GB2496013A - Reflecting apparatus for targeting electromagnetic waves. - Google Patents

Abstract

Reflecting apparatus has left and right eye mirrors 721l, 721r positioned along one of two separate axes 18l,18r, of the apparatus, then a series of reflecting devices formed from a pair of elliptical plane mirrors 723l, 724l, 723r, 724r, having central elliptical apertures, an annular conical mirror 717l, 717r and an angled mirror 734l, 734r all positioned on the axes 181l, 181r, where, in use, electromagnetic waves travelling along each of the two axes 181l, 181r, are reflected from one axis to the other via the reflecting surfaces and into input ends of the eye mirrors 721l, 721r, to be directed towards a target. A separate invention relates to assembling a dual multiple engine configuration in space.

Description

Optical recirculation with magnetic drive

1.0 Background to the invention.

This invention relates to a method and apparatus for inertial confinement fusion, and in particular, but not exclusively, to such a method and apparatus for use in the fields of defence as a directed energy weapon; propulsion by means of a beam or fusion; and terraforraing.

2.0 Prior art.

The prior art relating to optical recirculation comprises United Kingdom patent GB 2,305,516 B published as an application on the ggh April 1997 and as a patent on the 7th April 1999, and granted to the present inventor, which revealed method and ap-paratus for directing electromagnetic energy from an area or volume source, and which is incorporated herein by way of reference. As the present invention is limited to those embodiments of GB 2,305,516 B in which all the optical surfaces are reflective and axially symmetric about a common axis of symmetry, and in which each pair of defining rays whose intersection specifies a point on a defined mirror lie entirely in a respective plane through that axis of symmetry, such an apparatus will hereinafter be referred to as an "eye mirror". It equally follows that any ray in the plane containing a pair of defining rays also lies in a plane through the axis of symmetry and is therefore meridional.

The principle of optical recirculation of electromagnetic energy from the implosion of a target for inertial confinement fusion and the resultant fusion reaction(s) by a further alternate defined mirror either for the implosion of the next target, or that of a further part of the original target, is described in Section 6.17.2.1 of that application.

A further United Kingdom patent, GB 2,427,038 B, granted to the present inventor and relating to method and apparatus for directing electromagnetic energy from an area or volume source was published as an application on the 13th December 2006 and as a patent on the 11th March 2009.

Magnetic drive occurs when a magnetic field interacts with currents in the vehicle to produce a force on that vehicle. These currents may be in coils or be induced by changes

in that magnetic field.

The principle of the concave magnetic mirror produced by superconducting field coils was described by F. Winterberg in a paper entitled "Rocket propulsion by thermonuclear micro-bombs ignited with intense relativistic electron beams" (Raumfahrtforschung, 5, 208-217 (1971)). This concept was adopted in the "Project Daedalus" study, published in the Journal of the British Interplanetary Society (1978). It should be noted that the present invention does not use beams of electrons.

3.0 Objects of the Invention.

It is an object of the present invention to provide a method for, and an apparatus capable of, optically recirculating electromagnetic energy from the explosion of a cylindrical target for inertial confinement fusion for the implosion of a subsequent cylindrical target.

without any prior conversions of that energy into and from electricity and the losses of energy consequent thereon.

It is a further object of the present invention to provide simultaneous duai ignition of a cylindrical target for inertial confinement fusion by optical recirculation from two engines.

It is a further object of the present invention to provide a method for, and an apparatus capable of, the magnetic drive of a vehicle.

It is a further object of the present invention to provide a method for, and an apparatus capable of, the ignition of fusion reactions in deuterium-tritium fuel within a cylindrical target.

It is a further object of the present invention to provide a method for, and an appa-ratus capable of, the ignition of fusion reactions in deuterium helium three fuel within a cylindrical target with a deuterium-tritium seed.

It is a further object of the present invention to provide a met hod for, and an appa-ratus capable of, the ignition of fusion reactions in lithium deuteride tritide fuel within a cylindrical target.

It is a further object of the present invention to provide a method for, and an apparatus capable of, maintaining fusion reactions as an axial burn in a cylindrical target.

It is a further object of the present invention to provide a vehicle able to propel itself in exoatmospheric conditions.

It is a further object of the present invention to provide a method for, and an apparatus capable of, controlling the orientation of such an apparatus in exoatmospheric conditions.

It is a further object of the present invention to provide a method for, and an apparatus capable of, deaccelerating from, or accelerating to, a velocity whose magnitude is a few percent of the speed of light.

It is a further object of the present invention to provide a method for, and an apparatus capable of, forming a. plasma mirror for the reflection of a beam from an interstellar accelerator. -It is a further object of the present invention to provide a method for, and an apparatus capable of, magnetic sailing.

It is a further object of the present invention to provide a method for, and an apparatus capable of, magnetic shielding from stellar winds and cosmic rays.

It is a further object of the present invention to provide a vehicle with a crew com-partment of sufficient radius to furnish artificial gravity at its circumference by means of its rotation at an acceptable angular rotation.

4.0 Summary of the invention.

In view of the foregoing, a first aspect of the present invention provides an apparatus comprising eye mirrors, arranged on at least two separate but parallel axes of symmetry, on each of which axes of symmetry there is a rear elliptical plane mirror, a front elliptical plane mirror, an axially symmetric annular conical mirror arid an axially symmetric re-versed further alternate defined mirror as well as at least one eye mirror (which is axially symmetric by definition), the elliptical plane mirrors having elliptical holes, the projec-tions on a plane at right-angles to all the axes of symmetry of the outer edges of both the front and rear elliptical plane mirrors for each of those axes respectively being a common outer circle concentric about that axis, the projections on that plane of the inner edges of both the front and rear elliptical plane mirrors and the annular conical mirror for each of those axes respectively being a common inner circle concentric about that axis, with the projection on that plane of the reversed further alternate defined mirror for that axis lying within that respective common inner circle, such that an annular beam of electromagnetic energy collimated along one axis of symmetry from the rear of the apparatus towards its front with the same cross-section as the projection of the elliptical mirrors for that axis will be reflected sequentially from the rear elliptical plane mirror on that axis, from the front elliptical mirror on another axis, from the annular conical mirror on that other axis back through the holes in both the elliptical mirrors on that other axis, and finally from the reversed further alternate defined mirror on that other axis as well-directed input rays for the eye mirror(s) on that other axis, so that they will be directed by those eye mirrror(s) to or near to an aim point for a cylindrical target on or near that other axis where the implosion of that cylindrical target commences, with an optical recirculation period from a plane at right-angles to the axes of symmetry through the aim point on or near one axis to the aim point on or near another axis slightly less than or equal to the common period between the arrival of two successive cylindrical targets at each aim point.

According to a second aspect of the present invention there is provided a method of using the apparatus of the first aspect.

According to a third aspect of the present invention there is provided a method of assembling a dual multiple engine configuration in space.

According to a fourth aspect of the present invention there is provided a method of obtaining the simultaneous dual ignition of a cylindrical target.

5.0 Description of drawings.

Figure 1 is a schematic diagram showing a multiple engine configuration.

Figure 2 is a schematic diagram showing sections of a cylindrical target a further cylindrical target, a second further cylindrical target, and a third further cylindrical target through their respective axes of symmetry.

Figure 3 is a schematic diagram in the form of a section showing multiple eye mirrors arranged in tandem with a common axis of symmetry.

Figure 4 is a schematic diagram in the form of a section through its axis of symmetry of the nose of a cylindrical target together with an imaginary cylinder indicating the path of its future movement.

Figure 5 is a schematic diagram illustrating the implosion of a cylindrical target in the form of a section through its axis of symmetry.

Figure 6 is a graph showing the conditions which must be satisfied for the volume ignition of deuterium-tritium.

Figure 7 shows the geometry relating to a leaf in an eye mirror.

Figure 8 shows the geometry relating to the rotation of a leaf about its hinge in a meridional plane.

Figure 9 shows the geometry relating to a meridional ray.

Figure 10 is a wire diagrm showing art array of circular arrays of leaves.

Figure 11 is a pair of graphs showing both the rotation and the rate of rotation of a leaf.

Figure 12 is a front section of a leaf with a hinge and two actuators through the axis of that leaf.

Figure 12A is an enlarged section of a fibre optic cable in a plane at right-angles to its axis of symmetry.

Figure 13 is a side elevation of a leaf with a hinge and two actuators.

Figure 14 is a front elevation of a leaf attached to three actuators.

Figure 15 is a side elevation of a leaf attached to three actuators.

Figure 16 is a front elevation of a leaf attached to four actuators.

Figure 17 is a side elevation of a leaf attached to four actuators.

Figure 18 is a schematic diagram showing part of the surface of a cylindrical target whose trajectory is skew to the axis of symmetry of the eye mirrors.

Figure 19 is a schematic diagram showing an elliptical section of the surface of a cylindrical target in a plane at right-angles to the axis of symmetry of the eye mirrors.

Figure 20 is a schematic diagram of the control system for the leaves.

Figure 21 is a schematic diagram in the form of a half-section showing two recirculated beams through the axis of symmetry of a cylindrical target.

Figure 21A shows the geometry of an output beam.

Figure 22 is a schematic diagram in the form of a half-section showing overlapping bearnlets through the axis of symmetry of a cylindrical target.

Figure 22A is a schematic diagram in the form of a section of a hohlraum target through its axis of symmetry.

Figure 23 is a schematic diagram in the form of a half-section showing a single further alternate defined mirror.

Figure 24 is a schematic diagram in the form of a half-section showing several indi-vidual further alternate defined mirrors.

Figure 25 is a schematic diagram in the form of a half-section showing several indi-vidual truncated conical mirrors.

Figure 26 is a schematic diagram in the form of a half-section showing a single further alternate defined mirror for a directed energy weapon.

Figure 27 is a schematic diagram in the form of a half-section showing an individual further alternate defined mirror for a directed energy weapon.

Figure 28 is a schematic diagram in the form of a half-section showing an individual truncated conical mirror for a directed energy weapon.

Figure 29 is a schematic diagram of a small interstellar accelerator.

Figure 30 is a schematic diagram showing a plan and a side half-section of part of a fusion power station to which a number of off-axis directed energy devices are attached.

Figure 31 is a schematic diagram showing two sectional views of a sacrificial water-wall through its axis of symmetry, which is also the axis of symmetry of an off-axis directed energy device.

Figure 32 is a schematic diagram in the form of a half-section for the left side of the shield.

Figure 33 is a schematic diagram in the form of a half-section for the right side of the shield.

Figure 34 shows the geometry of part of the shield.

Figure 35 shows the shape of the heat wave and the shock wave from the explosion of a cylindrical target.

Figure 36 is a schematic diagram in the form of a section showing the conical shield in its forward position for ablative drive.

Figure 37 is a schematic diagram in the form of a section showing the conical shie1d in its rearward position for magnetic drive.

Figure 38 shows the double moving tripod in its rearward position for magnetic drive.

Figure 39 shows the double moving tripod in a null position for the rear moving tripod.

Figure 40 shows the double moving tripod in a null position for the front moving tripod.

Figure 41 shows the double moving tripod in its forward position for ablative drive.

Figure 42 is an exploded view of an extensible leg of the double moving tripod.

Figure 43 shows a rotation of the double moving tripod.

Figure 44 is a schematic diagram in the form of a section of a controllable pore array when not in use.

Figure 45 is a schematic diagram in the form of a section of a controllable pore array with the controllable tap in the open position.

Figure 46 is a schematic diagram in the form of a section of a controllable pore array with the central hole in the diaphragm closed.

Figure 47 is a rear elevation showing shield extensions on one side of the vehicle which are fully extended and shield extensions on the other side of the vehicle which are minimally extended.

Figure 48 is a rear elevation showing the shield extensions cycling.

Figure 49 is a rear elevation showing the shield extensions during reentry.

Figure 50 is a schematic diagram of a small boosted fission nuclearexplosive device.

Figure 51 shows the geometry of an explosive lens utilizing a cartesian oval.

Figure 52 shows a section of such an axially symmetric explosive lens through its axis of symmetry.

Figure 53 shows an icosahedron with one of its faces overlaid by a geodesated regular tessellation.

Figure 54 is a wire diagram showing an explosive lens trimmed to fit into a spherical array of explosive leiises.

Figure 55 is a schematic diagram in the form of a rear section of the rear inner and outer circular arrays of injector guns.

Figure 56 is a schematic diagram in the form of a rear section of the next rearmost, or second, inner and outer circular arrays of injector guns.

Figure 57 is a schematic diagram in the form of a rear section of the third inner and outer circular arrays of injector guns.

Figure 58 is a schematic diagram in the form of a rear section of the fourth inner and outer circular arrays of injector guns.

Figure 59 is an expanded view of the inside of Figure 55.

Figure 60 is an expanded view of the inside of Figure 56.

Figure 61 is an expanded view of the inside of Figure 57.

Figure 62 is an expanded view of the inside of Figure 58.

Figure 63 is a schematic diagram in the form of a sectional side elevation showing the rear half of the fuel injection system.

Figure 64 is a schematic diagram in the form of a sectional side elevation showing the front half of the fuel injection system.

Figure 65 is a schematic diagram in the form of a sectional side elevation showing the variable atmospheric intake.

Figure 66 is a sectional side elevation of a cartridge.

Figure 67 is a schematic diagram showing the cameras which measure the trajectory of a cylindrical target.

Figure 68 is a schematic diagram showing a sectional front elevation and a sectional plan of a dual engine configuration.

Figure 69 shows the return path of rays shown in Figure 68.

Figure 70 shows the geometry determining the maximum path length of the optica' recirculation in a single engine.

Figure 7lis a timing diagram showing the activities of a single engine in endoatmo-spheric operation and those of dual engines in exoatmospheric operation.

Figure 72 is a schematic diagram showing a sectional front elevation and a sectional plan of a twin dual engine configuration.

Figure 73 is a schematic diagram showing a sectional front elevation of a dual triple engine configuration Figure 74 is a schematic diagram showing a sectional plan of part of a dual triple engine configuration.

Figure 75 is a schematic diagram showing a sectional plan of a further part of a dual triple engine configuration.

Figure 76 is a timing diagram showing the activities of the engines in a dual triple engine configuration.

Figure 77 is a schematic diagram showing a sectional front elevation of a dual twin engine configuration.

Figure 78 shows the contour lines of the magnetic field for the magnetic drive.

Figure 79 shows the contour lines of the compressed magnetic field during the opera-tion of the magnetic drive.

Figure 80 shows the contour lines of the left half of the magnetic field produced by the front, rear and outer superconducting field coils.

Figure 81 is an elevation of an annular crew compartment attached to a single engine.

Figure 82 is a plan seen from the front of the vehicle of the annular crew compartment when rotating with sails extended.

6.0 Description of embodiments of invention.

6.1 Multiple engine configuration.

Figure 1 is a schematic diagram showing a sectional front elevation and a sectional plan of four plane mirrors, which have the same shape but different orientations. Since rays directed by the eye mirror(s) exit from the rear of the apparatus, the sectional front elevation is drawn below the sectional plan. The section, A-A, lies on the sectional plan.

Figure 1 also shows a left axis of symmetry 181, which lies in the plane 19 of the sectional plan, together with the defining mirror of a left eye mirror 7211, which is the outermost eye mirror on that axis, and a left conical shield 7221, both of whose axes of symmetry coincide with that axis of symmetry 181. Figure 1 also shows a right axis of symmetry lSr, which lies in the plane 19 of the sectional plan, together with the defining mirror of a right eye mirror 721r, which is the outermost eye mirror on that axis, and a right conical shield 722r, both of whose axes of symmetry coincide with that axis of symmetry 18r. Each of the plane mirrors is orthogonal to the plane 19 of the sectional plan. Figure 1 also shows the centre line 720 of the vehicle. It will be appreciated that neither the left eye mirror 7211 nor the right eye mirror 721r need comprise a directed energy weapon, as shown in Figure 1.

The radius of the base of each conical shield is as shown on the sectional frontS elevation. The inclination of the left rear plane mirror 7231 to the left axis of symmetry 181 is 6pl as shown on the sectional plan, while that of the left front plane mirror 7241 is 0pi The inclination of the right rear plane mirror 723r to the right axis of symmetry lBr is 0p( as shown on the sectional plan, while that of the right front plane mirror 724r is 0pl -ir. These angles are indicated by grey arcs.

Each of the plane mirrors has a hole in the shape of an ellipse, whose centre lies on its respective axis of symmetry, and whose minor axis is of length 2 b where = The projection of each such ellipse and the annular conical mirror on the sectional front elevation is a common inner circle of radius as shown on that sectional front elevation.

The major axis of each such ellipse lies in the plane 19 of the sectional plan and is of length 2bcscOj.

The outer edge of each of the plane mirrors also has the shape of an ellipse, whose centre lies on its respective axis of symmetry, and whose minor axis is of length 2 b0t. The projection of each such ellipse on the front elevation is a common outer circle of radius as shown on that sectional front elevation. The major axis of each such ellipse lies in

S

the plane 19 of the sectional plan and is of length 2 b0 csc Figure 1 shows those inner and outer rays lying in the plane 19 of the sectional plan of a left collimated annular beam 7161, which is reflected from the left rear plane mirror 7231, and then the right front plane mirror 724r, to replace the right collimated annular beam 716r.

Figure 1 shows those inner and outer rays lying in the plane 19 of the sectional plan of a right collimated annular beam 716r, which is reflected from the right rear plane mirror 723r, and then the left front plane mirror 7241, to replace the left collimated annular beam 7161.

The axial length along an axis of symmetry of each elliptical plane mirror is 2b0 cot 9. The left rear elliptical plane mirror 7231 is contiguous with the left front elliptical plane mirror 7241. The right rear elliptical plane mirror 723r is contiguous with the right front elliptical plane mirror 724r. The outer rays of the collimated annular beams are reflected from the outer edges of the elliptical plane mirrors in every case, as shown.

If the separation between the two eye mirrors 7211 and 721r respectively is a so that the distance between the two axes of. symmetry is 2rem + s then:-2rem + S tan26, = or 2 b cot B,, 2 2Tem + S -4b0 tan = 2rem + S The path length of any ray, which is initially collimated with respect to an axis of symmetry, between a rear elliptical plane mirror and a front elliptical plane mirror is (2rem + a) csc 2O,. The path length along that axis which is replaced by such a crossover is (2r6, + s) cot 20,,. Hence the increase in path length due to the crossover is:- (2rem + a) (csc 29,j -cot 24,i) = (2rem + a) tanO,t as may be verified from a geometric construction.

In Figure 1 s has been put equal to zero; so that the eye mirrors appear to touch.

As the explosion of a cylindrical target 101, 102, 103 or 104 respectively all of which are shown in Figure 2 on the left axis of symmetry 181 takes place some distance from the left conical shield 7221, and expands rapidly, much of the electromagnetic energy it emits, even though it is not collimated, follows similar paths to the left collimated annular beam 7161. Similarly for the explosion of a cylindrical target 101, 102, 103 or 104 respectively on the right axis of symmetry lSr. Each type of cylindrical target has an axis of symmetry 105.

Figure 1 shows a left annular conical mirror 7171, whose axis of symmetry coincides with the left axis of symmetry 181. Figure 1 shows a right annular conical mirror 717r, whose axis of symmetry coincides with the right axis of symmetry 18r. Figure 1 also shows a left variable atmospheric intake 7331 and a right variable atmospheric intake 733r.

Figure 1 also shows a left reversed further alternate defined mirror 7341 which is axially symmetric about the left axis of symmetry 181 and reflects electromagnetic energy as well-directed input rays into the left eye mirror 7211 and any other eye mirrors of the left engine and a right reversed further alternate defined mirror 734r which is axially symmetric about the right axis of symmetry lSr and reflects electromagnetic energy as well-directed input rays into the right eye mirror 721r and any other eye mirrors of the right engine. The radius of the outer edge of each reversed further alternate defined mirror is less than or equal to Figure 1 also shows the collimated annular beams after they are reflected by the annular conical mirrors, It will be seen that the reflections of both collimated annular beams are incident to the inside of a respective reversed further alternate defined mirror, so as to allow some badly collimated light to reach that mirror. As shown, the outermost rays of each beam are incident to a reversed further alternate defined mirror on its axis of symmetry In a further embodiment of the apparatus, a left cylindrical mirror 7351, whose inner surface is reflective, connects the hole in the left rear elliptical plane mirror 7231 with that in the left front elliptical plane mirror 7241, in order to prevent uncollimated light escaping from the reflection of the right collimated annular beam. And a right cylindrical mirror 735r similarly connects the hole in the right rear elliptical plane mirror 723r with that in the right front elliptical plane mirror 724r. Each end of each cylindrical mirror is truncated at the inclination of the elliptical plane mirror at that end: so that it forms an elliptical seal with that elliptical plane mirror.

It will be seen from Figure 1 that no beams cross each other between the front of a front elliptical plane mirror and its respective annular conical mirror. Figure 1 shows a left further cylindrical mirror 7361 and a right further cylindrical mirror 736r, whose inner surfaces are reflective, which enclose the beams and their reflections from the annular conical mirrors in those regions. A ray enclosure (not shown) mounted on the cylindrical mirrors, the plane mirrors, and the further cylindrical mirrors prevents uncollimated light from escaping from the beams into the vehicle.

Each of the elliptical plane mirrors, 7231, 7241, 723r and 724r respectively, both of the annular conical mirrors, 7171 and 717r respectively, both of the reversed further alternate defined mirrors, 7341 and 734r respectively, both of the cylindrical mirrors, 7351 and 735r respectively, both of the further cylindrical mirrors, 7361 and 736r respectively, and the enclosure are cooled.

It will be shown that this double engine configuration allows a period between the arrival of cylindrical targets for an engine equal to twice the sum of the duration of the implosion and burn, the time for which the point explosion usefully persists thereafter, and the crossover recirculation period less the overlap, which is equal to about half the implosion period plus the burn period, but plus some pulse stretching. Since the arrival of a cylindrical target for one engine must coincide with the arrival of a cylindrical target for the other engine, both recirculations occupy a common period.

Ablative drive occurs when a surface both receives momentum from, and imparts momentum to, material ablated from it, resulting in an ablation pressure on that surface.

The material may be matter from the surface itself and/or coolant upon it. The ablation is caused by heat from plasma in contact with the surface, or electromagnetic energy incident on it. Ablative drive using electromagnetic energy is known as a Teller-Ulam "radiation implosion".

6.2 Cylindrical target.

Figure 2 is a schematic diagram showing a section of the cylindrical target 101 through its axis of symmetry 105. The cylindrical target 101 comprises a cylindrical ablator 107 enclosing a cylindrical shell of cold fuel 108 both of whose axes of symmetry are also the axis of symmetry 105. The cylindrical ablator 107 is made of a material whose constituents each have a low value of the atomic number, Z. This may be a plastic with a formula such as (CH2), (CD2)_ or (CDT), or beryllium alloyS with about 1% of copper by weight to protect the cold fuel from being preheated by unwanted radiation between 100eV and lkeV.

The cold fuel consists either of a cylindrical porous shell containing deuteriurn-tritium, UT, in liquid form at its operational temperature below 25°K where DT fuel begins to condense to the liquid state, or a cylindrical shell of solid DT at its operational temperature below the melting point of DT of 19.8° K. The interior of the cylindrical target 101 contains UT gas 109 at the corresponding vapour pressure. The operational temperature may be chosen, for instance, as 18.3°K, for compatibility with hot-spot ignition in order to give the required vapour pressure and thus density in that mode of operation. In either case, the operational temperature is below 30°K where internal pressure could burst a plastic ablator.

Such a porous shell holds the liquid DT in place within pores of approximately 10pm in size. It may be made of polystyrene foam.

The uniformity of a solid layer of DT may be maintained by the beta-layering phe-nomenon, in which the self-heating due to beta decay of tritium into helium three, 2He3, warms the thicker areas more than the thinner areas and sublimates material from the thicker areas to the thinner. This is effective for cylindrical as well as spherical targets.

In a further embodiment of the cylindrical target 1D1, the cylindrical shell of fuel 108 consists of solid lithium deuteride tritide, at either ambient or cryogenic temperature, and the interior of the cylindrical target contains only gaseous helium three from the decay of the tritiurn.

The left-hand end of the cylindrical target 101 is sealed by the leading guide 113, while the right-hand end of that target is sealed by the trailing guide 114. Both guides are made of a dense high-Z material, such as gold, and their shape corresponds to the trajectory of the cylindrical ablator 107 and the cold fuel 108 during their implosion. The trailing guide 114 is covered by a ballistic cap 115, and the leading guide 113 is attached to extendable fins 116, to respectively minimise its drag and maximise its stability in an atmosphere when they are sprung open.

The intensity of the radiation on the ballistic cap of a cylindrical target during the explosion of the immediately preceding cylindrical target is very similar to that on the interior wall of a hohlraum. For this reason, it is made of a high-Z material, such as gold, so that both the amount of material ablated from it, and the ablation pressure on its surface, are relatively low, and the reflectivity of the plasma ablated from its surface is better than 90%. In consequence, the ballistic cap 115, and indeed the trailing guide 114, protect the cylindrical target 101 from the explosion of a preceding cylindrical target. The ballistic cap also reduces the heating of a cylindrical target by a gas during its injection, which is a problem for a conventional target even in a low-density buffer gas.

As the tangential velocity produced by rotation would prevent it from completing its implosion, this type of cylindrical target must be injected by a smooth-bore injector gun rather than a rifled-bore injector gun, unless provided with a slipping obturator. The low rate of rotation due to a slipping obturator, or to fins at a small angle to the airflow, reduces the dispersion of a cylindrical target.

Figure 2 also shows a further cylindrical target 102 in which those extendable fins are replaced by an ablative base 117 attached to the leading guide 113 by a bearing 118, which allows the ablative base 117 to be rotated by rifling, which engages with one or more driving bands on that ablative base, without the cylindrical target itself rotating.

The rotation of the ablative base 117 stabilizes the further cylindrical target 102 in both endoatmospheric and exoatmospheric use. The trailing guide 114 is covered by a ballistic cap 115. This target may have any of the types of fuel described above.

Figure 2 shows a second further cylindrical target 103 which is exactly similar to the cylindrical target 101 except in having two cylindrical shells of cold fuel, both of whose axes of symmetry coincide with the axis of symmetry 105. The inner cylindrical shell of cold fuel 112 is a DT seed of one of the types already described. In consequence, the interior of the second further cylindrical target 103 contains DT gas 109 at the vapour pressure corresponding to that target's storage temperature. The outer cylindrical shell of cold fuel 111 consists of a deuterium "honeycomb" with the interstices filled with liquid helium 3 whose boiling point is 4.22°K and whose storage temperature is 3K, as suggested in Project Daedalus.

Figure 2 finally shows a third further cylindrical target 104 which is exactly similar to the further cylindrical target 102 except in having two cylindrical shells of cold fuel as in the second further cylindrical target 103.

6.3 Multiple eye mirrors and/or multiple final stages in parallel.

Figure 3 is a schematic diagram in the form of a section showing multiple eye mirrors 121 to 123 respectively, arranged in tandem with a common axis of symmetry 18 in a plane 19 through that axis of symmetry. Each eye mirror is larger than the next higher numbered eye mirror so that its (recirculated) output beam is not masked by that higher numbered eye mirror. Such eye mirrors may be referred to as being in parallel to one another in the same sense as for stages in parallel in Section 6.14.5 of GB 2,305,516Th Section 6.15.9 and Figure 31 of GB 2,305,516B showed that a single final stage of an eye mirror may be replaced by multiple final stages in parallel. Section 6.15.10 and Figure 24 of GB 2,305,516 B showed how it is possible to make the physical output aperture of a final stage small when the common output angle, /3j, for each of its first defining rays is approximately equal to zero.

The trailing edge of the defined mirror of the final stage in a set of stages can only extend as far as the caustic or regular envelope to the defining rays. If the common output angle, th, is less than zero, and the coordinates at which a first defining ray is reflected from a defining mirror are r1, 91 then the point at which that ray is tangent to the caustic or regular envelope before its reflection from the defining mirror lies very close to that defining mirror when + Si + /3 (j3j C 0). In which case, the defined mirror must also lie very close to the defining mirror to give a small physical output aperture.

Similarly if there is no common output angle but all the output angles are nearly the same.

Section 6.15.9 and Figure 31 of GB 2,305,516B also showed how a defined mirror of a final stage may incorporate a mirror or mirrors on its reverse surface which mirror or mirrors each form a defining mirror or mirrors of the next parallel final stage inwards.

Similarly, the innermost defined mirror of the final stage of an eye mirror may incorporate a mirror or mirrors on its reverse surface which mirror or mirrors each form a defining mirror or mirrors of the outermost final stage of the next eye mirror inwards.

It is therefore possible to have a very large number of final stages in parallel, belonging to one eye mirror or more than one eye mirrors in parallel, in a relatively compact arrange-ment. For convenience, the eye mirrors are numbered monotonically from the outermost eye mirror inwards, the final stages are numbered monotonically from the outermost fi-nal stage inwards, and the recirculated beams are also numbered monotonically from the outermost recirculated beam inwards, irrespective of which final stage of which eye mirror directs which recirculated beam.

Both the power capacity, and the path length of recirculation, of each final stage is larger than that of the next higher numbered final stage.

Figure 4 is a schematic diagram in the form of a section in a plane 159 through the axis of symmetry 105 showing the nose of a cylindrical target 101, further cylindrical target 102, second further cylindrical target 103, or third further cylindrical target 104 together with an imaginary cylinder 130 indicating the path of its future movement to the right. The axis of symmetry 105 of the cylindrical target is also the axis of symmetry of the imaginary cylinder 130, and is therefore extended to the right. Figure 4 also shows recirculated beams 131 to 134, in this case from the four final stages 141 to 144 respectively (as indicated), which have already arrived at the surface of the imaginary cylinder 130.

Figure 4 shows nine sections numbered 91 to 99 through the imaginary cylinder 130 at right-angles to its axis of symmetry 105 which divide part of that imaginary cylinder into eight equal lengths and eight equal areas 21 to 28 respectively.

The recirculated beam 134 from the (highest numbered) final stage 144 has been directed to illuminate all those areas. The recirculated beam from each successively lower numbered final stage has been directed to illuminate only the rightmost half of the areas illuminated by the next higher numbered final stage. So that there are four different levels of illumination.

If the electromagnetic power emitted isotropically by an explosion at wavelengths which can be reflected is a function of time, and the powerto be recirculated, Pj,-, also a function of time, is contained between two cones 151 and 152 of half-angle 0min and °max respectively whose vertices lie at the centre of that explosion, as shown in Figure 3, then:- 2r(cos 0,nin -cos Pcirc = 4 where l)ern is the efficiency of the eye mirrors. However, neither the peak value, nor the time dependence, of P2i for the explosion whose recirculated energy implodes a cylindrical target and starts its burn can be predicted in advance, or are likely to be exactly repeatable.

If there are it »= 2 final stages in parallel and the recirculated power, Pejrc, is appor-tioried equally among them, then the power of each recirculated beam is P0/n. The number of equal areas is T'' and the number of different levels of illumination is it (as-suming that the illumination profile across each beam is flat).

The power on each of the leftmost areas is Pcjrc/ (2"1n). The power on the next 2' areas is:-cire circ - i 2 -2-'m 22n -2"-'n provided n »= 3.

The power on the rightmost area is:-p1+2+ +2"' -Pcirc 12 -Pcirc 2 -1 2mn\ ... )27_mn 1-2 The cylindrical target 101, 102, 103 or 104 moves into the recirculated beams 131 to 134 from left to right at a constant relative velocity, so that each point on it takes the same time tarea to traverse one of the equal areas. If a beam extends over 2' areas where in is a positive integer then its power on each area is P10/(2mn) but the time taken for each point on the target to cross that beam is 2"t area; so that the energy delivered to each area of similar size on the cylindrical target by each recirculated beam is tareaPcirc/ri. Since there are it beams, the total energy delivered to each such area is area' As any infinitesmal area of the cylindrical target 101, 102, 103 or 104 moves to the right, it is subject to rapidly and progressively rising power. When it reaches the rightmost recirculated beam the power has risen by a factor of 2 -1. If it = 9 this power factor is 511.

If the rightmost area is chosen to be smaller than the leftmost area, this power factor rises further (without reducing the total energy delivered to each area). Moreover, the rightmost recirculated beam comes from the largest final stage which can handle the greatest power.

However, in practice, the profile of the beams is smooth, rather than a series of steps, as the badly-directed rays associated with each beam spread out its illumination.

It will immediately be seen that if the illumination fraction is replaced by 3 where f> I then the nth level of power and illumination becomes:-p i tn -nrc -J f-1⁄4 1-f giving a power factor of (1 -fTh)/ (1 -f).

Clearly the limit for the pSer factor is extremely high. It should, however, be reit-erated that the respective fraction of the imaginary cylinder illuminated by a recirculated beam may have any value, and need not be equal to any of the respective fractions for the other recirculated beam(s). The above expression is merely intended to demonstrate how high the power factor can be.

Laser beams with a circular cross-section cannot be arranged to cover the entire surface of a spherical target uniformly. Each laser beam is therefore focussed on a point beyond such a spherical target. Each meridional ray from an eye mirror, however, intersects the axis of symmetry 18. And, since an eye mirror is axially symmetric, even badly directed rays output by it illuminate a cylindrical target uniformly.

As a right-circular section of the cylindrical target 101, 102, 103 or 104 implodes, its radius and any surface area defined by that radius decrease, and the intensity due to meridional rays from the eye mirrors on its surface increases by an additional factor.

The rapidly and progressively rising intensity on each right-circular section of the cylindrical target 101, 102, 103 or 104 as it moves to the right ensures its nearly isentropic compression. Moreover, the velocity of any right-circular section of the cylindrical target 101, 102, 103 or 104 is higher than the velocity of a similar section immediately to its left, not only because of the rapidly and progressively rising illumination, but also because it has been accelerated for a longer time. So that the portion of the cylindrical target 101, 102, 103 or 104 being illuminated becomes convex in shape with an axial, as well as a radial, velocity. But the shells of ablator and cold fuel cannot fold over beyond their tangent to the beams because that would cut off their illumination. For the same reason, those shells cannot split, even if there was a step increase in their illumination (which will not be the case, as aforesaid). The grazing angle of incidence with the convex surface not only reduces the intensity on that surface but also introduces refraction in the plasma corona blowing off from that surface with the possibility of resonance absorption as considered in Section 6.10.2.4 The implosion period of the cylindrical target 1111, 102, 103 or 104 may be of the order of 40 to TO xis. The recirculation period for the largest final stage may be of the order of 2üps. That for the smallest final stage may be several microseconds less than that. If the recirculation for the smallest final stage ceases before that for the largest final stage while the latter is illuminating the right-hand, or trailing, end of the cylindrical target, then the power factor during ignition will be reduced. So that the source of electromagnetic energy must persist sufficiently for the illumination of the cylindrical target by the smallest final stage to overlap that of the largest final stage by the implosion period. If the recirculation for the smallest final stage ceases thereafter, then the power factor during the subsequent burn of the cylindrical target will be reduced. But this is of much less consequence.

Since the path lengths of badly-directed rays through an eye mirror, each of whose stages is single, differs from that of the well-directed rays, badly-directed rays stretch pulses.

Synchronization of the recirculated beams with a cylindrical target is otherwise pro-vided by that target flying through those beams.

The principle of operation of an eye mirror is based purely on geometric optics; and is therefore independent of the scale applied to the geometry which produces area focussing, and thus the size of that eye mirror Moreover, both the power on, and the cooling of, each mirror therein are proportional to the area of that mirror. There is therefore no theoretical or practical limit to the size of a" eye mirror or its power output.

As the size of an eye mirror is increased, the number of multiple eye mirrors in tandem within it, and the number of multiple final stages in parallel in those eye mirrors, which it can conveniently accomodate, is also. So that the maximum power output of such a device is proprtional to its volume, as is the corresponding mass.

The thermal damage threshold of a mirror scales as the square root of the pulse length.

As even the longest cylindrical target need only be illuminated for O.2is, and thus about one thousandth of the period between the implosions of successive cylindrical targets, the recirculated power may be very high, provided all other illumination is prevented from entering the eye mirrors at times outside the period of recirculation.

Although each mirror in an eye mirror will be illuminated by electromagnetic energy with a range of wavelengths, over a range of angles of incidence, and be very large, there is no theoretical reason why its reflectivity cannot be very high.

Any combination of the above three approaches may be used to enable the recirculated power to be very high.

6.4 Cumulative implosions.

Scale-invariant similarity solutions may be used to analyse the èuxnulative implosion of a cylindrical shell, in which all the fluid elements (and all the shock waves) converge on the axis of that shell. The shock wave(s) in such a cumulative implosion may all arrive at that axis simultaneously with the fluid elements, or otherwise. An exact analytic solution exists for the singular point, known as F5, for such cumulative flow. For flow close to P5 as the time, t, tends to the implosion time, to, the trajectory R(a, t) in Lagrange coordinates of a particle starting from a R(a, 0) at time t = 0 is given by;-R(a, t) = R(a,O)t - as t -* t0 where n = 2 (for the cylindrical case), p = 2 / (7-1) and -y is the ratio of the specific heat at constant pressure to that at constant volume.

The ablation pressure driving the shell varies as:-pa(R(a,t),t) (çC5) (n(a,oflt -where C5 is one of the coordinates of the singular point P5 and thus constant.

For monochromatic light of low wavelength, as used for direct-drive, the intensity, i,, required to generate this pressure on a plane carbon surface is given subject to a number of assumptions by:-

I L

Pa = C1 I \ AL where AL is the wavelength of the incident light and c is a constant. In which case:-pg 3p'y 12 (R(a,o)t_-tof1('+M)c5) If the adiabatic exponent -y = for DT then L --toH3 as t -* t0.

Moreover, R(a, 0) ij for a cylindrical shell.

These solutions include the isentropic compression case necessary to achieve high compression without wasting energy in heating the fuel.

The corresponding mass ablation rate, tha, is given by:-/ ma = c2 ( -where c2 is a constant.

The exaust velocity of the ablated plasma is given by Pa I th0 so that it is proportional to also. Clearly the density of the plasma ablating from a plane surface does not depend on The mass ablation rate of a spherical target illuminated by light with a wavelength of 0.53 pm has been measured and fitted to a relation iita cx 10.76 6.5 Implosion.

Figure 5 is a schematic diagram illustrating the implosion of the cylindrical target 101 or the further cylindrical target 102 after the cold fuel 108 and the remains of the cylindrical ablator 107 enclosing it reach its axis of symmetry 105, aEld that cold fuel collides radially inwards. It has the form of a section in a plane 159 through that axis of symmetry. The areas of the imploding cylindrical ablator 107 illuminated by the recirculated beams 131 to 134 are also shown. The outer surfaces of all the recirculated beams approximately coincide at the target, while the inner surfaces of the recirculated beams are spaced at successively greater distances from their outer surfaces at the target. The length of that target illuminated by the recirculated beam 134 is ibea,ns. The illumination from all the recirculated beams falls within this length. The length of that portion of the cylindrical target 101 or 102 undergoing implosion is f beams where f »= 1. The effect of the beams is maximised if f 1, but the advantage reduces as I -÷ 1 due to shell convergence and the increasing obliquity of incidence.

Since the surface of the imploding cylindrical ablator 107 is at an angle to the axis of symmetry 105 during the latter part of its blow off, both it, and the cold fuel, will acquire axial, as well as radial, velocity from the plasma expelled normal to that surface.

An imploding conical shell 153 of cold fuel beyond the right-hand edge of the recirculated beam 134 is not being ablated, and is merely coasting inwards towards the axis of symmetry 1O5 at a constant approach angle, ?, to that axis.

As a result of the collision, the density of the cold fuel on or near the axis of symmetry rapidly increases, a high proportion of the kinetic energy of the remaining portion of the cylindrical ablator 101 and of all the cold fuel 108 is converted into internal energy, and the temperature of the cold fuel increases.

The cold DT gas 109 moving to the right with the cylindrical target 101 or 102 is subject to a shock wave 154 as it is deaccelerated by the implosion of the rightmost portion of that target.

Since the DT gas inside the imploding cylindrical shell of cold fuel escapes into the unirnploded region of the cylindrical target 101 or 102, it is not compressed to as high a pressure as it would be if trapped inside a spherical shell. It does not therefore deaccelerate that imploding shell significantly until the implosion reaches the leading guide 113. Such a deacceleration of a high density layer by a low density gas would be unstable, and lead to the mixing of that dense layer with the gas. In consequence of the absence of this instability, the convergence ratio of the cylindrical shell in this configuration may be a little higher than that of a spherical shell.

Similarly for a second further cylindrical target 103 or a third further cylindrical target 104 but with inner and outer shells of cold fuel and helium three as well as DT gas.

The illumination of the leading edge of the cylindrical ablator 107 by the recirculated beam 131 is liable to be impeded by plasma from the ablation of the leading guide 113 by the recirculated beams 132 to 134.

6.6 Ignition.

If the drive pressure and density of any element, either in a shell of cold fuel or the gas inside it, before collision are P0 and po respectively, while the stagnation pressure and density of that element just after the passage of a reflected shock rebounding from a central point or axis are p and p respectively, then:- 1 -1) fl n1a(1 a)_ and p 2 = I' n"a(1 -Q)(inhFB)(Thi)MO()IN) Pu where y is the adiabatic exponent, F2 (i + 1)/(y -1) is the gas constant, it = 2 for a cylindrical target, it = 3 for a spherical target, a is the isentrope parameter in the range 0.6 cc a cc 09, and M0 is the Mach number of the imploding shell in the range 2<M0<25.

For y = 3.6M, 2.4M0312 for spherical geometry, and Pu Ps 9/4 P 3/4 -cc, -cc M0 for cylindrical geometry Pu where M0 is the Mach number of the imploding shell in the range 2 < M0 < 25.

If the temperature at stagnation is 7' then:-T8 occ ==4 = 72(7 -1) (1 a)(n/ra_ny ?M1) where c is the adiabatic sound velocity.

Hence for = 3 Pa 3/2 -7-M0 for spherical geometry, and 2 P0 for cylindrical geometry Pci Numerical results for the pressure ratios Ps/PU over a range of Mach numbers are a factor of 12.5 lower for cylindrical geometry than for spherical geometry. The corresponding results for the density ratios ps/PU are a factor of 20 lower.

But these results assume that the shocks have rebounded symmetrically from a central point and axis respectively, which is not the case for the configuration under consideration.

Moreover, in a spherical or cylindrical target, the rebounding shock in the hot DT gas is subsequently incident to the inside of the cold fuel, and its reflection further heats the hot spot. In contrast, the shock wave in the initial implosion has axial as well as radial velocity and is conical in form so that its reflection is not incident to the inside of the cold fuel.

Even inside a spherical target, the gas is only heated to a temperature of a few hundred eV by the initial shock. So that a hot spot cannot form in the configuration described.

Even if the implosion velocity is raised, the temperature of the DT gas will still be too low for its ignition.

6.7 Low temperature volume ignition.

The compression ratio for a cylindrical target is equal to the square of the convergence ratio, so that it cannot be as high as that for a spherical target, which is equal to the cube of the convergence ratio. However, the power factor feasible with multiple eye mirrors and/or multiple final stages in parallel is particularly high, as explained in Section 6.3 And it may be further increased, as described in Section 6.23. The compression of the cold fuel due to multiple converging shocks may therefore be high. Moreover, the mass compressed may always be made sufficiently large, not only to render it optically thick to the electromagnetic energy from the hot fusion products, but also to enable it to contain a significant fraction of the neutrons released by its fusion reactions.

* It is therefore always possible to choose the mass compressed to be sufficiently large to satisfy the self-heating and confinement conditions and achieve low temperature volume ignition at temperatures which may be as low as 1 keV for DT.

6.8 Radial implosion velocity.

The radial kinetic energy of one gramme of matter whose radial implosion velocity is uu, cmf sec is v%np/2 ergs. One erg is i0 3. The particle energy of one gramme of matter at a temperature of T. keV is where 2'., refers to the temperature of the cold fuel after collision and 1B is the gas constant, which is 7.66 x 1014 erg g' keV1 or 7.66 x 1O 3 kg' keV' for equimolar DT. On that basis, the radial kinetic energy of a radial implosion with a radial velocity of 3.5 x io cm / sec, typical of direct and indirect drive by lasers, corresponds to a temperature of the cold fuel, after it has been heated by collision, of 0.53keV. Even this temperature is inadequate for low temperature volume ignition.

If, however, the radial implosion velocity is raised to 7 x I.O cm / sec by virtue of an absence of an upper limit to the intensity of direct drive by an eye mirror, as detailed in Section 6.10.2, then a temperature of 2.13 keV might be obtained in principle. The stagnation temperature of each element is, however, only raised by a factor of 23/2 = 2.828.

The assumption that kinetic energy transforms completely into internal energy is not accurate.

The radial implosion velocity can be raised not only by increasing the exaust velocity of the ablating plasma, but also by increasing the thickness, and thus the mass, of the cylindrical ablator 107. The energy efficiency of an ablative, or "rocket", drive peaks at a certain fractional ratio of the mass of the cold fuel 108 to that of the cylindrical ablator 107. The ratio generally used for direct drive by a laser is well above that optimum ratio.

So that the mass of the cylindrical ablator 107 may be increased by a factor of four with a consequential increase in that efficiency of about 50%.

When the burn commences, at a velocity, Vburn, relative to the cold fuel of approxi-mately 5 x io cm/sec. the corresponding stagnation temperature of the DT gas rises by a factor of (5O/3.5)3'2 = 54 over that of its radial implosion.

6.9 Admissable intensity for a laser.

Laser plasma instabilities and the reduction of the coefficient of collisional absorption at high laser intensities set an upper bound to the admissable power which may be used to drive a target directly using a laser. For a laser wavelength AL = D.35,um at normal incidence, the admissable intensity to avoid excessive laser plasma instabilities is close to Ij, io' W / cm2, where L is the intensity due to that laser. These figures give a typical radial implosion velocity of 3.5 x io cm / s. The threshold for the onset of such instabilities in a uniform plasma is ILA «= io' (W/cm2) jim2. Above this threshold, other mechanisms occur, which backscatter light and/or produce hot or suprathermal electrons, which preheat the cold fuel.

