GB2540644A - Master starter - Google Patents

Abstract

Apparatus for providing a pulse of electromagnetic energy is disclosed comprising a shock cavity 53 filled with gas 54 at a high pressure. Detonation of an explosive lens 51 causes the dissociation of said gas thereby generating said electromagnetic radiation, which is directed out of the cavity 53 via either a diaphragm 55 or an array of fibre-optic cables 58 by the mirrored inner surfaces 31, 33 & 35 of said cavity. The pulse of electromagnetic energy generated may be used, for example, to initiate inertial confine­ment fusion or for propulsion means. Alternatively, said pulse may be used to detonate the explosive lenses of further devices of a similar design.

Description

Master starter 1.0 Background to the invention.

This invention relates to a method and apparatus for providing pulses of electromagnetic energy through fibre-optic cables notably to flying plate detonators in starters which initiate inertial confinement fusion in a fusion power station, starship, or nuclear explosive device, and in particular, but not exclusively, to such a method and apparatus for use in the fields of defence as an explosive, neutron, radiological or directed energy weapon; propulsion by means of a beam or fusion; climate control; electricity generation; desalination; irrigation; and terraforming. 2.0 Prior art.

The prior art comprises United Kingdom patent GB 2,305,516 B published as an application on the 9th April 1997 and as a patent on the 7th April 1999, and granted to the present inventor, which revealed method and apparatus for directing electromagnetic energy from an area or volume source, and which is incorporated herein by way of reference. Any embodiment 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, will hereinafter be referred to as an “eye mirror”. Any ray in the plane containing such a pair of defining rays also lies in a plane through the axis of symmetry and is therefore meridional. 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 13ift December 2006 and as a patent on the lltft March 2009. A leaved eye mirror starship and a fusion power station with a beam launch to space facility were described in four patent applications by the present inventor published on the following dates:- GB 2,496,022 Ignition of a target 1st May 2013 GB 2,496,250 Ignition of a target and axial burn of a cylindrical target 8th May 2013 GB 2,496,012 Optical recirculation with ablative drive 1st May 2013 GB 2,496,013 Optical recirculation with magnetic drive 1st May 2013

Both these devices require a very powerful pulse of electromagnetic energy to initiate their operation. It is not desirable that this pulse is provided by a fissile nuclear explosive device inside a fusion power station, or for a starship taking off from a habitable planet, because of the radioactive products of fission. Section 6.23.1.3 of those applications therefore described a wire array Z-pinch system for the fusion power