The radial implosion velocity, Uimp, may be proportioned by:-(IL\215 imp CC for both normal and grazing incidence.

Hence doubling the implosion velocity requires an increase in IL/AL by a factor of about 180. This may be achieved in principle if AL = O.2prn and Ij = 1017W/cm2.

The corresponding value of the expression JLAj = 4 x 1015 (W/cm2) pm2 is above the threshold for the onset of laser plasma instabilities, but considerably less than the threshold of 1.37 x 1018 (WI cm2) jim2 beyond which relativistic effects occur. So that the latter threshold does not limit L But the absorption coefficient for a laser would be reduced by a factor of up to 7 at L = 1017 W/cm2 necessitating a further and counterproductive increase in ILP'L.

6.10 Comparison between lasers and eye mirrors.

6.10.1 Limitations of lasers.

The irradiation and implosion of a target is susceptible to laser plasma instabilities particularly in the low density plasma ablated from the inner wall of a hohiraum.

The principal instabilities are Stimulated Brillouin Scattering (SBS), Stimulated Ra-man Scattering (3113), and filamentation.

SRS produces hot electrons, as does resonance absorption.

6.10.1.1 Stimulated Urilloulu Scattering.

SBS causes backscattering of incident photons due to variations in the electric field of the incident light, producing sound waves which themselves cause scattering.

Various smoothing techniques including adding laser beam incoherence via induced spatial incoherence (131), temporal smoothing by spectral dispersion (SSD), and random phase plates (RPP) have been used to reduce SBS.

6.10.1.2 Stimulated R.aman Scattering.

8115 arises from interference between the incident light, and light scattered from it with a slightly different wavelength. Such light is scattered by molecular vibrations, which may be linear or rotational.

Lasers for the irradiation of a hohiraum are limited to short wavelengths to avoid 8113.

The hot electrons generated by 3113 in the plasma ablated from the inner wall of the hohlraum by light with a wavelength of 1.O6pm degraded the implosion of a target by preheating it.

6.10.1.3 Filamentation.

Filarnentation is an instability in which spatial modulations in the laser beam intensity are amplified as electrons are pushed away from regions of high laser intensity. Local enhancements in intensity lead to density depletions. Refraction of the light into regions of lower density increase the intensity perturbation, leading to a breakup of the beam into intense filaments. Monochromatic light with coherent phases tends to form interference patterns that seed the growth of such instabilities.

6.10.1.4 Resonance absorption.

The angle of incidence of meridional rays on the cylindrical target 101, 102, 103 or 104 or that on the limb of a spherical or cylindrical target may cause significant resonance absorption of p-polarized light. At the critical surface, a Langrrnnr wave is produced by resonant excitation-The amplitude of this wave increases as it encounters denser plasma nearer the ablating surface. When it breaks, it generates hot electrons. However, the s-polarized component cannot cause resonance absorption.

6.10.2 Advantages of eye mirrors.

6.10.2.1 Absence of interference effects.

Section 6.19.2 of GB 2,305,51GB described the wave surfaces and waveforms output by an eye mirror, whose source consisted of elementary radiators, in terms of geometric optics. The wave surfaces from an elementary radiator directed by an eye mirror towards a point are nearly spherical in shape, but not in extent. However, the waveforms resulting from a large number of elementary radiators will be irregular. The output may therefore be regarded as partially spatially coherent, but temporally incoherent, and incapable of producing observable fringes. Section 6.19.3 of GB 2,305,51GB described how the output may be split into part waves. Section 6.19.4 of GB 2,305,51GB rejected the formation of beam steering due to resultant wave surfaces, and pointed out that each wave surface from an elementary radiator is spaced over a considerable distance around the annular exit aperture of an eye mirror.

In consequence, those limitations of lasers associated with interference effects, such as SBS, SRS and interference patterns seeding filarnentation do not apply to an eye mirror-Furthermore, the spread of the output from each elementary radiator around the exit aperture, and their very large number, smooth that output, and avoid any perturbation which could give rise to filamentation.

Finally, the electric field responsible for the transverse quiver motion of the plasma electrons in a target is not periodic, which may affect the value of the coefficient of colli-sional absorption, it will also prevent any ripples forming in the corona of plasma escaping from the cylindrical ablator.

6.10.2.2 Short wavelengths.

As mentioned in Section 6.19.7 of GB 2,305,51GB, an eye mirror can use coherent or incoherent electromagnetic energy of any wavelength which may be wholly or partially reflected. Aluminium, for instance, can reflect very short wavelengths of 0.l2jm at normal incidence, when coated with Magnesium Fluoride, and of O.035pm at grazing incidence, provided an oxide layer is not allowed to form on its surface. And such electromagnetic energy may extend over a very wide waveband.

The use of shorter wavelengths maxirnises the absorption coefficient by enhancing collisional absorption in regions of higher plasma density. It further reduces any SItS.

The thickness of the conduction layer between the critical surface, where light of a particular wavelength is absorbed, and the front where ablation takes place is strongly dependent on that wavelength, AL. For planar geometry, it is proportional to A14/3: so that light of short wavelengths is absorbed very close to the ablation front. Bringing the deposition region of a laser closer to the ablation front makes it more susceptible to deposition non-uniformities of the type described in Section 6.10.1 This is not a problem for an eye mirror, whose output is spatially coherent and very smooth around a cylindrical target, as explained in Section 6.10.21 6.10.2.3 Wide waveband.

it was pointed out in Section 6.19.8 of GB 2,305,51GB that if the electromagnetic energy is distributed over a number of component wavelengths which cannot interact co-herently, SItS will not become significant until the energy of each such component exceeds the threshold at which said build up is considered to begin. And that if the source of electromagnetic energy for the apparatus has a wide waveband, as will be the case in this instance since that source is an explosion, SRS will be insignificant. And that, as a consequence, very high intensities may be produced on a target.

All stimulated scattering processes, such as SBS and SRS, are coherent processes requiring sufficient temporal and spatial coherence of the radiation source to allow a build up of the medium excitation responsible for the scattering by positive feedback leading to exponential amplification of the scattered radiation. So that the above consideration also applies to SBS, and all other stimulated scattering procees.

Moreover, there will not be a single critical surface at which light is absorbed, as for a laser, but an infinite number. This undermines the assumptions made when calculating a value for the threshold or critical intensity for collisional absorption.

6.10.2.4 Resonance absorption.

As shown in Figure 4, the beams are incident to the cylindrical target 101, 102, 103 or 104 at oblique angles of incidence which increase during its implosion, as shown in Figure 5. At oblique angles of incidence in the density gradient of the plasma blowing off from that cylindrical target, the p-polarized component of the incident electromagnetic energy undergoes resonance absorption, which greatly increases its absorption at any intensity and over a wide range of angles of incidence, albeit by different amounts. The maximum for that absorption generally occurs for angles of incidence below the initial angles of incidence of the beams. It should be mentioned that the period of illumination is greater than lOafs below which there is insufficient ion motion to produce resonance absorption.

As shown in Figure 84 and described in Section 6.18.3 of GB 2,305,516 B, the intensity for all the rays making up the output beam from an eye mirror of the resultant component of electromagnetic energy whose electric vector is normal to the plane of incidence will, in general, differ from that of the resultant component of electromagnetic energy whose electric vector is parallel to said plane of incidence, due to the different refiectivities at the various mirrors in that apparatus for other differently orientated normal and parallel components for each of said rays which arise from the non-normal incidence of those rays in that apparatus. As shown in Figure 74 and described in Section 6.18.1 of GB 2,305,516 B, the reflectivity of metal mirrors for p-polarized electromagnetic energy may be less than that for s-polarized electromagnetic energy. So that the amount of the p-polarized elec-tromagnetic energy in their output beams may be reduced by the choices of the surfaces of the eye mirrors.

6.11 Conditions for volume ignition.

Figure 6 is a graph showing the conditions which must be satisfied for the volume ignition of UT fuel with a uniform density of Pa = 190 g / cm3 in a cylinder of radius, rV'. This density will be assumed to be the highest that can be obtained by a cylindrical implosion. As the entire volume of fuel is heated, the conditions are isothermal, so that there is no hot spot. And there are no losses due to mechanical work. Curve 155 is the condition for self-heating in volume ignition, for which the power density deposited by the neutrons and a-particles which are the products of fusion, W, is greater than the power density lost by radiation, W7, and below which the fuel will cool without igniting. Curve 156 is the condition that the time required for self-heating, tsht, is less than the time for which the fuel will remain confined, Below curve 156, there will be insufficient time for self-heating to take place. Both conditions must be satisfied for volume ignition.

These curves are shown for a range of values of the volume ignition burn parameter = pcr' in g /cm2 and initial temperature T in keV.

Figure 6 also shows a curve 157, which shows the condition r]'t = ip, the Planck mean free path, above which the fuel is optically thin, and a curve 158 which shows the condition r1 = IR, the Rosseland mean free path. The derivation of these conditions may be found in Section 4.5 of "The Physics of Inertial Fusion" already referenced.

It will be seen that volume ignition can take place at pcr" = 7 g / em2, T = 2 keV.

(These conditions also suffice for the volume ignition of DT fuel with a density of Pc = g / cm3. Ignition temperatures for Li2DT of 8.1 keV with complete neutron energy redeposition, ttnd 3 keV if the fuel is also optically thick with pr' = 15 g/cm, were quoted in a paper entitled "Thermonuclear burn characteristics of compressed deuteriurn-tritium microspheres" (G.S. Fraley et al, The Physics of Fluids, Vol. 17, No. 2, Feb. 1914 p.485). A calculation similar to that for Figure 6 but for L4DT compressed to 190 g / cm2 indicates that it may be ignited at T = 2OkeV for pr' = 4.7g/cm2, or at T = 16kW for prV' = 7 g / cm2, but is not optically thick below pr1 = 20 g / cm2 because of its increased brernsstralhung.) Once a value for the volume ignition burn parameter has been chosen, the radius of the compressed fuel is determined by r'1 = prgY'/p0.

The mass of the fuel per unit length, M?', is given by:- 2 / vozign\ -I rcYl\ 7rIH3 M7t=?r(r)2pc kPcc) ________ Pc Pc Its radial kinetic energy per unit length is where Ujmp is the radial implo- sion velocity so that the energy required per unit length to implode the fuel is:-E -1M.cYt 2 req j ttjyp - and the power required to implode the fuel is at least:-c12 -,cyZ 2.ir(pcr1) 2 rrcq -iV1f UmpVbnrn -2Pc UimpUbnrn where Vburn is the velocity of the burn front relative to the cold fuel.

If the radial implosion velocity Uimp = 7 x 1O cm / sec and the burn velocity Vbrn = x 10 cm/Sec then the energy required per unit length to implode the fuel is 198.5 MJ / cm and the fuel power required to implode and ignite the cylindrical target 1011 102, 103 or 104 when the, or the inner, shell of cold fuel is DT is 99,249 TW. The recirculated power is Pcirc = Prsq/v where i is the overall coupling efficiency between the recirculated beams and the compressed fuel in the cylindrical target. Pcjrc = 1,240,619 TW when i = 0.08.

The condition for detonation of the cold fuel, or the DT gas, by a burn wave is:-Tbnrn > 4Pc Phurm where Tbur,-, and Pburn are the temperature and density of the burning fuel respectively, Pc is the density of the cold fuel after compression, or the DT gas, and the ignition temperature, Tign 75keV.

The density of the DT gas, Pc, is much lower than that of the burning fuel in volume ignition, so that Pc <<P,.n arid that gas will detonate. But as there is no density gradient in the DT gas along the axis of symmetry 105, this detonation will not propagate very far in advance of the implosion.

Since the imploding conical shell 153 of cold fuel has not yet collided on the axis of symmetry 105 of the cylindrical target 101, 102, 103 or 104, its density, Pc, is not only lower than that of the burning fuel in volume ignition, Pburn, but reduces as its radial distance from that axis increases. Hence a detonation wave will run into the conical shell 153 of cold fuel also, provided the burn temperature is some 30 keY, as will initially be the case.

As this detonation proceeds further from the axis of symmetry 105, the density gra-dient in the imploding conical shell 153 of cold fuel reduces. Moreover, that shell is less optically thick and less able to retain neutrons, in both dimension as well as density, than the core originally ignited. It also has a higher surface area, inside as well as outside, for losses of a-particles and neutrons to take place. So that such a detonation in the imploding conical shell 153 of cold fuel will fizzle out if the implosion does not keep pace with the burn.

Any undesirable preheating of a more distant section at right-angles to the axis of symmetry 105 of the cylindrical target of the imploding conical shell 153 of cold fuel by neutrons, photons and a-particles is inversely proportional to the distance of that section from the burn. Moreover, such a distant section is shielded from that burn by closer sections of higher density.

6.12 Gain.

Once ignition has been achieved in the cylindrical target 1D1, 102, 103 or 104, the gain from its burn must be just sufficient to provide the recirculated power necessary to implode the next cylindrical target, given the fraction of the radiated power recirculated.

The electromagnetic power emitted isotropically by the explosion at wavelengths which can be reflected, is then constant.

If the rate at which incident energy is converted to fuel energy at ignition is llPcirc where rj is the overall coupling efficiency for the implosion, then the gain, Gf, must be:-= = 4ir TIE'irc 2ir 7) ?)enz (cos 9,nin -cos Omaz) The gain depends on the compressed mass of fuel which generally appears in the results of numerical simulations as a parameter for a gain curve. If it is assumed that the recirculated beams are stationary, the energy, F?j, transferred to a compressed fuel element of length, d, is E1 = qPj,., d/ VtgL where Vtgt is the velocity of the cylindrical target. As will be revealed in Sections 6.17, 6.18 and 6.19, however, the recirculated beams may travel over the cylindrical target in the opposite direction to keep pace with the burn, at a velocity relative to the cold fuel near to the burn velocity, V1IIATTZ, in which case The limiting fuel gain, G}, may be approximated for a spherical target using DT fuel ignited by low-temperature volume ignition as:-= 1O00E'6 Hence the required gain, the compressed mass of fuel and the velocity of the target relative to the recirculated beams are interelated.

Since the a-particles from the thermonuclear reactions in the cold fuel heat both the imploding cold fuel and the DT gas, while the speed of the burn wave is itself sufficient to ignite that DT gas and detonate the cold fuel, the gain will rise rapidly after ignition. It may therefore be necessary to reduce the recirculated power during a burn in a predeter-mined way, as well as to control the recirculated power passing from one cylindrical target to the next.

In a target in which the thickness of cryogenic fuel is maintained by beta-layering, that thickness cannot easily he varied along the length of that target. But the thickness of the layer of fuel in other types of target may be varied to alter the gain along the length of that target. The thickness of the cylindrical ablator 107 may equally be varied for that purpose in any type of target.

6.13 Fast ignition.

In fast ignition, fuel is first compressed by all but one of the beams, and then ignited by the final trigger beam firing through the plasma blown off from the implosion. The trigger beam must deliver all its energy while the fuel remains compressed. In practice, the heating of that volume of fuel which undergoes ignition is so fast that it does not have time to expand at all before being ignited: so that the ignition conditions are isochoric.

Figure 5 shows the rightmost recirculated beam 131 from the outermost (lowest numbered) final stage 141 when used as a trigger beam 140. In consequence, the beam 131 is no longer present.

If the recirculated power is and there are n beams then the power in the outermost and most powerful beam is at least Pbeam = Prirrin. If Pcirc = 1,240,619 TW as for volume ignition and there are nine beams then Poeam = 137,846 TW.

/ The length of a cylindrical target illuminated by the well-directed rays in that beam may be in the range 0.0126 «= ltrbeam «= 0.126 cm, or iess. If the beams travel over that cylindrical target at a burn velocity of = 5 x 10 cm/s then each circular section of that cylindrical target will be illuminated by that beam for tjjirnn = itrbearn/Vf, so that 0.025 «= tjUum 0.25 us. If the overall coupling efficiency between that beam and the compressed fuel in that cylindrical target is 77 = 0.08 then the energy deposited in that cylindrical target by that beam per centimetre of length is Ed0 = VPbeam/Vo°J'm = 22 MJ / cm.

The radius of the cylindrical target is r'1 = 1.5cm initially and = 0.75cm when illuminated by the penultimate and second most powerful beam immediately prior to cutoff, while the initial aspect-ratio oi the cold fuel is Ac, 11.1. (Its in-flight-aspect-ratio at that peak illumination may be limited to A1 = 30.) The energy of Fermi degenerate compressed DT per centimetre of length for such a cylindrical target at 190 g / cm3 is 2.46 lvii / cm.

The isochoric self-heating condition for compressed DT fuel heated only by a-particles requires a temperature Th »= l2keV together with an areal density PRh »= 0.Sg/cm2 where the subscript /i signifies the hot part of that fuel. If the collision of the fuel along the axis of the cylindrical target raises its density to p = Pc = 190 g/cm3 then the required radius of the hot part Rh »= 26.3 pm with a corresponding length of 211,. »= 52.6 pm, which is less than the lower limit of ltrbeam at 126 pm.

The energy required for fast ignition, E19, of a cylinder of liT fuel of sufficient size, density and temperature for ignition whose length and diameter are equal when illuminated from one end is given by the computer simulation, DUED, described in a paper entitled "Inertial fusion fast ignitor: Igniting pulse parameter window versus the penetration depth of the heating particles and the density of the precompressed fuel" (S. Atzeni (1999) Phys. of Plasmas, 6, 3316-26), as:- = 140_185 = 42.7 kJ where 4ô is the fuel density in units of 100 g/cm3.

Since this amount of energy must be deposited in each cylinder of length 2Rh the energy per centimetre of length needed for the hot part of the fuel E9/2Rh = 8.1 M3/crn.

This is about 37% of the energy deposited per centimetre-If p = p = 100 g / cm3 so tha.t Rh = 5OMm and E9 = l4OkJ then Ejs,fl/2Rh = 14MJ/cm.

If PDT is the density of uncompressed DT then for p = Pc = 190 g / cm3 the radius of the compressed fuel, is given by:-1/2 = (2PnT r'1 = 0.02191 cm \pAoJ which is an order of magnitude more than Rh. So that the areal density component of the isochoric self-heating condition is amply fulfilled radially as well as axially.

Now the area! density of the compressed fuel is HJtt9Th = PCrCYI = 4.16306 g/cm2 there being less fuel in such a target than is ideal for volume ignition. (It is still close to the range of a neutron in DT at 4.lg/cm2.) A value for the classical range or area! density of DT fuel of PcTy = 22.5 g/cm2 is sufficient to stop 20 MeV electrons such as may be produced by incident intensities of 1019 W/cm2 or more.

If the temperature required for ignition is Th = 12 keV then the sound speed in the hot part of the fuel is c3 = 2.8 x i0T,"2 cm/s when 77h is in keV and the confinement time during ignition is tJ = Rh/c3 = O.027ns which is within the range for the illumination period of the trigger beam.

The burn of a deuterium target following fast ignition of a DT seed embedded in it has been simulated using DUED, as reported in a paper entitled "Burn Performance of fast ignited, tritium-poor ICF fuels" ((1997), Atzeni, S., & Ciampi, M.L., Nuclear Fusion, 37, 1665-77). The gain for a 20mg target requiring a driver energy of 7 MJ was still near 300 for a density of 200 g/cm3 when the total fractional tritium content was reduced to 1%. This, together with the figures given above, suggests that a very high proportion of the tritium could decay before a cylindrical target became unuseable for fast ignition.

6.14 Induced transparency.

When the radius of the compressed fuel is rt = 0.02191 cm and the illuminated length is 0.0126 < ttrbeam 0.126cm, the curved surface area illuminated by that trigger beam is A9 = 27r1ltvbam giving 0.001 73 A9t 0.0173 cm2.

Now the intensity, Jo, on such an area is Pbeam / As rgt is related to a burn parameter or areal density by rVt (prt1l) /Pc = H08tZ9/pc and:-Pcirc Preq - (H°')2 74mp'burn -fleam ---72 2np I vohgn\ 2 (MB) Vburm /2rnq 0 = r,rfastig7%, hILlB trbeam is independent of both Pc and r1 once a value for the areal density, HJffSt%9Th, has been chosen. For Poeam = 137,846TW, HaS9Th = 4.16306g/cm2 and 0.0126 «= 1trbeam «= 0.126 cm, the intensity, on it is 7.94669 x io' «= 1o < 7.94669 x i0-W/cm2 whatever the values of Pc and The plasma frequency, w, for electrons which have a relativistically enhanced mass, yme, is given by:-rez = /4lre2ne where -y = (i -v2/c2) h/2, v is the velocity of an electron oscillating in the electromagnetic field, c is the velocity of light in a vacuum, me is the mass of an electron, e is the electron charge, 1e is the electron density and (y) is an average value for -y.

As (-y) increases, the plasma frequency reduces allowing electromagnetic energy to propagate into those denser regions of the plasma blown off from the cylindrical target which are nearer that target. This effect is known as induced transparency.

The condition that the electrons have relativistically induced mass for a wavelength, A, is 10A2 > 1.37 x 1018 (W/cm2) pm2. For a minimum wavelength A,njn = 0.2 pm this becomes ja > 3.425 x io' W/em2.

If it is desired to reduce the wavelength for which induced transparency sets in, the number of beams used for the trigger may be increased.

Even in an underdense plasma, whose density is below the critical, the intense electro-magnetic energy gives rise to a beam of relativistic electrons, with energies of 1-20 MeV, travelling in the same direction as the incident electromagnetic energy within an angular divergence of a few degrees. This beam of electrons heats the fuel to the temperature necessary for ignition.

The effective instantaneous target for fast ignition is a cylinder of radius, r?t, and length, 1trbeant Although the hot part of the fuel has a length of tzrbeam c rY1 for tr1 0.027ns, the ensuing burn would propagate over a much longer length in the absence of the trigger beam, indeed, to the end of the cylindrical target. Purely, by way of comparison, the mass of fuel, M1, in mg of a cylinder of radius, rff", length 2rt, and density, Pc, is given by:-M1 = 20°°'Pc = 12.5577 mg The limiting gain, C?, for such a mass of fuel compressed with an isentrope parameter of a = 1.5 is given for fast ignition by:- = 4200M3/a°87 6305.55 One of the advantages of fast ignition is that the compressed fuel does not necessarily have to be symmetric as such. It suffices if the implosion has been sufficiently symmetric to raise the density of most of that fuel to the required value It follows that ignition may also be achieved by delaying the arrival of the most powerful beam on the cylindrical target until the cold fuel has reached its axis of symmetry.

This allows the recirculation period of the largest final stage to be longer.

6.15 Volume and fast ignition.

Induced transparency provides a route for energy to reach the fuel for either volume or fast ignition without non-isentropic compression raising the energy required for the compression of that fuel, or hot electrons preheating that cold fuel. The hot electrons produced by the trigger beam only arrive just in time for ignition.

Since there will be sufficient energy for volume ignition even if the shell of cold fuel cannot be accelerated to a sufficient speed to provide all that energy, it does not matter if the hot electrons do not deposit enough energy in the compressed fuel on the axis of symmetry of the cylindrical target for fast ignition.

If the hot electrons produced by the trigger beam reach the fuel before it arrives at the axis of symmetry of the cylindrical target, neither the density of that fuel nor its temperature will have been affected by its impact with itself. And the power of the trigger beam itself will have been spread out over a larger area of the surface of the fuel than necessary due to the excessive radius of the circle at which it was incident, and the high angle of that incidence: so that its intensity will not have been at the maximum possible.

If the hot electrons produced by the trigger beam reach the fuel just as it arrives at that axis of symmetry then both the density of that fuel and its temperature will have increased due to that impact-And the power of the trigger beam will have been spread over the smallest possible area of the surface of the fuel, possibly at a lower angle of incidence due to the collision, so that its intensity will be at the maximum possible.

On the assumption that all the kinetic energy of the fuel transforms into internal energy, that increase in temperature may be somewhere between 0.53 and 2.13 keV, significantly reducing the amount of energy which has to reach the axis for fast ignition.

If the hot electrons produced by the trigger beam reach the fuel after it has arrived at that axis of symmetry and rebounded from that impact then the density of that fuel and its temperature will have fallen slightly from their maximum. And the power of the trigger beam will have been spread out over a larger area: so that its intensity will have been lower.

As described in Section 6.23, the beamlets from the leaves are adjustable, so that the arrivals of the hot electrons produced by the trigger beam and the impact of the fuel at the axis of symmetry may be made to coincide.

As described in Section 6.28.1, the axis of symmetry of the cylindrical target cannot precisely coincide with that of the eye mirrors. However, if it did, the paths of those hot electrons produced by the trigger beam at a particular instant would lie between two cones whose axes coincided with the axis of symmetry of the cylindrical target and which intersected at the circle of origin of those hot electrons.

The hot electrons converge on the vicinity of the axis of symmetry of the cylindrical target. Their path to that vicinity is of the order of r3' csc. The spectra of the energy and speed of the hot electrons is biased in favour of lower energy and lower speed respec-tively. In fast ignition, r1 = 0.02191 cm. For a path of r'1 csc = 0.02191 csc cm and an areal density of pr1 csc = 5.887.c 22.5 g/cm2 sufficient to stop 20 MeV electrons as above, many of the hot electrons will reach that axis of symmetry on the basis of their classical range.

If none of the relativistic electrons had trajectories which were skew to the axis of symmetry of the cylindrical target, and the angles of those trajectories with that axis were all the same, then the current density would increase inversely with the distance to that aids. It is known that the current density in a plasma is limited.

S

The beam of relativistic electrons may be subject to instability, filamentation and anomalous stopping before it reaches the axis of symmetry of the cylindrical target. In any event, it is possible that the collision of the interconical beam of the hottest electrons on the axis of symmetry* of the cylindrical target will always prevent that beam from crossing that axis, so that most of their energy is deposited on that axis.

The deposition of energy may fulfill either the conditions for fast ignition, or those for volume ignition in a cylindrical target for fast ignition, which may be seen from Figure 6 to be T = 2.4 keY for DT with P. = 190 g/cm3 and per., = 4.16306g/cm2. Since the energy per unit length is:-cyi -a lr(pcrccvl)2

FBTCMJ -2 2

the cylindrical target for fast ignition requires less than half the energy per unit length to heat a target for which T = 2 keY and prg = 7 g / cm2 and achieve volume ignition.

It should be mentioned that this allows some of the beams previously used but no longer needed for heating to become additional trigger beams, particularly if the pow& factor for isentropic compression is maintained by the use of bearnlets as described in Section 6.23 -Moreover, the size of the target may be enlarged or reduced to arrange the deposition of the energy on the axis of symmetry of the cylindrical target for fast ignition. Or, alternatively, the size of the cylindrical target may be enlarged, and the amount of fuel therein increased, to increase pcrc and reduce T to fuffihl the conditions for volume ignition.

6.16 Burn of lithium deuteride tritide.

The deuterium ion, or deuteron, and the tritium ion, or triton, from lithium deuteride tritide can react:- + 1T3 -+ 211e4(3.49MeV) +rx(14.IMeV) (1) with a cross-section of up to 5 barns (which occurs at 64 keV). One barn is 10_28 in2.

The resulting fast neutrons can then react not only with the deuterons and tritons, but also with the naturally occurring isotopes of llthium according to the cross-sections indicated:-n + -* 2n + -6.26MeV (0.01 barns © 12MeV) (2) n + -* 2n + -2.22MeV (0.0105 barns © 14MeV) (3) n + 3Li6 -+ 2n + 2He4 + -3.7MeV (0.09 barns from 10 to 20MeV) (4) n + 3Li6 -* 2He4(2.OSMeV) + 1T3(2.7MeV) (0.02 barns © 11.5MeV) (5) n + 3Li7 -* 2n + 2He4 + -8.73 MeV (0.025 barus @14.1 MeV) (6) n+ 3Li7 -* 2n+ 3Li6 -7.25MeV (0.O4barns from 11 to 20MeV) (7) n + 3LiT -+ 3n + 2He4 + 1111 -10.95 MeV (neglible) (8) n + 3LiT -* n + 2He4 + 1T3 -2.47MeV (0.4barns © 11.5 MeV) (9) The protons produced by reactions (3), (4) and (8) can react with both 3Li6 and aLiT.

These reactions produce only charged particles:-ill' + 3Li6 -4 2He4 + 2He3 + 4.02MeV (10) 1H' + 3LiT 22He4 + 17.35MeV (11) Deuterons can react with each other as detailed in Section 6.27.2.1 One of the conditions selected for volume ignition is p,r0t = 7g 1cm2. The neutron cross-section for elastic collisions with deuteriumu at 14.1 MeV is 0.8 barns, while that for tritium at 14.1 MeY, and both 3Li6 and 3Li7 at all relevant neutron energies, is I barn. If the neutron meaxi free path is denoted by L and the density by p then p 1,., 4.7 g / cm2 for a cross-section of 0.9 barns, which is slightly below that for elastic collisions with lithium deuteride tritide at all relevant neutron energies. So that a neutron is likely to undergo one or two elastic collisions before escaping from the compressed fuel.

On average, a neutron will lose 2A/(A + 1)2 of its energy in an elastic collision with a nucleus of mass number A and thus 12/49 ths of its energy in such a collision with a 3Li6 ion, 7/32 nds of its energy in such a collision with a 3LiT ion, 3/8 ths of its energy in such a collision with a triton, or 4/9 ths of its energy in such a collision with a deuteron.

On that basis, the 14.1 MeV kinetic energy of a neutron from reaction (1) will be reduced to 10.6 MeV by a collision with a 3Li6 ion, or to 4.35 MeV by successive collisions with two deuterons. At the latter energy, the cross-sections of reactions (5) and (9) are both approximately equal to 3.1 barns. The energy lost by the neutrons will be transferred to their targets. So that those tritons and deuterons involved in such collisions will have high energies, and thus high probabilities of undergoing non-thermal fusion reactions.

Ideally, the cross-section of 5 barns for the deuteron triton reaction would be matched by a comparable figure for the combined cross-sections of the subsequent reactions.

For low temperature volume ignition, the fractional power deposition by neutrons, In pcr' / (pcry1 + ii) where H,, = 20 g / cm2; so that f 7/27 only.

The deuterori triton reaction (1) together with either of the lithium ion reactions (5) or (9) which produce a triton form a closed-chain reaction known as the Jetter cycle. A cycle cannot he maintained if more neutrons are lost from the compressed fuel than are produced by its reactions. Taking into account the cross-section of each reaction, together with their energy balance and the number of neutrons they react with and produce, a cycle of reactions (1) with either (4) or (5) absorbs less energy, reacts with less fast neutrons but more scattered neutrons and produces less slower neutrons than a cycle of reactions (1) with any of (6) through (9). As the other products of reactions (1) with (4) and (5) are charged particles, 3Li6 fuel might be more suitable for magnetic drive. But the number of reactions of fast neutrons with lithium, and the number of slower neutrons escaping, might both be increased by adding 3Li7 to the fuel, because of the high cross-section of reaction (9). This may be advantageous for ablative drive and/or for breeding tritium.

However, it is clearly possible to burn deuterium and tritium and at least some of the lithium if conditions are suitable. An initial excess of tritium, together with the lithium from whiêh it may be bred, over the deuterium allows for the decay of that tritium. Equally, some LiD may be included in the fuel to react with the tritium produced from lithium.

Since there are more electrons in Li2JJT than DT, more energy is required to compress it. If mD is the mass of a deuterium nucleus, niT is the mass of a tritium nucleus and rnL is the average mass of a nucleus for the combination of lithium isotopes used, the energy required to compress Li2DT in terms of that to compress DT by unit volume for the same compression factor is:-E(Li2DT) = ( (n +mTV2 PLt2DTEC(DT) = 2.7E(DT) (2mt +mp +mT)/8 PDT / if PDT 0,225 g / cm3, PLi2DT = 0.85 g /cm3 and mj4 = 6. The energy of Fermi degener-ate compressed L$DT per centimetre of length for the cylindrical target at 190gm / cm3 is 6.66MJ/cm.

The energy required for hot spot ignition is given by:-= FsThp where rB is the gas constant, Th is the temperature required by the appropriate self-heating condition, and p is the density.

The gas constant is (n +ne)kn/A,n where n is the number of ions, zi is the number of electrons, A is the mass number of the reactants and rn is the mass of a proton. 1c is the Boltzmann constant.

-. . B For equimolar DT, m = tie = 2 so that its gas constant is r8(DT) = mi3 + mT where m is the mass of a deuterium nucleus and mr is the mass of a tritium nucleus.

For Li2DT, n 2n = 8 so that its gas constant is F8(Li2DT) = 12k8 2mL + m + where 7Lj is the average nuclear mass for the combination of lithium isotopes used.

Hence F3(Li2DT) = (mn + mnT)14 r8(DT) = 0.88 Fn(DT) for Li = 6 (2mL + rn + mT)/12 A calculation similar to that for the volume ignition of DT for Figure 6 indicates that L$DT compressed to 190 g/cm3 may be ignited at T = 20 keV for pcrc°' = 4.7 g/cm2, or at T = 16 keY for pr' = 7 g/cm2, even through that fuel is not optically thick below pcr' = 20 g/cm2 because of its increased bremsstra)ung. Ignition takes place over the entire volume of fuel, and does not involve mechanical work. The ignition conditions in fast ignition would require a value of the temperature of the hot part of the fuel, Ti., some 4 keV higher for DT because of the mechanical work exerted by a hot spot in isochoric conditions.

Since that mechanical work is proportional to (128Th)3!2 an even higher temperature would be required for L$DT.

The temperatures required for the entire fuel for the volume ignition of Li2DT neces-sitate too much energy to be practical given the amount of fuel needed.

If 23, (DT) 12 keV for (isochoric) fast ignition while T (Li2DT) = 20 keV to burn Li2DT in the Jetter cycle then the energy required to ignite Li2DT in terms of that to ignite DT by unit volume for the same compression factor is:-E9(Li2DT) = 12(m +mT) T(Li2DT) PLI2DTEign(DT) = 5.SGEign(DT) 4(2mL + 7D + ?TIT) Tt.(DT) PDT if PDT 0.225g/cm3, PL2DT = 0,85 g/cm3 and mL = 6. At T(Li2DT) = 6OkeV, close to the energy of 64 keV at which the maximum cross-section of the DT reaction occurs, this rises to E9(Li2DT) = 16.67E9(DT). (On the assumption that all the kinetic energy of the fuel transforms into internal energy, a contribution of between 0.53 and 2.13 keV to the temperature will be provided by that kinetic energy.) The corresponding sound speed c(20keV) = 2.8 x 1O2',V2 = 12.52 x 1D cm/s gives a confinement time t07j = R4/c8(2OkeV) = 0.021 ns. While c8(6OkeV) = 21.69 x iO cm/s gives t00,-1 = 0.012 Us. However, the illumination period, may be reduced compar-atively easily. A higher number of the beams previously used but no longer needed for heating may become trigger beams, particularly if the power factor for isentropic com-pression is maintained by the use of beamlets as described in Section 6.23, and additional trigger beams may be provided, in order to deliver more energy to the hot part of the fuel.

These are the preferred options to allow the fast ignition of Li2DT.

As much of the tritium bred from lithium by neutrons in the explosion might not be burnt, tritium could be harvested from the exaust of a fusion power station, such as that outlined in Section 6.26 Since fused Li2DT is a solid of density 0.85 g/cm3, it follows that cryogenic targets are not required for either ablative or magnetic drive with fast ignition. Since the tritiuin in the cylindrical targets on board decays to 2He3, it remains desirable to burn the 211e3 extracted from those targets in magnetic drive, so that cryogenic targets are still required for that purpose. And cryogenic targets will survive closer to the explosion of an immediately preceding cylindrical target; so that even Li2DT targets are preferably cooled. Since the ablation of any coolant necessary to remove the kinetic energy of neutrons escaping from the burn of L12DT, together with the net energy released by their absorption by lithium isotopes in the lithium blanket, would prevent magnetic drive, arid might impose excessively high thrust in ablative drive, the ratio of 3Li6 to 3Li7 in the fuel must be chosen to minimise such neutrons. A fuel high in 3Li6 will be referred to as LigDT, while a fuel high in 3LiT will be referred to as LiDT, hereinafter, and it will be assumed that the former is more suitable for magnetic drive. The natural abundance of 3Li° is 7.4% while that of 3LiT is 92.6%.

The temperature to ignite deuteriuni and helium three is variously given as 18 keV and 60 keV. Since 211e3 requires a cryogenic target, DHe3 is most conveniently ignited by a DT seed as that must also be cryogenic.

Other hydrides, such as LiBD4+LiBT4, have been considered as fuels.

6.17 Target velocity.

The muzzle velocity of each cylindrical target 101, 102, 103 or 104 may be as low as io cm/sec for an injector gun using a chemical propellant, or as high as 106 cm/sec for a railgun. Each cylindrical target 102 or 104 with an ablative base 117 may be further accelerated by the blow-off from that ablative base driven by energy from one or more of the recirculated beams.

If in beams illuminate the ablative base for a time, t, while it -in > 0 beams later illuminate the cold fuel for the same time, t, with the same overall coupling efficiency, i, then the energy delivered to the ablative base is iiPcirct while that delivered to the cold n-rn fuel for its implosion is -qPcirct.

If the cold fuel comprises a fraction lJf of the mass of the cylindrical target, nt9, and VE9t is the axial velocity resulting almost entirely from the ablation and being much larger than the muzzle velocity then the axial kinetic energy of the cylindrical target is rn9jv?9. The radial kinetic energy of the radial implosion of the cold fuel is jrn9tu while the axial kinetic energy of the cold fuel is cot2 b where u1,, is the radial implosion velocity and 1' is the angle between the terminal velocity of the cold fuel and the axis of symmetry 105, in the reference frame of the target as before.

Equating the energy delivered to the kinetic energy in both cases gives:-in 2 n1Brirct mtgtvcgt ii = ymtgtup (i +cot24') So that:- 27)Pt 1 2 __________ 2 2 = = fri -m)fUtmhJ (i + cot 4)) Vtgt = in (1+cot24)) Uimp (it -m)f If in = 1, it = 9, f = 2 and 4) = so that cot 4) = 1 then Vt0 = $Aimp.

So that, for small values of in, the terminal velocity of each cylindrical target will be less than whatever the radial implosion velocity. As already mentioned, imp should be some 7 x iO cm/sec for volume ignition.

As the angle between the terminal velocity of the cold fuel and the axis of symmetry is 4), the axial component of the terminal velocity of that cold fuel is Uimp cot 4) in the opposite direction to Vt9t. The velocity of the burn front relative to the cold fuel, also in the opposite direction to Vt9t, is Vrn with a typical value for DT of 5 x iO cm/sec. Other fuels may have a different burn velocity. The axial velocity of the cold fuel on the axis of symmetry 105 18 Vtgt -Uimp cot sb C 0 as Vtgt C 1-4imp and cot 4) 1. In the reference frame of the vehicle and its eye mirror(s) this speed will increase the burn speed initially by subtraction of a negative value. Any DT gas in the cylindrical target, however, is still moving with the cylindrical target at a velocity of VtQt, and also detonates but with a potentially different burn speed. in that reference frame the burn may therefore be expected to propagate with a speed between Vburn -1timp cot 4)) initially and then if DT gas is present -V9 where v, is the burn velocity modified by the detonation of the DT gas.

6.18 Leaves.

Figure 7 relates to a leaved eye mirror 161 and includes a right-handed system of three dimensional cartesian coordinates it, v, vi in which the w-axis is aligned with the axis of symmetry 18.

The leaved eye mirror 161 has a final stage defining mirror 162, a portion of which is shown in Figure 7. Its defining surface 163 is a concave spherical mirror lying on a sphere 164 of radius rem with its centre 165 at the origin 0 of those coordinates.

The final stage defining minor 162 comprises an array of circular arrays 181 to 183 of hinged mirrors, or leaves, shown as a wire diagram in Figure 10. The reflective defining surface 163 of each leaf 191 is concave and a portion of a sphere of radius rem. Its axis of rotation 192 is tangent both to its reflective surface and the sphere 164, and it can be rotated so that its reflective surface lies on the sphere 164.

The edges of each leaf lie on two respective planes through the w-axis, and on two respective cones whose vertices are both at the centre 165 and whose axes are both the w-axis. There is sufficient clearance between adjacent leaves in both the meridional and latitudinal directions for each leaf to move without fouling its neighbours, irrespective of whether they also move.

Figure 10 also shows the ui-axis and part of each of the lines of intersection of one of those planes through the to-axis with the trailing cone 193.

The leaf axis 192 is tangent to the sphere 164 at spherical polar coordinates rem, t9e,n, Wem as shown in Figure 7.

The direction of the leaf axis is at right-angles to that plane through the to-axis which is at an angle Wem measured from the u-axis and in the uv plane. That direction is therefore When the reflective surface of the leaf 191 coincides with the sphere 164, a meridional ray 194 is reflected from a point P0 on that leaf whose spherical polar coordinates are j, g. This meridional ray has a dfrection g3, cot + r after reflection so that its angle of reflection is 7t --13o, its direction before reflection is 7i -2t9j -$o, çoi + ir and its direction cosines are:- -sin(29j + J3) cos çoj, -sin(261 + $) sin çoj, -cos(2t91 + /3) The cartesian coordinates of the point Phin9e at which the leaf axis is tangent to the sphere 164 are r,,1 Sill COS Wem, Tern 1fl ?m Slfl 4°em, Tern COS Z96m. A further meridional ray 195 is reflected from this point with a direction 13 hinge, Warn + it. It intercepts the aids of symmetry 18 at a point 1? which lies a distance iv9 from the centre 165. Applying the Law of Sines to the triangle /iOPhjflgeR in the plane through the axis of symmetry at an angle Warn to the u-axis gives:-Wtgt -Tern sin (it -9em /3hingc) -5111 /3hinge If the meridional ray 194 also passes through the point R then applying the Law of Sines to the triangle AOP0R in the plane through the axis of symmetry 18 at an angle pz to the n-axis gives:- _______________ -Tern sin(7r-ôi-/30) -sinfi0 Hence:-Wtgt = sin (t9ern + /3ainge) = sin (O + $a) sin [3 hinge sin ho sin 9; cosJ30 + cos9g sin$o sin cot$0 = (sin (z9em + hinge) -cosi) \ Slfl$Mnge sin (& + $hinge) =CSC13i -coti SIfl fihinge 6.18.1 Equation of leaf.

Figure 8 shows the meridional plane through the w-axis which is at an angle Yarn measured from the u-axis and in the uv plane. It includes the point Phinge at which the leaf axis 192 is tangent to the sphere 164.

If the leaf 191 makes a right-handed rotation through an angle w about an axis whose direction is, -then the centre C of that leaf moves to:-Tern (sin 29vn -sin (t9em -w)) COS Went, r (sin 29p -sin (t9 -w)) sin Warn, (COSYII -cos -w)) or 2 r cos (&rn -sin cos W' 2 Tam COS (tenz -sm1 sin Warn, -2rsin (z9em - The equation of the leaf becomes:- ( 2 ?ern cos (19cm -sin cos warn)2 + (v -2r cos (z9 -sin sin went)2 + (w +2rent sin (29cm -w) Li)2 = U2 + V2 + w2 +4 T Sin2 -4r (cos (oem) (uCoSWem +VSiflWem) -wsin (dem -= As shown in Figure 9, the meridional ray 194 intercepts the leaf 191 in its rotated position at a point P whose cartesian coordinates are zi, v, w. If the length of the short line from P to the original point P0 from which that ray was reflected is 1, a small distance, then:-it = r sinz9tcost -lsin(ir -2z91 -/30)cos (j + it) V = rem sint9 sinp -lsinUr --f3o)sin(yz +ir) w=remcosl9r-lcos(lr-2?91-13o) or it = r,-,1sin191coswz +lsin(2'i91 +flo)coscoz v rem sin y + I sin (229 + /Jo) sin = rem cosi9 + lcos(2ö1 +$o) Now it2 + v2 + = Tm + j2 + 2 remi (sin sin (2i9 + /%) cos2 yi + sin t9 sin (29, + $o) sin2 w +cost9zcos(219t +/9o)) =rm+l2+2remlcos&i+Po) This relationship may also be obtained from the Law of Cosines for the triangle AOP0P and the original angle of reflection LOP0P = it --1%.

And cos (l3em) (uCOSWem + VS1DWem) -wsin (29ern = cos (Oem -) (r sin 9i (cos em cos c0i + Sin Wern sin Wi) + 1 sin (26 + $0) (cos cos + sin Wem Mfl Wi)) sin (t9em -(rem cos t9j + I cos (229z + $o)) = Tem (cos (t9ern -sint9icos(z --sin (oem -) coso) + I (cos (L9em -sin (2O + $o)cos(Wi -em) -sin (Oem E) cos (2O + $o)) = Tern (cos29i (o. -+ + (t9em + cos(n -ern)) + t (cos(2t9i + flo)cos (Oem -+ + sin (2O + 3g) sin (Oem + cos(,i -em)) where each trigonometric factor represents the cosine of the angle between two lines.

So that the equation of the leaf may be written:-j2 + 2reml (cos (19i + !3o) -2 (cos (229t + i3o) cos (oem -* + sin(2i9i + $ü)sin (Oem + cos(j -Scent)) sin +r (i + 4 sin2 -4 (coso1 cos (oem -. +sinO1 sin (29 -+ cos(wj -ccem)) sin = 6.18.2 Perpendicular between ray and axis of symmetry.

The direction of the normal is from the inside of a surface to its outside. If ii, a and b are unit vectors in the direction of the normal, the incident ray, and the reflected ray, respectively, then:-b=a-2cosen where c is the angle between the incident ray and the normal given by cos c = an The normal at the point P comes from the centre of the leaf after its rotation. Its direction cosines are therefore:-U I (aJ\C) -2cos 9em -SRI tern V / -2cos çt9ern w) Sin SlflYem, tern Vi. / . W + 2 sin --Sin -tern 2i 2 Hence when the incident ray is the meridional ray 194:-cose = sin (2 + i3o) COSçO1 (2cos (9em -SI1 cos Yen. -L) tern + sin (2t91 + flu) sin (2 coB (tem -sin sin -ten.) -cos(2i91 +/3o) (2sin(l9em -)sin + 2 tern / / W\*W U V = sm(2i9, + øo) 2cos em -sin cos(w ---cos1 --Sifl \ tern tern -cos(2j + e%) (2 sin (t9em -sin + 2 t8 The direction cosines of the reflected ray are:- -sin(2ö1 + flo)cost -2cosc (L -2cos (6em) sin coswem) rem -sin(2, +$u)sinYz _2cose(2 _2cos(em -)sinsinwcm) tern -cos (2 + fib) -2 cose (r + 2sin (ern -Mn rem 2 2 If 1,], k are unit vectors in the directions of the tt, v, w axes respectively then the equation of the axis of symmetry 18 is r = sk. If the equation of the reflected ray is r = c + tb then the direction of the perpendicular between the reflected ray and that axis is b A k and the length, p, of that perpendicular is:-(bAk) c = Ak5 Now b = b11 +b2j + b3k so that b A k = b21 -b13 and Sb A k5 = (b + Hence:-c1b2 -c2bj = since c = c11 + c2j + c3k.

c1b2 -c2b1 = -(remsin?9jcosccj +lsin(2ö1 +Bo)cosço) (sin (2o +flo)sinyg + 2cosc -2cos (oem) sin sinwem)) \ tetTh + (rem sin th sin cpi + 1 sin (26 + fib) sin y) C (u sin (20 +fio)cospz + 2cose ( --2cos (Oem -)sin cosem)) \ rem = 2cosc(remsin6z +lsin(2i9t +fio))

C

sinj (--2cos (Oem -)sin coswe7fl) \ (v -cos1 -2cos (oem -)sinsinwem)) \ r Now usin2I-vcos?l= sinp1cos1 (rem sint9 +lsin(2i9i + j3o) -Tern sin01 -1sin(20 + Pb)) = 0 Hence:-I ()\ c1b2 -c261 = 4cose (rem sint9j + (sin (2O + /30D cos (19cm -sin sin(j -Wern) U2 V2 b + = sin2 (219 + fib) +4cos2 ( -m--+ + 4cos2 (19cm) sin2 . em cut ( u V)cos(19em-)sin) -COSe + S1fl2crn Tern / U +4sin (219 +fl0)cose (cosyz I -2cos (19cm -sin cosem) Iv +sinçoz I -2cos(9em -)sinsinern)) \Tem I2 = sin2 (219 +t3) +4cos2e (, --+ + 4cos2 (19cm -)sin2 em em

U V

-4 ( COSem + -nwn.) (19n. -sin \rem rem (u v +4sin (261 +/3o)cose -cosyt + -sin Wi \rem -2cos (19cm -cos -Yen.)) When is small:-1? 2\ b+bcisin2(2t9z+fio)+4cos2c(-j--+----) en. em,

U V

+4sin(2191+$o)cos(_coswz+_sinwi) Tern

U V ID

As Ten, >> /so sin19jcoswi, -sint9 sin çoj and cosi9,. Hence:-rem Tern U2 V2 + - sin2i9i and cn en.

U V

-cos + -sinoj sin61 so that rem Tern b + (sin (2i2 + fiç) + 2cosesini9i)2 and sin (26 + fig) (2cos (oem -sin C05 (w -coem) -sin 9) -cos(2t91 + flu) (2 sin (Oem -) sfrt + cost9t) For a typical embodiment, COS 6 > 0 and $ >> 0. If then 2O + /% >> ir. So that there is a useful range 0 <<i3 < f for which 2 -I-j3o > it. In which case sin t9j > 0 while sin (2z91 + $) < 0 and small. Since 1 is also small:- c1b2 -c2b1 4rem cos situ91 cos (oem -sin sin - Hence:- 4cosesiiu9 cos (oem -sin sin( -ern) 2 2 where Tern 5111 (2t9 + fib) + 2 cos sin 2 (sin (2)z + J3) cos (t9em) cos ( - -cos (2O + J3o) sin (oem -sin -cos (i9, + Thus for given values of the initial radius, of a cylindrical target and the radius, Tern, of an eye mirror, the coordinates rem, t2em, 92cm of the point at which a particular leaf axis is tangent to the sphere 164, the angle, /3, of the meridional ray 194, and the angle of reflection, c, (for which an approximte value may be used) it is possible to choose p < rgil and determine acceptable values for the rotation to in either direction for a position on either side of the leaf whose initial coordinates are rem, t2, 921.

The choice of p must allow for the implosion of the cylindrical target. As ablation practically stops after the shell has imploded to half its original radius p <0.5 r.

A common size for each leaf is chosen which gives an allowable range for a successful implosion along the axis of symmetry 18 which greatly exceeds the lengths of the various types of cylindrical target 101, 102, 103 or 104.

6.19 Beam velocity.

The velocity of all the recirculated beams 131 to 134 in the opposite direction along each cylindrical target 101, 102, 103 or 104 to its motion is Vbearns in the reference frame of the vehicle and its eye mirror(s). The beams must keep pace with the burn, For the reasons stated in Section 6.17, a steady state will be obtained somewhere in the region:- -- cot) < Vbcams «= g; -Clearly Vburn and depend on the type of fuel being burned.

The implosion period, tth,, must then be f lbearns/Vbeams. It is generally approxi-mately equal to rghhh/ujmp.

6.20 Actuators.

Figure 11 is a pair of graphs showing both the rotation, w, and the rate of rotation, of a leaf 191 as a function of time during one cycle of operation. It will be seen that the rate of rotation is sinusoidal except for the two linear sections 196 and 197 of duration ltgt/v&eams, where l is the length of the cylindrical shell of cold fuel 108 in the cylindrical target 101 or 102, or both the cylindrical shells 111 and 112 respectively in the cylindrical target 103 or 104, during the burn itself and the corresponding portion of the return respectively. The scale is arbitrary along each axis.

It follows that a piezoelectric actuator, such as a preloaded translator able to both push and pull, a preloaded amplified:PICZO actuator or the similar ultrasonic piezo actuator could produce such motion at a frequency approaching its resonant frequency, reson for a given additional mass, madam.

if there are no gaps between the cycles of operation, so that the motion is continuous and periodic, and a precalculated input signal is supplied to the actuator ahead of that motion and modified in closed loop operation, it is known that there will be almost no deviation from the desired motion if it is at half the resonant frequency of the actuator.

The resonant frequency at no load, f°', is given by:--1 2lrVmeff where /c is the stiffness and meff is the effective mass of the actuator.

The resonant frequency with an additional mass, madgrjn, is given by:-t 50Th = 1 2ir V mff + m0dd The time per cycle is then:-2 + 2 ,-esom "beams.1 assuming operation at half the resonant frequency.

As denoted in Sections 6.27.6 and 6.28.4 there are ni injector guns, each with a rate of fire of Thraje targets/sec. The time per cycle must be less than the time between the arrival of cylindrical targets, 1 / mjnjnratc; which sets an upper limit for the moment of inertia of the leaf.

if the leaf whose leaf axis 192 is tangent to the sphere 164 at rem, em, 40cm is symmetric about that leaf axis and the meridional plane through and the four points Tern, 29em± 4Ogj ± give acceptable values for the rotation, w, then the length of the arcs at the sides of the leaf 191 are 2 rem AO rneridionally and 2 rernA latitudinally. If the thickness of the material of the leaf is 4caf while its density is Plea! and the additional thickness of its coolant is d00t while its density is Pcoot then the areal density of the leaf is dleafPteaf + d00p00 except at its sides where material must replace the coolant to keep it in. The mass of the leaf, micaj, is: = 4 r,AO40 (dteaf 1eaf + d00ip00z) ignoring its curvature and the material at its sides.

The moment of inertia of the leaf, leaf, and its radius of gyration, kzeaj, about its leaf axis 192 are given by:- "eaf = = so that remI29 = ignoring its thickness.

If a piezo actuator 201 is in contact with the leaf 191 a perpendicular distance, kact, from the leaf axis 192, as shown in Figure 13, then:-/ -(klcaf \ maddn t. I 1f \ "act / since the moment of inertia of the leaf is unchanged.

Since the rotation, w, is very small, any change in kact as the leaf 191 rotates will be neglible.

Figure 12 is a front section of a leaf 191 through its leaf axis 192, in which the curvature of the reflective defining surface 163 and the reverse surface of that leaf have been exaggerated for clarity. It shows the leaf 191, its leaf axis 192, its hinge, a removable * leaf frame 205, one piezo actuator 201, and a respective defining mirror 206.

Since the leaf axis 192 is tangent to the reflective surface 163 of the leaf 191, its hinge comprises two needle bearings 203 and 204 on the* leaf axis 192 but at either side of the leaf 191, each within a recess provided for it in that leaf. These bearings are mounted on the removable leaf frame 205, which is in turn attached to the respective defining mirror 206.

Small reflective protrusions 207 and 208 are respectively provided to hold onto the needle bearings 203 and 204 with adequate strength. Alternatively, these bearings may be eliminated and the leaf 191 held by more than two piezo actuators, with a flexure provided to attach each such piezo actuator to the leaf 191, as described in Section 6.21.

The piezo actuator 201 being only able to push is in contact with the leaf 191 via a partially enclosed bail tip 209 which is free to rotate, so that it only allows normal forces to be transmitted, and isolates that actuator from both bending moments and lateral forces.

As that actuator can only push and not pull, two such actuators are provided, one at each end of the leaf. Figure 13 is a side elevation showing this arrangement. The bases of the two piezo actuators 201 and 202 are attached to the removable leaf frame 205, which is in turn attached to the respective defining mirror 206.

Figure 12 shows an input pipe 210 and an output pipe 211 in a coaxial arrange-ment within the leaf 191, through which cooling fluid 212 is passed. These pipes may be connected to a coaxial flexible pipe (not shown).

The leaf 191 incorporates a fibre optic cable (not shown due to its very small diameter) running from the reflective defining surface 163 of the leaf through the input pipe 210 and then a coaxial flexible pipe, such as the coaxial flexible pipe 236 shown in Figures 15 and 16, which supplies electromagnetic energy to a power sensor not shown here but described in Section 6.22 An Index Guiding Photonic Crystal Fibre made of undoped silica with a low OH content can sustain high power, have a high operating temperature range when covered with a polyimide buffer coating and withstand nuclear radiation.

A fibre comprising a low-index cladding, provided by a ring of holes, surrounding a high-index multi-mode core may transmit a broadband of electromagnetic energy in single-node operation, or be used for multi-mode operation, may have a numerical aperture as high as 0.9 in multi-mode operation in order to collect electromagnetic energy from a large solid angle, and may be used with an "open" end. Although electromagnetic energy entering the holes is unlikely to damage the cladding, the ends of the holes may each have a transparent seal to prevent liquids entering by capillary action. The end of such a fibre optic cable would preferably be flush with and at right-angles to the reflective surface 163. The power sensor may sense one or more of the modes of the fibre optic cable in multi-mode operation.

Figure 12A is an enlarged section of such a fibre optic cable 213 in a plane 215 at right-angles to its axis of symmetry 214. It shows a fused silica structure 216 forming both the core 217 and the cladding 218 of that fibre, a ring of holes 219 reducing the refractive index of that cladding, and a polyimide buffer coating 220.

In interstellar space, almost all of the thermal radiation reaching a piezo actuator 201 will come from other parts of the vehicle, as will the thermal conduction. Each piezo actuator 201 must be in close proximity to its respective leaf 191. Waste heat from the vehicle may be used to keep the cooling fluid 212 from freezing, before being radiated by the leaf 191. Alternatively, heat from the operation of a piezo actuator 201 may be used to melt cooling fluid which has frozen in its respective leaf 191 prior to a burn, in which case that piezo actuator 201 will have to function below the freezing point of the cooling fluid 212. During a burn, a leaf 191 may be at a temperature close to the boiling point of that fluid. In any event, a piezo actuator 201 will have to operate over a wide temperature range.

A typical range of working temperatures for a low voltage piezo actuator 201 based on a soft ceramic is -40°C to 80°C, but they have been tested to -196°C, where their total displacement is only one third of that at room temperature. A temperature sensor may be mounted on the piezo actuator 201 to facilitate compensation.

6.21 Tilting leaves and their actuators.

The injector guns 801 to 872 respectively are not aligned with the axis of symmetry 451 of the conical shield 420, as described in Section 6.28.1, so that the trajectories of the cylindrical targets 101, 102, 103 or 104 which they fire cannot be. Moreover, the dispersion of those projectiles, when fired by the injector guns 801 to 872 respectively, around their aim point 679 may be much larger than their radius, rg".

In a small eye mirror, such targets can be tracked by small movements of the de-fined mirror of the final stage in a series of stages, as described in Section 6.16.0 of GB 2,305,5163. Such defined mirrors in the present invention are, however, extremely large, with very high inertia, and cannot, therefore, be moved sufficiently far in the time available between the arrival of successive cylindrical targets.

Figures 14 and 15 are respectively front and side elevations showing a further embod-iment of the leaf 191 in which it is attached to three preloaded piezo actuators 221, 222 and 223 by three respective fiexures 231, 232 and 233. Each of the piezo actuators 221, 222 and 223 is able to both push and pull in order to hold the leaf 191. This provides rotation about an axis through the point Piringe which is orientated in any direction. Figures 16 and 17 are respectively front and side elevations showing a similar further embodiment of the leaf 191 in which there are four preloaded piezo actuators 221, 222, 223 and 224 and four respective flexures 231, 232, 233 and 234. (The preloaded piezo actuator 221 and its respective flexure 231 are hidden in both of these figures.) Both these embodiments may radially position, rotate and tilt a leaf.

The bases of the piezo actuators in all these figures are attached to an alternative removable leaf frame 235 which is in turn attached to the respective defining mirror 206.

Figures 15, 16 and 17 show a coaxial flexible pipe 236, which supplies cooling fluid 212 to, and removes it from, the leaf 191.

Figure 18 is a schematic diagram showing the axis of symmetry 105, and part of the surface, of a cylindrical target 101, 102, 103 or 104, whose trajectory is skew to the axis of symmetry 18, together with the incidence on that surface of two bearniets 239 and 240 respectively from two diametrically opposite leaves 241 and 242 (as indicated) from the same circular array of leaves (not shown) in the form of a section through that axis of symmetry 1D5. The skew of the trajectory has been exaggerated for clarity. It will be appreciated that the axis of symmetry of the cylindrical target might be skew to its trajectory.

Figure 18 also shows two sections 243 and 244 through that target at right-angles to that axis of symmetry 105-The rotation of these two leaves 241 and 242 has been adjusted so that the beamlets 239 and 240 both illuminate the surface of the cylindrical target 1017 102, 103 or 104 only between the sections 243 and 244.

Figure 19 is a schematic diagram showing the elliptical section 245 of the surface of the cylindrical target 101, 102, 103 or 104, its axis of symmetry 105 and the projections 247 and 248 of the bearniets 239 and 240 respectively in a plane 19 at right-angles to the axis of symmetry 18. The size of the beamlets has been exaggerated for clarity. The leaves 241 and 242 have been tilted so that the beamlets 239 and 240 approximately converge on the axis of symmetry 105 of the cylindrical target 101, 102, 103 or 104.

Each leaf 191 is able to rotate and tilt so that the reflection of its respective further meridional ray 195 through its respective point hinge passes along the axis of symmetry of the cylindrical target 101, 102, 103 or 104 in exact and simultaneous alignment with those of all the other leaves in its circular array of leaves.

The illumination of such a cylindrical target cannot, of course, be exactly symmetrical.

There is therefore an allowable range perpendicular to the axis of èymmetry 18 over which a successful implosion of a cylindrical target can take place.

The response of each of the piezo actuators 221 to 223 or 224 is determined by the sophistication of the controller provided for it. A simple controller limits the useable closed-loop tracking bandwidth of a piezo actuator to 1/10th of its resonant frequency, giving a response time of 10/f TCSOTh It is known that a more sophisticated approach can reduce the response time to between i/f?30n and 2/fresorz as aforesaid.

6.22 Control system.

Figure 20 is a schematic diagram of the control system for the leaves 191. It shows a leaf controller 251 that supplies signals to an actuator system 252 which comprises one or more actuators and rotates, and optionally tilts and/or moves radially, a leaf 191. A sensor 253 measures the position of the leaf 191, which comprises its rotation, and optionally its tilt and/or radial position, and reports it to the leaf controller 251. The sensor 253 may comprise a laser whose beam is reflected specularly from the reverse surface of the leaf 191 into a camera which measures the rotation and tilt of that leaf. This arrangement may be combined with an interferometer which measures changes in the radial position of that leaf. Alternatively, one sensor may be provided for each actuator to measure its position.

A further sensor 254 is provided for each actuator to measure its temperature, and report it to the leaf controller 251. These sensors enable closed-loop operation of the actuator system 252.

Since electromagnetic energy for the implosion of a cylindrical target has come straight from the reflective surface of a leaf, every part of the reflective surface of each leaf is in line of sight of the subsequent explosion, and may incorporate a power sensor able to monitor that explosion over the shortest possible path with the smallest possible delay. fri order to minimise timing delays and maximise redundancy, a power sensor 255 is provided in this embodiment for each actuator system 252 to monitor the power of the electromagnetic energy from the explosion of the previous target, and thus obtain a measure of its gain subject to the energy absorbed by the gas surrounding it, with a timelag of the order of rem/c where Tern is the radius of the largest (lowest numbered) eye mirror and c is the velocity of light in a vacuum; Each power sensor receives electromagnetic energy from a fibre optic cable, such as that shown in Figure 12A, running from the reflective defining surface 163 of the leaf 191 through the input pipe 210 shown in Figure 12 and the coaxial flexible pipe 236 shown in Figures 15, 16 and 17. The power sensor 255 reports the power of the explosion together with the time at which it was measured to the leaf controller 251.

Each leaf controller 251 has a digital input 257 attached to a fibre-optic digital data bus 256 which may be used not only for this purpose, but also to receive similar information from the power sensors for other actuator systems. An interface controller 273 also receives this information over the fibre-optic digital data bus through its digital input/output 274, and calculates an average of the power measurements and an average of the time of their measurement for transmission to any other engines to which electromagnetic energy froth this engine may be forwarded.

If the electromagnetic energy from the previous explosion was too high, one or more circular arrays of leaves, such as 181 to 183, do not take part in the implosion. Such a choice of leaves maintains the axial symmetry of the implosion. The choke is made according to a predetermined algorithm stored in each leaf controller 251. It will be seen from Figure 11 that nearly three-quarters of a cycle of operation, between the end of a burn and the start of a cycle, is available to make this choice.

A double tripod controller 271, which operates the six extensible legs 421 to 426 respectively, shown in Figures 38 to 41 and 43 and described in Section 6.27.6.3, responsible for the position arid orientation of the conical shield 420, shown in Figures 36, 37, 63 and 64 and described in Section 6.28.1, sends a digital signal to each leaf controller 251 with the position and orientation of the axis of symmetry 451 of that conical shield 420 relative to the axis of symmetry 18. The position and orientation of the conical shield 420 may be measured by a position sensor 272. The conical shield 420 contains the injector guns 801 to 872 respectively shown in Figures 55 to 64 and described in Section 6.28.1 The initial angle of rotation, w0, of the leaves 191, and their various tilts, position the recirculated beams 131 to 134 beyond the point 258 near the axis of symmetry 451 at which the implosion of the cylindrical target liii, 102, 103 or 104 is to commence, as shown in Figure 67 and described in Section 6.28.4. When one of the injector guns 801 to 872 respectively fires a cylindrical target 101, 102, 103 or 104, an analogue or digital signal from its muzzle velocity sensor 261 representing the muzzle velocity attained by that target, or a pair of pulses at the times when a position on that cylindrical target passed over two respective sensors, is sent to a camera controller 262. The camera controller 262 sends a digital signal detailing the time at which that cylindrical target was fired and that muzzle velocity to each of the leaf controllers 251 over the fibre-optic digital data bus 256 to its respective digital input 257. If a figure for that muzzle velocity is not available, a predetermined figure may be assumed and transmitted. The camera controller 262 instructs a pair of image-intensifiers 265 and 266 to gate the exposure of respective charge injection device cameras 267 and 268 at an interval after firing predicted from that muzzle velocity to allow for the arrival of that cylindrical target in their field of view.

The camera controller 262 receives respective frames from these cameras and uses them to measure the position of the cylindrical target 101, 102, 103 or 104 at that time, as described in Section 6.28.4, and then sends a further digital signal containing that position and the time of its measurement to each of the leaf controllers 251 over the fibre-optic digital data bus 256 to their respective digital inputs 257. Each leaf controller 251 also receives information over the fibre-optic digital data bus 256 to its respective digital input 257 from an inertial measurement unit 269, attached to the main body of the vehicle (rather than the conical shield described hereinafter). This inertial measurement unit has three ring laser gyroscopes which measure the angular velocities of the vehicle 270 shown in Figure 81 and described in Section 6.37 around three mutually orthogonal axes and three accelerometers which measure the accelerations to which the vehicle 270 is subjected along those three mutually orthogonal axes. All these measurements enable each leaf controller 251 to predict the future trajectory relative to the vehicle of the cylindrical target 1011 102, 103 or 104. The density of the ablated gas or plasma behind the shield must be estimated in order to establish its resistance to the motion of the cylindrical target. An

S

initial prediction of that future trajectory may be made on the basis of the muzzle velocity when the cylindrical target 101, 102, 103 or 104 is fired, followed by a more accurate prediction based on the position of the cylindrical target when in the field of view of the charge injection device cameras.

The actuator systems for those cylindrical arrays taking part in the burn then accel-erate their respective leaves 191 rotationally and adjust their tilt so that the velocity of the recirculated begins 131 to 134 along the trajectory of the cylindrical target 101, 102, 103 or 104, but in the direction in which that burn will take place, becomes equal to the beam velocity, Vbaams, and the leftmost edge of those beams intercepts the front of the cylindrical target 101, 102, 103 or 104 at the point 258 on that trajectory when and where its implosion is to start. It will be appreciated that as the trajectory of the cylindrical target does notcoincide with the axis of symmetry 18 of the eye mirror(s), these rotations and tilts will be different for each leaf, so that the necessary calculations may be most conveniently performed by that leaf's controller. The rotation and tilt of each leaf 191 is adjusted so that the reflection of its further meridional ray 195 through its respective point Phinge will pass along the expected position of the axis of symmetry 105 of the cylindrical target 101, 102, 103 or 104 in exact and simultaneous alignment with those of all the other leaves in its circular array of leaves.

The recirculated beams 131 to 134 maintain the beam velocity on the trajectory of the cylindrical target 101, 102, 103 or 104 by rotation and tilt until the burn is complete.

Thereafter, they deaccelerate, and return, not quite to their initial position, but to a position from which the trajectory of the next cylindrical target may best be intercepted.

6.23 Overlap.

As the leaves 191 may rotate independently, any set of leaves may act as an additional final stage in parallel, and further increase the power factor and thus the rate at which the power progressively rises on a point on the cylindrical target 101, 102, 103 or 104, provided

S

the axial symmetry of the illumination of that cylindrical target is maintained.

Figure 21 is a schematic diagram in the form of a half-section in the plane 159 through the axis of symmetry 105 showing the recirculated beams 131 and 132, in this case from the (two lowest numbered) eye mirrors 121 and 122 respectively (as indicated), which have already arrived at the surface of the imaginary cylinder 130 (similar to that shown in Figure 4).

The (lowest numbered) eye mirror 121 has six circular arrays of leaves 281 to 286 so that the recirculated beam 131 comprises six respective beamlets 291 to 296. The right-hand side of the recirculated beams 131 and 132, and of any other such beams, coincides with the right-hand side of the beamlet 296.

Figure 22 is similar to Figure 21 except that the bearnlet 294 overlaps with the bearniet 292 on the imaginary cylinder 130, and the bearnlets 295 and 296 overlap on that part of the imaginary cylinder 130 illuminated by the beamlet 293. And the right-hand side of all the recirculated beams, such as 131 to 134 in Figure 4, coincides with the right-band side of the beamlets 293, 295 and 296 at the surface of the imaginary cylinder 130. The angles of the bearnlets 294, 295 and 296 have been greatly exaggerated for clarity.

It will be seen that this adjustment incleases the rate at which the power rises on each area of the cylindrical target 101, 102, 103 or 104 as it moves to the right. As this affects the burn, it may also be used to control the gain.

It will be appreciated that many such overlapping schemes are possible. And that at least three circular arrays of leaves are required to provide more than one level of illumination. While one or more bearnlets may act as a trigger beam.

Since the recirculation path, and thus the recirculation period, for the various sets of leaves is substantially the same, the difference between the highest and lowest such recirculation period is very low, and the persistence required of the illumination from the source approaches the period over which the implosion of the cylindrical target is driven.

Moreover, the choice of overlapping scheme may be varied during use to adjust the illumination profile to suit different modes of operation: such as, for instance, endoatmo-spheric operation as well as exoatmospheric operation; arid fast as well as volume ignition.

6.23.1 Low recirculation power.

For a small target to burn, when imploded by the relatively low recirculated power and energy produced by the fusion of another small target, a well known technique known as hot spot ignition must be employed, rather than volume or fast ignition.

6.23.1.1 Hot spot ignition.

The energy density of DT compressed sufficiently to absorb a significant fraction of the a-particles released by the fusion of DT is almost two orders of magnitude less than that required to compress and heat the same amount of DT to the density and temperature required for ignition.

Unlike the DT gas inside a cylindrical target, which can escape from the imploding shell, the DT gas inside a spherical target is trapped and compressed by the imploding shell.

A strong shock, intensified by spherical rather than cylindrical convergence, propa-gates through the DT gas. This shock converges on the centre of the spherical target and is reflected from that collision. The DT gas behind the reflected shock stagnates.

The reflected shock hits the inner surface of the dense shell, which deaccelerates and reflects the shock back to the centre of the target for a further collision.

A sequence of such shocks heats the DT gas to the temperature necessary for its fusion.

At the same time, the kinetic energy of the cold shell is converted into internal energy, and the DT fuel in that shell is compressed.

A burn wave is propagated outwards into the cold shell by the a-particles released by fusion, which that shell is sufficiently dense to contain.

6.23.1.2 Hohlraum target.

Figure 22A is a schematic diagram in the form of a section through its axis of symmetry 297 of a hohiraum target 287 comprising a hohlraum 288, made of a high-Z material, such as gold, containing a spherical target for inertial confinement fusion by indirect X-ray drive consisting of a spherical ablator 289 enclosing a spherical shell of cold fuel 290 with which it is concentric. The hohlraum 288 has an axially symmetric trailing entrance hole or window 275 and an axially symmetric leading entrance hole or window 276. The spherical ablator 289 is attached to the hohlraum 288 by a tripod (not shown) whose legs are in planes through the axis of symmetry 297 of that hohlra.um equally spaced around that axis and at right-angles to that axis. Otherwise, the spherical ablator 289 may be similar to the cylindrical ablator 107. The cold ffiel consists either of a spherical porous shell containing DT in liquid form, or a spherical shell of solid DT, as for a cylindrical target.

The interior of the spherical shell of cold fuel 290 contains DT gas 109 at the vapour pressure corresponding to that target's operating temperature, as for a cylindrical target.

The leading end of the hohlraum 288 is attached to extendable fins 116, which clear beams entering the leading entrance hole 276 at that end when they are extended. A cylin-drical support 299 is inserted through the leading entrance hole 276 so that its spherically concave top fits the spherical ablator 289 and its base seals that entrance hole. It both supports that spherical ablator and prevents gas from a cartridge entering the hohiraum target 287 when that hohlraum target is fired from an injector gun. It is then jettisoned by the same mechanism (not shown) as that which opens the extendable fins 11. The cylindrical support can be supplemented or replaced by low density plastic foam in which a thermal wave will propagate supersonically with almost no hydrodynamic effect. Since the explosion of a hohiraum target is less energetic than that of a cylindrical target, a succeed-ing bohlraum target will survive such an explosion at a closer range. In consequence, the muzzle velocity of the hohiraum target, and thus the acceleration necessary to reach that velocity over a particular barrel length, may both be relatively low. The rate of rotation must be low, as for a cylindrical target.

The recirculated power from a hohlraum target will never be high enough to exceed the thermal damage threshold of the eye mirror(s), or ablate sufficient vapour to block the optical path of that recirculated power.

In order to provide enough recirculated power for a long enough period to illuminate a succeeding target, a hohiraum target must be exploded in a buffer gas. Since the period over which that recirculated power persists exceeds the recirculation period, the beams illuminating the hohlraum will already be present when that hohlraum reaches the position at which that illumination is intended to commence.

A prepulse is therefore provided by only allowing the widest and least powerful beam in a set of overlapping beams to enter a window initially. A main pulse is then supplied by one or more of the narrowest and most powerful beam(s) in that set entering that window as the hohiraum target moves to the right, as for a cylindrical target. In order to avoid wasting energy unnecessarily, it is desirable for that widest beam to continue entering that window during the entire implosion of the spherical target.

While the recirculation period remains the same for all types of target, the period for which the explosion of a hohiraum target provides adequate illumination for the recircu-lated beams may be considerably lower, for the reasons explained in Section 6.27.7; so that the rate of fire of the hohiraum targets may have to be higher. For a given muzzle velocity of any guns provided to inject targets, the spacing between the hohiraurn targets will be correspondingly smaller. However, hohiraum targets are able to survive the explosion of a previous hohiraum target at a much smaller separation because of its lower power, as aforesaid.

But if the main beam was provided by a final stage without leaves, its width would have to be inconveniently narrow for it to enter a window within a. short rise time for its pulse if the muzzle velocity was low-A higher relative velocity between the beams and the hohiraurn target may, however, be provided by leaves fitted to such a final stage. (Since the beams do not have to keep pace with the burn, as with a cylindrical target, they could otherwise be stationary.) It should be noted that each cylindrical array of leaves may operate independently of any other cylindrical array; so that the rise time of the pulse due to a particular beanilet is a matter of choice.

A sacrificial mirror 298, made of a bigh-Z material, such as gold, is attached to the hohlxaum 288 by a tripod (not shown) whose legs are in planes through the axis of sym-metry 297 of that hohlraum 288 equally spaced around that axis, which may be the same planes through the axis of symmetry 297 as those of the tripod attaching the spherical ablator 289 to the hohlraum 288. The sacrificial mirror 298 is covered by a ballistic cap 115, made of a high-Z material, such as gold, which need not be as substantial as that required for the more powerful cylindrical targets.

OverLapping trailing beams, such as 277 and 278 respectively shown above the hohiraum target 287, enter the gap between the hohlraum 288 and the sacrificial mit-rot 298 progressively as the hohiraum target passes through those beams. They are then reflected by the sacrificial mirror 298 through the trailing entrance hole 275 to illuminate a first ring of the inside wall of the hohlraum 288. This first ring is a certain distance from a plane at right-angles to the axis of symmetry 297 and through the centre of the spherical target. This ring is ablated to a plasma of high opacity which reradiates most of the absorbed energy as X-rays-The overlapping trailing beams provide a shaped, and rising, pulse of electromagnetic energy as the hohiraum target 287 passes through them.

Such overlap may be provided by multiple eye mirrors and/or multiple final stages, as described in Section 6.3. It may also be provided by beamlets from the leaves of one or more eye mirror(s), as described in Section 6.23. The overlapping trailing beams 277 and 278 respectively come from the outermost and thus larger eye mirror(s), which have the highest power(s), so as to compensate for the losses due to reflection from the sacrificial mirror 298 and interference to the entrance of electromagnetic energy into the hohlraurn 288 due to the tripod legs attaching it to that hohlraum.

Overlapping leading beams, such as 279 and 280 respectively shown above the hohiraum target 287, which provide the inside wall of the hohiraun with a pulse of iden-tical profile and timing to that supplied by the overlapping trailing beams, progressively enter the hohlraum 288 through the leading entrance hole 276 to illuminate a second ring of the inside wall of the hohlraum 288 symmetrically with the first ring about a plane at right-angles to the axis of symmetry 297 and through the centre of the spherical target.

The overlapping leading beams 279 and 280 respectively come from the next outermost eye mirror(s). They must not be present until the hohlraum target 281 reaches the posi-tion where its spherical target is to be imploded. Otherwise they will enter the trailing entrance hole 275 as the hohlraum target passes through them-This may be ensured by not triggering a source of electromagnetic energy for starting until that trailing entrance hole has passed through the region where the overlapping leading beams would otherwise be. Both the first and second rings are illuminated progressively from the inside to the outside of the hohiraum 288. Both the beams 278 and 280, and the beams 277 and 279, are kept a fixed distance apart by the operation of the cylindrical arrays of leaves to ensure that they illuminate their respective entrance holes simultaneously as the hohlraumu target flies through them.

As the period over which the recirculated power persists exceeds the recirculation pe-nod, it would be difficult to avoid the leading beams illuminating the trailing entrance hole prematurely during idling with multiple hohiraum targets, particularly if the recirculated beams are provided solely by multiple eye mirrors and/or multiple final stages. If the eye mirror(s) are leaved, the profile of the beams from those next outermost eye mirror(s) may be reversed, and their beamlets may approach the hohiraum target from the front towards its leading end in order to avoid illuminating the trailing entrance hole prematurely. But the second ring of the inside wall of the hohlraum 288 will then be illuminated progres-sively from the outside to the inside of that hohiraum, and thus introduce an undesirable asymmetry. Moreover, in order to synchronize the arrival of a leading beam at the leading entrance hole 276 to 1 ns, it would be necessary, inter alia, to be able to measure the po-sition of the hohlrauni target 287 to a corresponding accuracy. Even at a relative velocity between the leading beam and that hohlraum target of 5 krn/s, the corresponding accuracy is 5pm. If the hohiraum target has a length of 140 mm and fills a sensor frame of 1000 pixels in width then each pixel extends over 140 zm of the length of that target, which is much higher. It should be mentioned that reliable synchronization is essential for idling, but that a lower probability of synchronization suffices for starting, as multiple attempts may be made.

In a further embodiment, three corner-cube retro-reflectors (not shown) are attached to the leading end of the hohlrauin 288, equally spaced around the leading entrance hole 276 and facing 45° away from the axis of symmetry 297. Each corner-cube retro-reflector receives three single pulses of attosecond duration, each of a different wavelength from a respective laser positioned at one corner of a triangular base, all of which pulses are dispatched simultaneously at a known time. Three cameras, each of which has a filter to receive only the return pulse from a respective laser, time their return pulses so as to enable the position of that corner-cube retro-reflector to be triangulated to micrometre accuracy. The position of all three corner-cube retro-reflectors is found simultaneously to establish the position and orientation of the hohlraum target.

The X-rays reach all parts of the interior of the hohiraum at the speed of light, and ablate it, generating more X-rays. So that plasma rapidly covers the entire surface of the inside of the hohiraum. As the flux radiated by an area of the plasma is proportional to T4, where T is its temperature, the temperatures of all the areas of plasma tend to equalize (subject to losses out of the two entrance holes). The transfer efficiency from the source to a spherical target or fusion capsule is (Nf + f)/(Nf + 1) where N is the re-emission number and f is the ratio of the combined area of that capsule arid the two hohiraum entrance holes to the area of the hohlraum. As N 20 and f 0.238, it decreases by only 25% as the capsule implodes.

The geometry of the hohlraurn 288 and the outside radius of the spherical ablator 289 are optimised to provide nearly symmetric illumination of that spherical ablator by X-rays throughout its implosion. In a hohlraum illuminated by lasers, a further set of overlapping trailing beams would generally be provided to illuminate a third ring on the inside wall of the hohlraum 288, which is wholly or partially separate from the first ring, while a further set of overlapping leading beams would be provided to illuminate a fourth ring on the inside wall of the hohlraum, which is wholly or partially separate from the second ring.

This would, however, require four further beams, which would not then be available to increase the power factor. In practice, many more than two overlapping trailing beams, and many more than two overlapping leading beams, are provided by beamlets from the leaves to give a high power factor (albeit not as high as that for a direct drive target).

The amount of fuel in this type of hohiraum target is between one and two orders of magnitude less than in a cylindrical target of the same radius.

This hohlraum target is about five times the size of that used in the National Ignition Facility. The high-Z plasma from its inside wall will not penetrate far into its interior, particularly if that inside wall is coated with a layer of low-Z material, such as CR, to reduce its motion.

This type of target requires a symmetric implosion. The reflection of beams from the sacrificial mirror 298 not only reduces their intensity but also becomes non-specular when the surface of that mirror ablates, and thus introduces a left-right asymmetry into the implosion of the spherical ablator 289 and the spherical shell of cold fuel 290. This may be partially compensated if those reflected beams comprise more, or more powerful, beams, as aforesaid. The sacrificial mirror 298 is not necessarily plane as shown in Figure 22A.

However, if the gap between the hohlraum 288 and the sacrificial mirror 298 with the ballistic cap 115 is increased to allow beams from the right to enter the entrance hole 275 at the trailing end of the hohlraum 288 directly, then the spherical ablator 289 may be illuminated from both ends symmetrically. In a fusion power station, two opposing sets of eye mirror(s) on a common axis of symmetry 18 can be provided. As the hohlraum target is moving away from one set of eye mirror(s), and towards the other set, the profile of the beams from the latter must be reversed to provide a rising level of illumination. The beams are kept a fixed distance apart and the hohlraurn target flies through them as before. The appropriate beams are shown as dashed lines below the hohhaurn target 287. The right beam illuminates the first ring of the inside wall of the hohlraum 288 progressively from the outside to the inside of that hohlraum and thus introduces an undesirable asymmetry. The illumination from the left and right beams must, of course, commence simultaneously, and the left beams must not be present until the trailing entrance hole has passed through the region where those beams would otherwise be, which again restricts operation to starting unless the position of the hohlraurn target 287 is measured to micrometre accuracy (as the problem of synchronizing moving beams with the hohlraum target otherwise prevents idling). The exaust from the explosions in such an arrangement flows of necessity at right-angles to the axis of symmetry 18 of those eye mirrors.

6.23.1.3 Wire array Z-pinch.

A typical wire array Z-pinch device consists of a cylindrical array of some 240 con-ductors, each about 7.5 jim in diameter, and made of a metal such as tungsten, which are simultaneously vaporized into a plasma by a pulse of electricity rising to 20 MA in 100 ns.

The magnetic field generated by the parallel currents pulls the plasma towards the central axis of the cylindrical array. The subsequent collision provides a hot dense plasma emitting the majority of its thermal energy as soft IC-rays. It may be difficult to scale up such a device beyond a peak X-ray power of 280 1W. Moreover, the pulse width may be as short as 4 ns, whereas a pre-pulse of 20 ns at lower power followed by a pulse of 10 ns at higher power is needed for a hohlraum target, so that the pulse shape of a single such device is not suitable for inertial confinement fusion.

An eye mirror may, however, combine and smooth the output of multiple sources, as detailed in Sections 6.17.2, 6.17.2.1 and 6.19.2 of 082,305,516B, each of whose outputs will be spread out over a considerable distance round its annular exit aperture, as detailed in Section 6.19.4 of GB 2,305,616B; so that as many such devices as are needed may supply the power required for a hohlraum target. While a pulse duration which is too short may be extended by providing such devices for more than one set of such sources and staggering their operation. And the number and/or power of such devices in each set may be varied to assist in shaping the pulse.

Any beam profile, such as a rapidly rising pulse rate for a direct drive target, may be furnished by multiple beams, as described in Section 6.3, and/or by multiple beamlets, as detailed in Section 6.23. The prepulse may be delivered by a small number of beams and/or beamlets, while the main pulse may be delivered by all the beams and/or a large number of beainlets.

The most convenient driver for a wire array Z-pinch X-ray source is a Linear flans-former Driver (or LTD) for the reasons explained in a paper entitled "A New High Current Fast 100 ns LTD Based Driver for Z-pinch IFE at Sandia" (MG. Mazarakis & C.L. Olson Fusion Engineering 2005, 2l IEEE/NRS Syposium on). Each LTD cavity contained 40 individual circuits (or "bricks"), each comprising a 200-ky dry air gas switch and two Ca-pacitors, feeding in parallel through an accelerating cavity gap made of an iron tape core to give a current of 1 MA at 100 kV. Sixty such cavities were stacked around their common soft iron core to form a 60-cavity voltage adder module giving 6 MV. The cavity diameter was of the order of 3m, Typically 60 60-cavity voltage adder modules were connected in parallel by a single transmission line sequence 31 m in length, because of the diameter of the cavities, to the Z-pinch load. Much smaller and simpler configurations are, however, possible.

Two papers respectively entitled "The Magnetic Flux Compression Scheme as a Power Amplification & Pulse Shaping Stage" (M. Bavay et al, Power Modulator Symposium, 2002 and 2002 High-Voltage Workshop, Conf. Rec. of the 2M" mt. p.343) and "GD Numerical Modelisation and Optimization of Flux Compression Experiments" (P.L.'Eplattenier et a!, Pulsed Power Plasma Science, 2001, PPPS-2001, Digest of Technical Papers p.65) described a wire array Z-pinch device in which a further wire array in a primary circuit collapsed and compressed the magnetic flux in a secondary circuit containing the wire array Z-pinch device itself, and thus increased the current in it, together with a driver for that magnetic flux compression device with 120 similar LTD stages for a primary generator in a different arrangement to that described above, but probably providing 400kV, along with 40 such similar LTD stages for a secondary generator. A test of the flux compression device on the Z machine at Sandia gave an output pulse of 20 TW or more over 5 ns with a peak power output of 30 TW, albeit at a plasma temperature of 110 eV, which would emit some wavelengths too low for any eye mirrors themselves to reflect.

Each wire array Z-pinch device may be partially enclosed by a sacrificial mirror to direct its X-ray output towards a further alternate defined mirror, described in Section 6.24. The axis of symmetry of the wire array Z-pinch device may be aligned with an axis of symmetry of the sacrificial mirror.

The complexities of driving a wire array Z-pinch device were explained in a paper entitled "Architecture of petawatt-class z-pinch accelerators"(W.A. Stygar et al, Physical Review Special Topics -Accelerators and Beams 10, 030401 (2007)) together with its references. Clearly an X-ray power output of 20 TW over 5ns requires at least 100 kJ.

Each LCD cavity can provide a wire array kinetic energy of 2.5 kJ. So that at least 40 LCD cavities would be needed for each flux compressor, perhaps arranged in 4 modules with 10 cavities each.

Each flux compressor may be in close proximity to three LTD modules for its primary circuit giving 3 MA at 1 MV and a single LTD module for its secondary circuit giving 1 MA at 1 MV, together with the pumping stations required to charge their capacitors. A number of such flux compressors may be mounted in a circular array, either on the inside of a cylindrical mirror, such as the cylindrical mirror 428 shown in Figures 36, 37 and and described in Section 6.27.7.1, or on the outside of a compartment like the reactor compartment 437 shown in Figure 65 and also described in Section 6.27.7.1 Nine circular arrays of twenty-eight such assemblies could provide an X-ray output of TW for 20 us followed by 2240 TW for iOns, giving a total driver energy of 2.52 MJ. A relatively low energy from such devices may ignite a hohiraum target whose recirculated energy may in turn ignite a short cylindrical target.

6.24 Further alternate defined mirrors.

Figure 23 is a schematic diagram in a plane 19 through the axis of symmetry 18 in the form of a half-section showing a single further alternate defined mirror 171, which reflects electromagnetic energy into all the eye mirrors 311 to 313 respectively, each of which may be of any type. As the power loading on such a single mirror is very high, it is a sacrificial mirror of either of the types described in Section 6.18.6 of GB 2,305,516B and shown in Figures 87 and 88 thereof or detailed in Section 6.27.6.4 hereof. If mercury is used as the sacrificial reflecting surface and coolant then it should be precooled to its melting point of -38.87°C so that the cooling it provides is maximized and the amount of high-Z vapour released may be minimized if necessary.

The intensity of the electromagnetic energy from the burn of a cylindrical target is very high, but of short áuration. Sufficient high-Z vapour may be released to block that energy from reaching the eye mirrors, arid thus prevent that energy from damaging them.

When the burn itself ends, that vapour flows through the converging annular shock tube 427, shown in Figures 36 and 37 and described in Section 6.27.7.i, past the conical shield 420 also shown in those figures, whose function is described in Section 6.27.6.2.1, and then out along the axis of symmetry 18. It also helps protect that conical shield against excessive illumination.

The high-Z vapour both clears the optical path, and cools. The recirculated beams are unblocked and are reflected by the single further alternate defined mirror 171 to enter the eye mirror(s). In this way, the pulse width of the electromagnetic energy incident to those eye mirror(s) may be limited to keep the illumination of those eye mirror(s) below their damage threshold.

Another path, to which ingress is controlled and which does not lie in the optical path, may be provided for the escape of the high-Z vapour, so that the period during which the recirculated beams are blocked may be varied.

Fig.ire 65 described in Section 6.27. 7.1 shows the single further alternate defined mirror 171 and a cylindrical array of controllable valves 685 which control the escape of high-Z vapour to respective steel condensers 686 so as to remove that high-Z vapour from the optical path at a chosen distance from that single further alternate defined mirror, and thus at a chosen period after the burn. A number of such circular arrays of controllable valves and steel condensers are provided to enable the period during which the recirculated beams are blocked to be varied. The condensed mercury is returned to the sacrificial further alternate defined mirror 171.

If the burn of a cylindrical target takes place further away from the recirculation aperture 429, shown in Figures 36 and 37 and described in Section 6.27.7.1, then the intensity on the single further alternate defined mirror 171 of the electromagnetic energy it emits is reduced, less high-Z vapour is released by the sacrificial further alternate defined mirror 171, and the recirculated beams are unblocked more quickly.

Since eye mirrors collimate, focus or otherwise direct electromagnetic energy input to them over a wide range of angles, there is no necessity for the single further alternate defined mirror 171 either to maintain a particular shape, or even to reflect electromagnetic energy specularly. However, that part of its surface area near the axis of symmetry 18 which reflects electromagnetic energy into the (highest numbered) eye mirror 313 is small.

This reduces the amount of electromagnetic energy which passes into that eye mirror.

Moreover, not all of the surface of this single further alternate defined mirror reflects rays which are collimated along the axis of symmetry 18 into the angular input apertures of points on the first stage defined mirrors of the three eye mirrors. And all of the leading edges of those three defined mirrors are far from that axis of symmetry.

Figure 24 is a schematic diagram in a plane 19 through the axis of symmetry 18 in the form of a half-section showing individual further alternate defined mirrors 301 to 303 respectively, each of which reflects electromagnetic energy into a respective eye mirror 311 to 313. The surface area of all these mirrors combined cannot be higher than that of the single further alternate defined mirror 171, so that they must be sacrificial. However, the shape and position of each of these individual further alternate defined mirrors may more easily be chosen so as to reflect electromagnetic energy into their respective eye mirror; if necessary at the expense of reducing their combined surface area. Moreover, the surface area of the (highest numbered) individual further alternate defined minor 303 may be chosen to be larger than that part of the surface area in Figure 23 which reflects electromagnetic energy into the (highest numbered) eye mirror 313, so that it does not restrict the amount of that electromagnetic energy.

Figure 25 is a schematic diagram in a plane 19 through the axis of symmetry 18 in the form of a half-section showing individual truncated conical mirrors 321 to 323 respectively with low half-angles to which electromagnetic energy from the explosion of targets is inci-dent at high angles of incidence, so that their reflectivities to such electromagnetic energy are high. The inner (highest numbered) individual truncated conical mirror 323 reflects electromagnetic energy towards the inner (highest numbered) individual further alternate defined mirror 303. The middle individual truncated conical mirror 322 reflects electro-magnetic energy towards the middle individual further alternate defined mirror 302. The outer individual truncated conical mirror 321 reflects electromagnetic energy towards the outer individual further alternate defined mirror 301. This is the preferred embodiment for ablative drive for which the power loading is the highest due to the proximity of the explosions to these mirrors, as explained in Section 6.27.6.3. The individual truncated conical mirrors are also sacrificial.

Since the eye mirror(s) must maintain both their shape and reflectivity, it is unde-sirable for them to be sacrificial, to be subject to thermal expansion, or even to require excessive cooling. The mirror(s) preceding the eye mirror(s) along the optical path from the explosions are thus chosen to absorb wavelengths below those which those eye mirror(s) can reflect. The reflectivity of a metal decreases sharply below the critical wavelength cor-responding to its plasma frequency. The leading edges of the first stage defined mirrors of all the eye mirrors are far from the axis of symmetry 18.

6.25 Directed energy weapon.

As described in Section 6.17.2.1 of GB 2,305,516B, one or more outermost parallel final stages may direct an output beam, while the remaining parallel final stages illuminate an inertial confinement fusion target. And the further alternate defined mirror 171 reflects the electromagnetic energy from the inertial confinement fusion into an intermediate stage of the apparatus such that some of it forms the output beam.

Figure 26 is a schematic diagram in a plane 19 through the axis of symmetry 18 in the form of a half-section showing a single further alternate defined mirror 171. The leading edge of this single further alternate defined mirror 171 extends further to the left than is necessary to reflect electromagnetic energy into the outermost (lowest numbered) eye mirror 311 of those which provide recirculated beams so as to reflect electromagnetic energy into the outer eye mirror 310 which acts as a source of a beam for the acceleration of another object, and/or as a directed energy weapon.

Figure 27 is a schematic diagram in a plane 19 through the axis of symmetry 18 in the form of a half-section showing an individual further alternate defined mirror 300 which reflects electromagnetic energy into the outer eye mirror 310 which acts as a source of a beam for the acceleration of another object, and/or as a directed energy weapon.

Figure 28 is a schematic diagram in a plane 19 through the axis of symmetry 18 in the form of a half-section showing an individual truncated conical mirror 320 which reflects electromagnetic energy towards an individual further alternate defined mirror 300.

The individual further alternate defined mirror 300 reflects electromagnetic energy into the outer eye mirror 310 which acts as a source of a beam for the acceleration of another object, and/or as a directed energy weapon. Alternatively, the individual truncated conical mirror 320 may reflect electromagnetic energy towards an (outer) further defined mirror of the type described in GB 2,427,038 B. This has the advantage of containing stray electromagnetic energy within the outer eye mirror 310.

Figure 29 is a schematic diagram in a plane 19 through the axis of symmetry 18 of a small interstellar accelerator, which includes an apparatus 331 as shown in any of Figures 23, 24 or 25 firmly attached by legs 332 to a very large mass 333 in order to limit its movement to that of said very large mass. Electromagnetic energy from successive explosions 334 is directed by further eye mirrors 341 to 344 respectively in parallel, which act as sources of respective beams for the acceleration of another object, and/or as a directed energy weapon. It will be seen that utilizing part of the other hemisphere of those explosions 334 allows a higher proportion of the electromagnetic power to be collected and

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directed by the further eye mirrors 341 to 344 respectively over a longer period for each explosion than any of the embodiments shown in Figures 26, 27 or 28. Moreover, the larger diameter of that small interstellar accelerator reduces the diffraction of its output beam.

The further eye mirrors 341 to 344 respectively are attached to the very large mass 333 by further legs 351. The exaust from the successive explosions 334 escapes through the exaust aperture 352.

The single final stage of any of the eye mirrors shown in Figures 23 to 29, or any of the further eye mirrors 341 to 344 respectively, may be replaced by multiple final stages in parallel to each other, as described in Section 6.15.9 of GB 2,305,516 B, so as to reduce the annular thicknesses of their respective output beams.

The beams from all the embodiments shown in Figures 26 to 29 may be partially focussed, rotated or distorted as described in Section 6.16.0 of GB 2,305,516 B. Further or in the alternative, the defining mirrors of the final stages of the eye mirrors therein may be provided with leaves which rotate and tilt, as described in Section 6.21 of this application, for those purposes. Such leaves may also disperse those beams over a wide angle when they are not required.

6.26 Fusion power station.

Since the exaust from the small interstellar accelerator shown in Figure 29 is not contained, it is only suitable for use in space. However, an off-axis directed energy device may be attached to a horizontal fusion power station on a planet to provide a vertical beam of electromagnetic energy for the launch using ablative drive of a very large vehicle equipped with a shield and including some means to control its own attitude. So that such a vehicle typically includes a single engine. As the solid angle subtended by the further alternate defined mirror for such an off-axis directed energy device at the fusion explosion must inevitably be much smaller than that subtended by the shield of such a very large vehicle at its fusion explosion, the illumination of that shield must also be lower than in its normal operation. But the flow of coolant through that shield may be increased to provide sufficient thrust for the launch of its parent vehicle, as may be seen in Sections 6.27.6, 6.27.6.4, 6.27.7J and 6.34 Before launch, the very large vehicle and the off-axis directed energy device share both the same angular velocity and the same tangential velocity. After launch, the very large vehicle retains that tangential velocity, but its angular velocity reduces as it is inversely proportional to the radius of that vehicle from the centre of the planet. So that the attitude of the very large vehicle must be adjusted to provide some horizontal thrust and increase its tangential velocity if it is to remain vertically above the off-axis directed energy device.

The very large vehicle may escape the planet's gravity in a vertical climb. Alterna-tively, once it has left the atmosphere vertically, its engine may be started so that it may provide thrust away from the vertical and enter an orbit as required. Equally, since the first stage of an eye mirror may accept electromagnetic energy over a wide range of angles without preventing its final stage(s) from focussing, collimating or otherwise directing that energy, a small off-axis directed energy device may tilt away from the vertical while in op-eration. In addition, the beam from any off-axis directed energy device may be rotated as described in Section 6.16.0 of GB 2,305,516 B. Moreover, the defining mirrors of the final stage(s) of the eye mirror(s) therein may be provided with leaves which rotate and tilt, as described in Section 6.21 of this application for that purpose. So that the beam from an off-axis directed energy device can follow a vehicle turning away from the vertical in any case.

Figure 30 is a schematic diagram in the form of a plan of four launch tables or pads 326, 327, 328 and 329 respectively and four off-axis directed energy devices 336, 337, 338 and 339 respectively in a beam Launch facility attached to a fusion power station, together with a side half-section below it of the two largest off-axis directed energy devices 336 aM 337 respectively in that facility through both of their axes of symmetry (when vertical)

I

together with part of that fusion power station 355.

The diameters shown in the plan of the apertures 346, 347, 348 and 349 respectively in the four launch pads 326, 327, 328 and 329 respectively are equal to or slightly greater thai' the diameters of the four off-axis directed energy devices 336, 337, 338 and 339 respectively positioned vertically below them. The diameters of the four off-axis directed energy devices 336, 337, 338 and 339 respectively are in the ratios 8:4:2:1 so that the power in the beams from those off-axis directed energy devices are in the ratios 64:16:4:1. If a ratio ii: 1 is chosen for the respective diameters of two off-axis directed energy devices then the power in their beams is in the ratio n2: 1.

A shock wave 334 resulting from the implosion and burn of a cylindrical target 101, 102, 103 or 104 is positioned vertically below the second largest off-axis directed energy device 337 on the axis of symmetry 18 of the fusion power station 355 in the side half-section. There is an allowable range for that implosion along that axis of symmetry, as described in Section 6.18.2, and perpendicular to that axis of symmetry, as described in Section 6.21, which is utilised by altering the rotation and tilt of the leaves 191. The trajectories of the cylindrical targets are altered as described in Section 6.27.6.3. So that the burn may take place vertically below any of the off-axis directed energy devices 336, 337, 338 or 339 respectively. Moreover, it will be seen from the plan that there is room to incorporate more smaller off-axis directed energy devices into the beam launch facility without greatly increasing the distance of the burn from the axis of symmetry 18. Moreover, shorter cylindrical targets may be used to reduce the power even further, provided they chamber correctly in any guns provided to inject them into the reaction chamber of the fusion power station. Hence the power range of the beam launch facility may be even higher than 64:1 in order to launch vehicles of widely different masses.

The shield of the vehicle being launched must be sufficiently far above the off-axis directed energy devices that the ablation from it does not damage those devices. The vehicle may be supported on legs, which fit round the cluster of launch pads rather than on one of them. This is feasible with a large vehicle having long legs. Equally, the vehicle may rest on an elevated launch pad over the off-axis directed energy devices, and thus be a safe distance above those devices. Alternatively, the launch pad may be at ground level, a suitable distance above its respective off-axis directed energy device, which is below ground. Finally, a launch pad or table may be raised into an elevated position from ground level, and then swung over an off-axis directed energy device. In consequence of the various alternatives, the launch pads or tables are not shown in the side half-section.

It is necessary to isolate the interior of the fusion power station from the atmosphere of the planet. Even a cooled window would be unable to withstand the intensity of the electromagnetic energy from the fusion explosion.

Figure 31 is a schematic diagram showing two sectional views through the axis of symmetry 354 of an axially symmetric sacrificial water-wall 358 which provides a sealed window between the fusion power station 355 and the off-axis directed energy device 336, whose axis of symmetry coincides with that axis of symmetry 354.

The sacrificial water-wall 358 consists of a window 359 of fused quartz, a bottom tray 360 and a top tray 369. Pipes 363 supply the water. The window 359 may have any shape, and need not be formed by rotation, provided it is axially symmetric for dynamic balance, including the cylinder shown. Similarly for the top and bottom trays, each of which may be annular.

In the first view 361, the sacrificial water-wall 358 is stationary and the pipes 363 have filled the bottom tray 360 with water 364 which is horizontal. An inner seal 366 between a moveable further alternate defined mirror 357 and an annular bottom enclosure 973, together with bottom and top seals 367 and 368 respectively between the window 359 and the annular bottom enclosure 973 and a top enclosures 974 respectively, isolate the fusion power station 355 from the atmosphere of the planet.

The defining unit and the fixed defined unit of an eye mirror are attached by the three legs of a fixed tripod as shown in Figures 45 to 47 of and described in Section 6.16.1.1 of GB 2,305,516 B. Figure 30 shows the defining unit 975 and the fixed defined unit 976 of the off-axis directed energy device 336.

The annular bottom enclosure 973 supports the defining unit 975 while the fixed defined unit 976 supports the top enclosure 974.

The path for the load andJor thermal expansion between the annular bottom enclosure 973 and the top enclosure 974 is therefore short and rigid enough for any variations in load or temperature not to break the seals 367 and 368 respectively. Similarly for the off-axis directed energy devices 337, 338 and 339 respectively.

The tilt of a small off-axis directed energy device may be accomplished by replacing such attachments by actuators whose operation is controlled for that purpose.

In the second view 362, the sacrificial water-wall is in constant rotation about the axis of symmetry 354 and the surface 365 of the water 364 has adopted a parabolic shape in which its gravitational potential energy and its rotational kinetic energy are equal and the water is in equilibrium. The top tray 369 retains the top of the water 364. The moveable further alternate defined mirror 357 is raised so that it is in alignment with the sacrificial water-wall. (An interlock prevents the moveable further alternate defined mirror 357 from being raised unless the sacrificial water-wall has achieved the necessary rotational speed.) An actuator (not shown) to raise and lower the moveable further alternate defined mirror 357 is attached to tile top enclosure 974. A motor (not shown), attached to the outside of the annular bottom enclosure 973, drives the sacrificial water-wall 358.

Electromagnetic energy emitted by the fusion explosions in the interior of the fusion power station 355 is reflected by the moveable further alternate defined mirror 357 onto the surface 365 of the water 364, where part of it is reflected. The water 364 absorbs some of the electromagnetic energy not reflected and evaporates at a certain rate, while the pipes 363 supply water at the same rate in order to maintain the sacrificial water-wall.

The electromagnetic energy not absorbed passes through the water 364 and the window 359 into the off-axis directed energy device 336, which directs it as a vertical beam. The steam is extracted and condensed. The inoveable further alternate defined mirror 357 is also water cooled. Water absorbs wavelengths below 0.186pm, so that the off-axis directed energy device 336 is protected from those wavelengths.

When the off-axis directed energy device 336 is in operation, the sacrificial water-wall 358 is the only seal between the interior of the fusion power station 355 and the atmosphere of the planet. However, the pressure in that interior is maintained below atmospheric pressure: so that gas only flows into that interior through any imperfections in that seal.

Moreover, the launch only requires a few minutes. Further seals (not shown) are mounted outside the sacrificial water-wall on the attachment between the annular bottom enclosure 973 and the defining unit 975, and closed when the off-axis directed energy device 336 is not in use.

The side half-section in Figure 30, whose interior is not to scale, shows the reaction chamber 977 of the fusion power station 355, its inner wall 985, a partially spherical lithium blanket 978, a conical lithium blanket 9W! inside a cylindrical aperture 979 for the off-axis directed energy device 336, and a conical lithium blanket 982 inside a cylindrical aperture 980 for the off-axis directed energy device 337. Further conical lithium blankets are provided inside cylindrical apertures for the off-axis directed energy devices 338 and 339 respectively Some 80% of the energy produced by the fusion of DT is carried away by neutrons, and most of this energy passes through the inner wall 985 of the reaction chamber 977 arid is then absorbed in the various lithium blankets by nuclear reactions which may be exotherrnic or endothermic, including the partially spherical lithium blanket 978 and the conical lithium blankets 981 and 982 respectively, within their common thickness of about one metre.

The angle of each cone forming an outer surface of a conical lithium blanket is chosen so as to maximise the entrance of the cylindrical aperture for the respective off-axis directed energy device, and yet not provide a direct route for neutrons from the fusion of a cylindrical target to reach the respective sacrificial water-wall. The top and annular bottom enclosures 974 arid 973 respectively are sufficiently thick not only to absorb any scattered thermal neutrons which reach them but also adequate to absorb neutrons from a cylindrical target which explodes in the wrong position.

It is desirable to retain the capability to launch vehicles using the full power of the fusion power station. But that power level is at least two orders of magnitude larger than the highest terrestial requirement for power currently envisaged.

A primary pump 98 supplies liquid lithium at a low temperature, somewhat above its melting point of 180°C, through an outer coaxial pipe 987 to the conical lithium blanket 981 for the off-axis directed energy device 336 from where it is forced through an inner coaxial pipe 988 into a conical lithium storage chamber 991 at a temperature below its boiling point of 1330°C. There is a similar arrangement for the conical lithium blanket 982 for the off-axis directed energy device 337 (which arrangement is omitted for clarity) and for those of each of the off-axis directed energy devices 338 and 339 respectively.

As the lithium in the lithium blankets may be heated up by neutrons in as little as two seconds when burning DT or LiDT, a multitude of similar arrangements, of which only three are shown, are provided for the partially spherical lithium blanket 978 and its partially spherical lithium storage chamber 995. It is, of course, feasible to burn DT or LiDT for a second or two to heat up the lithium blankets, and then switch to LiDT or DHe3.

Each conical lithium storage chamber is supported by the partially spherical lithium storage chamber 995 through a respective tripod (not shown for clarity) in the cylindrical aperture for its respective off-axis directed energy device.

A secondary pump 996 supplies hot liquid lithium from the partially spherical lithium storage chamber 995 to a steam generator 997 and then to a tritium recovery unit 998 before returning the cooled liquid lithium to that chamber. The steam is used to generate electricity and/or desalinate salt water. A temperature of 500°C is desirable for the thermal efficiency of the former.

As the available power is very high, a multitude of such secondary pumps, steam generators and tritium recovery units is provided for the partially spherical lithium storage chamber 995.

However, it is not convenient to provide such a secondary pump for a conical lithium storage chamber 991 as it lies below its respective sacrificial water-wall. Instead, cooled liquid lithium is injected into a conical lithium storage chamber by a further pump (not shown) mounted on the partially spherical lithium storage chamber 995 through a passage in one of the tripod legs supporting that conical lithium storage chamber. Hot liquid lithium is then forced out of that chamber through two similar passages in the other two legs of that tripod into the partially spherical lithium storage chamber 995.

Each primary pump 986, each secondary pump 996, and each further pump may all be a high-temperature annular linear induction pump with both inner and outer stators comprising Invar windings and an outer core and a hollow inner core made of Hiperco-27 alloy. In each primary pump 986 and each further pump, the flow is initially through the inner core's hollow centre in the reverse direction to the output flow. The exaust 999 is also supplied to energy and tritium recovery units.

The waste energy from a launch is thus available for use over a period two orders of magnitude longer than the duration of a launch. Such a low duty cycle greatly extends the lifetime of the fusion power station.

Various designs for fusion reactors were described in a book entitled "Nuclear Fusion by Inertial Confinement: A Comprehensive Treatise" (G. Velarde et a! (1993)). This book reproduces a performance map for ICF target chamber first surface protection concepts (from Monsler, M.J. et al., Nuci. Technol. Fusion, 1, 302, 1981) as Figure 7 in Chapter 25.

At low power, a dry wall of steel or a refractory metal will suffice. At a much higher power, a wetted wall of a liquid metal, such as lithium, may be used. Pore arrays, similar to those described in Section 6.27.6.4 but sealed when closed by a fixed stop instead of a moveable extension in a.n actuator, and in a lithium blanket instead of a sealed compartment, may be used to provide either a dry or a wetted wall depending on the pressure in that lithium blanket. This allows operation at either a low power level or a higher power level. The lithium is also recovered from the exaust The lithium vapour from the wall does not enter the beams from the eye mirrors. And if the lithium in the blanket boils, the annular metal diaphragms for the pore arrays act as safety valves discharging lithium vapour into the reaction chamber.

The axially symmetric configuration allows both magnetic protection of the inner wall and the direct extraction of energy from the exaust by magnetohydrodynaruic (MHD) or other devices. An inhomogeneous magnetic field may also remove burn and debris ions from the vicinity of the point at which the implosion of the next cylindrical target is to take place, to prevent them absorbing electromagnetic energy from the recirculated beams.

But a magnetic field used for protection will impede the pumping of the liquid lithium.

The tritium produced may be left to decay into helium three in order to provide a more suitable fuel for spacecraft and terrestial power stations.

6.27 Shield.

6.27.1 Functions and composition.

Figures 32, 33, 36 and 37 are schematic diagrams illustrating the function of the shield 370 and the items associated with it. All these figures are in the form of a section of the shield 370 through the axis of symmetry 18, which is also its axis of symmetry. Figure 32 shows the left half of the shield 370, Figure 33 shows the right half, and Figures 36 and 37 both show the middle portion of that shield. Since the shield 370 is axially symmetric, the hatching of the sections in all these figures is axially symmetric; so that it would remain in the same orientation if the direction of view rotated about the axis of symmetry 18.

The primary purpose of the shield is to ptotect the apparatus during its coasting and deacceleration phases of flight from that bombardment by electrons, protons and dust particles in space which results from its velocity. It may also protect the apparatus frpm electromagnetic energy when it is being accelerated or deaccelerated by a beam, either by reflecting that beam, and/or by having material ablated from its surface by that beam. It may equally protect the apparatus from the hot gas or plasma generated by reentry into an atmosphere. As it may be eroded and/or ablated, the shield 370 may be replaceable.

Figures 32 and 33 also respectively show closed and open shield extensions 384 and 375 which rotate inwards to close the output apertures of the eye mirrors 311 to 313, each of which may be. of any type, in order to protect those eye mirrors when they are not in use.

Figure 32 shows a pump 521 which supplies coolant to the shield extension 384 through its hinge 554 by means of a pipe 524, part of which lies behind that shield extension. Figure 33 shows a pump 531 which supplies coolant to the shield extension 375 through its hinge 545 by means of a pipe 534. Both the pump 531 and the pipe 534 lie in front of the section of the figure and are therefore shown in grey.

The shield 370 may merely consist of an ablative material which is not thermally 1 DO conductive. Alternatively, it may consist of an ablative material which is thermally con-ductive: for instance, beryllium; a beryllium aluminium alloy, such as a two phase matrix composite; or a carbon-carbon composite. This material may be porous, and a cooling fluid may be pumped through it to its outside surface where that fluid ablates. The utility of such a coolant is to prevent the material of the shield from melting, rather than ablating.

Figures 32 and 33 show controllable pore arrays 391 through the shield 371) and their shield extensions 384 and 375 respectively together with the coolant 392. The ablation pressure of the material of the shield and/or the coolant generates thrust. The ablated material provides plasma or gas, which may be of substantially uniform density, behind the shield 370.

The shield 370 may equally consist of a mirror, whose reflective surface is sacrificial, or consists of a liquid which is sacrificial, as described in Section 6.18.6 of GB 2,305,516B.

The shield 370 protects the apparatus from both the electromagnetic energy and the plasma resulting from the explosion of the DT or other fuel. A beryllium or carbon shield also acts as a neutron moderator and reflector.

In magnetic drive, the shield acts as a radiator as it is then undesirable to reduce the velocity of the charged fusion products, such as a-particles, and the exaust by adding coolant to that exaust. The rear surface of the shield also conducts eddy currents whose interaction with the magnetic field produces an impulse on it. The material of the rear surface of the shield must then be electrically conductive, and thus thermally conductive.

6.27.2 Particle emissiOnS.

As shown in Figure 34, the area of an element 401 of a spherical shell 402 of radius rshield at an angle, 0, to a point explosion at its centre 0 measured from the x-direction along the axis of symmetry 18 is:- 27r Tshield sinG r3lddG The emission of electromagnetic energy and particles from the explosion of part of the cylindrical target 101, 102, 103 or 104 is not isotropic. The imploding conical shell 153 of cold fuel and the leading guide 113 in the forward direction together with the trailing guide 114 in the rearward direction absorb some of those emissions In the forward direction this protects the starter injector 577 and the inj&tor guns Sot to 872 housed inside a conical shield 420 as shown in Figures 55 to 64 and described in Section 6.28.!, any further alternate defined mirror 171, any individual further alternate defined mirrors 300 or 301 to 3D3, and any individual conical mirrors 320 or 321 to 323 from those particles and excessive levels of electromagnetic energy. It equally protects those cylindrical targets 101, 102, 103 or 104 which are in flight towards the points at which their respective implosions will take place, and may thus be very close to the point explosion. The conical shield itself masks those mirrors from such emissions from the burn and the early expansion of the subsequent explosion. It should be mentioned that the presence of high-Z material in the cylindrical target 101, 102, 103 or 104 from the leading guide 113 and the trailing guide 114 enhances its soft X-ray emisssions while reducing its hard X-ray output. However, where that high-Z material lies between the explosion and the conical shield, and when it is heated to a temperature at which it is well-ionized, it will also attenuate radiation below 1 keV quite considerably. Further details are given in Section 6.27.7 if the total momentum of all the particles escaping isotropically from such a point explosion is the product of their total mass, mz0t, and their weighted average velocity, wav, and that shield lies inside a cone 398 of half-angle iv -Oshidmin whose vertex coincides with that point explosion, and outside a cone 399 of half-angle ivOshL4max whose vertex coincides with that point explosion, as shown in Figure 34, then the momentum of those particles which impinge on the shield resolved in the x-direction along the axis of symmetry 18 is:-P1IOahldmar mtotu.wav: 2 Ttotttwav 2 6ohtdma 4irr2 j --2TrrShCws1nOcosOdG = 4 sin 9L_eazrtain shieLd ?t 6shld,ntn * 2 * 2 = (sin 8shlcimax sin Osi.iarmim) The particles impinging on the shield from the fusion of DT consist of 14.1 MeV neutrons with a velocity of 5.19379 x iO cm / a, and, in the absence of a buffer gas, 3.5 MeV a-particles with a velocity of 1.29 x 10° cm / s in a vacuum but roughly four times as much rest mass. However, the mass of these particles which will be released during the burn of a cylindrical target is much less than the mass which will be ablated from the shield 370 by that burn in ablative drive. Moreover, the a-particles, together with the other charged particles, will be slowed down by the plasma ablated from the shield well before they reach that shield. It should be mentioned that this loss of velocity also reduces their momentum in the exaust after deflection by an inhomogeneous magnetic field.

Neutron multiplication may take place in any beryllium in the shield due to the endothermic reaction:-n+ 4Be° -22He4 -(-2n---1.67 MeV (2-3 barns © 2-14MeV) The half-life of tritium is 12.6 years due to the reaction:- -2He3 +Y(18.6llceV) During a long voyage, therefore, it will be necessary to breed tritium, to fill any cylindrical targets 101, 102, 103 or 104 which need DT on board, using two of the reactions listed in Section 6.16:-n+ 3Li6 -# 2He4(2.OSMeV) + 1T3(2.T IvLeV) (0.02 barns@1l.5 MeV) (5) n + 3LiT n + gHe4 + 1T3 -2.47MeV (0.4barns©11.5MeV) (9) Since most of the neutrons from the fusion reactions will escape into space, rather than collide with the shield, neutron multiplication in the shields may be required to breed sufficient DT.

Figures 32 and 33 both show a liquid lithium blanket 403 inside a container 404 for the breeding of DT. The amount of helium produced as a by-product may suffice for a coolant for the shield in magnetic drive, described in Section 6.33 6.2T.2.1 Burn of deuterium helium three.

The 211e3 from the decay of tritium may be burnt if the DT seed in a cylindrical target 103 or 104 reaches the conditions necessary for its ignition at the axis of symmetry of that cylindrical target, either due to its implosion velocity being high enough, or sufficient hot electrons reaching that axis, and it proves possible for the ensuing DT burn to ignite the reaction:- + 2}1e3 -* 2He4 + 1H' + 18.35 Mev (up to 0.9 barns at 0.25 MeV) The products of this reaction all comprise charged particles which may be diverted by an inhomogeneous magnetic field. However the following equiprobable deuterium reactions may also take place:- 1D2 + 1D2 -+ 2He3(0.82MeV) +n(2.45MeV) (up to 0.11 barns at 1.75MeV) 1]D2 + -* 1T3(1.O1MeV)+ 2W(3.O2MeV) (up to 0.09ö barns at 1.25MeV) The first reaction produces a neutron, while the second reaction produces a triton which can react with a deuteron to produce a neutron. The helium three in the fuel may absorb a neutron by means of either of the reactions:-m+ 2He3 -p 21)2(0.1 barns©12MeV) n+ 2Jile3 -4 1T3+ 1H'(O.l barns©I2MeV) Both the number of neutrons produced, zmd the fraction of those produced escaping from the fuel, are likely to be small and the flow of coolant needed in ablative drive when burning DHe3 to remove the energy they deposit in the shield is of the correct order for the vapour from that coolant to enable optical recirculation in ablative drive from behind the shield in exoatmospheric operation if the cylindrical targets are sufficiently large, as described in Section 6.27.7.2. During a long voyage, tritium must be bred, but only sufficient for the DT seed if enough DHe3 is available.

Since the boiling point of helium is only 4.22°K the 2He3 from the decay of DT does not recondense in the shell of fuel in a cylindrical target containing solid DT, other than by diffusion, but builds up in the inside of that cylindrical target. It has to be extracted and loaded into a different type of shell consisting of a deuterium "honeycomb" with the interstices filled with liquid helium 3, as suggested in Project Daedalus. The deuterium tritium trigger would be an inner shell of cold fuel 112 as shown in the second further cylindrical target 103 or the third further cylindrical target 104 in Figure 2.

6.27.3 Confinement time.

If V0 is the initial volume of the cylinder of burning fuel, V(t) is its volume at time, t, Rj is the initial radius of the burning core, R(t) is its radius at time, t, and c8 (or cT) is the isothermal sound velocity, then for a cylindrical target 101, 102, 103 or 104:-V(t) = (11(t))2 (icst)2 If the fuel is confined during burning for a period, Tcr,nf, equal to R / c then the effective confinement time is:- ftconf V(t) = jRf/cs (i -L (f -3c5 R1} Rf 3 Cs 6.27.4 Energy balance.

If (cv) is the averaged reactivity, defined as the probability of reaction of cross-section, cr(v), per unit time per unit density of target nuclei averaged over a range of relative velocities, v, between a projectile and a target nucleus with their distribution function normalised to one, and n0 is the ion number density of the plasma then the total number of fusion reactions1 Nf3, in the effective confinement time is given by:-rt V0R1 (crv)--3c3 However, in low temperature volume ignition, effective burn starts when part of the fuel is no longer confined, so that the burning fuel mass and effective confinement parameter are smaller than the initial values, and the usual formula for burn efficiency derived from the above does not apply and a value must be assumed for it.

We may use the simplifying assumption that volume ignition of UT fuel leads to the a-particles and neutrons, together with all their energy, being retained within the remaining fuel and achieving thermal equilibrium within that fuel.

If one third of the DT fuel is burnt in the reaction 1D2 + 1T3 -2He4 + it + 17.6 MeV then for each reaction there will be six electrons, two unburnt deuterium ions, two unburnt tritium ions, one a-particle and one neutron in the fuel, making twelve particles in all. The thermal energy for each such particle is k3T where Boltzmann's constant It8 = 1 eV / eV if the temperature, T, is in eV. Hence the energy balance is:-

S

7r = 17.6 x 106 so that T = 0.97 MeV At this increased temperature, even with a density of 190g / cm3. the burnt fuel becomes optically thin, and the electromagnetic power it emits is proportional to where p is the density of the burnt fuel.

If the radius of the compressed fuel is rla then the confinement time during burning is given by Tconf r1 / c. The sound speed, c3 = i.IFfBT where pUeI is the gas constant for the burnt fuel. This is equal to 12kg / (15m) in the above case where m is the mass of a proton. Hence for r1 = 0.02191 cm, Tnf In a vacuum, the outside of the burnt fuel would expand at the velocity of the 3.5 MeV a-particles, and thus 1.29 x cm / s. The remainder of the fuel would expand at its local sound speed of 2.8 x 107(T/ 1000)1/2 cm/s where the local temperature, T, is in eV. These velocities are radial. Any axial expansion of the burnt fuel will be much less than Vburn = 5 x 108 cm / a. But, in practice, the burnt fuel is surrounded along its length by plasma ablated from the cylindrical ablator 107, and at its ends by plasma from the remainder of the cylindrical target, including the leading guide 113 and the trailing guide 114.

6.27.5 Relative positions of heat wave and shock wave.

In the direct drive of a target, the mass ablation rate and the exaust velocity from that target both have the same weak dependence on the intensity of illumination, as described in Section 6.4, so that the density of the plasma ablated from the cylindrical ablator 107 during the implosion is largely independent of the rapidly and progressively rising intensity on that ablator.

As a result of the burn, a heat front expands cylindrically from the length of the cylindrical target 101, 102, 103 or 104, and spherically from its ends, into the plasma ablated from the cylindrical ablator 107. Since that burn starts at the trailing end of that target, the expansion is greater at each point of time at the trailing end. In an ideal target comprised only of a cylindrical ablator enclosing a cylindrical shell of fuel, the heat wave 405 therefore approximates to the exterior surface of a body formed by two spheres 406 and 407 respectively connected by a cone 408 tangent to both their surfaces, as shown in Figure 35. The shock wave 40, which is initially inside the heat wave, has a similar shape.

For a constant mass rate, iii, and a constant flow, u, the flow out of a cylinder of radius, r, and length, 1, is constant, being given by th = 2ir riup where p is the density at the surface of the cylinder. in which case, p x 1 / r and p = g0r1 where 90 is a constant.

But the flow out of a cylindrical target as a result of ablation is not necessarily constant with respect to the radius from its axis of symmetry. in subsonic flow, it would slow down as that radius increases. But in supersonic flow, it will speed up as that radius increases.

Hence p = goø where sc C -1 for supersonic flow and -1 cc,c C 0 for subsonic flow.

Similarly, such a constant flow out of asphere of radius, r, is given by iii = tic r2up, a constant. In which case, p cc 1 /r2 and p = g0r2. Hence for a sphere p = gor' where c < -2 for supersonic flow and -2 cc c < 0 for subsonic flow.

If a similar expression were to be fitted to a rarefaction wave, with respect to an origin moving in time so as to coincide with the point reached by that wave, its exponent, ,c, would be a function of time, starting at a very negative value and increasing to a negative value much nearer zero.

The relationship between the heat wave and the shock wave from strong point explo-sions in an ambient gas has been considered in a paper entitled "The point explosion with heat conduction" by P. Reinicke and J. Meyer-Ter-Vehn (Phys. Fluids A, Vol. 3, No. 7, July 1991, p.180.?).

Only if the ambient gas density decays with a given power of the radius from the point explosion, can a completely self-similar solution be obtained: in which case, the relative position of the shock wave and the heat wave does not depend on time. The shock wave must remain in the same position relative to the heat wave, and behind it. If the ambient gas density is uniform, the solution cannot be completely self-similar and the shock wave can overtake the heat wave. If the heat conductivity is x = XOPaTb where Xc, a and b are constants such that a «= B and b »= 1 then the condition for complete self-similarity is believed to be:- (2b -1)n + 2 sothat -n<K<U 2b -2a + 1 and the adiabatic exponent y <y > 0 where 2(b+1)(n-1)--(3n-2)a 3 2b(n-a(n-2) 7'2 where ri = 3 for the spherical case and n = 2 for the cylindrical case but the precise value for 71 is at present undetermined.

For radiative heat conduction in a fully ionized plasma a = -2 and b = iS / 2 so that this condition becomes:-Bn+1 21n-19 3 9 and7c'yj>Owhere1517ay1 Said paper obtained an estimate for the time when the shock front overtakes the heat front in a uniform gas by equating the shock front location from a book entitled "Similarity and Dimensional Methods in Mechanics" (L. L Sedov (1959)) with the heat front location from a work entitled "Similarity, Self-Similarity and Intermediate Asymptotics" (G. I. Barenbatt (1979)).

It is very unlikely that the shock wave will overtake the heat wave until it reaches the substantially uniform plasma ablated from the shield 370 where ic = 0. This eventuality is treated in Section 6.27.7 6.27.6 Burn and heat wave.

As the heat wave is outside the shock wave, the electromagnetic power emitted by the burnt fuel as hard X-rays is extremely high, and it cools quickly. The rate of energy loss declines quite slowly as the temperature reduces, being proportional to p2J'h/2 per unit volume for temperatures above one keV. Indeed, if there were no expansion, almost all the energy would be radiated within 2 ns. If the intensity on the shield were to be excessive as a result of this high power, a supersonic heating wave, which involves no hydrodynamic motion, and thus neither thrust nor ablation, would ensue. However, not all of the cylindrical target 101, 102, 103 or 104 burns at the same time, and the burn lasts for a time 1tgi / Vbeams >> Tconf where 1tgt is the length of the cylindrical shell(s) of cold fuel in that target. During this period, the power radiated at all wavelengths, Prad, is fairly constant by design. So that if the shield comprises a portion of a sphere of radius, r9hjd, whose centre coincides with the burning target, and there is no buffer gas to absorb the hard X-rays (as may be the case for the first explosion in a series of explosions in exoatmospheric conditions, or before the shield or a coolant reaches its operating temperature, whatever the design parameters), then the X-ray ablation pressure, Pa, on the low-Z material of the shield due to an ablative heating wave is given by:-Prad 1 Pa 2 47rr5h6ld J4 FSiTskieza where FffBZZd is the gas constant for the shield material and Thjd is the temperature of the plasma ablating from its surface.

The mass ablation rate per unit area, Vfla, from the shield is given by:-Prad 1 ma = 2 A pshieldrn - £ B shield so that the mass ablated per unit area from the shield by a single explosion, m", is th19t /Vbea,ns.

Since both Pa and tha are inversely dependent on rhjeld, both the total thrust on the vehicle, and the total mass ablated from the shield by a single explosion, being proportional to the area of the shield, are independent of the radius of that shield.

The exaust velocity, u,,, is given by:-Pa IA r'shield'ri 1/2 tL01 -¶ B -tshield) ma Similarly for a coolant. Since the gas constant for the coolant, pfQLant = (1 + Z)lcB / Am where Jc is Boltzrnann's constant, Z is the atomic number of the coolant, A is its mass number and ni is the mass of a proton, hydrogen has the highest exaust veloc-ity; so that liquid hydrogen is an attractive coolant for the shield as well as an excellent neutron moderator. It is transparent in all its phases other than a plasma.

The condition that a supersonic heating wave does not form is:-Q Prad <4 (rtdTBhCj43/2 where hetd is the initial density of the shield.

The highest values of the exaust velocity occur for the highest values of T3hla, which reduce the value of the dimensionless drive parameter, Q. The smallest radius of the shield for any shield material may be chosen using this condition given some assumption for T8h6,d.

If the minimum and maximum acceptable accelerations for the vehicle are g,,-j,,, and 9mac respectively, then the final velocity of the vehicle, veh, is given by the rocket equation:-Uveh = Uex log(gmx/gmjn) The time, tveh, taken to reach this velocity is equal to the total mass of the material in the exaust over the entire acceleration divided by the rate at which it is fed into the exaust, and is thus given by:-(1 __ __ 9fltifl flynaa, flmzn It is therefore proportional to the final velocity of the vehicle.

There is a further condition involving the radius of the shield. If the shield 379 is a flat disk of radius equal to rshjeja then the beams from the eye mirrors will typically meet a distance rshieia from it, and the burn will take place at that position If the shield 370 contains a spherical indentation 390 of radius rshjeja such as that shown in Figure 36 with the geometry shown in Figure 34 then those beams will meet at the centre of that spherical indentation 390, or close to it. In either case, the radius of the shock wave from the burn when it reaches the shield will be approximately Tshjeja. If there are injector guns, each with a rate of fire of rate cylindrical targets per second, then the period between cylindrical targets is 1/minjnrate seconds. The gas ablated from the shield acts as a buffer gas which absorbs hard X-rays and reduces Praa. If the exaust velocity of the gas ablated from the shield is Uez then that gas will fill a space between burns extending ue/mimjnrate from the shield. The condition that the shock wave is still entirely within the ablated gas when it meets the shield is therefore uew/minjnrats > 2 r8h1d. The shock wave is optically thin. So that this condition ensures that both hemispheres of the shock wave provide electromagnetic energy for optical recirculation in the form of soft X-ray-s or light of longer wavelengths.

If the mass ablated per unit area from the shield by an explosion, m?1, expanded normally from a plane surface into a box of unit surface area and length uex/minjnrate in the time between explosions, 1/mjnjmrate, then it would have a density minjnrate if evenly distributed (in an exoatmospheric burn). This expression may be used as a starting point for the density of the ablated gas, po, provided uex/mjmjnrote > 2Tshiecd As m' is inversely proportional to rshie,a it may be increased by reducing r8h1d and decreased by increasing r3h1d. If the shield 370 contains a spherical indentation 390 then the surface of that indentation will be closest to the explosion, and the density of the ablated gas will be highest on the axis of symmetry 18, and reduce rapidly away from that axis. The blast reaching that spherical indentation may be between one and two orders of magnitude larger than that generally envisaged for a reactor, depending on its radius and the amount of fuel in a cylindrical target. The blast reaching the outside of the shield is much lower than that generally envisaged for a reactor, whatever that amount of fuel.

Moreover, the outer part of the shield presents a very high angle of incidence to the shock wave from the explosion, as may be seen in Figures 32 and 33. And a further advantage of this arrangement may be that the path of any neutrons escaping from that explosion through the shield to the periphery of the apparatus, where a crew compartment may be located as in Figure 81, is high, particularly in magnetic drive.

The total energy radiated during the burn is ltgt/voeams. Only a proportion of this energy is incident to the shield.

6.27.6.1 Transfer of momentum.

That electromagnetic energy from the explosion which is incident to the shield 370 ablates material and/or coolant from it. The blow-off of this plasma imparts momentum to the shield 370.

The velocity of the shield increases by Au at intervals of At. If the remainder of the vehicle experiences a constant acceleration a1 > 0 for fAt, where 0 c f cc 1, followed by a constant acceleration a2 for (1 -flAt then the conditions that the vehicle has the same velocity as the shield, and has maintained its position relative to the shield, after an interval At are:-ajfAt + a2(l -= Au and aif2At2 + aifAt(1 -DAt-I-a2(1 -f)2At2 = L\uAt = (ai -a2)f + a2 = aJ -a112 + + a2f2 -a21 2 ______ f = whereo<f<landai>O a2 -a1 Ifa2=OthenfO. Hence a2O.

If a2> Dthena2 > a2-a1 so that f>1 ifa2 > a1 orf2 <0 if a2 <a1. Hencea2 <0.

If a2 = -a1 then f = and Au/At = (V-1)ai so that AulXt = (s/ -1)aiAt2.

If the shield 370 contains all the material to be ablated, then Au increases from a low value to a high value as material ablates and the mass of that shield reduces. The * magnitude of the acceleration on bound, a1, and that on rebound, a2, must therefore increase, so that the forces accelerating the remainder of the vehicle must also increase, even though the mass of that remainder remains constant.

If the remainder of the vehicle contains all the material to be ablated, then Au is a constant but high value. The magnitudes of the accelerations, a1 and a2, are thus constant but high. As the material ablates and the mass of the remainder of the vehicle reduces from a high value, the forces accelerating it also reduce from high values.

The final values of the forces are the same for both these alternatives.

In order to provide these varying forces, the shield 370 is attached to the remainder of the apparatus 410 by an array of active vibration control units 411 shown in Figures 32, 33, 36 and 37. If the maximum value of a1 = -a 98.lm/s2 and At = 1/5000sec then AuAt = 1.6 pm. Such a displacement at such a frequency is compatible with high voltage piezoelectric shock absorbers.

It should be mentioned that the damping coefficient for a typical beryllium aluminium alloy is a factor of between six and ten times better than that of aluminium (depending upon the resonant frequency).

The gas ablated from the shield 370 then both tamps the expansion of the burnt fret towards the shield, and acts as a spring to absorb the shock and transfer the momentum of the plasma in it to the shield.

6.27.6.2 Control.

6.27.6.2.1 During a burn with ablative drive.

The shield and its extensions provide three methods of controlling the orientation of the vehicle during a burn with ablative drive. Firstly, the position of the point explosion may be moved relative to the shield by moving the conical shield 420 shown in Figures 36, .37 and 63 and thus the aim of the injector guns housed within it. Secondly, the flow of coolant through one sector of the shield may be varied. And thirdly, one or more shield extensions in a sector of the shield may be deployed further outwards than those which diametrically oppose them. These methods may be used separately or together as commanded by a control system.

Displacement of a burn away from the axis of symmetry 18 brings it nearer to those areas of the shield which are in the direction of that displacement, or near to it, and increases the irradiance (per unit area) on those areas. Conversely, such a displacement takes the burn further from those areas of the shield which are in the opposite direction, and decreases the irradiance on those areas. Both the ablation pressure, and thus the impulse due to the ablation from any area, are proportional to the irradiance on that area, and normal to it. Such a displacement therefore imparts an angular impulse to both the shield and the vehicle to which it is attached about the centre of gravity of that vehicle, and may be used to control the orientation of that vehicle. As the radius of an eye mirror, rem, is much greater than that of the shield indentation, rshjela, the allowable range perpendicular to the axis of symmetry 18 over which a successful implosion of a cylindrical target can take place is large in relation to r3hLd, and corresponds to a large displacement requiring appreciable movement of the conical shield 420.

Since the conical shield 420 is always orientated towards the burn, the shock wave from that burn alone cannot generate asymmetric aerodynamic forces on it. There may, however, be such forces on components which cannot be moved, such as the outside of the converging annular shock tube 427 and the cylindrical mirror 428 shown in Figures 36 and 37. Moreover, the gas flow around the cylindrical side of the conical shield may exert asymmetric forces on it. But the sense and magnitude of all these effects depends on the position as well as the orientation of the conical shield, both of which may be adjusted as required. If the fusion reactions produce neutrons, and they escape from the fuel and are absorbed in the shield or a lithium blanket inside it, their momentum will also impart an impulse to that shield, which may equally be asymmetric. Such impulses are, however, neglible.

Similarly, increasing the flow of coolant through an area of the shield increases the mass flow from it, and thus the ablation pressure and the resulting impulse if the exaust velocity is not significantly affected. The flow of coolant may be varied asymmetrically on diametrically opposed areas. If the fusion reactions produce neutrons, and they escape from the fuel and release energy in a lithium blanket or the shield, coolant must be forced through the shield to remove that energy. The area of the shield at which this takes place, may, however, be a matter of choice, provided no part of the shield approaches its melting point.

Deploying a shield extension further outwards increases the moment of the force upon it about the centre of mass of the vehicle.

6.27.6.2.2 During reentry.

There are also three methods of controlling the orientation of the vehicle during reentry under the command of a control system.

While the shield extensions are normally closed during reentry to protect the eye mirrors 310 or 311 to 313, each of which may be of any type, the gas being encountered may not be sufficiently hot and dense as to damage those eye mirrors. In which case, the shield extensions may be used to control the orientation of the vehicle during such a reentry.

The position and orientation of the conical shield may both be varied, so as to affect the gas flow around its conical and cylindricai surfaces and elsewhere in the converging annular shock tube, and thus generate asymmetric aerodynamic forces.

If the gas is sufficiently hot and dense as to heat the shield significantly, the flow of coolant through the controllable pores may be varied asymmetrically over that shield and its extensions, and thus generate asymmetric forces on their surfaces.

6.27.6.3 Double moving tripod.

Figures 36 and 37 include representations from which much of the detail has been omitted of the conical shield 420, the extensible leg 421, which is one of three extensible legs 421, 422 and 423 respectively forming a front moving tripod, and the extensible leg 424, which is one of three extensible legs 424, 425 and 426 respectively forming a rear moving tripod. The extensible leg 424 lies substantially in the plane of these figures. The extensible leg 421 lies in front of the plane of these figures and is therefore shown in grey.

As much of the detail of the structure of the conical shield has been omitted, so has its hatching.

Figure 36 shows the conical shield 420 in its forward position for ablative drive, while Figure 37 shows the conical shield 420 in its rearward position for magnetic drive. The conical shield 420 houses the injector guns 801 to 872 and also a starter injector 577, as aforesaid The shield end of the extensible leg 421 is attached either to the shield 370, its spherical indentation 390, or a cylindrical mirror 428 (as shown in Figures 36 and 37) by a spherical bearing 4311, while its conical shield end is attached to the conical shield 420 by a further spherical bearing 441. Similarly for the remaining five extensible legs 422, 423, 424, 425 and 426 respectively, five respective spherical bearings 432, 433, 434, 435 and 436, and five respective further spherical bearings 442, 443, 444, 445 and 446.

Both figures show front cameras 447 and 448 respectively and rear cameras 449 and 450 respectively.

Figure 38 shows the double moving tripod in its rearward position for magnetic drive.

It includes the extensible legs 421, 422 and 423 respectively for the front moving tripod together with the three respective spherical bearings 431, 432 and 433 and the three re-spective further spherical bearings 441, 442 and 443 for that tripod. The mountings on the shield 370 for the three extensible legs 421, 422 and 423 in the front moving tripod are in a plane at right-angles to the axis of symmetry 18. The mountings on the conical shield 420 for the three extensible legs 421, 422 and 423 in the front moving tripod are in a plane at right-angles to the axis of symmetry 451 of that conical shield. Figure 38 also includes the extensible legs 424, 425 and 426 respectively for the rear moving tripod together with the three respective spherical bearings 434, 435 and 436 and the three re-spective further spherical bearings 444, 445 and 446 for that tripod. The mountings on the shield 370 for the three extensible legs 424, 425 and 426 in the rear moving tripod are in a plane at right-angles to the axis of symmetry 18. The mountings on the conical shield 420 for the three extensible legs 424, 425 and 426 in the rear moving tripod are in a plane at right-angles to the axis of symmetry 451 of that conical shield. The position of the conical shield is indicated by that part of its axis of symmetry 451 which lies between the plane of the three further spherical bearings for the rear moving tripod and the plane of the three further spherical bearings for the front moving tripod. The separation between the two planes of the mountings on the shield is different from the separation between the two planes of the mountings on the conical shield. In order to provide some perspective, the further spherical bearings 441, 442 and 443 respectively are connected by light grey lines and the further spherical bearings 444, 445 and 446 respectively are also connected by light grey lines.

The extensible legs 421, 422 and 423 of the front moving tripod are skew to the axis of symmetry 18 in one rotational direction, while the extensible legs 424, 425 and 426 of the rear moving tripod are skew to that axis in the opposite rotational direction. So that any attempt to move the conical shield 420, either linearly or rotationally, without changing the lengths of those extensible legs, is opposed by the double moving tripod in the same manner as for a hexapod. Both the double moving tripod and the hexapod provide three linear degrees of freedom and three rotational degrees of freedom.

The conical shield 420 is moved from one of those positions shown in Figures 36 and 37 to the other linearly along its axis of symmetry 451 by retracting all six extensible legs 421 to 426 so that all three legs in one moving tripod reach their minimum length for that move, at which they all lie in the same plane and are unable to continue the rotation they have been making (irrespective of whether they remain skew to the axis of symmetry 18 and could therefore rotate in that plane, or otherwise), and are in a null position, where they cannot move either themselves or the conical shield linearly. All three extensible legs in the other moving tripod are retracted at the same time, in unison with those of the first moving tripod, but do not reach their minimum length as soon as those of the first moving tripod; so that their further retraction is able to drive the first moving tripod through its null position, from which all three extensible legs in that first moving tripod are extended beyond that null position (in reverse to their original orientation if measured from the spherical bearings towards the further spherical bearings). The extension of the three extensible legs in the first moving tripod and the retraction of the three extensible legs in the second moving tripod continues until the second moving tripod teaches its null position. The first moving tripod then drives the second moving tripod through its null position in turn with all six extensible legs extending.

Figure 39 is exactly similar to Figure 38 except that the double moving tripod is in a null position for the rear moving tripod and the view point has been altered so that no part of any leg is hidden.

Figure 40 is exactly similar to Figure 38 except that the double moving tripod is in a null position for the front moving tripod and the view point has been altered so that no part of any leg is hidden.

Figure 41 is exactly similar to Figure 38 except that the double moving tripod is in its forward position for ablative drive and the view point has been altered so that no part of any leg is hidden.

Figure 42 is an exploded view of the extensible leg 421 comprising both a side elevation and a front elevatibu above it of a double worm 461, a side section of the shield end 462 of the extensible leg 421 and a side section of the conical shield end 463 of that extensible leg 421 through the axis of symmetry of the double worm 461. Figure 42 also shows a side elevation of a laxge splined shaft 464 and the electric motor 465 which drives it.

Figure 42 shows a front elevation of the shield end 462, both a front elevation and a side elevation below it of a leg shield 466 and a rear elevation of the conical shield end 463.

The conical shield end 463 includes the further spherical bearing 441 and a double start right-handed female helical thread 471. The shield end 462 includes the spherical bearing 431 and a double start left-handed female helical thread 472.

The double worm 461 comprises a double start right-handed male helical thread 473, which engages with the double start right-handed female helical thread 471, and a double start left-handed male helical thread 474, which engages with the double start left-handed female helical thread 472. The double worm 461 may be driven in either rotational direc-tion. Its interior contains male splines 475 which engage with female splines 476 on the large splined shaft 464. The electric motor 465 fits inside the recess 477 in the conical shield end 463 and is attached to that conical shield end.

The interior of the leg shield 466 contains male splines 479 which engage with female splines 480 on the shield end 462 and with female splines 481 on the conical shield end 463 to prevent those ends from rotating with respect to each other, and thus altering the length of the extensible leg 421 without any rotation of the double worm 461. Such unwanted rotations of the ends may also be prevented by replacing the spherical bearing and the further spherical bearing with universal joints, but this would weaken the extensible leg 421. The cutaways either end of the leg shield 466 allows it to fit over the spherical bearing 431 and the further spherical bearing 441 respectively. Coolant is provided to the leg shield 466 through a flexible pipe 482 and exausted through conlrol1able pore arrays such as 491, 492, 493 and 494 respectively which are indicated schematically together with the coolant cavity. A further pipe 495 may be provided to supply coolant to the conical shield 420 from a reservoir in the vehicle through the leg shield 466. Other services, such as the supply of electricity from one or more generators attached to the shield to the injector guns in the conical shield, may be routed through a leg shield.

A right-handed rotation of the shaft of the electric motor 465 with the thumb placed along the large splined shaft 464 increases the length of the extensible leg 421, while a left-handed rotation reduces its length.

The helical threads may be single or multiple start, and the handedness of the threads may be interchanged. Similarly for the remaining five extensible legs 422 to 426 respec-tively.

Appropriate retractions arid extensions of the six extensible legs 421 to 426 respectively rotate the conical shield 420 through some chosen angle from the axis of symmetry 18 in any plane through that axis as for a hexapod. The centre of such a rotation does not necessarily lie on that axis. (Rotations in a plane which do not pass through that axis are also possible if required.) Figure 43 is exactly similar to Figure 38 except that the double moving tripod has rotated from its rearward position in a plane through the axis of symmetry 18 through an angle ir/18 about the centroid of the further spherical bearings for the rear moving tripod and the view point has been altered so that no part of any leg is hidden. Said plane is at an angle of ir/6 to the plane through the axis of symmetry 18 and the spherical bearing 431 for the front moving tripod.

It will be seen that the bearings of the electric motor 465 are insulated from impulses transmitted from the conical shield 420 either to the shield 370, its spherical indentation 390 or the cylindrical mirror 428 through the extensible leg 421 by virtue of linear movement of the male splines 475 relative to the female splines 476. And that an arrangement with a single helical thread of the same pitch would have half the travel per rotation.

Current may be passed through the windings of the electric motor 465 prior to a movement or a burn to raise their temperature, and that of the extensible leg 421, to their minimum operating temperature. Alternatively, strip heaters may be provided for those purposes.

The electric motor 465 is cooled during a burn by gas evaporated from cryogenic drum magazines housed inside the conical shield 420 shown in Figure 63 and described in Section 6.28.1. A flexible gas pipe (not shown) runs from the conical shield to the extensible leg 421.

Since the threads 471, 472, 473 and 474 respectively are subject to high and shock loads, at both low as well as high speeds, both low and high temperatures, long periods of disuse, high vacuum and nuclear radiation, and a coefficient of friction below 0.1 is desirable, their lubrication, and that of the spherical bearings 431 to 436 respectively, the further spherical bearings 441 to 446 respectively, and the splines 475, 476, 479, 480 and 481 respectively, is provided by burnished or bonded films of solid molybdenum disulphide or poiytetrafluoraethylcne.

In the bonded case, the molybdenum disuiphide must be bonded to the surfaces of the threads and splines by an inorganic binder, such as sodium silicate, which withstands nuclear radiation.

The centre of the spherical defining mirror of a final stage of an inner eye mirror ties at or near to the centre of the outermost spherical defining mirror of the outermost (lowest numbered) eye mirror 311. The single or individual further alternate defined mirror(s) lie close to the outside of that outermost spherical defining mirror, whose radius is Tern, and thus at a distance slightly less than Torn to the front of the latter centre.

In the configuration shown in Figure 36 for ablative drive, the explosion of a cylindrical target takes place slightly in front of the centre of the spherical indentation 390 in the shield 370, a distance slightly less than Tern to the rear of the latter centre.

The ratio of the direct illumination of the further alternate defined mirror, the indi-vidual further alternate defined mirror(s) or the individual conical mirror(s) to that of the spherical indentation 390 iii the shield 370 is thus approximately:-/ ( T8/04 where Tsiezd <<rem \2Tem) so that this ratio is low. However, a great deal of the electromagnetic energy entering the recirculation aperture 429 reaches those mirrors and the power loading is at its highest in ablative drive.

In the configuration shown in Figure 37 for magnetic drive, the explosion takes place further to the rear; so that the direct illumination of the further alternate defined mirror, the individual further alternate defined mirror(s) or the individual conical mirror(s) is even lower. So that leth high-Z vapour is released from those sacrificial mirrors, and the recirculated beams are unblocked more quickly. This is partially offset by reduced masking of the illumination by the conical shield.

6.27.6.3.1 Response time required of conical shield.

Clearly a rotation of the axis of symmetry 451 of the conical shield 420 in a certain plane through the axis of symmetry 18 will produce a rotation of the vehicle in the same plane and the same rotational direction during a burn. But the linear acceleration of the vehicle is riot necessarily along that axis of symmetry. It is, however, almost certain to lie in that plane. If the linear acceleration of the vehicle at an angle -< a C to the forward direction of the axis of symmetry 18 in that plane is i-i g where g is the acceleration due to gravity at the surface of the Earth, the radius of the periphery of the vehicle is rmaz, the angular velocity, Ô, in that plane is zero, and the maximum perinissable acceleration at that radius is mmazg then the maximum permissable angular acceleration, 6max, in that plane is given by:-nycosa +rmaxO maw = The maximum permissable rate of rotation, O,,, in the absence of any angular acceleration is limited to:-ngsina + rmax9ax = t'rnaxg Since the angular acceleration, 0(t), at time, t, is tangential, while the acceleration due to the rate of rotation, O(t), at time, t, is radial, the magnitude of their resultant is:-1(2 rmax (e(fl2 + O(t)) But clearly the direction of that resultant varies with time. However, we may impose the worst case limit where the linear acceleration and the resultant of the angular and centripetal accelerations axe in the same direction:-2/2 rmaz (9(t)2 + = (nmaw 72)9 Hence we have:-dA(t) = Ü(t) = ((@taw --a(t)4) t Since (nmar -n) g / rmax is a constant, we may simplify the notation by putting sin a 1; so that:-dO(t) - -è 4'\1/2 dt kmam U) The minimum time taken for rotational acceleration from zero to is given by:- -dO -/r(5/4) -Jo --Omax F(3/4) ) if umax -n = 10,g = 9.81 rn/s2 and max = l000m then O,flax = 0.313209 radians/sec and t = 4. 18579 sec. Similarly for decceleration from °max to zero.

If the burn is to continue beyond the end of such adjustments, then the conical shield must be aligned with the axis of symmetry 18 at the end of that period.

6.27.6.4 Controllable pore array.

Figure 44 is a sectional schematic diagram of a controllable pore array when not in use, such as 391 (as shown), 491 to 494 respectively, or the conical shield controllable pore array 683, shown in Figure 63 and described in Section 6.28.2. It includes a portion of a shield such as the shield 370 (as shown) with large diameter individual pores 501 and small diameter individual pores 502. The large diameter individual pores allow bubbles of vapour to escape, while any capillary action is higher in the small diameter individual pores. An annular metal diaphragm 503 with a circular central hole 504 is attached to the edges of a recess 505 in the inner wall of the shield 370 and isolates those pores from the supply of coolant. The extension 506 of an actuator 507 rests against the annular metal diaphragm 503 and forms a seal.

The base of the actuator 507 is attached to a sealed compartment 511 which contains a number of similar actuators. The sealed compartment 511 incorporates a controllable tap 512 which is in its closed position. This tap may be opened or closed by a control system and prevents leakage from the interior of the shield 370 of the cooling fluid 513 when the cooling system is not in use. It also allows the controllable pore arrays within it to be taken out of use when the cooling system is in use.

Figure 45 is similar to Figure 44 except that the controllable tap 512 is in the open position. Pressure inside the shield 370 has forced cooling fluid 513 into the sealed compart-ment 511 and forced the annular metal diaphragm 503 open, so that some of the cooling fluid 513 has entered the recess 505 and the individual pores 501 and 502 respectively.

If the pressure inside the shield is not sufficiently high, capillary action may keep the cooling fluid 513 inside those pores 501 and 502 respectively. In which case, both the shield 370 and the tooling fluid 513 may be ablated by a burn.

If the pressure inside the shield is sufficiently high, the cooling fluid 513 will spread over the surface of the shield 370, and only that fluid will be ablated by a burn.

In either case, shock waves will pass through both the cooling fluid 513 and the shield 370, but not necessarily at the same speed.

The duration of a burn is of the order of 0.2zs while the period between burns is of the order of 200,us. The resonant frequency of the diaphragm is of the order of 1 nis. The position of the extension 506 of the actuator 507 may be adjusted more quickly to reduce, or prevent, any unwanted flow of the cooling fluid 513 back into the sealed compartment 511 during a burn.

Figure 46 is similar to Figure 45 except that the extension 506 has moved to seal the circular central hole 504 in the annular metal diaphragm 503, and prevent further flow of the cooling fluid 513 into the recess 505 and the individual pores 501 and 502 respectively to provide control. After a timelag for those pores to partially dry up, the ablation of the cooling fluid ceases. This period may be longer than the time taken for the extension 506 to close the circular central hole 504, which may be of the order of I ins at most.

Alternatively, the large and small diameter individual pores may be replaced by a biporous wick, in which the recession of the mensici and/or the formation of bubbles in the large pores increases the number and thus the surface area of the meriisci in the small pores with which they are connected, as explained in a paper entitled "Biporous Heat Pipes for High Power Electronic Device Cooling" (Jinuiang Wang & Ivan Catton (2001) j7th IEEE SEMI-THERM Symposium p.211.). Such a biporous wick may be formed by sintering particles which contain small pores so as to leave large pores between the particles.

Figure 32 shows pumps 521, 522 and 523 respectively supplying coolant to the shield extension 384, the shield 370 and the spherical indentation 390 through respective pipes 524, 525 and 526. Figure 33 shows pumps 531, 532 and 533 respectively supplying coolant to the shield extension 375, the shield 370 and the spherical indentation 390 through respective pipes 534, 535 and 536.

Controllable pore arrays may be used with a liquid metal instead of a coolant to provide a sacrificial mirror as required for any further alternate defined mirror 171, any individual further alternate defined mirrors 300 or 301 to 303 and any individual truncated conical mirrors 320 or 321 to 323 described in Sections 6.24 and 6.25 If a high exaust velocity is not required, water and/or heavy water may be used as a coolant. Both are excellent neutron moderators. The protons have a very high cross-section for the capture of neutrons to produce deuterons. Deuterons have a very small neutron capture cross-section, but produce tritons.

6.27.6.5 Deployment of shield extensions.

Figure 47 is a rear elevation showing shield extensions 371 to 379 on one side of the vehicle which are fully extended, and shield extensions 380 to 388 on the other side of the vehicle which are minimally extended only so far as not to impede the beams from the eye mirrors 311 to 313, each of which may be of any type, at which orientation they present the least surface area to the burn.

Each shield extension 371 to 388 is mounted on a respective hinge 541 to 558 tangent to a circle in a plane at right-angles to the axis of symmetry 18, whose radius exceeds that of the trailing edge of the final stage defining mirror of the outermost of those eye mirror(s) which can take part in the implosion of a target. Alternatively, if there is an outer eye mirror, 310, this radius may exceed that of the trailing edge of the final stage of its defining mirror. And the shield extensions extend so as to clear its beam. The hinges are attached to whichever is the outermost trailing edge of the eye mirrors 311 to 313, and 310 if protected.

If the shield 370 is rotating, the shield extensions may be extended and retracted cyclically so as to maintain a torque around some fixed axis through the centre of mass of the vehicle. Figure 48 is a rear elevation showing the shield extensions performing such a cycle during a burn, with the shield extension 375 at its maximum extent, and the shield extensions 380 to 388 at their minimum extent.

Figure 49 is a rear elevation showing shield extensions 380 to 388 which are closed, and shield extensions 371 to 379 at their maximum extent, for a manouevre during reentry into a cold thin gas when the shield is not rotating.

6.27.7 Shock wave.

The energy remaining in the explosion of the burnt fuel when the shock wave overtakes

S

the heat wave is small in comparison to that released by its burn, but is still large.

Table 1

Laser Ion beam target direct drive with a layer of Low-Z High-Z Neutrons 75% 70% Hard X-rays 6% Hard & soft X-rays 22% Debris 19% 8% Table 1 shows the fractional output power split at the first wall of a reactor for typical reactor-size targets containing DT fuel with both low-Z and high-Z outer layers from "The Physics of Inertial Fusion" ((2004) S. Atzeni & 3. Meyer-Ter-Vehn Table 3.3 page 69). The low-Z figures originated in a paper entitled "Preliminary Conceptual Design of SIRIUS, A Symmetric Illumination, Direct Drive Laser Fusion Reactor" (B. Badger, H.A. Attaya, T.J. Barth!, ML. Corradini, ILL. Engeistad, G.L. Kulcioski, E.G. Lovell, GA. Moses, KR.

Peterson, ME. Sawan, IN. Sviatoslavsky, L.M. Goldman, R.E. Hopkins, L.D.Lund, ILL.

McCrory, S. Skupsky and K. Walsh (Report UWFDM-568, (1984) University of Wisconsin Fusion Technology Institute, Madison) at page 4-29. This paper envisaged that "including neutron deposition in the calculation would reduce the neutron percentage by about 10%, with the energy going mainly to the charged particles" at page 4-13. This direct drive concept did not use a buffer gas.

Table 2

Direct drive Indirect drive CH Coated Significant yield Low-Z High-Z Neutrons 81% 66% Hard X-rays 1% Hard & soft X-rays 18% Debris 18% 15% Table 2 shows similar calculations in which the low-Z outer layer for the direct drive target is CH, while the high-Z outer layer comprised by the hohiraum for the indirect drive target is gold, extracted from a paper entitled "Response of National Ignition Facility First Wall Materials to Target X Rays and Debris" (R.R. Peterson (Report UWFDM-1018, (1996) Fusion Technology Institute University of Wisconsin, Madison). No buffer gas is mentioned in this paper. The increase in X-rays from direct to indirect drive is entirely due to soft X-rays emitted by the high-Z material.

There will be more neutron scattering inside a target of the size used in volume ignition, so that it will emit less neutrons and the temperature of the burnt fuel will be higher, increasing the proportion of the energy radiated as X-rays or remaining in ion debris. The high-Z material in the cylindrical target also increases the proportion of the energy in soft X-rays. But the high-Z material from the leading guide 113 and the trailing guide 114 is confined to the ends of such a target. It seems likely that the output of neutrons from a large cylindrical target containing DT will account for less than 60% of the energy, while the energy in the X-rays will be high.

The X-rays may be of too short a wavelength to be reflected (even by sacrificial mirrors). The amount of bigh-Z material in the leading guide may be increased to reduce the energy at these wavelengths (as may be the amount of material remaining from an ablative base).

The BUCKY 1-D Radiation-Hydrodynamics Code has been used to simulate energy deposition in a gas as described in a presentation entitled "Response of Dry Wall Graphite Chamber Designs to the Output Spectrum from a Directly Driven Laser IFE Target" (D.A.

Haynes and R.R. Peterson, Fusion Technology Institute University of Wisconsin and the High Average Power Laser HAPL team).

If the gas behind the shield has a density 0110 mTorr, characteristic of a low density buffer gas, only a small proportion of the energy of the hard X-rays, some 9%, an even smaller proportion of the energy of the a-particles and other fusion products, at 1%, but a significant fraction of the energy remaining in the debris ions comprised by the unburat fuel and other target materials, about 28%, will be stopped by that gas. Clearly the a-particles and other fusion products have sufficient kinetic energy to penetrate a buffer gas which is sufficiently dense to stop both the debris ions, because of their lower kinetic energy, and the hard X-rays.

A similar study has been made using the CONRAD radiation-hydrodynamic code, the IONMIX equation of state and opacity code, and a detailed non-LTE (Local Thermal Equilibrium) radiation transport calculation in a paper entitled "Implications of Non-LYE Buffer Gas Effects on ICF Target Chamber Design" (J.J. MacFarlane, P. Wang and GA.

Moses, Report UWFDM-831 (October 1990) Elision Technology Institute University of Wisconsin).

It seems that absorption cross-sections are high at the frequencies where the emissivity is also high, resulting iii "self-attenuation" which dramatically reduces the radiative heat flux.

So that if the gas behind the shield had a density of 1 Torr, characteristic of a high density buffer gas, about 95% of the energy of the hard X-rays and the debris ions would be stopped in that buffer gas. The debris ions would be completely stopped in the gas by about 1 j.ts after the target explosion and within a radius of 2.5 metres for the energy of the explosion considered. Apparently their absorption would produce a second shock front ahead of the shock wave at times less than 10 ps.

in these circumstances, the hard X-rays from the burn would be replaced by soft X-rays from the shock wave, which would fulfill their functions of ablation and control.

If 19% of the energy of a typical medium length cylindrical target remains in the shock wave then the density of the gas behind the shield must be 24 Ton to supply enough recirculated energy. If 38% of the energy of a typical medium length cylindrical target remains in the shock wave then the density of the gas behind the shield must be 18.4 Tort to supply enough recirculated energy. If 19% of the energy of a typical long cylindrical target remains in the shock wave then the density of the gas behind the shield must be 14.6 Tort to supply enough recirculated energy. These densities reduce as the length of such a cylindrical target is increased. But a gas of sufficient density to provide adequate recirculated energy from a cylindrical target which is sufficiently short to survive its accel-eration during injection as detailed in Section 6.28.2 will stop the charged a-particles and other fusion products. So that the apparatus and methods of operation described in the next. three sub-sections must be adopted.

6.27.7.1 Endoatinospheric operation.

A strong point explosion of energy, E, in a uniform gas of density, P0, is known to produce a shock front of radius, r3h (t), velocity, Vsh (t), and temperature, T3h(r, t), at time, t, given by:-/ \1fS E0 ISt2/5

I P

flI 7-i \1J5 v (t) -± ( ° 5t3Th sh - a3()) Po 2/5 8(y-1) / FL?0 \ -2/5 -5/5 25(+1)2 a5()) Pa t where y is the adiabatic exponent, rB is the gas constant, c('y) is in the range 0.15 C a3(-y) <2 and a3(1.4) 0.85, for that point explosion.

Similarly:-I L' \1/4 LJQ I -1/441/2 shU) -I I / \1/4 if E0 -1/4-1/2 1/2 FT -1 E0 \ -1/2_i s 34(r,t) -2(7+1)2 PU t where ac(7) is in the range 0.15 c ac(7) < 2 and c(1.4) 1, for an axial explosion.

In either case, the density at the shock front, PSh, is given by:-y+l Psh.71P0 The above relations are derived using certain approximations which apply when, as will be the case, the Mach number of the shock, M(t) > 10.

It will be seen that increasing the density, po1 does not greatly reduce the radius of the shock front. Conversely a gas or plasma with a ow density will suffice to reduce the rate at which the burnt fuel expands. Indeed, that plasma ablated from the shield which is near a cylindrical target about to undergo implosion must be well below the critical density for the recirculated beams to reach it. And, since the plasma from the previous target contains ions of high-Z as well as low, it too must be clear of the target. This may, however, be ensured by the provision of an inhomogeneous magnetic field.

The radius of the shock front must be sufficiently small, and its density and temper-ature must be sufficiently high, for adequate electromagnetic energy to be recirculating when the next cylindrical target arrives at the position where it is to be imploded. It should be noted, however, that the temperature of the shock wave is not sufficiently high for it to emit radiation of such low wavelengths as to stress the individual conical mirrors 320 or 321 to 323, the individual further alternate defined mirrors 300 or 301 to 303, or the further alternate defined mirror 171.

The bremsstralung power radiated per unit volume of an optically thin shock wave is:-2Z2 2 1/2 9C5 -2 P85th (t) where the Gaunt factor, g 2v'/ir, C5 is a constant, z = >.i: = 2 = Z, is the ion charge of the jth component of the plasma, A3 is its mass number, and x is the fraction of the plasma comprised by that component-For beryllium, the bremsstrahlung constant A5 = 9C5Z3/A2 = 153 x 1024 erg cni3 r2 ke'C"2.

The thickness of the shock wave may be taken as 0.05 rah(t).

if the shield indentation comprises a portion of a sphere of radius, r3h6jd, whose centre coincides with that of a point explosion, then the power of the radiation per unit area on it is:- 0.05 rsh(t)5 2 1(2 -0.05Aoph ( 8(y -1) 1/2 (____ -4/5 3/5 2 bPsh -2 1 nrf rl\2F I ( ( Pci rhietd LnJ7 U') Bj \sCY)I Thus, for a time, the radiated power will increase, unless the loss of energy reduces the temperature of the shock wave. Such a loss may, however, be partially ofet by reflections from the shield of electromagnetic energy emitted by the burn. But it is unlikely that any of the power recirculated from the burn through the eye mirror(s), which could be incident to the shock wave as the leaves return to their starting position, will arrive in time to heat that shock wave.

The X-ray ablation pressure as a function of time, pa(t), on the low-Z material of the shield due to an ablative heating wave is given by:- 0.05 rh(t)3 AophTs,t(t)1i'2 p(t) -2 rShC1d I4 where pffÜ'id is the gas constant for the shield material and Tshjejd is the temperature of the plasma ablating from its surface.

The mass ablation rate per unit area as a function of time, tha(t), from the shield is given by:- -0.05 r8h(t)3 AbphTsh(t)1"2 ma(t) 2 A-rshieIdm --L shieLd As before, both the total thrust on the vehicle, and the total mass ablated from the shield by a single explosion, are independent of the radius of that shield.

The condition for efficient drive by an ablative heating wave rather than a supersonic heating wave which involves no hydrodynarnic motion is:-Q(i) = 0.05 rS,L(t)AopShTs,%(t) <4 2 sMeld frshietdT -3/2 rShld Po \ sheLdJ The radius of the shield for any shield material must also satisfy this condition.

The exaust velocity as a function of time, uez(t), is given by:-zz(t) = = 24.ield(j) = where c1'(t) is the isothermal speed of sound in the shield material as a function of time.

Figures 36 and 37 also show the cylindrical mirror 428, which prevents light which is not collimated along the axis of symmetry 18 from escaping from the recirculation path, and ensures that light entering the recirculation aperture 429 is reflected so as to Teach such further alternate defined mirror 171, individual further alternate defined mirrors 300 or 301 to 303 and individual truncated conical mirrors 320 or 321 to 323 as are fitted to the vehicle. Although a section of the cylindrical mirror 428 lies in the respective plane of each of the figures, it is shown in grey to differentiate it from the extensible leg 424 and the spherical bearing 434.

The outer edge of the recirculation aperture 429 is provided by either the inner edge 389 of the shield 370 or its spherical indentation 390 (as shown). It is aligned with the inside of the cylindrical mirror 428. The conical shield 420 and either the inner edge of the shield 370 or its spherical indentation 390 (as shown) together with the inside of the cylindrical mirror 428 form a converging annular shock tube 427, which increases the strength of that part of the shock wave which enters that recirculation aperture 429, and preserves it for the period during which it travels up that shock tube. Since the enhanced and preserved shock wave continues radiating, this increases the allowable time between implosions. Moreover, the whole, or a part, of the fluid used to cool the lithium blankets 403 is discharged into the converging annular shock tube 427 from the conical shield 420, the leg shields 466 of the extensible legs 421 to 426 respectively, and/or into its forward end through a circular array of cooling nozzles 393 to increase the density of the gas within that shock tube, and thus the recirculated energy. As a firther advantage, the density of the gas behind the remainder of the shield is reduced, and does not therefore impede the a-particles or other fusion products in magnetic drive in exoatmospheric conditions.

The cylindrical mirror 428 is provided with a cooling cavity 430 with pores if required.

Either a single further alternate defined mirror 171, individual truncated conical mirrors 320 or 321 to 323 and/or individual further alternate defined mirrors 300 or 301 to 303 lie at the front of the shock tube.

Figures 65 shows the axis of symmetry 18, a variable atmospheric intake 565 and its conical door 566, which is closed in exoatmospheric operation and opened in endoatmo-spheric operation in order to increase the density P0 behind the shield 370. The variable atmospheric intake 565 is connected to the recirculation aperture 429 by means of the passage between the cylindrical mirror 428 on the outside and a reactor compartment 437 and the conical shield 420 on the inside. The rear of the reactor compartment 437 is itself conical to obtain a smooth gas flow. The reactor compartment is described in Section 6.28.2. Both the variable atmospheric intake and the front surface of the vehicle, which may be the reverse surface of the defining mirror of the outermost eye mirror, must be sufficiently robust to withstand endoatmospheric use.

It will be appreciated that the gas between the explosion and the shield 370 together with any spherical indentation 390 in it is the result of the time dependent explosion of the cylindrical target 101, 102, 103 or 104, the time dependent ablation of the shield 370 together with any spherical indentation 390, and the shapes of those components, which affect both their ablation and the subsequent flow of plasma away from their surfaces, together with any gas flows through the recirculation aperture 429.

That plasma will never, therefore, be uniform; so that the shock wave in it cannot be spherical. In any case, that optimum shape for the shield 370 which produces the most thrust along the axis of symmetry 18 is a plate at right angles to that axis, rather than a portion of a sphere. And on the other hand, the mass ablation rate per unit area varies with the distance of any point on the shield 370 from the explosion. So that, if the mass ablated from the shield 370 is high, the surface of that shield will be ablated so as to become a sphere whose centre is the origin of the explosion.

Operation within a closed chamber has been described in Section 6.26. It is also possible to operate within a partially closed chamber in space. Since the density may be maintained above the required density, P0, by operation within such a partially closed chamber, this type of operation is effectively endoatmospheric. There must, however, be a path for the recirculated beams from the eye mirrors to reach each cylindrical target, as envisaged in Section 6.26.

In low endoatmospheric operation, the dense atmosphere rapidly cools the low density plasma ablated from the shield; so that its radiation makes no contribution to the recircu-lated power. The shock wave is sufficiently dense to radiate adequate recirculated power.

The increase in temperature of the shock wave due to an increase in the temperature of the atmosphere, T0, caused by the ablated gas may therefore be neglected in any event.

And as M(t) > 10, the pressure and temperature of the gas ahead of the shock will have neglible effect on that shock.

6. 2T.T.2 Exoatmospheric operation.

In exoatmospheric operation, the temperature of the plasma ablated by either hard or soft X-rays, depending on the density of the buffer gas, from the surface of a shield with minimal cooling, Tshjejd, is very high, but the density of that plasma, p, is very low. The exaust velocity of that plasma, Uez, is very high being given by:- -2 f-nshiefdm 1/2 - - B -shiehl) -LcT where f6l is the gas constant for the shield material and or is the isothermal sound velocity.

The shock wave 409 initially has the shape shown fin Figure 35 and expands at a velocity which is higher than but its velocity v8h(t) rapidly falls below U3 so that it ceases to expand in the direction of the shield. The density of the shock, psh(t), is given by:- (y + 1)M(t)2 Psh(t) = (y -1)M(t)2 + where -y is the adiabatic exponent, and the Mach number, M(t), is given in the direction of the shield by:-M(-t) = vsh(t) + Ue = vh(t)+ 2CT 2 For an ideal or perfect gas, the shock temperature, T3h(r, t), is given by:- (7M(t)2 -( -1)/2) (( -1) /2 M(t)2 + 1) Tqh(r,t) - ((y+1)/2)2M(t)2 As the Mach number is small, psh(t) is only about twice Pa and T8h(t) is only about twice T5hJd. Although T3hzd and T3h(t) may be several hundred eV, they are not suffi-ciently high to outweigh the very considerable reduction in ph(t) from the endoatmospheric case in the formula for the power radiated per unit volume of an optically thin shock wave:-Abp8h (t)2T8h (i)'t2 It follows from the radius and thickness of the shock that the power radiated will not suffice for optical recirculation, even though a similar contribution is made by the plasma itself, which is of greater thickness. However, the density of the plasma may be increased sufficiently for that purpose by ablating coolant from the surface of the shield. Enough material must be ablated from the shield 370 to be compatible with the rate at which cylindrical targets 101, 102, 103 or 104 can be injected. If there are injector guns 801 to 872, each with a rate of fire of rate targets/sec, then this rate is m,1 2rate The various relationships may be rewritten with Tcooiane in place of T3hjd and pc5oolant in place of The two sets of relationships may also be combined together.

If the fusion reactions produce neutrons, and they escape from the fuel and then release energy in a lithium blanket or the shield, coolant must either be forced through the shield or into the converging annular shock tube 427 to remove that energy in any event.

The rate at which coolant must be provided for the kinetic energy of unwanted neutrons from cylindrical targets enclosing DHe3 fuel with a DT seed is of the correct order for the vapour from that coolant to enable optical recirculation in ablative drive from behind the shield if that target is sufficiently large. That rate may be modified up or down by exo or endothermic reactions with lithium isotopes.

It must be stressed, however, that the resulting density of gas behind the shield is so high that it will stop the a-particles or other fusion products and thus prevent magnetic drive. Discharging as much of the coolant as possible into the converging annular shock tube 427, as described in Section 6.27.7.1, is the preferred option. It must be emphasized that if all the coolant that was not required to prevent the shield 370 or its spherical indentation 390 from melting was discharged into the converging annular shock tube 427, then it would not be possible to use that coolant for control, as described in Section 6.27.6.2.1. But this is not of consequence, as magnetic drive may be iriterupted for rapid manouevres to be performed in ablative drive.

The rate at which coolant must be provided for the kinetic energy of neutrons produced by DT or LiDT fuel is more than sufficient for optical recirculation from behind the shield, and would provide a very high thrust.

6.27.7.3 Gaseous and atmospheric breakdown.

The intensity of the output beam from an eye mirror is about three orders of magnitude below the intensity threshold for the atmospheric breakdown of clean air at a pressure of one atmosphere immediately after leaving that eye mirror. The intensity of a beam with a focus, being inversely proportional both to the distance to its focus and its radial distance to the axis of symmetry of the eye mirror, only reaches that threshold when it nears that ajcis of symmetry. But at such a distance, the beam from a leaved eye mirror is slewing at a tangential velocity close to Vbeams = s x i0 cm/s. And the velocity of the gas behind the shield in the opposite direction is also high. This velocity is much higher than that of a cylindrical target, and will give rise to a shock wave from the leading end of each cylindrical target.

Figure 21A shows the geometry of such an output beam 514 at an angle f3lzinge to the axis of symmetry 18 with a focal circle 515 symmetric about that axis output from a leaved eye mirror 161.

The thickness of the output beam at a point 516, a distance, r, from the focal circle 515 is t1, while its thickness at a point 517, a distance, 2, from the focal circle 515 is t2, so that:-

-

-

If the radius of the focal circle 515 is r and the area of the frustrum at the point.516 is A1 while the area of the frustrum at the point 517 is A2 then:-A1 = -ic (2 (rj 5111 -r) -4-t1 cos t1 A2 = it (2 (72 5Uh I3hin9e -r) + t2CO5f3hn9)t2 = it (2 (73 Slfl/3hinge -r) + tir2/rj cos I3tuinge) t1r2/ri If the intensity on the frustrurn at the point 516 is I while that on the frustrum at the point 517 is 12 then:--!i A2"r as r1 >> r, i >> t1, r2 >> r and 73 >> t2.

If the section of the output beam 514 shown rotates about the point 516 then the radial distance of the point 517 is r -r2 while that of the point 520 on the axis of symmetry 18 is i -r csc The tangential velocities are proportional to these radial distances.

Atmospheric breakdown is a cascade ionization process, requiring initial electrons, where the intensity threshold is a function of some inverse power of the period of illumina-tion. The period of illumination of any point on the cylindrical target may typically vary from 64 ns for the lowest intensity beam down to 0.25 ns or less for the highest intensity beam used for implosion. So that the time during which a beam is vulnerable to atmo-spheric breakdown near that target is extremely limited, and may not be long enough for it to occur in any event.

The coefficient of collisional absorption for a plasma depends on its temperature, density, and degree of ionization; together with the wavelength of light incident upon it.

That degree of ionization depends on both its density and its temperature. Near to the axis of symmetry of the eye mirrors, the temperature rise of the plasma due to a beam is limited by its slewing. At high intensities, that coefficient is reduced substantially. At very high intensities, induced transparency occurs-Ideaily, that one of those beams which is used for the compression of cold fuel and has the highest intensity at the cylindrical target should be able to illuminate that target at or near the limit of intensity below which collisional absorption is effective.

With ablative drive in exoatmospheric operation, the density of the plasma behind the shield is low arid cannot prevent such beams as are necessary for the compression of cold fuel for fast ignition from reaching a cylindrical target.

In endoatmospheric operation when the vehicle is already in forward motion, the density behind it will also be low because of its considerable frontal area, as will the pressure. The atmosphere will spill over the edges of the shield extensions into the low pressure behind the vehicle.

The variable atmospheric intake 565 shown in Figure 65 controls the flow of the atmo-sphere, initially along the axis of symmetry 18, and is used not only to adjust the density behind the centre of the shield, but also to douse the temperature of the plasma ablat-ing from that shield towards the position where the cylindrical targets will be imploded.

Hence both the density and temperature may be chosen to prevent atmospheric breakdown impeding the beams.

Beams used to compress the fuel in a cylindrical target have to travel over that entire target together at a common velocity, Vbeama. Beamlets used for the fast ignition of that compressed fuel only need to briefly illuminate the trailing end of the cylindrical target.

The geometric optics of a beaxnlet cannot be altered. So that a beamlet with a very high intensity at the cylindrical target would have to transit regions where its intensity was sufficient to break down the gas on its way to that target, on the basis of geometric optics alone. But the diffraction of a beamlet from a single leaf with an orientation differing from that of its neighbours may be much higher than that from a set of leaves forming a spherical surface. Similarly for a single circular array of leaves.

If in beamlets are required to overlap at a cylindrical target for only a very short interval, they may be brought together only for that interval. So that the intensity of each individual beamlet when not overlapping is 1/rn, or less when diffracted, of the intensity of the beamlets when overlapping. And the time for which the undiffracted part of each beamlet passes through a particular region of gas is also reduced by a factor of in. Moreover, the velocities of the beamlets over the cylindrical target may range from Vbeams to several times that velocity.

In this way the onset of gas or atmospheric breakdown by the trigger beams may be avoided. The assembly of the trigger beam from beamlets may be precisely synchronized * with the arrival of their cylindical target by the same means as that described in Section 6.23.1.2 for successive bohlraum targets.

6.27.7.4 Directing energy.

Only the effect of the atmosphere itself need be considered when a directed energy weapon is in endoatmospheric operation. The shock wave will not have time to reach those outermost final stage(s) of the eye mirror(s) which are used for that weapon in the presence of an atmosphere.

In exoatmospheric operation, the density of the gas behind the shield is made higher near the axis of symmetry 18 and reduced further from said axis in so far as is consistent with the need for control by means of the controllable pore arrays.

If the density distribution is p = gor then the invariants of the hydrodynanic equa- tions for an explosion are:-f j, \ a/2 I 1_/o (r=(o%-I anda= \go) where n = 3 for a point explosion.

The velocity of the shock is Vsh (t) = a (t1. So that the velocity of the shock will increase with time if a> 1 and thus if, < -8. In which case the velocity of the shock wave will increase when it reaches the lower density gas further from that axis of symmetry.

The directed energy weapon outputs electromagnetic energy from the burn almost one recirculation period after the explosion of a cylindrical target, and from the shock wave until just before the implosion of the next cylindrical target (when the gas associated with the explosion of that previous cylindrical target will have had time to dissipate, possibly under the influence of a magnetic field). Both the recirculated energy, and part of its input energy, will have been emitted from the shock wave a fraction of the period between cylindrical targets alter the explosion of that previous cylindrical target, when the radius of the shock wave is preferably of the same order as that of the recirculation aperture.

By the time the directed energy weapon completes its output of electromagnetic en-ergy, the shock wave will have expanded much further. But the density of the gas away from the axis of symmetry would have to be extremely low for the shock wave to have reached the outermost final stage(s) used for that weapon at that time.

6.27.8 Starter.

Now the power required to initiate volume and/or fast ignition is very high. Moreover, there will be no gas remaining from a previous explosion to help tamp the first explosion and to maintain the recirculated power for the necessary period. Hence in space the first explosion is most conveniently provided by a small boosted fission nuclear explosive device, with minimal containment to enable the electromagnetic energy to escape and ensure that :144 no fragments survive its detonation to damage the shield, such as that described in Fourth Generation Nuclear Weapons (A. Gsponer & i-P. Hurni 5th Ed. (1999) at page 11).

Figure 50 is a schematic diagram of a small boosted fission nuclear explosive device 571 comprising a spherical shell 572 of 4kg of steel forming a tamper, concentric abOut a common centre with and enclosing a further spherical shell 573 of 4 kg of plutonium 239 and/or uranium 235, inside which cold DT gas 574 has been introduced immediately prior to detonation at a pressure of 10 atmospheres-The device is imploded by the assembly of 10kg of high explosive 575 which surrounds it, shown here as the schematic by which it is often represented. Fast neutrons from an external neutron generator 576 initiate the fission chain reaction. The inside radius of the fissile shell is about 6cm. The yield of this device may be reduced to enable a take-off from a planet (other than Earth) during which its explosion would be partially contained by the surface of that planet, by reducing the amount of DT gas 574 injected by limiting the stroke of a piston in a cylinder or otherwise.

The tamper may alternatively consist of beryllium.

Figure 63 shows a starter injector 577 for this device, which is aligned with the axis of symmetry 451 of the conical shield 420. Neither the muzzle velocity nor the acceleration of the small boosted fission nuclear explosive device down the barrel need be high. Equally the propellant charge in the starter injector 577, and its recoil, may be low. Provided a small boosted fission nuclear explosive device merely provides the first burn in a sequence of burns but takes no part in that sequence thereafter, the starter injector 577 need not be reloaded quickly. If, however, a planetary atmosphere (other than Earth's) impedes the recirculated beams from thc eye mirror(s), the starter injector 577 may be multiplicated and each starter injector reloaded quickly to provide a succession of small boosted fission nuclear explosive devices for operation in that atmosphere. The explosion of the small boosted fission nuclear explosive device may take place at any point along the axis of symmetry 451 of the conical shield 420 at which it provides adequate electromagnetic

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energy for recirculation, but does not overstress that conical shield, the shield 370 or its spherical indentation 390.

6.27.8.1 Explosive lens.

It is well known that in a vacuum a hyperboloid lens whose refractive index, n, is equal to its eccentricity, e, will collimate parallel to its transverse axis those rays incident to it which come from that one of its foci which is exterior to it.

It is equally well known that an explosive lens with a hyperboloid boundary between a fast explosive, whose detonation velocity is vj, on the incident side and a slow explosive, whose detonation velocity is v2, on the transmitted side of eccentricity vl/v2 > I will convert a spherical detonation front expanding from the focus on the incident side into a plane detonation front on the transmitted side orthogonal to the transverse axis and travelling along it.

Figure 51 shows the geometry of a more general explosive lens utilizing a cartesian oval. It shows the point of detonation, F, and the centre of a sphere, C, connected by a transverse axis 581 of length, c.

Figure 51 also shows a boundary 582 between such a fast explosive 583 and such a slow explosive 584. A ray 585 from the point of detonation, F, at an angle to the transverse axis 581 intersects the boundary 582 after a distance, 1, at a point, P. It is refracted as a ray 586 to the centre, C. So that the explosion is focussed, rather than being merely collimated along the transverse axis.

The normal 587 to the boundary 582 at the point, P, intersects the transverse axis 581 at a point, C. The coordinates of the point, P, from an origin at C are r, 6. Those from an origin at G are g,'y. The ratio n/v2 = it.

The boundary 582 meets the transverse axis 581 at a point, A, a distance a from F. By the Law of Sines:-9 1 9 r = . and = so sin* sin'y sin6 siny gsin7 = isin = rsin8 Equating the optical path length through P with that along the transverse axis:-l+rn=a+(c-a)n or gsiny(csccb+ncsc9)=a+(c-a)fl (1) Equating the horizontal components of the path through P with the length of the transverse axis:- 1cos + rcosO = c or gsin-y(cotç5+ cot9) =c (2) By Snell's Law:-sin(i'+Ø) =nsin('y-O) or sin'ycos' + cos-ysinØ = nsirvycosO -ncos'ysinO sinty(cos_ncos9)+cos7(sin+flS1n9) = 0 (3) We therefore have two coordinate variables (g, -y) plus two parameters (0, ) connected by three equations with three constants (a1 c, n). This system represents a line and may be solved numerically.

This line is the boundary 582 in Figure 51. A branch of the hyperbola through the point, A, with eccentricity n is shown as a dashed line 588 for comparison. It will be seen that this has a wider base than the cartesian oval and is thus only able to collimate an explosion.

Figure 52 is a section of an axially symmetric explosive lens 591 with the geometry of Figure 51 through its axis of symmetry 592. It shows the detonator 593, a truncated cone of fast explosive 594, the slow explosive 595, and an inner spherical shell of fast explosive 596.

A regular polyhedron is a convex polyhedron, each of whose faces is a regular polygon and identical to all of the other faces, and each of whose vertices is surrounded alike.

There are only five kinds of regular polyhedra, of which the icosahedron has the most faces, numbering twenty and comprising equilateral triangles.

Each face may be inlaid by a regular tessellation of order in by splitting each edge into in equal edges to give 3(m -1) new vertices on those edges. If in = 3 there is also a new vertex in the centre of that face, while if in = 4 there are three new vertices. Alt these new vertices are triangulated to give in2 new equilateral triangles.

Such a tessellated regular polygon may be geodesated by moving each new vertex radially onto the sphere circumscribing that polyhedron and sharing its centre.

This procedure makes a polyhedron which has 80 faces for in = 2, and 180 faces for m = 3. A larger number of smaller faces reduces the volume of explosive required.

Figure 53 shows an icosahedron 599, one of whose faces is overlaid by a geodesated regular tessellation of order 2 for that face. For clarity, this geodesation is expanded onto a sphere of slightly greater radius than the one circumscribing the icosahedron. The inner triangle 600 is an equilateral triangle, while the three outer triangles 601, 602 and 603 respectively are isosceles triangles.

In Figure 54 the edges of this inner triangle 600 are shown as dashed lines, and an explosive lens 604, similar to the one in Figures 51 and 52 but with smaller maximum values for 0 and, is trimmed so as to fit into this triangle with the outer surface 605 of the inner spherical shell of fast explosive 596 coinciding with the circumscribing sphere.

Figure 54 is a wire diagram.

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The detonator 593 is shown protruding from the face 6D6 of the truncated cone of fast explosive 594 symmetric about a line through the centroid of the inner triangle 600.

There are three identical cuts 611, 612 and 613 respectively through the explosive lens 604 to allow it to fit into a spherical array of explosive lenses which are identical before being cut. The respective boundary 621, 622 and 623 of each cut 611, 612 and 613 with the surface of the truncated cone of fast explosive 594 is a hyperbola. The respective boundaries 631, 632 and 633 between the slow explosive 595 and the truncated cone of fast explosive 594 on each cut 611, 612 and 613 are also shown. The point of detonation 635 of the detonator 593 lies on a line through the centroid of the inner equilateral triangle 600.

An adjacent explosive lens for the smaller isosceles outer triangle 601 has a similar cut for the face it shares with the larger equilateral inner triangle 600; so that its point of detonation is symmetric with respect to and equidistant from that shared face with the point of detonation 635 of the detonator 593 for the inner equilateral triangle 600. But the cuts for its other two sides are closer to its point of detonation, which does not therefore lie on a line through its centroid.

The points of detonation of explosive lenses for any two adjacent outer triangles are also symmetric with respect to and equidistant from their shared face.

This arrangement of symmetric and equidistant points of detonation for two different types of faces cannot be obtained with a truncated icosahedron because all the edges of its hexagons and pentagons have the same length.

Since all the "optical" path lengths from the point of detonation 635 to the inside of the inner spherical shell of fast explosive 596 in the explosive lens 604 are the same, and equal to the "optical" path lengths for all the other explosive lenses in the spherical array of explosive lenses, all the detonations for the array are triggered simultaneously by a common trigger.

Each detonation may be effected by a hot-wire exploded with a pulse of electricity.

Alternatively, each detonation may be achieved by direct laser ignition via a fibre-optic cable of the same length, either with or without a focussing lens system. In the latter case, a return fibre-optic cable may be provided for each detonator, so that its function may be verified before use.

A laser-driven metal flyer plate can reliably shock detonate insensitive high explosive.

Such a metal flyer plate can be coated directly onto the tip of an optical fibre leaving a small gap between its surface and that of the high explosive parallel to it. This would, however, prevent any testing of that optical fibre prior to use.

A reversed pair of thick pIano-convex aspheric fused silica lenses may be interposed between the tip of the optical fibre and the metal flyer plate to respectively collimate and then focus the light from that tip onto that plate. In which case, the metal flyer plate may be coated onto the plane surface of the focussing lens leaving a small gap between its surface and that of the high explosive parallel to it. It is known from Figure 8 of U.S. Patent 5,914,458 that the optical fibre may be offset slightly from the common axis of symmetry of those lenses, and light of too low an intensity for ignition reflected back for testing purposes by a plane fused silica window between the convex surfaces of those two lenses into a return optical fibre offset from that common axis of symmetry by the same amount in the symmetrically opposite direction.

Each optical fibre may receive electromagnetic energy from a respective laser diode within a pulsed laser diode array which is electrically wired in parallel through a cylindrical lens or a respective spherical microlens.

6.28 Fuel injection.

6.28.1 Injector guns.

Each injector gun may have either multiple revolving chambers, or multiple revolving barrels. Since a cylindrical target 101, 102, 103 or 104 fired from a revolving barrel will have both a tangential velocity as well as its muzzle velocity when it leaves the muzzle of that barrel, the aim and the orientation of the firing position of each injector gun with a revolving barrel is arranged to make the resultant velocity pass through a common aim point on the axis of symmetry 451 of the conical shield 420. It is also possible for an injector gun with a single barrel to hold more than one round, all of which can be fired seperately in succession.

A typical revolving barrel gun can fire 4200 rounds! mm with a mean time between failure of 100,000 rounds if maintenance is carried out every 15,000 rounds. This would allow operation for some period greater than 3.6 minutes but less than 23.8 minutes for a set of conventional injector guns. An injector gun with a revolving barrel takes some 0.5 seconds to reach full speed, during which time the burn cannot commence because the cylindrical targets 101, 102, 103 or 104 would be too widely spaced for optical recirculation to take place at a sufficient power level. Since jettisoning debris at relativistic velocities is undesirable, cylindrical targets should not be fired by injector guns with revolving barrels during a run up to full speed unless they will be vaporized by the fireball from the small boosted fission nuclear explosive device. So that injector guns with multiple revolving chambers may be preferred.

A rate of fire of 5000 cylindrical targets per second is required. The muzzle velocity of a typical medium calibre cannon using a chemical propellant is 1000 metres / sec and varies by ±1%, but this is mainly a systematic error due to the temperature of that propellant. At that muzzle velocity and rate of fire, such a variation would allow a faster cylindrical target to close on a slower preceding cylindrical target. While the launch time of a projectile can vary by a time an order of magnitude larger than the period between firing cylindrical targets. This would also affect the spacing of the cylindrical targets.

Clearly, the muzzle velocity of each cylindrical target fired from each injector gun must be almost exactly the same with a neglible error in the required launch time to obtain a stream of equally spaced cylindrical targets. Moreover, it is preferable if the spacing is the same in all conditions. It is therefore desirable, at the least, for such a chemical propellant to be ignited by a variable amount of electrical energy chosen so as to compensate for the variation in performance of that propellant with temperature and to reduce the variation in launch time.

Figure 55 is a schematic rear section showing the rear inner and outer circular arrays of injector guns. Figure 59 is an expanded view of the inside of Figure 55. Both show the axis of symmetry 451 of the conical shield 420 and the starter injector 577 whose line of fire is on that axis. A rear inner circular array 791 of injector guns 801 to 809 is surrounded by a rear outer circular array 792 of injector guns 810 to 818 arranged so that their barrels are as close to the axis of symmetry 451 as possible when firing. Each respective feed 901 to 909 runs radially inward from a respective cryogenic drum magazine 1001 to 1009 to its respective injector gun 801 to 809 in the rear inner circular array 79L Each respective feed 910 to 918 runs radially inward from a respective cryogenic drum magazine 1010 to 1018 to its respective injector gun 810 to 818 in the rear outer circular array 792.

Figures 56 and 60 are similar to Figures 55 and 59 respectively but show the next rearmost, or second, inner circular array 793 of injector guns 819 to 827 respectively together with the next rearmost, or second, outer circular array 794 of injector guns 828 to 836 respectively.

Figures 57 and 61 are similar to Figures 55 and 59 respectively but show the third inner circular array 795 of injector guns 837 to 845 respectively together with the third outer circular array 796 of injector guns 846 to 854 respectively.

Figures 58 and 62 are similar to Figures 55 and 59 respectively but show the fourth inner circular array 797 of injector guns 855 to 863 respectively together with the fourth outer circular array 798 of injector guns 864 to 872 respectively.

If every cylindrical target had an identical muzzle velocity, neglible error in its launch time and zero dispersion from its intended trajectory, all the implosions could commence * either at a common point on the axis of symmetry 451 of the conical shield 420, or in a common plane at right angles to that axis. Since each inner or outer circular array is at a different distance from such a common point or common plane, the timings of the firings of its injector guns must be adjusted to avoid an incorrect gap between cylindrical targets from different circular arrays. For this reason, it is convenient to fire all the injector guns in a particular circular array sequentially.

Figure 63 is a schematic side elevation through the axis of symmetry 451 showing that injector gun 801 from the rear inner circular array 791 which lies in the vertical plane in Figures 55 and 59 and that injector gun 814 from the rear outer circular array 792 which lies in that vertical plane, together with their respective cryogenic drum magazines 1001 and 1014 and their respective feeds 901 and 914. Figure 63 also shows the starter injector 577.

The cryogenic drum magazine 1001 is power driven to minimise jamming. It has multiple layer helical tracks in order to accommodate a very large number of rounds: 46,500 in the example shown. Alternate helical tracks have opposite senses. So that if their axial rails rotate in the same direction, the rounds in them move in opposite directions axially.

A common direction of rotation facilitates the transfer of each round from one layer to another at either end of the cryogenic drum magazine.

The feed 901 comprises both a feed chute and a return chute, separated by a thermal insulator to prevent the warmer spent cartridges from heating the cryogenic fuel, and is a linkless feed system.

As the cryogenic drum magazine 1001 is very long in order to contain a very large number of rounds, it is not convenient for the return chute to go to the other end of that magazine, as is the normal practice. Moreover, it is not desirable to store the warm spent cartridges in the cryogenic drum magazine iDOl in case they heat the cryogenic fuel.

Instead, a power driven storage drum 1101 is provided to store the empty cartridges in multiple layer helical tracks or otherwise. The interior 1301 of this drum houses a super-conducting permanent magnet electric motor which drives the cryogenic drum magazine, the linkless feed, and the storage drum itself. Each injector gun is driven by its own electric motor, which is synchronized with the superconducting permanent magnet electric motor in its respective storage drum.

The interior 1201 of the cryogenic drum magazine iDOl houses the cold side of a heat pump utilizing a solid hydrogen refrigerant at approximately 12 to 13°K, while the interior 1301 of the storage drum includes its warm side. The heat circulated by this pump helps keep the feed mechanism lying between the two drains free of ice, even when it is not in use. Similarly for all the other cryogenic drum magazines 1002 to 1072; their respective storage drums 11D2 to 1172 and their respective linkless feeds 902 to 972.

Figure 63 also shows that injector gun 819 from the next rearmost, or second, inner circular array 793 which lies in the plane approximately -from the vertical in Figures 56 and 60 and that injector gun 832 from the next rearrnost, or second, outer circular array 794 which lies in that plane, together with their respective cryogenic drum magazines 1019 and 1032, their respective storage drums 1119 and 1132, and their respective feeds 919 and 932.

All these items are enclosed in a schematic section of the conical shield 420 through its axis of symmetry 451 in the vertical plane. Respective trajectories 1401 to 1472 from the injector guns 801 to 872 pass through respective holes 1501 to 1572 in the nose of that conical shield. Part of the nose of the conical shield has been further cut away to reve& fourteen of those holes 1501 to 1572 which lie nearest to that section Figure 64 is a schematic side elevation showing that injector gun 837 from the third inner circular array 795 which lies near the vertical plane in Figures 57 and 61 and that injector gun 850 from the third outer circular array 796 which lies near that vertical plane, together with their respective cryogenic drum magazines 1037 and 1050, their respective interiors 1237 and 1250, their respective storage drums 1137 and 1150, their respective interiors 1337 and 1350, and their respective feeds 937 and 950.

Figure 64 also shows that injector gun 855 from the fourth inner circular array 797 which lies near the vertical plane in Figures 58 and 62 and that injector gun 868 from the fourth outer circular array 798 which lies near that vertical plane, together with their respective cryogenic drum magazines 1055 and 1068, their respective interiors 1255 and 1268, their respective storage drums 1155 and 1168, their respective interiors 1355 and 1368, and their respective feeds 955 and 968.

All these items are enclosed in a schematic section of the conical shield 420 through its axis of symmetry 451 in the vertical plane.

The injector guns in Figures 56, 57 and 58 are at larger distances from the axis of symmetry 451 than those in Figure 55. Their cryogenic drum magazines and storage drums are, however, at identical distances from that axis of symmetry as that shown in Figure 55. The total number of injector guns in this example is 72 giving a rate of fire of 5040 cylindrical targets per second. This rate of fire is adequate to maintain optical recirculation in both endoatmospheric and exoatmospheric operation with ablative drive. It will be seen from the timing diagrams in Figure 71 described in Sections 6.30.2 and 6.30.4 that more injector guns giving an even higher rate of fire are necessary for optical recirculation in exoatmospheric conditions with magnetic drive. Moreover, it will be shown in Section 6.39.4 that much larger cryogenic magazines must be provided in order to increase the amount of ammunition by a factor of at least twenty for ablative drive to that needed for acceleration to, or deacceleration from, values of veh which are a fraction. of one thousandth of the speed of light. The corresponding factor for magnetic drive to or from a few percent of the speed of light is much larger still, because more of the vehicle's mass is comprised of cylindrical targets 103 or 104 filled with DHe3 and less of coolant and/or material to be ablated. The exaust is mainly debris from the cylindrical targets. The exaust velocity is much higher, but the thrust is lower, and the acceleration takes place over a longer period to a higher final velocity using a correspondingly larger number of cylindrical targets. Figure 76 described in Section 6.32.1.1 shows a timing diagram appropriate to magnetic drive with the preferred engine configuration.

Figure 59 shows the trajectories 1401 to 1409 for the injector guns 801 to 809 re-spectively together with the trajectories 1410 to 1418 for the injector guns 810 to 818 respectively as points in its plane. Figure 60 shows the trajectories 1419 to 1427 for the injector guns 819 to 827 respectively together with the trajectories 1428 to 1436 for the injector guns 828 to 836 respectively. Figure 61 shows the trajectories 1437 to 1445 for the injector guns 837 to 845 respectively together with the trajectories 1446 to 1454 for the injector guns 846 to 854 respectively. Figure 62 shows the trajectories 1455 to 1463 for the injector guns 855 to 863 respectively together with the trajectories 1464 to 1472 for the injector guns 864 to 872 respectively.

All these trajectories are shown unnumbered in Figure 55. Figures 56 and 57 show unnumbered only those trajectories from their own injector guns and those of the injector guns in front of them which pass by their own injector guns. Figure 58 only shows unnum-bered the trajectories from its own injector guns as there are no injector guns in front of them.

The sequence of firing for the injector guns may be such that the trajectory of a cylindrical target is close to the trajectory of the immediately preceding cylindrical target; so that the shielding of the cylindrical target from the burn and the subsequent fusion explosion of the immediately preceding cylindrical target is maxirnised by the debris from its leading guide 113, and either its extendable fins 116 or its ablative base 117.

If the points at which implosions commence are in a plane at right-angles to the axis of symmetry 451 of the conical shield 420, rather than at a point on that axis, this will introduce a systematic asymmetric variation of the thrust on the shield 370. However, this variation will be randomized by the dispersion of the cylindrical targets. Moreover, a burn may take place with some of the injector guns out of service. The choice of the sequence of firing may therefore be chosen in operation.

6.28.2 Cryogenic propellant.

Chemical propellant may be ignited by a plasma injector external to the cartridge, a laser injector, or an exploding wire. However, if a plasma injector was incorporated into a cartridge, as would be convenient given the large number of rounds required, it would increase its length and reduce the rate of fire of the injector gun.

Figure 66 is a sectional side elevation showing a cartridge 673 at the required tem-perature of 18.3°K for the DT fuel, filled with cryogenic propellant 674 such as hydrogen, which is thus below its boiling point of 20.4°K at a pressure of one standard atmosphere, or deuterium, which is thus below its triple point of 18.72°K and 0.171 bar, to which energy is supplied on firing by an exploding wire 675 (as shown), or a coil of wire, between two electrodes, to cause that propellant to vaporize and expand.

Liquid hydrogen is transparent at wavelengths between 0.186 jim and 1 Mm. The trans-parency of liquid deuterium should be similar to that of liquid hydrogen. Solid hydrogen and deuterium are also transparent. As the exploding wire 675 is at a temperature of the order of 20,000°K, the energy is transported by radiation into the whole volume of the transparent cryogenic propellant 674 and the instability of the penetration of the denser cryogenic propellant 674 by the less dense plasma from the exploding wire 675 is not of con-sequence. A more complicated, but less robust, multi-site exploding wire is not therefore useful.

A cathode 677, the exploding wire 675 and an anode 676 are connected to form a coaxial arrangement whose magnetic fields substantially cancel each other out. An insulator 680 isolates the anode from the cathode. The role of the anode and cathode may be interchanged-The breach of each injector gun contains a coaxial cable for the electrical energy, which is connected to the cathode 677 and the anode 676 only on firing.

Its chamber for the cartridge 673 is electrically isolated from it. These two measures remove that electrothermal (ET) injector gun from the high-voltage electrical circuit, as

well as minimizing the magnetic field from it.

The anode includes large perforations 678 for the gaseous propellant to pass through.

The anode is shown attached to the ablative base 117 of a further cylindrical target 102, or a third further cylindrical target 104, which forms one half of the bearing 118. It may equally be attached to a pusher plate for a cylindrical target 101, or a second further cylindrical target 103. The cylindrical ablator 107 may be extended to the left in Figure 2 to connect with this pusher plate, and be provided with slots for the extendable fins 116 to pass through when deploying. Such a light working fluid has the high sound velocity necessary to maintain the pressure along the barrel at a relatively low temperature. On the one hand, a high muzzle velocity is desirable to maximise the distance between a cylindrical target and the explosion of the immediately preceding cylindrical target. On the other hand, it would -be useful for the gaseous propellant to remain sufficiently cool after its explosion to keep the barrels of the injector guns 801 to 872 at their working temperature without further cooling, and thus minimise their erosion. However, it is more important to inaximise the spacing of the cylindrical targets and their distance from previous explosions.

The maximum temperature of the propellant gas at which barrel erosion is not ex-cessive is 4,700°K. At that temperature the velocity of sound in molecular hydrogen is 5,013 metres/sec, while that in molecular deuterium is 3,545 metres/sec when calculated from the high-temperature limiting value of the adiabatic exponent for a diatomic gas of 1.286. The fins on a projectile fired at ambient temperature with a velocity of 5km/s in an atmosphere with a pressure of one bar would melt rapidly. At an altitude of 15km in the Earth's atmosphere, and thus at a pressure of 90.85 Torr, the ablation of a blunt nosetip made of a carbon-carbon composite at a velocity of Skin/s is about 0.1 millimetre per kilometre of path. Each cylindrical target has to survive multiple shock waves of in-creasing severity from the explosions of preceding targets. The extendable fins 116 fired at cryogenic temperature in the thinner atmosphere behind the shield 370 may survive long enough to reach the point 258 at which the implosion of the cylindrical target 101 or 103 to which they are attached is to commence.

The acceleration of a cylindrical target to a velocity of 5,000 metres/sec over a barrel length of 2.1 metres is 5,952,381 metres/sec2. The length of the ablator in a cylindrical target for a 30mm injector gun would be at least 7cm. The density of beryllium is 1.85 g/cm3. The ultimate tensile strength of an extruded beryllium rod is 827 MPa at room temperature and some 20% higher than that at cryogenic temperature. At room temperature, the compressive yield strength is ten percent higher than the tensile yield strength. Such an ablator would therefore be able to withstand the 770 MPa at its base necessary to accelerate itself. As the dynaánic compressive yield strength of a metal may be three times as much as its static compressive yield strength for very short periods an ablator with an initial aspect ratio of 10 should also be able to accelerate the high-Z ballistic cap.

The force required to give such an acceleration to a layer of DT of density prir = 0.225 gm/cm3 which is 0.15cm thick and one square metre in extent is 2 MN. The shear strength of solid hydrogen at 10°K is only 0.75 MPa. If the adhesion of the cold DT fuel to the ablator is also 0.75 MPa then a muzzle velocity of 3,055 metres/sec can be obtained over the same barrel length.

The ultimate tensile strength of warm pressed polycrystalline lithium hydride at room temperature is up to 54.9 MPa. The compressive strengths of ceramics are about twelve times their tensile strengths. So that its compressive strength may be as high as 658.8 MPa.

The base of a 7cm long cylinder of warm pressed polycrystalline L12DT fuel with a density of 0.85 gm/cm3 under acceleration to a muzzle velocity of 5,000 metres/sec along a barrel of length 2.1 metres is exposed to only 354 MPa and should therefore be able to support itself A projectile for a typical revolving barrel gun with a calibre of 30mm has a length of 14cm and a mass of 425 gm. A cylindrical target of that length could have a mass as little as one quarter as much. Since a longer projectile is preferred, the following calculation assumes a mass of 425 gm.

If 15 MJe is supplied to each cartridge and 72 injector guns fire at 70 rounds/sec then the average electrical power used for the injector guns will be some 75.6 GWe. If 15 MJe is supplied to a cartridge in one milliscond, then the peak power for a single injector gun will be 15 OW,. The optimum choice of power supply for the injector guns depends on the number of rounds they are required to fire during a burn. If a very large number of rounds are needed, as with magnetic drive to several percent of the speed of light, then the power should come from generators able to satisfy the entire load of 75.6 GWe. In a study entitled "A Potassium Rankine Multimegawatt Nuclear Electric Propulsion Concept" (E.

Baumeister et al (1990) Proc. of the 25th. Intersociety Energy Conversion Engineering Con-ference, 1990, IECEC-90, IEEE p.121) a 200 MW power system (less its nuclear reactor and shield) was envisaged to have a mass of 412,616 kg. So that a load of 75.6 GW6 would necessitate auxiliary power systems with a mass of 155,968,848 kg. If fitted, such power systems would be situated in front of the shield 370 or its spherical indentation 390, as they receive heat from the liquid lithium blanket 403 therein, as described in Section 6.33.4. If the requirement is only for a burn of 16,800 rounds per injector gun for 72 injector guns, as with ablative drive within the solar system, high power lithium-ion batteries will provide the desired energy and power for a mass of 120,960,000 kg. Such batteries may be charged by a space qualified nuclear fission reactor. If fitted, those batteries and such a reactor may be situated in a separate reactor compartment 437 forward of the conical shield 420, as shown in Figure 65.

All the injector guns 801 to 872 are aimed at the aim point 679 shown in Figure 67 on the axis of symmetry 451 of the conical shield 420. The implosion of a cylindrical target 101, 102, 103 or 104 occurs before it reaches that aim point in ablative drive, but after it passes that aim point in magnetic drive Figure 63 shows a conical shield 420, perforated by a hole 681 for the starter 571 and by circular arrays of holes 1501 to 1572 for the cylindrical targets 101, 102, 103 or 104 to pass through, which protects the starter injector 577 and the injector guns 801 to 872 from the explosion of each cylindrical target 101, 102, 103 or 104. The gaseous propellant passes through the barrels of the injector guns 801 to 872 and then through the hole 681 and the circular arrays of holes 1501 to 1572. It is diluted by sufficient gas evaporating from the cryogenic drum magazines to cool both it and the apex of the conical shield 420, as well as purge any propellant gases from the starter injector. The remainder of the conical shield 420 is provided with a cooling passage 682 filled with cooling fluid and a large number of conical shield controllable pore arrays 683 of the type described in Section 6.27.6.4 (but not necessarily taking part in the control of the vehicle) to allow the ablation of that cooling fluid. Since the conical shield always points towards the point at which the implosion of a cylindrical target takes place, the cylindrical portion of its wall cannot be subjected to electromagnetic energy from the resulting fusion explosion until the radius of its shock wave exceeds that at which the conical shield is positioned, and then only at very high angles of incidence. The cylindrical portion of the wall forms part of the converging annular shock tube 427. In both ablative and magnetic drive therefore, hot plasma may pass over it, but this plasma is of very low density. In order to conserve coolant, it is thus preferable if the cylindrical portion of the wall can be cooled by conduction rather than controllable pore arrays.

Since the single starter injector 577 is only used to initiate the burn, the hole 681 in the shield, through which the small boosted fission nuclear explosive device 571 comprising the starter passes, is sealed after use by a rotating or sliding cap 684, but with sufficient clearance to allow the cooling gas to escape. The starter injector 577 is, however, provided with an automatic loader (not shown) in order to allow more than one burn. The circular arrays of injector guns, their cryogenic drum magazines, their storage drums and the starter injector are all mounted on the conical shield and thus move with it. The hole 681 and the circular arrays of holes 1501 to 1572 are sufficiently large to allow for the respective dispersion of the starter 571 and the cylindrical targets 101, 102, 103 or. 104 plus any relative acceleration between the vehicle and those projectiles.

6.28.3 Size of cylindrical target.

If the cylindrical targets are small then the energy from the explosion of a cylindrical target may be insufficient to provide sufficient recirculated power from a gas of low density behind the shield (but not from a gas in the converging annular shock tube). And the areal density of the cold fuel may be inadequate to stop hot electrons produced by any trigger beam(s), or provide volume ignition.

Increasing the radius of the cylindrical targets raises the calibre, size and mass of each injector gun.

Increasing the length of the cylindrical targets not only raises the size and mass of each injector gun but also reduces its rate of fire. It also increases the stress in each cylindrical target under acceleration, unless the muzzle velocity is reduced, or the length of the barrel of each injector gun is increased. It is undesirable to reduce the muzzle velocity as that shortens the distance of each cylindrical target from the explosion of the immediately preceding cylindrical target. So that it is preferable to increase the barrel lengths-Insufficient information is available about the characteristics in inertial confinement fusion of fuels other than DT to decide the required size of their cylindrical targets. While insufficient information is available about the strengths of materials at cryogenic temper-atures to decide the feasible size of their cylindrical targets.

6.28.4 Trajectory sensors.

Figure 67 shows a pair of charge injection device cameras 701 and 702, each of whose exposures is gated by a respective image-intensifier 703 or 704, arranged so that their respective optical axes 705 and 706 are orthogonal, and those optical axes both intersect the axis of symmetry 18 at the point 707. Those optical axes are not necessarily at right-angles to the axis of symmetry 18. The cameras 701 and 702 have lenses 709 and 710 respectively.

A muzzle velocity sensor 713 on that injector gun 801 to 872 which fires the cylindrical target 101, 102, 103 or 104 sends an analogue or digital signal representing a muzzle velocity, or a pair of pulses at the times when a position on that cylindrical target passes over two respective sensors, to a camera controller 714 which triggers the image intensifiers 703 and 704 after a delay after firing predicted from that muzzle velocity to allow for the arrival of that cylindrical target in their field of view. The camera controller 714 has already sent a digital signal detailing that muzzle velocity and the time at which it was measured to each leaf controller 251, as described in Section 6.22.

A cylindrical target does not contain a magnet. It does not therefore provide a mag-netic held for a Hall-effect sensor to detect. Nor does its passage provide a varying magnetic field for an inductive pick-up coil to detect. A cylindrical target does not contain any fer-rous material. It does not therefore provide a magnetic path for a variable reluctance sensor to detect. If a permanent magnet was added to a cylindrical target then a Hall-effect sensor or an inductive pick-up coil would detect its passing. If some ferrous material was added to a cylindrical target then a variable reluctance sensor would detect its pas-sage. The muzzle velocity sensor shown comprises two inductive proximity sensors, each of which includes a radio-frequency pick-up coil able to detect non-ferrous metals, spread apart along the trajectory of the cylindrical target arid shown as circles.

Such sensors would be suitable for ablative drive, provided the magnetic fields from the ET injector guns are shielded, but not for magnetic drive because of the high and varying magnetic field inherent in that mode of operation. It should also be mentioned that NdFeB cryogenic permanent magnets have lower remanent magnetization and may be more easily demagnetized below 140°K.

An optical sensor may be obscured by residue from chemical propellant deposited on its window but not by the cryogenic propellant described in Section 6.28.2 which does not produce any such residue. However, its image may be obscured by hot gas blowing by a cylindrical target. A stripe on a cylindrical target in a plane at right-angles to its axis of symmetry improves the contrast between that target and any such hot gas enabling an optical muzzle velocity sensor to be used with cryogenic propellant in both ablative and magnetic drive. There must be either two such stripes spaced a known distance apart along each cylindrical target, or two such optical sensors spaced a known distance apart along the trajectory of the cylindrical target.

The cameras 701 and 702 respectively measure the position at that time and thus the trajectory of a cylindrical target 101, 102, 103 or 104 very precisely. As described in Section 6.22 and shown schematically in Figure 20, an inertial measurement unit 269 with three ring laser gyroscopes, which measure the angular velocities of the vehicle 270 around three mutually orthogonal axes, and three accelerometers, which measure the accelerations to which the vehicle 270 is subjected along those three mutually orthogonal axes, is provided.

All these measurements are used by each leaf controller 251 to predict the future trajectory of that cylindrical target 101, 102, 103 or 104, and the rotation and tilt of each leaf 191 is adjusted so that the reflection of its respective further meridional ray 195 through its respective point.Phjnge would pass along the axis of symmetry 105 of the cylindrical target 101, 102, 103 or 104 in exact and simultaneous alignment with those of all the other leaves in its circular array of leaves at the beam velocity, t/beamg.

If there are injector guns, each with a rate of fire of,-t targets/second, the rate of fire, of the injector guns 801 to 872 is mjnjnrate. If the frame rate of a charge injection device camera 701 or 702 is faarn, then at least CEILING(rnin3nrate / fcara) pairs of such cameras are provided. The timelag between a cylindrical target 101, 102, 103 or 104 leaving the muzzle of an injector gun 801 to 872 and reaching the point 258 at which its implosion is to commence is sufficiently long for the calculations to predict its future trajectory to be performed and the rotations and tilts of the leaves to be adjusted accordingly.

In practice, the field of view of each camera may be reduced to the larger of the sum of the length of the cylindrical target plus twice the positive value of the worst case error due to uncertainties in the muzzle velocity, launch time and drag of those targets, or the sum of the diameter of the cylindrical target plus twice the worst case error due to the dispersion of those targets (taking into account the geometry shown in Figure 67). This enables both those errors to be measured with maximum accuracy. In which case, multiple pairs of cameras are provided t&detect cylindrical targets on trajectories from both the inner and outer injector guns even when the axis of symmetry 451 of the conical shield 420 has rotated and/or moved away from the axis of symmetry 18. In consequence, the point at which the optical axes of a pair of cameras meet is no longer necessarily on the axis of symmetry 18. The lens for each such camera may be a zoom lens in order to allow it to cover the field of view of an adjacent camera which has failed, albeit with reduced accuracy of measurement.

The cylindrical target 101, 102, 103 or 104 is illuminated first by the burn, either of the small boosted fission nuclear explosive device 571, or of a previous cylindrical target, at a very high level; and then by the subsequent shock wave at a lower, but still high, level. No light reaches the image intensifier for a camera directly. Since the ballistic cap is an ogive, or similar shape, any specular reflection will spread out over a wide solid angle, as will any diffuse reflection. So that the light level reaching an image intensifier will be reduced by six orders of magnitude for specular reflection.

In addition to gating the charge injection device camera, the image intensifier may protect both itself and that camera from very high light levels, and compensate for vary-ing light levels, by automatically reducing the voltage to its photocathode and/or its microchannel plate. The lens may be preceded by a filter to reduce the light level reaching the image intensifier.

The light from the burn of a previous cylindrical target may, of course, be used as a strobe.

6.29 Dual engine configuration.

Figure 68 is a schematic diagram showing a sectional front elevation and a sectional plan of four plane mirrors, which have the same shape but different orientations. Since rays directed by the eye mirror(s) exit from the rear of the apparatus, the sectional front elevation is drawn below the sectional plan. The section, A-A, lies on the sectional plan.

Figure 68 also shows a left axis of symmetry 1SL, which lies in the plane 19 of the sectional plan, together with the defining mirror of a left eye mirror 721L, which is the outermost eye mirror on that axis, and a left conical shield 722L, both of whose axes of symmetry coincide with that axis of symmetry 18L. Figure 68 also shows a right axis of symmetry 1SR, which lies in the plane 19 of the sectional plan, together with the defining mirror of a right eye mirror 72111, which is the outermost eye mirror on that axis, and a right conical shield 72211, both of whose axes of symmetry coincide with that axis of symmetry 18R..

Each of the plane mirrors is orthogonal to the plane 19 of the sectional plan. Figure 68 also shows the centre line 720 of the vehicle. It will be appreciated that neither the left eye mirror 7221 nor the right eye mirror 721R need comprise a directed energy weapon, as shown in Figure 68.

The radius of the base of each conical shield is r0,, as shown on the sectional front elevation. The inclination of the left rear plane mirror 723L to the left axis of symmetry 18L is as shown on the sectional plan, while that of the left front plane mirror 724L is -The inclination of the right rear plane mirror 72311 to the right axis of symmetry 1811 is as shown on the sectional plan, while that of the right front plane mirror 72411 is 0p1 -ir. These angles are indicated by grey arcs.

Each of the plane mirrors has a hole in the shape of an ellipse, whose centre lies on its respective axis of symmetry, and whose minor axis is of length 2b. The projection of each such ellipse on the sectional front elevation is a common inner circle of radius as shown on that sectional front elevation. The major axis of each such ellipse lies in the plane 19 of the sectional plan and is of length 2 csc The outer edge of each of the plane mirrors also has the shape of an ellipse, whose centre lies on its respective axis of symmetry, and whose minor axis is of length 2 b0t. The projection of each such ellipse on the front elevation is a common outer circle of radius b0t, as shown on that sectional front elevation. The major axis of each such ellipse lies in the plane 19 of the sectional plan and is of length 2 b,,,± csc 0p1 The projection of the defining mirror of the left eye mirror 721L on the sectional front elevation is a circle of radius rem as shown on that sectional front elevation.

The projected area of each elliptical plane mirror on the front elevation is it (b - The projected area of each elliptical hole less that of the conical shield within it on the sectional front elevation is iv -r0). These two areas are equal; so that:- 1k2 k2\-1b2 2 \ or 2 _0L2 2

- -

Figure 68 also shows those inner and outer rays lying in the plane 19 of the sectional plan of a left inner collimated annular beam 725L which passes through the elliptical hole in the left rear elliptical plane mirror 723L and then the elliptical hole in the left front elliptical plane mirror 724L, and those inner and outer rays lying iii the plane 19 of the sectional plan of a right inner collimated annular beam 725R which passes through the elliptical hole in the right rear elliptical plane mirror 723R and then the elliptical hole in the right front elliptical plane mirror 724R.

Figure 68 shows those inner and outer rays lying in the plane 19 of the sectional plan of a left outer collimated annular beam T26L, which is reflected from the left rear elliptical plane mirror 723L, and then the right front elliptical plane mirror 724R, to replace the right outer collimated annular beam 726R.

Figure 68 shows those inner and outer rays lying in the plane 19 of the sectional plan of a right outer collimated annular beam 726R, which is reflected from the right rear plane mirror 72311, and then the left front plane mirror 724L, to replace the left outer collimated annular beam 726L.

The axial length along an axis of symmetry of each elliptical plane mirror is 2b0 cot O,j. The left rear elliptical plane mirror 723L is contiguous with the left front elliptical plane mirror 724L. The right rear elliptical plane mirror 723R is contiguous with the right front elliptical plane mirror 72411. The outer rays of the outer collimated annular beams are reflected from the outer edges of the elliptical plane mirrors in every case, as shown. If the sei3aration between the two eye mirrors 721L and 72111 respectively is a so that the distance between the two axes of symmetry is 2re,n + s then:-2rem + S tan = or 2 b0 cot °pl 2 2Tem + S -4b0 tan 6,,= 2rem + .5 The path length of any ray, which is initially collimated with respect to an axis of symmetry, between a rear elliptical plane mirror and a front elliptical plane mirror is (2rem + s) csc 201,1. The path length along that axis which is replaced by such a crossover is (2r87_ + a) cot 2O. Hence the increase in path length from an inner collimated annular beam to an outer collimated annular beam dueto the crossover is:- (2r + a) (csc29i -cot 28pL) = (2r_ + a) tan Opt as may be verified from a geometric construction.

The separation, s, allows room for the opening of those of the shield extensions 371 to 388 respectively which are positioned where these adjacent eye mirrors are closest. As such shield extensions only need to be minimally extended so far as not to impede the beams from their respective eye mirrors, rather than control reentry, and the shield extensions are much smaller than the shield 370, rem >> s. In Figure 68, and all similar figures, a is therefore put equal to zero; so that adjacent eye mirrors appear to touch.

The simultaneous arrival of a pulse of electromagnetic energy and a cylindrical target at the point 258 at which its implosion is to commence for an engine are synchronised by the leaves for that engine independently of any other engine.

As the explosion of a cylindrical target 101, 102, 103 or 104 on the left axis of symmetry 18L takes place some distance from the left conical shield 722L, and expands rapidly, much of the electromagnetic energy it emits, even though it is not collimated, follows similar paths to the inner and outer left collimated annular beams 725L and 726L respectively.

Similarly for the explosion of a cylindrical target 101, 102, 103 or 104 on the right axis of symmetry 18R.

Figure 68 shows a left outer annular conical mirror 732L, and a left inner annular conical mirror 731L, which have slightly different cone angles, and whose axes of symmetry coincide with the left axis of symmetry 18L. Figure 68 shows a right outer annular conical mirror 732R, and a right inner annular conical mirror 731R, which have slightly different cone angles, and whose axes of symmetry coincide with the right axis of symmetry ISR.

Figure 68 also indicates the locations of a left variable atmospheric intake 733L and a right variable atmospheric intake 733R.

Figure 68 also shows a left reversed further alternate defined mirror 734L which is axially symmetric about the left axis of symmetry 18L and reflects electromagnetic energy as well-directed input rays into the left eye mirror 721L and any other eye mirrors of the left engine and a right reversed further alternate defined mirror 734R which is axially symmetric about the right axis of symmetry 18R and reflects electromagnetic energy as well-directed input rays into the right eye mirror 121R arid any other eye mirrors of the right engine. The radius of the outer edge of each reversed further alternate defined mirror is less than or equal to Each reversed further alternate defined mirror may be replaced by two or more reversed individual further alternate defined mirrors.

Figure 68 only shows the collimated annular beams until they reach the annular conical mirrors. Figure 69 is identical to Figure 68 except that it only shows those beams after they are reflected by the annular conical mirrors. The reflection of the left inner collimated annular beam 725L is shown on the left of that figure, while that of the left outer collimated annular beam 726L is shown on its right. It will be seen that the reflections of both inner and outer collimated annular beams are incident to the inside of each reversed further alternate defined mirror, so as to allow some badly collimated light to reach that mirror.

As shown, the outermost rays of each beam are incident to a reversed further alternate defined mirror on its axis of symmetry.

In a further embodiment of the apparatus, shown in both Figures 68 and 69, a left cylindrical mirror 735L, whose inner surface is reflective, connects the hole in the left rear elliptical plane mirror 723L with that in the left front elliptical plane mirror 724L, in order to prevent uncollimated light escaping from the left inner annular beam. And a right cylindrical mirror 735R similarly connects the hole in the right rear elliptical plane mirror 723R with that in the right front elliptical plane mirror 72411. Each end of each cylindrical mirror is truncated at the inclination of the elliptical plane mirror at that end: so that it forms an elliptical seal with that elliptical plane mirror.

It will be seen from Figures 68 and 69 that no beams cross each other between the front of a front elliptical plane mirror and its respective annular conical mirrors. Figures 68 and 69 both show a left further cylindrical mirror 736L and a right further cylindrical mirror 736R, whose inner surfaces are reflective, which enclose the beams and their reflections from the annular conical mirrors in those regions. A ray enclosure (not shown) mounted on the cylindrical mirrors, the plane mirrors, and the further cylindrical mirrors prevents uncollirnated light escaping from the beams into the vehicle.

Each of the elliptical plane mirrors, 723L, 724L, 72311 and 72411 respectively, each of the inner arid outer annular conical mirrors, 731L, 732L, 73111 and 73211 respectively, both of the reversed further alternate defined mirrors, 734L and 73411 respectively, both of the cylindrical mirrors, 735L and 73511 respectively, both of the further cylindrical mirrors, 736L and 73611 respectively, and the ray enclosure are cooled.

The power of each of the annular beams 725L, 72511, 726L and T261t on output from the eye mirror(s) on an axis of symmetry is Pcjrc/ qem, and thus sufficient on its own to implode a cylindrical target 101, 102, 103 or 104 and cause its ignition.

6.aO Timing.

6.30.1 Maximum path length of optical recirculation in a single engine.

A simple approximate relationship may be found between the radius, Dem, of an eye mirror and the maximum path length of the optical recirculation in a single engine shown in Figure 70 when the aim point lies on the axis of symmetry 18 of the eye mirror and the explosion of a cylindrical target occurs at that aim point.

If the beam 716 originates from a point 727 on the spherical defining mirror 728 with coordinates re,,., while the cylindrical target 101, 102, 103 or 104 is much smaller than that mirror, then the separation between the centre 729 of that mirror and the centre 718 of the cylindrical target 101, 102, 103 or 104 when at the aim point is approximately rem cos 01r +pl where p1 = -rem sin °lr cot (Oir + O) and 9 is both the angle of incidence to and reflection from that point 727. While the length of the beam from that point 727 to the centre 718 of the cylindrical target neglecting the size of that cylindrical target is approximately p2 = r sin 61r csc (Ui,. + O).

We may assume that the fusion products remain near the centre 718 of the cylindrical target 101, 102, 103 or 104 at the aim point. The distance back along the axis of symmetry 18 between that point and the inside of the spherical defining mirror 728 at the point 719 is p1 + rem cos 6jr + rem. The length of the arc of the inside of the spherical defining mirror 728 between its intersection with the axis of symmetry 18 and the start of the beam 716 at the point 727 is r,(ir -Or,.). Hence the maximum path length for the recirculation in a single engine is approximately:-rem (1 + ii--Or,-+ cosO1,-+ sin 9 (csc(91 + 9) -cot(91,-+ 9))) It will be appreciated that this path length may be increased for a single engine by substituting a reversed further alternate defined mirror for a further alternate defined mirror, and providing an annular conical mirror.

6.30.2 Single engine in endoatmospheric operation.

When the rear (trailing) edge of the cold fuel in a cylindrical target arrives at the position where its implosion is to commence, the front (leading) edge of the innermost recirculated beam, which has the shortest path length, must be present at that point-The front (leading) edge of the next innermost recirculated beam, which may have a slightly longer path length, must be present when the rear (trailing) edge of the cold fuel has passed through that portion of the innermost recirculated beam where it is the sole source of illumination to reach the selected illumination fraction of that beam, as described in Section 6.3. As the eye mirror(s) always accept energy for all the recirculated beams and/or beanilets, including any trigger beam(s), those beams will all be present subject to any blocking by high-Z vapour in the optical path, the delays depending on their different path lengths and the stretching of their pulses by badly-directed rays. -in volume ignition, or compression for fast ignition, the recirculated beams must last until the outermost recirculated beam finishes illuminating the partially imploded front (leading) end of the cold fuel, immediately before it starts to coast, and thus for a time equal to about half the implosion period, timp, plus the burn period of the cylindrical target.

In fast ignition, the recirculated trigger beam(s) must last almost until the hot elec- trons reach the rear (trailing) edge of the cold fuel on the axis of symmetry of that cylin-drical target, and thus only for a time equal to the implosion period. Once ignition has been achieved, the burn should proceed in the absence of any trigger beam(s).

But in volume ignition, the recirculated beams will have to last for longer than the burn period of the fuel. As the rays in the recirculated beams will have many different paths while being directed by the eye mirror(s), they will have different path lengths, and the duration of those beams will be extended accordingly.

The initial expansion of the shock wave overlaps the burn of a cylindrical target.

Figure 71 is a timing diagram. it shows the activities of a single engine with ablative drive in endoatmosperic operation comprising the very short implosion and burn 737 of a cylindrical target, the period 738 during which the electromagnetic energy emitted from the point explosion remains sufficiently high to implode the next cylindrical target, and the period 739 required for an optical recirculation, over several cycles of operation. As the implosion and burn of each cylindrical target takes a very short time in comparison to the other periods, it appears almost as a thick vertical line. It overlaps with the recirculation period 739 as explained above.

6.30.3 Path lengths in a dual engine configuration.

It will be seen from Figure 69 that rays on a return path must converge towards their respective axis of symmetry (irrespective of whether they actually cross that axis) in order to pass through the hole in their respective front elliptical plane mirror. This concentration of electromagnetic energy may ionise any atmosphere entering the respective variable atmospheric intake.

The axial distance between the centre of a front elliptical plane mirror and the base of an outer annular conical mirror must be sufficient for the outer rays reflected back along the return path from the latter to pass through the hole in the former. It is therefore at least:- (3b0w -2b) cot 9pt The axial distance through the whole of a rear elliptical plane mirror and half a front elliptical plane mirror is 3b0 cot The recirculation path length for the inner collimated annular beam, which does not include a crossover, is therefore:-rpm (1 + it-O +cosOir +sin9i (csc(6j,. i-O) -cot(9i + OiD) + 6 b0 cot 0,, + (3bont -2b) cot Oi The increase in path length from an inner collimated annular beam to an outer colli-mated annular beam due to the crossover is (2rem + s) tan O,,z where s U if the adjacent eye mirrors are contiguous, as aforesaid.

6.30.4 Dual engines in exoatmospheric operation.

Figure 71 also shows the activities of dual left and right engines with ablative and/or magnetic drive in exoatmospheric operation comprising the very short implosion arid burn 747 of a cylindrical target, the short period 748 during which the electromagnetic energy emitted from the point explosion remains sufficiently high to implode the next cylindrical target for the opposite engine, and the period 749 required for a crossover recirculation, over several cycles of operation. Clearly the burns are separated by shorter intervals than in endoatmospheric operation, and a much higher rate of fire is required, albeit spread over two engines. This part of Figure 71 is equally applicable to a double engine configuration.

Both dual and double engine configurations allow a period between the arrival of cylindrical targets for an engine equal to twice the sum of the duration of the implosion

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and burn, the time for which the point explosion usefully persists thereafter, and the crossover recirculation period less the overlap, which is equal to about half the implosion period plus the burn period, but plus some pulse stretching. Information about the power of the explosion in one engine must be passed to the other engine so that its leaf controllers may make a choice of the circular arrays of leaves to take part in the implosion of the next cylindrical target for that other engine. Clearly the recirculation path in a dual engine configuration for the inner collimated annular beam, which does not include a crossover, is shorter than the period 749, and recirculation along it must commence during either the very short burn 747 or the short period 748. It cannot therefore implode the next cylindrical target for the same engine. But this path may be used for optical recirculation within a target from one position on it to another, as envisaged in Section 6.17.2.1 of GB 2,305,516 B. It is only available in the dual engine configuration.

Since the gain of an explosion is controlled by the choice of circular arrays of leaves to take part in the implosion causing that explosion, and those circular arrays form part of the eye mirrors within one engine only, there is no need with optical recirculation within a target in dual operation without a crossover for information about the power of the explosion in another engine merely to control that gain.

It is, however, necessary in any mode of operation that the target gain is the same for both engines in straight flight, or differs by the amount necessary to alter the orientation of the apparatus and effect a left or right turn otherwise.

6.31 Twin dual engine configuration.

Figure 72 is a schematic diagram showing a front elevation and a sectional plan of an upper and lower copy of the apparatus in Figure 68. Figure 72 also shows the centre line 730 of the vehicle, the axis of symmetry of the upper left engine 18UL, the axis of symmetry of the upper right engine 18UR, the axis of symmetry of the lower left engine ISLL and the axis of symmetry of the lower right engine I8LFt.

The operation of the lower left and the upper right engines are synchronised. The operation of the lower right and the upper left engines are synchronised. In this way, the thrust is symmetric about the centre line 730 at all times in straight flight.

This configuration is capable of making turns in any plane by varying the gain of the engines.

6.32 Dual multiple engine configurations.

Multiple engine configurations, in which one engine recirculates electromagnetic en-ergy to another, may be reconfigured as dual multiple engine configurations.

6.32.1 Dual triple engine configuration.

Figure 73 is a schematic diagram showing a similar sectional front elevation to that in Figure 69 in the plane 19 of the paper of a dual triple engine configuration. It shows a bottom left axis of symmetry 18BL, a bottom right axis of symmetry I8BR, a bottom up axis of symmetry ISBU, a top left axis of symmetry 18TL, a top right axis of symmetry 18TH, and a top down axis of symmetry ISTD. It also shows a centre line 740 of the vehicle.

Figure 73 also shows the defining mirror of a bottom left eye mirror 721BL and a bottom left conical shield 722BL whose axes of symmetry coincide with the bottom left axis of symmetry 1SBL, the defining mirror of a bottom right eye mirror T21IBR and a bottom right conical shield 722BR whose axes of symmetry coincide with the bottom right axis of synmietry 1SBR, the defining mirror of a bottom up eye mirror 721BU and a bottom up conical shield 722BU whose axes of symmetry coincide with the bottom up axis of symmetry 1SBU, the defining mirror of a top left eye mirror 721TL and a top left conical shield 722TL whose axes of symmetry coincide with the top left axis of symmetry 18TL, the defining mirror of a top right eye mirror 721TR and a top right conical shield 722TR whose axes of symmetry coincide with the top right axis of symmetry 18TH, and the defining mirror of a top down eye mirror 721TD and a top down conical shield 722TD whose axes of symmetry coincide with the top down axis of symmetry 18TD. Each of these eye mirrors is the outermost eye mirror on its respective axis of symmetry. It will be appreciated that these eye mirrors may or may not be directed energy weapons. The radius of the base of each conical shield is r0 as shown in Figure 73.

Figure 73 also shows six front outer plane mirrors, with six rear outer plane mirrors hidden behind them, all of which have the same shape but different orientations. Figure 74 is a schematic diagram showing a sectional plan of the bottom left axis of symmetry 1SBL together with the defining mirror of the bottom left eye mirror 721BL, which is the outermost eye mirror on that axis, and the bottom right axis of symmetry 18BR together with the defining mirror of the bottom right eye mirror 721BR, which is the outermost eye mirror on that axis, both of which lie in the plane 19 of Figure 74. Figure 74 shows two of the outer plane mirrors each of which is orthogonal to the plane 19. The inclination of the bottom left rear outer plane mirror 742BL to the bottom left axis of symmetry 18BL is 0pll as shown in Figure 74. The inclination of the bottom right front outer plane mirror 744BR is Up" -it, as shown in Figure 74. These angles are indicated by grey arcs.

Each of the outer plane mirrors has a hole in the shape of an ellipse, whose centre lies on its respective axis of symmetry, and whose minor axis is of length 2 b1. The projection of each such ellipse on the front elevation is a common inner circle of radius b, as shown in Figure 73. The major axis of each such eLlipse lies in the plane 19 in Figure 74 and is of length 2 csc The outer edge of each of the outer plane mirrors also has the shape of an ellipse, whose centre lies on its respective axis of symmetry, and whose minor axis is of length 2 The projection of each such ellipse on the front elevation is a common outer circle of radius as shown in Figure 73. The major axis of each such ellipse lies in the plane 19 in Figure 74 and is of length 2 5ouj csc 1 78 The projected area of each outer elliptical plane mirror on the front elevation is iT - The projected area of each elliptical hole less that of the conical shield within it on the front elevation is it (b -r0). These two areas are equal; so that:- 1k2 7,2.... (A2 2 \ iT -°jn) - -or A2.....c)h2 2 uout -11i7. -COfl Figure 74 shows a bottom left outer annular conical mirror 746BL, and a bottom left inner annular conical mirror 745BL, which have slightly different cone angles, and whose axes of symmetry coincide with the bottom left axis of symmetry ISBL. Figure 74 shows a bottom right outer annular conical mirror 746BR, and a bottom right inner annular conical mirror 745BR, which have slightly different cone angles, and whose axes of symmetry coincide with the bottom right axis of symmetry 18BR. Figure 74 also indicates the positions of the bottom left variable atmospheric intake 733BL and the bottom right variable atmospheric intake 733BR.

Figure 74 also shows a bottom left reversed further alternate defined mirror 734BL whose axis of symmetry coincides with the bottom left axis of symmetry 18BL and a bottom right reversed further alternate defined mirror 734BR whose axis of symmetry coincides with the bottom right axis of symmetry 18BR. Each reversed further alternate defined mirror may be replaced by two or more reversed individual further alternate defined mirrors.

Figure 74 shows those outer rays lying in the plane 19 of the paper of a bottom left outer collimated annular beam 762BL, which is reflected from the bottom left rear outer elliptical plane mirror 742BL, and then the bottom right front outer elliptical plane mirror 744BR, to replace the bottom right outer collimated annular beam 762BR (not shown).

Figure 74 shows the reflections of both those inner and outer rays lying in the plane

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19 of the paper of that outer collimated annular beam from the bottom right outer annular conical mirror 746BR to the bottom right reversed further alternate defined mirror 734BR.

An exactly similar arrangement to that in Figure 74 applies with the bottom right axis of symmetry 1SBR together with the bottom up axis of symmetry 18BU. An exactly similar arrangement to that in Figure 74 applies with the bottom up axis of symmetry 1SBU together with the bottom left axis of symmetry 1SBL.

An exactly similar arrangement to that in Figure 74 applies with the top right axis of symmetry 18TR together with the top left axis of symmetry ISTL. An exactly similar arrangement to that in Figure 74 applies with the top left axis of symmetry 1STL and the top down axis of symmetry 18TD. An exactly similar arrangement to that in Figure 74 applies with the top down axis of symmetry 18TD and the top right axis of symmetry 18Th.

Figure 73 also shows six front inner plane mirrors, with six rear inner plane mirrors hidden behind them, all of which have the same shape but different orientations. Figure is a schematic diagram showing a sectional plan of the bottom right axis of symmetry 1SBR together with the defining mirror of a bottom right eye mirror 721BR, which is the outermost eye mirror on that axis, and the adjacent top down axis of symmetry 18T1) together with the defining mirror of a top down eye mirror 721TD, which is the outermost eye mirror on that axis, both of which lie in the plane 19 of Figure 75. Figure 75 shows two of the inner plane miirors each of which is orthogonal to the plane 19. The inclination of the bottom right rear inner plane mirror 741BR to the bottom right axis of symmetry 1BBR is 0p12 as shown in Figure 75. The inclination of the top down front inner plane mirror 743TD to the top down axis of symmetry 1STD is ir -9p12, as shown in Figure 75.

These angles are indicated by grey arcs.

Each of the inner plane mirrors has a hole in the shape of an ellipse, whose centre lies on its respective axis of symmetry, and whose minor axis is of length 2r00. The projection of each such ellipse on the front elevation is a common circle of radius as shown in Figure 73. The major axis of each such ellipse lies in the plane 19 in Figure 75 and is of length 2r0 csc The outer edge of each of the inner plane mirrors also has the shape of an ellipse, whose centre lies on its respective axis of symmetry, and whose minor axis is of length 2 b. The projection of each such ellipse on the front elevation is a common inner circle of radius as shown on that front elevation in Figure 73. The major axis of each such ellipse lies in the plane 19 of the sectional plan in Figure 75 and is of length 2 csc Ojil2.

Figure 75 shows a top down outer annular conical mirror 746TD, and a top down inner annular conical mirror 745TD, which have slightly different cone angles, and whose axes of symmetry coincide with the top down axis of symmetry I8TD. Figure 75 shows a bottom right outer annular conical mirror 746BR, and a bottom right inner annular conical mirror 745BR, which have slightly different cone angles, and whose axes of symmetry coincide with the bottom right axis of symmetry 18BR. Figure 75 also indicates the positions of the top down variable atmospheric intake 733TD and the bottom right variable atmospheric intake 733BR.

Figure 75 also shows a bottom right reversed further alternate defined mirror 734BR whose axis of symmetry coincides with the bottom right axis of symmetry I8BR and a top down reversed further alternate defined mirror 734TD whose axis of symmetry coincides with the top down axis of symmetry 1STD. Each reversed further alternate defined mirror may be replaced by two or more individual reversed further alternate defined mirrors.

Figure 75 shows those outer rays lying in the plane 19 of the paper of a bottom right inner collimated annular beam 761BR., which is reflected from the bottom right rear inner elliptical plane mirror 741BR, and then the top down front inner elliptical plate mirror 743TD, to replace the top down inner collimated annular beam 761TD (not shown).

Figure 75 shows the reflections of both those inner and outer rays lying in the plane 19 of the paper of that inner collimated annular beam from the top down inner annular conical mirror 745TD to the top down reversed further alternate defined mirror 734TD.

An exactly similar arrangement to that in Figure 75 applies with the top down axis of symmetry 1STD together with the adjacent bottom left axis of symmetry 18BL. An exactly similar arrangement to that in Figure 75 applies with the bottom left axis of symmetry 18BL together with the adjacent top left axis of symmetry 1BTL. An exactly similar arrangement to that in Figure 75 applies with the top left axis of symmetry 18TL together with the adjacent bottom up axis of symmetry I8BU. An exactly similar arrangement to that in Figure 75 applies with the bottom up axis of symmetry 1SBTJ together with the adjacent top right axis of symmetry 1STR. An exactly similar arrangement to that in Figure 75 applies with the top right axis of symmetry l8Tlt together with the adjacent bottom tight axis of symmetry 18BR.

As the explosion of a cylindrical target 101, 102, 103 or 104 on the bottom right axis of symmetry 183R takes place some distance from the bottom right conical shield 722BR, and expands rapidly, much of the electromagnetic energy it emits, even though it is not collimated, follows similar paths to the bottom right inner and outer collimated annular beams 7C1BR and 762BR respectively. Similarly for the explosion of a cylindrical target 101, 102, 103 or 104 on any of the other axes of symmetry.

It will be seen from both Figure 74 and Figure 75 that rays on a return path must converge towards their respective axis of symmetry (irrespective of whether they actually cross that axis) in order to pass through the hole in their respective front outer elliptical plane mirror. This concentration of electromagnetic energy may ionise any atmosphere entering the respective variable atmospheric intake. Since this engine configuration is designed for magnetic drive in space, this may be accepted. (These intakes are retained so that the engines in this configuration may also be used as single engines.) The distance between the axes of adjacent eye mirrors is 2r,-,. + s where s = 0 if those eye mirrors are contiguous. The path)ength of any ray, which is initially collimated with respect to an axis, between a rear inner elliptical plane mirror and a front inner elliptical plane mirror is therefore (2rem + s) csc 2Oz2. The path length along that axis which is replaced by such a crossover is (2rem + a) cot 29p12 Hence the increase in path length due to a crossover between adjacent axes is:- (2rem + a) (csc 2O12 -cot 20p12) = (2re + s) tan 8p12 The distance between the axes in a triple engine configuration is /(2rem + a) where $ = 0 if the adjacent eye mirrors are contiguous. Hence the increase in path length due to a similar crossover between two of these axes is:-v'i (2rem + a) (csc 207311 -cot 2O) = + a) tan 6pll These increases in path length axe the same if:-tan 9p2 = V5tanO2li For the embodiment of interest > 6n > 0pli The spacing between a rear elliptical plane mirror and a front elliptical plane mirror, whether those mirrors are both inner or both outer, is dependent on the inclination of the rear elliptical plane mirror. As Oji < 9pn it is the inclination of the outer elliptical plane mirrors which affects the position of the annular conical mirrors. The axial distance between the centre of a front outer elliptical plane mirror and the base of an outer annular conical mirror must be sufficient for the outer rays reflected back along the return path from the latter to pass through the elliptical hole in the former. It is therefore at least:-b0t- (o01 cot 0jdl + V (2r + a) cot 20,ii) + b0 cot 9pi It will be seen from Figure 74 that this is about long enough for those outer rays to pass through the elliptical hole in the front inner elliptical plane mirror also. And that those mirrors may be moved to the rear in order to enable those rays to pass through.

The axial distance through half a rear outer elliptical plane mirror is b cot 0pll* The recirculation path length for the outer collimated annular beam is then at least:-rem (1 + ir -O,-+ cos 61r + sin Oj (csc(Gir + O) -cOt(O + Oi))) + 2 b01 cot 9pti + -s/a (2r,-, + s) (csc2Otj + cot 2Opn) 2b0,t- (b cot + /1 (2r6,1 + s) cot 2Opa) + 2b0 cot Oui = rem (1 + 71 -Olr + cosoi,. -4-sin 0k,. (csc(0i + 9) -cot(9i,. + B))) +4b01cot0ii -÷ /a(2rem + s)cot0ti + (oot cot Gpti + v(2rem +s)cot2epn) where s = 0 if the adjacent eye mirrors are contiguous.

It will be seen from the front elevation in Figure 73 that the line 757 in the plane 19 of the paper joining the bottom right axis of symmetry 18BR to the bottom up axis of symmetry 18BU is at right angles to the line 758 in the plane 19 of the paper joining the bottom right axis of symmetry lEER to the top down axis of symmetry 1STD. The projection of the major axes of the ellipses delineating the edges of the bottom right rear outer elliptical plane mirror 742BR lie on the line 757. The projection of the major axis of the ellipse delineating the outer edge of the bottom right rear inner elliptical plane mirror 7413R lies on the line 758. Consideration of the paths of the rays reflected from the bottom right rear inner elliptical plane mirror 741BR shows that they clear the bottom right rear outer elliptical plane mirror 742BR when the centre of the bottom right rear inner elliptical plane mirror 741BR is forward of the centre of the bottom right rear outer elliptical plane mirror 742BR, even if the centres of those mirrors are very close together.

It will also be seen from Figure 73 that the line 759 in the plane 19 of the paper joining the top right axis of symmetry 18TR to the bottom right axis of symmetry 18BR is at right angles to the line 760 in the plane 19 of the paper joining the bottom left axis of symmetry 1SBL to the bottom right axis of symmetry 1SBR. In consequence, the rays incident to the bottom right front inner elliptical plane mirror 743BR clear the bottom right front outer elliptical plane mirror 744BR if the centre of the bottom right front inner elliptical plane mirror 743BR is to the rear of the centre of the bottom right front outer elliptical plane mirror 744BR, even if the centres of those mirrors are very close together.

These two conditions are both satisfied when 0pZl < 93,12 It will be appreciated that the functions of the inner and outer elliptical plane mirrors may be interchanged. This would, however, require the centres of the larger outer elliptical plane mirrors to lie inside those of the smaller inner elliptical plane mirrors and necessitate a less compact arrangement.

It will be seen from Figure 73 that the projections of the crossovers of the inner collimated annular beams on that front elevation do not cross any of the projections of the crossovers of any of the other collimated annular beams, and cannot, therefore, pass through any other beam in three dimensions. It will equally be seen from Figure 73 that the apparent intersection of each pair of crossovers of outer collimated annular beams on that front elevation occurs at different distances from the rear outer elliptical plane mirror of each member of that pair. Since those crossovers are at an angle to the plane 19 of that figure, as shown in the sectional plan comprising Figure 74, those crossovers cannot, therefore, pass through each other in three dimensions. All of the crossovers are thus enclosed in respective cylindrical mirrors to prevent uncollimated light from escaping the beams.

It will be seen from Figures 74 and 75 that both the remainder of the beams, and their reflections from the annular conical mirrors, may also be contained within cylindrical mirrors.

Figure 74 shows the crossover cylindrical mirror 750BL for the bottom left outer collimated annular beam 762BL, the bottom left cylindrical mirror 751BL, and the bottom right cylindrical mirror 751BR, as a plan superimposed over the ras in the plane 19 of the paper.

The bottom left cylindrical mirror 751BL includes an exit aperture 764BL for the bottom left inner collimated annular beam 761BL, an entry aperture 763TD for the top down inner collimated annular beam 761TD, and an entry aperture 765BU for the bottom up outer collimated annular beam 762BU.

The bottom right cylindrical mirror 751BR includes an exit aperture 766BR for the bottom right outer collimated annular beam 762BR, an exit aperture 764BR for the bottom right inner collimated annular beam 761BR, and an entry aperture 763TR for the top right inner collimated annular beam 761TR.

Figure 75 shows the crossover cylindrical mirror 750BR for the bottom right inner collimated annular beam 7G1BR, the bottom right cylindrical mirror 751BR, and the top down cylindrical mirror 751TD, as a plan superimposed over the rays in the plane 19 of the paper.

The bottom right cylindrical mirror 751BR includes an exit aperture 766BR for the bottom right outer collimated annular beam 762BR, an entry aperture 763TR for the top right inner collimated annular beam 761TR, and an entry aperture 765BL for the bottom left outer collimated annular beam 762BL.

The top down cylindrical mirror 751TD includes an exit aperture 766TD for the top down outer collimated annular beam 762TD, an exit aperture 764TD for the top down inner collimated annular beam 761TD, and an entry aperture 765TL for the top left outer collimated annular beam 762TL.

All of the inner and outer elliptical plane mirrors, the inner and outer annular conical mirrors, the crossover cylindrical mirrors, the cylindrical mirrors and the reversed further alternate defined mirrors are cooled.

The power of each of the inner and outer annular beams on output from the eye mirror(s) on an axis of symmetry is Peire / 7)em, and thus sufficient on its own to implode a cylindrical target 101, 102, 103 or 104 and cause its ignition.

6.32.1.i Timing.

Figure 76 is a timing diagram showing the activities of all six engines in a dual triple engine configuration. The operation of engines which are opposite to each other with respect to the centre line 740 of the vehicle are automatically synchronised: so that the thrust is symmetric about that centre line at all times in straight flight.

The firing order of both triple engine configurations is either anticlockwise as seen in the front elevation of Figure 73, which corresponds to this example; or clockwise.

The recirculation path length is the same for both the inner elliptical plane mirrors and the outer elliptical plane mirrors-But the direction of the crossovers in that recirculation for the inner elliptical plane mirrors as seen in the front elevation of Figure 73 is the opposite of that for the outer elliptical plane mirrors. Otherwise, firing one engine will ignite all six engines simultaneously in five further cycles. The direction of the crossovers in the recirculation is indicated by arrows on the lines in the plane 19 of the paper joining the axes of symmetry.

The time axis in Figure 76 is horizontal. The implosion and burn of each cylindrical target takes a very short time in comparison to the period between such events. The period for which each resulting point explosion usefully persists thereafter in exoatmospheric operation is also very small. So that each implosion and burn and its subsequent point explosion is therefore shown as a short thick vertical line 767. The periods of the implosions and burns together with the point explosions for a particular engine are arranged along a labelled horizontal line for that engine.

The recirculations in the outer elliptical plane mirrors for a triple engine configuration are shown as diagonal lines 768. The recirculations in the inner elliptical plane mirrors between adjacent engines are shown as diagonal lines 769. It will be seen that a diagonal line 768 and a diagonal line 769 intersect on each vertical line 767 and each cylindrical target in the first part of the burn is imploded simultaneously by an inner and an outer recirculation to give simultaneous dual operation.

The dual triple engine configuration allows a period between the arrival of cylindrical targets for an engine equal to three times the sum of the duration of an implosion and burn, the time for which the resulting point explosion usefully persists thereafter, and the common recirculation period less the overlap, which is equal to about half the implosion period plus the burn period, but plus some pulse stretching. The common recirculation period may be made as high as is required by increasing both the inner and outer recir-culation path lengths by the same distance. The outer recirculation path length may be increased by extending the axial distance between the centre of each front outer elliptical plane mirror arid the base of its respective outer annular conical mirror. As a respective inner annular conical mirror is attached to that outer annular conical mirror, the inner recirculation path length is thereby increased by almost exactly the same amount.

It allows the persistence of the point explosion to be low, and thus facilitates magnetic drive in a medium of sufficiently low density for that purpose. It also allows the rate of fire of cylindrical targets in each engine to be low, despite such low persistence. And it equally enables the number of cylindrical targets which can conveniently be stored in magazines to be increased by providing six conical shields, and thus maxirnises the final velocity of the vehicle, Uveh. It equally provides a longer period between burns for the shield 370 and its spherical indentation 390 to radiate excess heat from the electromagnetic energy and any unwanted neutrons from the resulting explosion incident upon it, and thus avoids the use of cooling fluid. The dual triple engine configuration is thus the preferred embodiment for an interstellar mission.

A dual multiple engine configuration provides two time windows for the arrival of a cylindrical target at the point of implosion. These windows may overlap, be contiguous, or be separated by an interval. They may accordingly provide a margin for the time of arrival of a cylindrical target. When they overlap, they will provide more energy for its implosion and increase the gain of the subsequent explosion.

The failure of one single cylindrical target to explode successfully will not stop the burn of subsequent cylindrical targets. indeed, all the cryogenic drum magazines for an engine may be refilled with cylindrical targets, all the power driven storage drums for that engine may be emptied of spent cartridges, while all the injector guns for that engine may be maintained, without interupting the ignition of cylindrical targets for the other engines.

Any successful explosion will synchronise the implosions of the next pair of opposing engines via the recirculations for the multiple engine configuration and those for adjacent engines. The implosion of a target commences with the earliest recirculation arriving at that target when at the point of implosion. In consequence the leaf controllers 251 for an engine make a choice of the circular arrays of leaves to take part in the implosion of the next cdindrical target for that engine from the information they receive about the power of an explosion which will provide sufficient power for a successful implosion and arrive at the earliest time, taking into account the appropriate recirculation path length.

In the contingency that the power from two explosions will arrive either simultaneously or overlapping, the leaf controllers make that choice on the basis of their combined power.

As described in Section 6.22, information about the power of an explosion and the time of its measurement is sent from each power sensor 255 in an engine over a fibre-optic digital data bus 256 to an interface controller 273 for that engine which calculates an average for that power and an average for that time of measurement. The interface controller for each engine is connected to the interface controller(s) of those other engines to

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which its electromagnetic energy is recirculated by further fibre-optic digital data bus(es) whenever a multiple, dual or dual multiple engine configuration is assembled. The interface controller for each of these other engine(s) supplies these average figures for power and time of measurement to each of the leaf controllers in their engine over its fibre-optic digital data bus. There is, of course, more time available for this information to reach an engine in a multiple, dual or dual multiple engine configuration, as compared to a single engine, due to their longer recirculation path(s).

This configuration is capable of making turns in any plane by varying the gain of the engines.

6.32.2 Dual twin engine configuration.

Figure 77 is a schematic diagram showing a sectional front elevation in the plane 19 of the paper of a dual twin engine configuration. All the items in Figure 73 for the dual triple engine configuration are present in Figure 77 except those for the bottom up axis of symmetry and the top down axis of symmetry.

The top left eye mirror I21TL and the top right eye mirror Y21TR become adjacent as in Figure 75, and the top left inner collimated annular beam TG1TL replaces the top right inner collimated annular beam 761TR.

The bottom right eye mirror 721BR axd the top left eye mirror 721TL become twins as in Figure 74, and the bottom right outer collimated annular beam 762BR replaces the top left outer collimated annular beam 762TL, and vice versa.

The bottom right eye mirror 721BR and the bottom left eye mirror 7213L become adjacent as in Figure 75, and the bottom right inner collimated annular beam 761BR replaces the bottom left inner collimated annular beam 7G1BL.

The bottom left eye mirror 721BL and the top right eye mirror 721TR become twins as in Figure 74, and the bottom left outer collimated annular beam 762BL replaces the top right outer collimated annular beam 762TR, and vice versa.

It will immediately be seen from Figure 77 that all four engines have to fire simul-taneously to provide simultaneous dual implosion and ignition of each cylindrical target.

And that firing one engine will ignite all four engines in three further cycles and establish simultaneous dual operation thereaftr.

The distance between opposite axes is./(2rcm + s) where s = 0 if the adjacent eye mirrors are contiguous. The condition that the increase in path length due to a crossover between two inner elliptical plane mirrors is the same as that between two outer elliptical plane mirrors is:-csc 2Ol2 -cot 2O2 = (csc 20p11 -cot 2Opll) or tan 0p12 = v'tan62ii For the embodiment of interest > 0pi > 0pll' The spacing between a rear elliptical plane mirror and a front elliptical plane mirror, whether those mirrors are both inner or both outer, is dependent on the inclination of the rear elliptical plane mirror. As 62u C 9p2 it is the inclination of the outer elliptical plane mirrors which affects the position of the annular conical mirrors. The axial distance between the centre of a front outer elliptical plane mirror and the base oi an outer annular conical mirror must be sufficient for the outer rays reflected back along the return path from the latter to pass through the elliptical hole in the former. It is therefore at least:-b0-b cot 9pU + -f (2r + s) cot 28) + bo,g cot 9p11 This is generally long enough for those outer rays to pass through the elliptical hole in the front inner elliptical plane mirror also. Those mirrors may, in any case, be moved to the rear in order to enable those rays to pass through.

The axial distance through half a rear outer elliptical plane mirror is b0,.1 cot The recirculation path length for the outer collimated annular beam is at least:-rem(l +rOir +cosOir+sinOir(csc(Oir-i-Oi)-cot(Oir+Oifl) + 2 b0 cot 9pll + (2rem + a) (csc 2Ogi + cot 2Opzi) + 260 (b0 cot 6p11 + (2r + a) cot 2G) + 2b0 cot 6,ii = rem (1 +ir -Olr + COSOlr + SlflOlr (csc(Ojr + Ci) -COt(Oir + 6fl) + 4 b0 cot 0pn + v@ (2rem + s) cot 0pI1 + 2b0; b, (b0 cot °pll + + s) cot 29) where a = 0 if the adjacent eye mirrors are contiguous.

It will be seen from the front elevation in Figure 77 that all the lines in the plane 19 of the paper joining the axes of symmetry of adjacent eye mirrors are at an angle of 45° to the lines in the plane 19 of the paper joining the axes of symmetry of eye mirrors which are opposite each other. As 0ptl < 9pe, the centres of the inner elliptical plane mirrors may lie between those of the outer elliptical plane mirrors, as for a dual triple engine configuration, with adequate ray clearance.

It will be seen from Figure 77 that all four crossovers of outer collimated annular beams on that front elevation intersect at equal distance from their respective rear outer elliptical plane mirrors, and thus in three dimensions. All the crossovers are thus enclosed in respective pairs of cylindrical mirrors, whose inner surfaces are reflective, around a central eight-way junction, whose inner surface is reflective, to prevent uncollimated light escajiing from the beams. This eight-way junction is also cooled.

6.33 Magnetic drive.

It is important to note that ablative and magnetic drive are not incompatible. Indeed, a magnetic field may be used to remove burn and debris ions from the vicinity of the point at which the implosion of the next cylindrical target is to take place, to prevent them absorbing electromagnetic energy from the recirculated beams. Equally, there must be some gas to provide recirculated electromagnetic energy, even though it impedes the a-particles which are diverted by the magnetic field. Magnetic drive is applicable to all engine configurations, including a single engine configuration.

Figure 36 showed the central part of the shield 370 with its spherical indentation 390 in the form of a portion of a spherical shell whose centre coincided, at least approximately, with that of a point explosion in ablative drive. Figure 36 also shows an axially symmetric front superconducting field coil F behind the inner edge 389 of the spherical indentation 390 and just outside the recirculation aperture 429, together with an axially symmetric rear superconducting field coil It, for magnetic chive. If the material of the shield 370 and its spherical indentation 390 is not ferromagnetic or ferrirnagnetic, or so thick as to provide some magnetic effect otherwise, as is preferred, the field from these coils will pass through the shield unaltered. The shield may be retracted to disperse its ablation over a larger area, But in a preferred embodiment, the centre of the point explosion is moved further away from the shield to disperse the illumination of the shield 370 and its spherical indentation 390 over a larger area in magnetic drive. This also reduces any neutron flux. The spherical indentation 390 may equally be retracted to move it further away from the point explosion (as shown in Figure 37). This has the effect of reducing any magnetic shielding of the rear superconducting field coil R. It also provides a line of sight for multiple pairs of cameras, such as 447 and 448. But it has no effect on the neutron flux through the shield itself.

6.33.1 Allowable range of point explosion.

There is an allowable range along the axis of symmetry 18 for the position of the implosion of a cylindrical target relative to the eye mirrors, beyond which some rays become excessively skew to that axis. There is an allowable range perpendicular to the axis of symmetry 18 for the position of that implosion, beyond which the illumination of the cylindrical target becomes excessively asymmetric. (Perpendicular offsets also cause asymmetric thrust, as explained in Sections 6.27.6.2.1 and 6.33.3.) Since the injector guns cannot be on the axis of symmetry 451 of the conical shield 420 and the trajectory of the cylindrical targets cannot therefore be aligned with that axis, the distance between the conical shield and the implosion affects the position of the implosion perpendicular to that axis, and must therefore also fall within some allowable range.

The aim point(s) of each pair of cameras must be sufficiently behind the conical shield for errors in the trajectories of the cylindrical targets to become measurable, and sufficiently in front of the position of the implosion for the consequent adjustments to be made by the leaves.

As already detailed, the position of the implosion in magnetic drive is arranged to be further from the shield 370 and its spherical indentation 390 than that position in ablative drive, so as to reduce any neutron flux and spread the illumination over a wider area of the shield, and reduce the density of the gas or plasma ablated, or even eliminate that ablation almost entirely. The neutron flux and mass ablation rate from any given area are inversely proportional to the square of its distance from the resulting point explosion. The conical shield 420 is also moved rearward for magnetic drive so that its distance from the point explosion stays within the allowable rauge. Either the multiple pairs of cameras 447 and 448 which monitor the trajectories of the cylindrical targets must move with the conical shield 420, or separate multiple pairs of cameras 449 and 450 must be provided for that purpose in ablative and magnetic drive respectively (as shown). But the distance between the aim point of each pair of cameras and the conical shield need not be exactly the same for both ablative and magnetic drive (and may even be varied at will).

If the distance between the conical shield 420 and the point 258 at which an implosion is to commence is at the high end of the allowable range in magnetic drive rather than at the low end of the allowable range in ablative drive then not only the perpendicular distance between that point and the axis of symmetry 18 due to a rotation of the conical shield, but also the errors due to variations in the muzzle velocity, launch time, drag and dispersion of the cylindrical targets, will be correpondingly higher. Since it is undesirable to reduce the accuracy of the measurement of those errors, the field of view of the individual cameras for magnetic drive would ideally be the same as those for ablative drive. In which case, not only must multiple pairs of cameras be provided, as detailed in Section 6.28.4, but their number must be further increased for magnetic drive. The distance of a camera from its aim point will generally be higher in magnetic drive than in ablative drive: so that its angular field of view must be smaller. The aim point of the injector guns on the axis of symmetry 451 of the conical shield 420 will, in general, be equidistant between the points at which implosions are to commence in ablative and magnetic drive for every injector gun; in which case the perpendiculas distances of those points from that axis are equal.

6.33.2 Magnetic field.

Figure 78 shows the front and rear superconducting field coils F and It respectively, the rear surfaces of the shield 773 and that of its spherical indentation 774, the contour lines 775 of the magnetic field produced by those superconducting field coils and the field lines, or lines of force, for the lowest 13.5% of the field (in grey). These contour lines delineate successively higher levels of magnetic field. Such higher levels could also be represented by providing more numerous lines of force.

A single charged particle moving in a constant and uniform magnetic field describes a helical orbit around an axis in the common direction of the magnetic field lines. If those magnetic field lines become closer together as it spirals around them, so that the field has a radial component varying in the direction of some central axis, then it will experience a deaccelerating component of force back along the axIs of its spiral because of its orbital velocity and the radial component of the magnetic field. If those magnetic field lines become further apart as it spirals around them, then it will experience an accelerating component of force along the axis of its spiral, as the radial component of the magnetic field will have the reverse direction. There is, of course, a further component of force due to the axial velocity of that particle and the radial component of the magnetic field.

Following the burn of a target, the plasma expanding from that explosion rapidly compresses the magnetic field and raises its strength, producing a cavity therein within a few microseconds. This induces eddy currents in the rear surfaces of the shield 773 and its spherical indentation 774, rather than in the superconducting field coils F and B.. The interaction of these eddy currents with the magnetic field produce an impulse on the shield 370 and its spherical indentation 390 to drive the vehicle.

Figure 79, which is similar to Figure 78, illustrates the compression of the magnetic field against the shield 370 and its spherical indentation 390 as the compressed contour lines 776.

Thereafter the process goes into reverse. The magnetic field rebounds, and accelerates the charged particles, but in the reverse direction, along the expanding field lines. It will be appreciated that the energy from the plasma is first stored in the magnetic field and then returned from the magnetic field to the plasma, and that the superconducting field coils do not supply that energy.

Radiation produced by the acceleration of the charged particles is emitted in the infrared and microwave portions of the electromagnetic spectrum, which are not useful for target implosion or the optical recirculation which drives such implosion. Moreover, the speed of the a-particles ensures that they will escape from the vicinity of the recirculation aperture 429 in a few microseconds.

6.33.3 ControL With multiple, dual or dual multiple engine configurations, the orientation of the vehicle may most conveniently be changed by varying the gain of the engines, as already described, in either ablative or magnetic drive. There are two methods of controlling the

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orientation of a vehicle with a single engine during a burn with magnetic drive. These methods may also be employed by one or more engines in a multiple, dual or dual multiple engine configuration.

If the position of the burn is moved off the axis of symmetry 18 so as to be closer to one region of the shield 370 and its spherical indentation 390 then the magnetic field near that region will be compressed more, increasing the field in that region of the shield, while the magnetic field near the opposite region of the shield 370 and its spherical indentation 390 will be compressed less, decreasing the field in that opposite region of the shield.

Moreover, the eddy currents produced by the magnetic field will be similarly asymmetric, at least transiently. So that the interaction of the asymmetric magnetic field and the asymmetric eddy currents will produce both an impulse acting through, and an angular impulse around, the centre of mass of the vehicle.

In pure magnetic drive, in the absence of any ablation by electromagnetic radiation, the magnetic field protects the shield 310 and its spherical indentation 390 from the plasma from the burn by deflecting the charged particles which comprise it. If the asymmetric magnetic field fails to prevent those charged particles from reaching that region of the shield 370 and its spherical indentation 390 which is nearest the burn then the ablation of that region, or of coolant flowing through it, increases the angular impulse around the centre of mass of the vehicle.

In pure magnetic drive, the shield 370 and its spherical indentation 390 act as radiators to remove the kinetic energy of unwanted neutrons from DD reactions in the DHe3 fuel which are absorbed in them, together with the ohmic heating from the eddy currents. In a dual triple engine configuration, the period between burns for any one engine is adequate for all that energy to be radiated.

In a single engine configuration, some flow of coolant through the shield 370 and its spherical indentation 390 might be necessary to dissipate that portion of the electromag-netic energy from the burn which they absorb, together with the heat generated by the absorption of neutrons in the liquid lithium blanket 403 and the ohmic heating from the eddy currents, in order to prevent that shield melting. But such flow is preferably dis-charged into the front of the converging annular shock tube 427, as described in Section 6.27.7.1 6.33.4 Power supplies.

Since the vehicle will spend extended periods coasting, a source of electrical power for the onboard systems must be provided by one or more space qualified nuclear fission reactors. Since the annular crew compartment 785 may be separated from the single engine 781, as shown in Figure 81 and described in Section 6.37, two or more such reactors may be situated near the inner cylindrical surface 783 of that crew compartment and arranged axially symmetrically about its axis for dynamic balance. A further such reactor must be provided in the single engine 781 in front of its conical shield 420, as shown in Figure and described in Section 6.28.2, to supply electrical power to the heat pumps in the cryogenic drum magazines and their respective storage drums.

During a burn, extra electrical power must be provided to the single engine 781 for its injector guns, the piezo actuators 201 and 202 or 221 to 224 respectively for its leaves, the piezoelectric shock absorbers in its active vibration control units 411, and the various methods of control. But this power may be obtained from waste heat from the cooling of the liquid lithium blanket, the shield and/or the eye mirrors, energy generated by the piezoelectric shock absorbers in the active vibration control units 411, and/or light emitted by the fusion products incident to a "solar" array outside the outer edge of the shield. It is not desirable to reduce the energy in the exaust by means of an induction loop.

Since there is no requirement for a lithium storage chamber in a space vehicle, the liquid lithium blanket 403 is in close proximity to any pump mounted on the front of the shield 370 or its spherical indentation 390. This allows a thermoelectric electromagnetic pump to be used, as the temperature of its primary inlet from the liquid lithium blanket will become high as soon as neutrons reach that blanket. Such a pump circulates hot liquid lithium from the liquid lithium blanket, cools it, and then returns it to that blanket, through a primary heat transport loop. It also circulates cooler liquid lithium to a Potas-shun Rankine power conversion system, cools it, and then supplies it to a tritium recovery unit before returning it to the pump, through a secondary heat rejection loop. A plurality of such pumps is needed to satisfy such a power system.

A thermoelectric electromagnetic pump is described in two papers respectively en- titled "Thermoelectric electro-magnetic pump design for the SF-lOU reference flight sys-tem" (F.M. Zarghami et ad (1989) IEEE Proceedings of the 24th Intersociety Energy Conversion Engineering Conference, 1989, IECEC-89, p.1227) and "STEPAC-AN SP-thermoelectric-electromagnetic pump analysis code" (J.J. Buksa et al (19S9) IEEE Proceedings of the 24th Intersociety Energy Conversion Engineering Conference, 1989, IECEC-89, p.81).

6.34 Endoatmospheric and exoatmospheric operation.

If either DI or LiDT is used as the fuel, the flow of coolant must be sufficient to remove the kinetic energy of the neutrons from their fusion reactions, together with the net energy released by their absorption by lithium isotopes, out of a lithium blanket and the shield without either of those components melting. In consequence, the mass ablation rate, ablation pressure and thrust are very high, but the temperature of the shield and the exaust and final velocities are very low. So that D11e3 and LiDT fuels are preferred for both endoatmospheric and exoatmospheric operation, and will be the only fuels considered in the following.

In (very) high endoatmospheric or exoatinospheric operation with ablative drive, the flow of coolant and/or the amount of ablation together with the temperature of the shield, T3hld, and the exaust velocity, u,, which is dependent on that temperature, are dictated not only by the need to remove energy, but also by the requirement to maintain the density of either the ablated gas behind the shield, p0, or that in the converging ann&ar shock tube at a sufficient level to allow optical recirculation. In low endoatmospheric operation, the atmosphere of the planet itself is capable of providing a sufficiently high level of pg. Indeed, that density may have to be reduced to prevent gaseous and atmospheric breakdown blocking the beams from the eye mirror(s), as mentioned in Section 6.27.7.3 If the vehicle is already in forward motion, the pressure behind it will be low because of its considerable frontal area. Variable atmospheric intakes, such as 733L and 733R shown in Figure 68, are used to adjust the density behind the vehicle. As the a-particles will be slowed down by the gas in both endoatmospheric and exoatinospheric operation with ablative drive, they cannot be deflected by a magnetic field so as to become the most energetic part of the exaust and provide magnetic drive. The magnetic field can, however, be used to remove plasma from the point at which the explosion of a cylindrical target will take place.

In ablative drive, the mass ablation rate, tha, and the ablation pressure, Pa, are both high, so tha.t the thrust on the vehicle is also. But the exaust velocity is low, so that the final velocity of the vehicle, Uveh, would be also, if such a mode of operation was continued in space. In low endoatmospheric operation, it may be necessary to increase the thrust sufficiently to overcome gravity by increasing tha and Pa In exoatmospheric operation, the only reason for using ablative drive is to effect a rapid manoueuvre.

In exoatmospheric operation with magnetic drive, using multiple, dual or dual multiple engines, no minimum thrust is required, and it is only necessary to ensure that the shield does not melt either by radiating sufficient energy and/or by using sufficient coolant and/or ablated material to carry away the heat, and to maintain the optical recirculation. As much of the coolant as possible is discharged into the front of the converging annular shock tube 427 to maximise the density of the gas in that shock tube, and minimise the density of the gas behind the shield. The temperature of the shield may be as high as the shield material(s) will allow, and the vaLues of the exaust velocity and the final velocity of the vehicle may be maximised. The thrust on the vehicle, being inversely proportional to will be lower, but is no longer required to overcome gravity. Similarly, the mass ablation rate per unit area, being inversely proportional to Tshjeld, is reduced, as is the ablation pressure, being inversely proportional to TS'/ld. In this regard, it may be mentioned that the specific heat of beryllium is 1.9253 / (g °C) while its melting point is 1285°C. The values for a typical beryllium aluminium alloy are L54913/(g °C) and 645°C respectively.

The shield 370 and/or its spherical indentation 390 may be retracted. The conical shield 420 is certainly moved to its rearward position, and the point explosion is moved to the rear of the aim point to disperse the illumination of the shield 370 and its spherical indentation 390 over a wider area. If the distance of the point explosion from the spherical indentation 390 is removed to 3.3 times the radius of that indentation then both that illu-mination and any unwanted neutron flux will be reduced by about an order of magnitude.

The flow of coolant and/or the amount of ablation is either minimised or eliminated en-tirely, so that the fraction of the exaust comprised by the fusion products becomes larger or unity. In particular, the a-particles have a longer range in the less dense gas from the shield or previous explosion and those heading towards that shield can be diverted by the field from the superconducting field coils F and R respectively into the exaust with a higher velocity than any gas from the shield.

Optical recirculation is maintained, even for a very short burn period and despite the possibly lower persistence of the fusion products in the absence of ablation, without increasing the rate of fire of any one engine, by providing more engines with a longer recirculation path, as in a dual triple engine configuration. The longer recirculation path also enables the shield 370 and its spherical indentation 390 to radiate more heat between burns.

It is convenient for each engine to be provided either with a single further alternate defined mirror 171 or individual further alternate defined mirrors 301 to 303 respectively, with or without individual truncated conical mirrors 321 to 323 respectively, in order to take off from a planet on its own using ablative drive. These mirrors may then be stowed or removed and a multiple, dual or a dual multiple engine configuration assembled in space. Since an engine is capable of independent operation, it may be provided with a crew compartment to the rear of the conical shield to fulfill the combined functions of bridge and engine room.

6.35 Plasma mirror.

Ideally, all the power in the beam from an interstellar accelerator would be reflected by the shield. Since the power of the beam from a very large interstellar accelerator would be extremely high, its light pressure alone would be more than adequate to accelerate or deaccelerate the vehicle without any ablation.

Unfortunately, the reflectivity of a shield cannot be sufficiently high for that purpose, and its ability to absorb power is also too limited. It is therefore necessary to accept some ablation to remove excess heat in the earliest stage of an acceleration by a very large interstellar accelerator. In which case, it is desirable that the exaust velocity of the resulting plasma should be as high as possible, so that its temperature must be also.

The coupling coefficient between the impulse exerted on a target and the energy of a beam incident on it remains at a high level until the onset of plasma shielding of that target from the beam, after which it decreases. In a vacuum, the density of the plasma is almost zero a few millimetres from the solid surface of the target.

The surface area of the projection on a plane at right angles to a beam along the axis of symmetry 18 of the shield 370 and its spherical indentation 390 together with its shield extensions 371 to 388 respectively through the outer edges of those shield extensions is approximately ?rrm, where rem is the radius of the outermost eye mirror. Clearly the plasma expanding in a cylinder with that cross-section continues to take part in the absorption of the beam. While the only leakage of the plasma from the plasma mirror occurs from the curved surface of that cylinder, whose periphery is 2ltTRm. If the density an axial distance x rearwards from the outer edge of the shield extensions is p(x) then the leakage through an element of axial length dx and surface area 2irremdx at a radial velocity v(x) is 2irrp(x)v(x)dz. For values of x Cc rem/2, the surface area of the leakage is much less than that cross-sectional area. So that the density of the plasma will be maintained much further from the solid surface of the shield.

The coupling coefficient is increased by a factor of ten over that in a vacuum at a pressure of one atmosphere. So that a thrust similar to that provided by ablative drive may be obtained from a beam but with much less ablation.

Once plasma shielding occurs, electromagnetic energy can only propagate in the ab-lated plasma up to the critical electron density corresponding to its wavelength. Since the beam is constant, a stationary ablative heat wave develops with a constant mass ablation rate. If the intensity of the beam is I and it is assumed that all its component wavelengths are absorbed in a region where the critical electron density is Pc and that it keeps the ablating plasma of lower density outside that critical region isothermal then the exaust velocity, which is also the sound velocity, outside the critical region, CT, is given by:-/ I \1f3 = I -\ 1Pc the constant temperature in that region, T, is given by:- 2 1 ( T\2/3

T CT S

C -FR -B

where F8 is the gas constant for the ablated material; the mass ablation rate, tha, is given by:- = PcCT = (PC)2)3 and the ablation pressure, Pa, jS given by:-Pa = 2p4 = (Pc)113 j2/3 The energy in the exaust, is proportional to the intensity.

As the ablation pressure and the product of the mass ablation rate and the exaust velocity are both proportional to P3, the intensity may be increased to enhance the accel-eration until collisional absorption strongly decreases above iD'5 W/ cm2. Unfortunately, the exaust velocity, and thus the final velocity attained by the vehicle for a given mass ratio, are only proportional to P13. It is therefore preferable that the beam should heat the exaust and increase its velocity, rather than maintain its temperature and keep it isothermal. A temperature of 3 x i07 °}C may be obtained in coronal equilibrium. The reflectivity of the plasma increases with its temperature.

Now, the plasma is fully ionized. So that the plasma may be contained by a magnetic field and redirected along the axis of symmetry 18 of the eye mirror(s), as described in Section 6.33, to further reduce the leakage, and thus the actual mass ablation rate, as well as increasing the thickness of the plasma mirror. Since the diffusion coefficient across the magnetic field lines is proportional to T112 where T is the temperature of the plasma, the leakage from the hotter region of the exaust is lower.

The magnetic field produced by the front and rear superconducting field coils F and R respectively does not need to be high, as it is raised to a much higher level when it is compressed by the expansion of the plasma from the explosion of a cylindrical target.

No such compression is provided by a steady-state beam from a very large interstellar accelerator, so that the magnetic field from the front and rear superconducting field coils will remain constant at a low level.

For this reason, an outer superconducting field coil 0 is provided, as shown in Figures 32 and 33, which has a much higher radius, current and magnetic field. Figure 80 shows the front, rear and outer superconducting field coils F, It and 0 respectively, the contour lines 777 of the magnetic field produced by those superconducting field coils on the left half of the shield and the field lines for the lowest 8% of the field (in grey). This magnetic field increases the exaust velocity of the ablated plasma.

The plasma mirror is contained radially by the magnetic field and axially from the rear by light pressure. The beam from a very large interstellar accelerator heats the exaust to a very high temperature and a very high velocity. The plasma becomes very reflective.

The shield, and thus the vehicle to which it is attached, are accelerated by both the exaust and the light pressure which maintain the pressure inside the plasma mirror together with

the magnetic field.

Provided the vehicle can withstand very high accelerations, much higher velocities can be attained than for magnetic drive.

6.36 Magnetic sails.

The utility of magnetic sails for deaccelerating interstellar probes was pointed out in a paper entitled "Magnetic Sails and Interplanetary Travel" by R.M. Zubrin and D.G.

Andrews (AIAA 89-2441 25th Joint Propulsion Conference (1989)).

In the particle model presented therein the drag obtained scales as I Rm, where I is the current in the magsail loop and Rm is its radius, as does the mass of the magsail loop.

In which case, there is no advantage in choosing a low current and a high radius over a high current and a low radius if high current is available.

If a magnetosphere boundary can be created, the drag obtained scales in the fluid model presented therein as (I R)2"3, and it is advantageous to choose the highest possible value of Tim consistent rith the necessary conditions for same. In consequence, the drag which results from the ionization of the interstellar medium due to the much smaller front and rear superconducting field coils F and R respectively, despite the high currents therein, is three orders of magnitude smaller than that of the proposed magsail, and neglible for a vehicle which is much more massive. While that from the outer superconducting field coil 0 is similar to that of the proposed magsail. But both are available without penalty as those coils are required for propulsion. If the vehicle and its superconducting field coils are orientated at an angle to the direction of motion of the vehicle, lift is generated perpendicular to the motion of the vehicle, as well as the drag in the opposite direction to the motion of the vehicle. Such lift can be used to manoeuvre the vehicle.

It should be noted that the magnetic field from a magsail, or the superconducting field coils, provides additional shielding from stellar winds and cosmic rays over and above that of the shield 370. A magsail may be deployed from or a magnetic field may be generated by either a single or a multiple engine configuration; so that a multiple engine configuration can separate into several single engine configurations, which will still benefit from the deacceleration and shielding provided by their own magsails or magnetic fields.

When it is in operation in the interstellar medium, the lealcge from the plasma mirror inflates its magnetic field equatorially and the larger cross-section increases the drag from that medium. Acceleration by such an effect in the solar wind was detailed in a paper entitled "Large-Scale Mini-Magnetosphere Plasma Propulsion (M2P2) Experiments" by R.M. Winglee et a! ((2001) Marshall Space Flight Center Doc. ID 20010048753) at page 2.

The field inflates into a magnetic bubble until equilibrium between the thermal pressure of the plasma and the magnetic pressure of the field is achieved, so that the bubble expands in response to decreasing thermal pressure, and the drag remains constant whatever the density of that medium. In a paper entitled "Advances in Magnetized Plasma Propulsion and Radiation Shielding" by Robert Winglee ((2004) Proc. of the 2004 NASA/DoD Con-ference on Evolvable Hardware (EH'04) IEEE Computer Society), a simulation predicted that the cross-section of a magnetosphere could be extended by a factor of about 64 by the injection of plasma into the magnetic field. If the vehicle is being deaccelerated by a beam from a large interstellar accelerator, and the plasma is provided only by that leakage, there is clearly no performance penalty. Moreover, the energies of charged particles against which shielding would be provided was predicted to increase by a factor of 200. Similarly if the plasma is provided only by the debris from cylindrical targets.

6.37 Annular crew compartment.

Figure 81 is an elevation of a vehicle 270 comprising an annular crew compartment 785 attached to a single engine 781 by a ring 782. The inner cylindrical surface 783 of that annular crew compartment is shown as a dashed line as it is hidden from view. The visible parts of the single engine 781 comprise the reverse surface 784 of the defining mirror of its outermost eye mirror, its shield extensions 371 to 388 respectively, and part of its shield 370.

The ring 782 serves as a bearing which allows the annular crew compartment 785 and the single engine 781 to be rotated in opposite directions to each other, and as a geared, or friction capstan, drive to give the opposing torques responsible for the opposing angular accelerations, or deaccelerations, necessary to vary those rotations. The drive motor or motors are internal to the annular crew compartment, and therefore not shown. The ring 782 may also act as a locking mechanism to allow the annular crew compartment 785 and the single engine 781 to engage with, and disengage from, each other.

The outer radius of the annular crew compartment 785 is of similarly large size to that of the single engine 781, and thus able to provide artificial gravity at a rotational rate which is sufficiently slow to provide a near Earth-like gravitational environment.

Cylindrical decks Dl to D7 respectively inside the annular crew compartment are shown as dashed lines. In practice, their radii are the same as or only slightly less than that of the outer radius of the annular crew compartment. Decks Dl and D2 are extended into a horizontal plane as disks to provide living and working areas when the vehicle is accelerating linearly and thus providing artificial gravity without any rotation. In the alternative, a linear car may be provided along each chord of a regular polygon, whose centre lies on the axis of symmetry and rotation and which lies in a horizontal plane, and suspended on an axis above its centre of mass, so that it adjusts its orientation to be below that axis whatever the direction of its acceleration. However, the floor of such a car is only at right-angles to a radius from the centre of rotation at the mid-point of the chord, so that the upward direction varies either side of that mid-point while the floor does not.

Moreover, the connection between a car and an adjacent car, and that between a car and the remainder of the vehicle, must vary as the car changes its orientation.

The hole 880 in the annular crew compartment allows a planetary atmosphere to reach the variable atmospheric intake of the single engine 781 in ablative drive. It also allows a cylindrical mirror, such as the cylindrical mirror 751BL in a dual triple engine configuration, to be fitted to the single engine 781 for magnetic drive.

The annular crew compartment 785 must be sufficiently robust to withstand the condi-tions it will encounter during use: which will generally include endoatmospheric operation, and bombardment during the latter part of the acceleration phase by electrons and protons not deflected by any magnetic field, and dust particles. Its front surface 881 provides a suitable mounting surface for phased array or parabolic communications antennae, due to its large extent.

Figure 81 also shows a leg 882 of the landing gear in a partially stowed position. It comprises a front arm 883 and a longer rear arm 884 whose inner ends are attached to the single engine 781 and whose outer ends locate the leg housing 885. The leg housing 885 contains outer, middle and inner telescopic struts 888, 889 and 890 respectively. A foot 891 rotates around a ball mounting on the rear end of the inner telescopic strut 890.

Figure 81 also shows a further leg 887 of the landing gear with the front and rear arms 883 and 884 respectively partially rotated outwards towards their position for landing.

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The outer, middle arid inner telescopic struts 888, 889 and 890 respectively have partially extended from the leg housing 885. The foot 891 has also been rotated so as to spread the load on the ground.

Clearly the landing gear must have at least three legs. An arrangement presupposing an even number of large legs is shown for clarity. A fairing (not shown) may be provided to reduce the drag of the legs in endoatmospheric operation with doors through which those legs may be deployed.

6.38 Sails.

Sails are of particular utility for the acceleration of interstellar probes.

A microtruss fabric of discontinuous carbon fibres joined to one another hy node-bonding, supported by carbon fibre spun into ropes, and coated on one side with a thin layer of rhodium would be sufficiently robust to elastically self-deploy from rolled stowage and be able to operate at a high temperature.

The power per unit area required to fill a high-temperature sail is about 9MW/rn2 on a continuous basis. The spot corresponding to normal diffraction from the small in-terstellar accelerator described in Section 6.25 and shown in Figure 29 would have such an intensity averaged over its duty cycle up to nearly 0.03 light years. And its diffraction could be reduced as described in Section 6.15.11.4 of GB 2,305,516 B to increase that range.

Moreover, the physical geometry of an eye mirror with a very large number of final stages in parallel might be chosen to bring the well-directed rays inside the spot due to normal diffraction without severely reducing its efficiency. However, it is not at present known how to manufacture very large concave spherical defining mirrors to a corresponding accuracy of 2 in 1011. Fortunately, such a long reach is not necessary to launch interstellar probes.

Providing a beam can beifiaintained for a sufficient period, a sail system whose total areal density is 7g/m2 will receive enough energy to accelerate itself to a useful speed. An acceleration over 5.42 x 1 0 light years requiring 1.2 days will confer a speed of 0.003 c, where c is the velocity of light, several times that for ablative drive. An acceleration over 0.0005 light years taking 12.16 days will result in a speed of 0.03 c similar to that for magnetic drive. However, the small interstellar accelerator cannot conveniently provide a beam over the latter period as that would require not only a large supply of coolant but also a vast number of cylindrical targets. Other sources of energy or lighter sails are preferable for the latter mission. It should be noted that sails of total areal density as low as I g/m2 are under consideration.

if a sail can accelerate itself in a beam to more than the required speed, it can clearly supply a net contribution to the acceleration to, or deacceleration from, that speed of a larger vehicle in the same beam.

Figure 81 also shows sails 892 furled into sail cylinders 893 mounted around the periphery of the annular crew compartment 785.

Figure 82 is a plan seen from the front of the vehicle of the annular crew compartment 785 and its sail cylinders 893 when rotating with the sails 892 extended so as to obtain thrust from the beam of an interstellar accelerator or the electromagnetic radiation from a star.

Such rectangular sails can be unrolled from and rolled up into such cylindrical sail cylinders repeatedly.

6.39 Missions.

6.39.1 Climate control.

6.39.1.1 Electricity generation, desalination and irrigation.

The fusion power station described in Section 6.26 may generate electricity at a power level at least two orders of magnitude larger than the highest terrestial requirement for power currently envisaged.

Many fields in arid areas are irrigated with 1.5 metres of water per annum. Irrigating one million square kilometres at that rate would require 1.5 x 1012 m3 of water each year.

Reverse osmosis needs up to 21.6 MJ / in3 of electricity to desalinate sea water with a high salt content. Multi-stage flash distillation and multi-effect distillation requiTe up to 720 MJ / in3 of heat. So that reverse osmosis to irrigate a million square kilometres requires 1 TW of electricity while distillation needs 34.2 TW of heat.

Very large scale desalination, irrigation and soil restoration would allow the production of food, timber and biofuel, with the sequestration of sufficient carbon dioxide to lower the amount of that greenhouse gas in the atmosphere significantly.

The atmosphere of the earth contains 2.13 billion metric tonnes of carbon for each part per million of atmospheric carbon dioxide.

In the forests of the Northeast United States, each hectare 010.01 km2 holds 185 metric tonnes of carbon in the form of vegetation, roots, dead wood, litter and soil organic matter.

So that a forest of one million square kilometres could sequester 18.5 billion metric tonnes of carbon and absorb 8.685 parts per million of atmospheric carbon dioxide.

In order to obtain the greatest possible benefit, it is desirable that the heat escaping from the desalination plant, and the water vapour released locally by the irrigation process, both be minimised. Water vapour is a more significant greenhouse gas than carbon dioxida The desalinated water would convey heat at a rate of several terawatts. A binary cycle plant can generate electricity at an efficiency of 10% from water at 57°C. So that an irrigation system could supplement an electricity grid.

6.39.1.2 Maintaining therniohaline circulation.

The North Atlantic Drift is the northern branch of the Gulf Stream It is driven by thermohaline circulation.

Evaporation from the Gulf Stream both cools its sea water and makes it saltier. Sea ice forms at high latitudes, further increasing its salinity. The dense cold brine sinks in polar regions. This drives a circulation via the southgoing North Atlantic Deep Water.

It has been suggested that global warming could increase the supply of fresh water to northern oceans, dilute the brine, and consequently slow down thermohaline circulation.

This would reduce the warming of northern Europe provided by the heat in the North Atlantic Drift.

Large quantities of brine and/or salt will be a byproduct of large scale desalination, which could be discharged into the ocean at a suitable position to maintain such a ther-mohaline circulation.

6.39.1.3 Solar radiation shielding.

Mirrors or refractive screens in space could deflect sufficient solar radiation away from the Earth to counter global warming. Mirrors may equally direct heat and light towards the Earth to prevent global cooling, to solar power stations on the ground for energy generation, and to cities for lighting. They may also heat selected regions of the Earth in a controlled manner so as to modify the weather. Such systems could be removed from space if that was required.

A paper entitled "Earth Rings for Planetary Environmental Control" (Jerome Pearson et al (2002) International Astronautical Federation IAF-02-U.1.01) describes such a concept with a total mass of 5 million metric tonnes in Earth orbit. It also reviews other Climate Control Methods.

A paper entitled "Feasibility of cooling the Earth with a cloud of small spacecraft near the inner Lagrange point (Li)" (Roger Angel, 17184-17189 PNAS, Nov. 14, 2006, vol. 103, no. 46) describes another concept with a total sunshade mass of 20 million tons in solar orbit. The extra masses of the launch vehicles envisaged in this paper added a further 40 million tons, which would have to be disposed of safely after escaping from the Earth.

The beam launch facility of the fusion power station described in Section 6.26 could propel a mass of the order of a million tons into space and facilitate such concepts.

6.39.2 Diversion of asteroid or long-period comet.

The existence and orbits of many periodic, or short-period, comets are known. The arrival of aperiodic, or long-period, comets cannot, however, be predicted. They could be detected optically from Earth between 2 and 6 months before crossing the orbit of the Earth, depending on whether their approach was from behind the sun or otherwise, together with other factors, such as their size, composition and velocity.

However, an asteroid has no tail, and cannot be detected optically in daylight from Earth. It may be detected by radar provided that radar has been cued onto its approximate position, but then only at a comparatively low range giving 3 to 6 days warning of its impact. It is therefore clear that a space-based detection system is necessary to detect asteroids approaching the daylight hemisphere of Earth.

For a comet or an asteroid to be diverted by one Earth radius in the last month of its approach requires a velocity change of 2.46 in/s.

There are three methods by which the apparatus can change the velocity of a massive object:-a series of impulses produced by the pulses of the beam from its directed energy weapon vaporizing mass from that object; the dynamic pressure of its exaust (in conjunc-tion with any such impulses); and its own thrust when in direct contact with that object.

Smaller objects can be vaporized entirely, which has the advantage of preventing them from having any future encounters with Earth. Smaller objects can also be diverted by the gravitational attraction of a very large spacecraft.

The coupling coefficient between the energy in a pulse and the resultant impulse on a target has to be found emphirically. It maybe taken as 8 dyne sec/J or 8 x io-N sec/J.

Thus diverting an object of 10 billion metric tonnes by a velocity change of 2.46 rn/s with a beam whose average power is 1000 TW as may be obtained as a pulse from the burn, or over a longer period from the shock wave, from any one of the embodiments shown in Figures 26, 27 or 28 takes 308 seconds. Mirrors of very high reflectivity might enable the average power to be increased by up to two orders of magnitude.

This period is so low that there is little point in direct contact with the object even though that method is more energy efficient.

Since the effective range of the directed energy weapon is some 20 < 106 1cm, and its beam is available for two orders of magnitude longer than 300 seconds, and thus able to deflect a comet or asteroid of this mass through a much larger velocity change than 2.46 mIs, it is apparent that it is not necessary for the apparatus even to intercept any such body The diversion of such a comet or asteroid may be performed by the directed energy weapon from the vicinity of Earth and not long before that body arrives at Earth's orbit.

The asteroid responsible for the Cretaceous-Tertiary (K-T) Extinction was probably two orders of magnitude more massive than that in the example above. The directed energy weapon is sufficiently powerful to divert such a massive asteroid, provided it stays in one piece. if, however, a very large asteroid broke up into fragments, there might not be sufficient time to target all those fragments. And there might not even be an immediate opportunity to target some fragments if they were initially hidden from view in the break-up. In such circumstances, intercepting and rendezvousing with an asteroid or comet is desirable.

The vehicle would either take off from Earth on a vertical beam as described in Section 6.26, or from a planet other than Earth using ablative drive, accelerate very quickly to a high speed using ablative drive to intercept that target, deaccelerate equally quickly using ablative drive to adjust its velocity and trajectory to that of the target, before diverting that target using the high thrust available with ablative drive. The vehicle itself must thereafter deaccelerate.

6.39.3 Terraforming Mars.

There are a number of possible requirements for the delivery of rnega-payloads to Mars.

Nitrogen on present-day Mars has only been measured in its atmosphere. it is con-ceivable that nitrogen atoms may have undergone non-thermal escape from Mars to space, and that there is now insufficient nitrogen on Mars for terraforming. It may therefore be desirable to transport large quantities of nitrogen to Mars from somewhere else in the solar system. It may, however, only be necessary to deliver a mega-payload to the source of the nitrogen, from where it could be propelled in smaller quantities to Mars by solar sails or an accelerator.

A paper entitled "Technological Requirements for Terraforining Mars" by KM. Zubrin and C.P. McKay evaluated some of the requirements for warming and thickening the Martian atmosphere.

The orbiting mirrors, in the form of solar sails, necessary to raise the temperature at the south pole by 5°K arid cause the carbon dioxide in the south polar cap to vaporize in a runaway greenhouse effect would have a mass of only 200,000 tonnes. This would endow Mars with an atmosphere of 50 to 100 mint.

In favourable circumstances, this would give rise to a second runaway greenhouse effect caused by the carbon dioxide in the Martian soil, raising the atmospheric pressure to 300 mbar.

In the least favourable circumstances, four outer solar system asteroids made of a frozen greenhouse gas such as ammonia, each with a mass of 10 billion metric tonnes, would have to be found and given a velocity change of at least 300 rn/s to cause them to collide with Mars after an encounter with Uranus or Saturn. (Forty such asteroids would double the nitrogen content of Mars' atmosphere.) The energy of the impacts would produce liquid water on Mars' surface and the ensuing water vapour would cause a third runaway greenhouse effect Providing an object of B) billion metric tonnes with a velocity change of 300 rn/s using a beam whose average power is 1000TW takes 37500 secs. Dynamic pressure on or direct contact with, the object would be more efficient.

Alternatively, increasing the number of mirrors by a factor of 3 would melt some of the permafrost and release water vapour to cause the third runaway greenhouse effect, if suitable asteroids do not exist, transporting to, or producing on, Mars 423 million tonnes of chiorofluorocarbons, CFCs, would have a similar effect. (Perfluorcarbons, PFCs, are preferable, as they would not destroy the ozone layer.) It may be advisable to surround Mars with a magnetic field like Earth's in order to protect it from the solar wind.

6.39.4 Interstellar.

The beam from any eye mirror whose output is directed along its axis of symme-try may be modulated by defocussing that beam, as described in Section 6.16.2.1.i of GB 2,305,516 B. For large eye mirrors, for which the inertia of a final stage defined mirror would be high, the frequency of such modulation would be low.

if, however, the outer eye mirror 310, which acts as a directed energy weapon as described in Section 6.25, includes a final stage defining mirror 162 equipped with leaves 191, as described in Section 6.18, then its beam may be modulated at a much higher frequency by the rotation of those leaves. The small interstellar accelerator, described in Section 6.25 and shown in Figure 29, may have such an outer eye mirror with a final stage defining minor equipped with leaves.

Such a modulated beam may be used for communication over interstellar distances with an advanced civilization in another star system. But caution is advised, as the use of this technology implies a capability to launch a kinetic energy weapon at relativistic speeds.

Payloads of tens of thousands of tonnes may be accelerated to a fraction of one percent of the velocity of light by the action of the beam originating in space from the small interstellar accelerator on an ablator and/or a plasma mirror. So that probes may be launched in order to take a close-up view of a target stellar system when flying past it, and establish whether it could usefully be the subject of a manned or unmanned mission.

An interstellar mission might comprise a craft with a single engine configuration burn-ing D11e3 fuel and using ablative drive with liquid hydrogen coolant if a very long duration at a velocity a fraction of one thousandth of the speed of light was acceptable for that mission. If the exaust velocity, U,,, is 4.70634 x 106 cm/see, g = 0.2g and Ymaa = lOg, where g is the acceleration due to gravity at the surface of the Earth, then the final velocity of the vehicle, veh, is D.000614135 c where c is the velocity of light, and the acceleration time, t,, is 6.53 hours. If the vehicle is unmanned, or the crew is fitted with g-suits of much higher performance than is currently available, so that g,, is the same but Ymaz = 50 then that fined velocity is 0.000866795 c, and the acceleration time, uch, 5 increased to 6.64 hours. In either case, about 20 times as much ammunition is required than the 100,000 rounds for each of the 72 injector guns mentioned in Section 5.28.1 Otherwise, six single engines would either take off from Earth on a vertical beam as described in Section 6.26, or from a planet other than Earth using ablative drive and gen-erating some tritium in their lithium blankets during that launch, as described in Section 6.27.2. Their payloads would include the mirrors for the dual triple engine configuration described in Section 6.32.1 and shown in Figures 73, 74 and 75. Their payloads for a manned mission would include a large interstellar accelerator and at least one shuttle to enable return journeys to be made.

A dual triple engine configuration would be assembled in space, and then accelerated towards the target star system by the beam of a very large interstellar accelerator. If there was a suitable means of deaccelerating the craft, such as a very large cloud of dust or gas, en route to the target star system, the velocity attained may be high. If, however, that deacceleration has to rely principally on magnetic drive, that velocity must be limited to a few percent of the speed of light.

When this linear acceleration became so low as to provide inadequate artificial gray-ity, the craft would manoeuvre so as to leave the beam from the very large interstellar accelerator, which would in any case be terminated after a predetermined interval. The crew compartment(s) on respective individual engine(s) in the configuration would then be spun up to provide an alternative source of artificial gravity.

Some of the tritium in the cylindrical targets loaded before launch, and of that gen-erated during launch in the lithium blanket, will decay to 2He3 within its half-life of 12.6years. It is, of course, preferable to burn 2He rather than 1T3 as its reaction with 1D2 gives a proton rather than a neutron. But tritium is necessary to ignite that reaction and the deacceleration using magnetic drive must commence before there is insufficient tritiurn in those cartridges for them to be useable. The deacceleration burn will generate more tritium in the lithium blanket, which will be harvested and used to refill cylindrical targets on board. If the exaust velocity, u, is io cm/sec, 9mj,, = O.08g and gmaz 4g then the velocity of the vehicle, Uveh, may be O.13c, with a deacceleration time of 144.528 days requiring an extremely large number of cylindrical targets. These might be stored in disposable tanks, and used to refill the cryogenic drum magazines during maintenance of the injector guns.

All available means, including solar and magsails, would be used to deaccelerate the craft, so as to minimise journey time while conserving fuel. If there is sufficient drag available from a very large cloud of dust or gas, artificial gravity may be provided by the resultant linear deacceleration. Similarly for single engine configuration(s) disassembled from a multiple engine configuration.

For a return journey, the shuttle would be accelerated by the large interstellar accel-

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erator at the target star, and deaccelerated by the very large interstellar accelerator at the sun. Because of the small mass of the shuttle, such a return journey may attain relativistic velocities. A starship with an outer eye mirror 310 could aiso accelerate the shuttle.

Claims (1)

1. <claim-text>CLAIMS.1. An apparatus comprising eye mirrors, arranged on at least two separate but parallel axes of symmetry, on each of which axes of symmetry there is a rear elliptical plane mirror, a front elliptical plane mirror, an axially symmetric annular conical mirror and an axially symmetric reversed further alternate defined mirror as well as at least one eye mirror (which is axially symmetric by definition), the elliptical plane mirrors having elliptical holes, the projections on a plane at right-angles to all the axes of symmetry of the outer edges of both the front and rear elliptical plane mirrors for each of those axes respectively being a common outer circle concentric about that axis, the projections on that plane of the inner edges of both the front and rear elliptical plane mirrors and the annular conical mirror for each of those axes respectively being a common inner circle concentric about that axis, with the projection on that plane of the reversed further alternate defined mirror for that axis lying within that respective common inner circle, such that an annular beam of electromagnetic energy collimated along one axis of symmetry from the rear of the apparatus towards its front with the same cross-section as the projection of the elliptical plane mirrors for that axis will be reflected sequentially from the rear elliptical plane mirror on that axis, from the front elliptical plane mirror on another axis, from the annular conical mirror on that other axis back through the holes in both the elliptical plane mirrors on that other axis, and finally from the reversed further alternate defined mirror on that other axis as well-directed input rays for the eye mirror(s) on that other axis, so that they will be directed by those eye niirrror(s) to or near to an aim point for a cylindrical target on or near that other axis where the implosion of that cylindrical target commences, with an optical recirculation period from a plane at right-angles to the axes of symmetry through the aim point on or near one axis to the aim point on or near another axis slightly less than or equal to the common period between the arrival of two successive cylindrical targets at each aim point.</claim-text> <claim-text>2. An apparatus as claimed in claim 1 in which there is an inner rear elliptical plane mirror, an inner front elliptical plane mirror and an axially symmetric inner annular conical mirror on each axis of symmetry, these inner elliptical plane mirrors having elliptical holes and the projections on a plant at right-angles to all the axes of symmetry of the outer edges of both the front and rear inner elliptical plane mirrors and the inner annular conical mirror for each of those axes respectively coincides with the inner circle concentric about that axis projected by those elliptical plane mirrors, which have become the front and rear outer elliptical plane mirrors, while the projection on said plane of the inner edges of both the front and rear inner elliptical plane mirrors and the inner annular conical mirror for that axis is respectively a common circle concentric about that axis and inside said inner circle, such that an inner annular beam collimated along one axis from the rear of the apparatus towards its front with the same cross-section as the projection of the inner elliptical plane mirrors for that axis will be reflected sequentially from the rear inner elliptical plane mirror on that axis, from the front inner elliptical plane mirror on another axis, from the inner annular conical mirror on that other axis back through the holes in all the inner and outer elliptical plane mirrors on that other axis, and finally from the reversed further alternate defined mirror on that other axis as well-directed input rays for the eye mirror(s) on that other axis, said other axis not being the same other axis as for the outer front and rear elliptical plane mirrors.</claim-text> <claim-text>3. An apparatus as claimed in claim 2 in which the common inclination of the outer elliptical plane mirrors, 0pLl, and the common inclination of the inner elliptical plane mirrors, 8p12, to their axes of symmetry is such that the optical recirculation period for each path through the outer elliptical plane mirrors is the same as that for each path through the inner elliptical plane mirrors, so as to provide simultaneous dual ignition of each cylindrical target.</claim-text> <claim-text>4. An apparatus as claimed in claim 3 in which there are six axes of symmetry passing through the vertices of a regular hexagon in a plane at right-angles to them alt 5. An apparatus as claimed in claim 4 in which the cross-overs from a rear elliptical plane mirror of one type to the front elliptical plane mirror of the same type on another aids of symmetry are between adjacent axes of symmetry, while the cross-avers from a rear elliptical plane mirror of the other type to the front elliptical plane mirror of that other type on another axis of symmetry are between axes of symmetry passing through the vertices of an equilateral triangle in a plane at right-angles to those axes, there being two such triangles with mutuaily exclusive vertices.6. An apparatus as claimed in claim 5 in which the cross-overs between adjacent axes of symmetry are between the inner elliptical plane mirrors while those between non-adjacent axes of symmetry are between the outer elliptical plane mirrors.7. An apparatus as claimed in claim 5 in which the cross-avers between adjacent axes of symmetry are between the outer elliptical plane mirrors while those between non-adjacent axes of symmetry are between the inner elliptical plane mirrors.8. An apparatus as claimed in any of claims 5, 6 or 7 in which the direction of the projections on a plane at right-angles to all the axes of symmetry of the cross-overs between adjacent axes of symmetry and the direction of the projections on a plane at right-angles to all the axes of symmetry of the cross-overs between non-adjacent axes of symmetry are in opposite senses.9. An apparatus as claimed in any of claims 3 to 8 in which tan = tan 10. An apparatus as claimed in any of claims 4 to 9 in which for each crossover the rays crossing from one axis of symmetry to another are enclosed in a cylindrical mirror whose inner surface is reflective.ii. An apparatus as claimed in claim 10 in which the rays, when travelling back and forth along each axis of symmetry, between the respective eye mirror and the respective annular conical mirrors, are enclosed in respective cylindrical mirrors, whose inner surfaces are reflective, and which have entry and exit apertures connecting with the cylindrical mirrors enclosing the crossovers.12. An apparatus as claimed in claim 3 in which there are four axes of symmetry passing through the vertices of a square in a plane at right-angles to them all.13. An apparatus as claimed in claim 12 in which the cross-avers from a rear elliptical plane mirror of one type to the front elliptical plane mirror of the sane type on another axis of symmetry are between adjacent axes of symmetry, while the cross-overs from a rear elliptical plane mirror of the other type to the front elliptical plane mirror of that other type on another axis of symmetry are between opposite axes of symmetry.14. An apparatus as claimed in claim 13 in which the cross-overs between adjacent axes of symmetry are between the inner elliptical plane mirrors while those between opposite axes of symmetry are between the outer elliptical plane mirrors.15. An apparatus as claimed in claim 13 in which the cross-overs between adjacent axes of symmetry are between the outer elliptical plane mirrors while those between opposite axes of symmetry are between the inner elliptical plane mirrors.16. An apparatus as claimed in any of claims 3 or 12 to 15 in which tan 9p12 = /tan 0pll* 17. An apparatus as claimed in any of claims 12 to 16 in which for each crossover between opposite axes of symmetry the rays crossing from one axis of symmetry to its opposite axis of symmetry are enclosed in a pair of cylindrical mirrors, whose inner surfaces are reflective, arranged on opposite sides of a central eight-way junction, whose inner surface is reflective.18. An apparatus as claimed in claim 17 in which the rays, when travelling back and forth along each axis of symmetry, between the respective eye mirror and the respective annular conical mirrors, are enclosed in respective cylindrical mirrors, whose inner surfaces are reflective, and which have entry and exit apertures connecting with the cylindrical minors enclosing the crossovers 19. An apparatus as claimed in claim 1 in which there is an axially symmetric inner conical annular mirror on each axis of symmetry, and the projection on a plane at right angles to all the axes of symmetry of the outer edge of the inner annular conical mirror on that axis of symmetry respectively coincides with the inner circle concentric about that axis projected by those elliptical plane mirrors, such that an inner annular beam collimated along that axis from the rear of the apparatus towards its front will pass through the holes in both the elliptical mirrors on that axis and then be reflected sequentially from the inner annular conical mirror on that axis back through the holes in both the elliptical plane mirrors on that axis and from the reversed further alternate defined mirror on that axis as well-directed input rays for the eye mirror(s) or' that axis.20. An apparatus as claimed in claim 19 in which there is a cylindrical mirror, whose inner surface is reflective, on each axis of symmetry which connects the hole in the rear elliptical plane minor on that axis with the hole in the front elliptical plane mirror on that axis.21. An apparatus as claimed in either of claims 19 or 20 in which there is a further cylindrical mirror, whose inner surface is reflective, on each axis of symmetry between the front of the front elliptical plane mirror on that axis and the annular conical mirror on that axis, which has become the outer annular conical mirror on that axis.22. An apparatus comprising an upper and a lower copy of the apparatus as claimed in any of claims 19, 20 or 21 in which there are four axes of symmetry, referred to as the upper left, upper right, lower left and lower right axes of symmetry respectively.23. An apparatus as claimed in claim 22 in which the operation of the lower left and upper right engines are synchronised and the operation of the lower right and upper left engines are synchronised.24. An apparatus as claimed in any of claims 1 to 23 in which the outermost rays of the reflections of a collimated annular beam from an annular conical mirror are incident to a reversed further alternate defined mirror, on, or near to, its axis of symmetry, such S. reflections from inner and outer collimated annular beams overlapping, so that some badly collimated electromagnetic energy reaches that reversed further alternate defined mirror.25. An apparatus as claimed in any of claims 2 to 18 in which for each axis of symmetry the centres of the inner elliptical plane mirrors on that axis lie inside the centres of the outer elliptical plane mirrors on that axis.26. An apparatus as claimed in any of claims 2 to 25 in which there is a conical shield on each axis of symmetry, whose axis of symmetry coincides with that axis and the radius of whose base is the radius of the common outer circle is b02, the radius of the common inner circle is b, the radius of the common circle inside the inner common circle is r and = 2b -rL where r0 c( bin < 27. An apparatus as claimed in any of claims 1 to 26 in which there is on each axis of symmetry at least one axially symmetric superconducting field coil and at least one conducting shield, so that plasma expanding from an explosion on that axis compresses a magnetic field produced by the superconducting field coil(s) on that axis, which in turn induces eddy current(s) in the rear surface(s) of the shield(s) on that axis, the interaction of those eddy current(s) with that magnetic field producing impulse(s) on the shield(s) on that axis and thus magnetic drive, and each shield radiates electromagnetic energy equal to that incident upon it plus the energy deposited in or on it by neutrons, plasma and/or electromagnetic radiation and the ohmic heating due to the eddy currents less any energy removed by a cooling and/or power generation system in the period between the explosions on. that axis.28. An apparatus as claimed in claim 27 in which the aim point(s) or line(s) of the recirculated beam(s) from the eye mirror(s), which cause a target for inertial confinement fusion to implode and ignite fusion, may be moved.29. An apparatus as claimed in claim 28 in which the aim point(s) or line(s) may be moved along their respective axis of symmetry away from the shield(s) on that axis of symmetry so as to reduce any ablation from those shield(s) which may be caused by the resulting explosion on that axis of symmetry.30. An apparatus as claimed in either of claims 28 or 29 in which the aim point(s) or line(s) may be moved off their respective axis of symmetry so as to provide asymmetric impulse(s) on the shield(s) on that axis of symmetry, by asymmetrically compressing themagnetic field on that axis of symmetry.31. An apparatus as claimed in any of claims 28, 29 or 30 in which the aim point(s) or line(s) may be moved off their respective axis of symmetry so as to provide asymmetric impulse(s) on the shield(s) on that axis of symmetry, by asymmetrically ablating the material of the shield(s) on that axis of symmetry or coolant on their surface(s).32. An apparatus as claimed in any of claims 27 to 31 in which at least one shield is retracted away from the aim point(s) or line(s) on its respective axis of symmetry of the beam(s) from the eye mirror(s), which cause a target for inertial confinement fusion to implode and ignite fusion, so as to reduce any ablation from those shield(s) which may be caused by the resulting explosion on that axis of symmetry.33. An apparatus as claimed in any of claims 27 to 32 in which the gain of each engine is controlled individually and the respective gains of two or more engines are adjusted to differ, so as to alter the orientation of the apparatusfor the purpose of effecting a turn.34. An apparatus as claimed in any of claims 2 to 33 in which the hole in each inner annular conical mirror forms a variable atmospheric intake with a conical door to allow the atmosphere of a planet to reach the position on its respective axis of symmetry where a target for inertial confinement fusion explodes and ablates the material of the shield(s) on that respective axis of symmetry or coolant on their surface(s) to produce impulse(s) on them in ablative drive.35. An apparatus & claimed in any of claims 2 to 34 in which the power of each annular beam is sufficient on its own to implode a target for inertial confinement fusion and cause its ignition, on output from the eye mirror(s) on an axis of symmetry.36. An apparatus as claimed in claim 1 in which there is on each axis of symmetry at least one shield, the ablation of material from the surface of which produces an impulse on that shield, and the hole in each annular conical mirror forms a variable atmospheric intake with a conical door to allow the atmosphere of a planet to reach the position on its respective axis of symmetry where a target for inertial confinement fusion explodes and ablates material from the surface(s) of the shield(s) on that respective axis of symmetry to produce impulse(s) on them iii ablative drive.37. An apparatus as claimed in claim 36 in which a further alternate defined mirror is provided on an axis of symmetry to reflect the annular beam(s) of electromagnetic energy collimated and approximately collimated along that axis of symmetry from the rear of the eye mirror(s) on that axis as well-directed input rays for those eye mirror(s), such that those eye mirror(s) may be detached from the remainder of the apparatus to form a single engine.38. An apparatus as claimed in claim 36 in which individual further alternate defined mirrors are provided on an axis of symmetry to reflect the annular beam(s) of electromag-netic energy collimated and approximately collimated along that axis of symmetry from the rear of the eye mirror(s) on that axis as well-directed input rays for those eye mirror(s), such that those eye mirror(s) may be detached from the remainder of the apparatus to form a single engine.39. An apparatus as claimed in claim 36 in which individual conical mirrors and individual further alternate defined mirrors are provided on an aids of symmetry to reflect the annular beam(s) of electromagnetic energy collimated and approximately collimated along that axis of symmetry from the rear of the eye mirror(s) on that axis as well-directed input rays for those eye mirror(s), such that those eye mirror(s) may be detached from the remainder of the apparatus to form a single engine.40. An apparatus as claimed in any of claims 27 to 39 in which there is an outer superconducting field coil axially symmetric about an axis of symmetry of the largest radius which can be accommodated within the eye mirror(s) on that axis, so as to mantarn a plasma mirror behind the shield on that axis, and/or enable magnetic sailing.41. An apparatus as claimed in any of claims 34 or 36 to 40 in which there is an annular crew compartment which rotates to provide artificial gravity at its circumference in the absence of a linear acceleration of the vehicle sufficient for that purpose, the hole in its centre allowing a planetary atmosphere to teach the variable atmospheric intake.42. An apparatus as claimed in claim 41 in which sail cylinders containing rolled-up lightweight sails are mounted around the periphery of the annular crew compartment, from which those sails can be unfurled when that annular crew compartment is rotating, and therebye extended so as to obtain thrust from a beam or other electromagnetic radiation.43. An apparatus as claimed in any of claims 1 to 42 in which each engine has a fibre-optic digital data bus to which various of its controllers and various of its sensors are connected.44. An apparatus as claimed in claim 43 in which each engine has au interface controller connected to its respective fibre-optic digital data bus which may be connected to the inter-face controller for another engine to which its electromagnetic energy is to be recirculated, so that information about the power of an explosion and the time of its measurement may be sent from the first engine to the second engine.45. An apparatus as claimed in any of claims 27 to 33 in which there is an aim point near the vehicle on an axis of symmetry for cameras in ablative drive and an aim point further away from the vehicle on that axis of symmetry for cameras in magnetic drive, at least one pair of cameras on respective optical axes which pass through the camera aim point for ablative drive and are orthogonal to each other, and at least one pair of cameras on respective optical axes which pass through the camera aim point for magnetic driveIand are othogonal to each other.46. An apparatus as claimed in claim 45 in which there is at least one further pair of cameras on respective optical axes which are othogonal to each other and pass through a point which is not on that axis of symmetry but is in a plane at right-angles to that axis through the camera aim point for ablative drive, and at least one further pair of cameras on respective optical axes which are orthogonal to each other and pass through a point which is not on that axis of symmetry but is in a plane at right-angles to that axis through the camera aim point for magnetic drive.47. An apparatus as claimed in any of claims 1 to 46 in which at least one of the mirrors is cooled.48. A method of optically recirculating electromagnetic energy with magnetic drive comprising the steps oE- (a) providing an apparatus as in any of claims ito 47; and (b) injecting a cylindrical target; and (c) providing a source of electromagnetic energy by other means at or near the position where a cylindrical target will subsequently be imploded.49. A method of assembling a dual multiple engine configuration in space comprising the steps of: (a) providing multiple single engine configurations, with the other components making up that dual multiple engine configuration and at least one annular crew compartment as their payloads; and (b) launching all those single engine configurations with their respective payloads, either from Earth on a beam from a fusion power station, or from another planet using ablative drive; and (c) assembling the dual multiple engine configuration in space; and (d) connecting each interface controller to the interface controllers of those other engines to which its electromagnetric energy is to be recirculated.50. A method of obtaining the simultaneous dual ignition of a cylindrical target com-prising the steps of (a) providing a dual multiple engine configuration as in any of claims 3 to 18; and (b) injecting a cylindrical target for a first engine; and (c) injecting cylindrical targets for the other engines so that they will be at the respective point at which their respective implosion will commence when respective electromagnetic energy arrives at that respective point; and (d) providing a source of electromagnetic energy by other means at or near the position where a cylindrical target will subsequently be imploded in an engine which recirculates electromagnetic energy to that first engine.51. A method of controlling the orientation of a vehicle with a single engine comprising the steps of:- (a) providing an apparatus as in either of claims 30 or 31; and (b) commanding the leaf controllers in that vehicle's engine to move the aim point(s) or lines(s) off the axis of symmetry.52. A method of maintaining a plasma mirror comprising the steps of:- (a) providing an apparatus as claimed in claim 40; and (b) establishing an electric current in the outer superconducting field coil; and (c) providing coolant to the shield to be ablated by a beam incident to that shield.</claim-text>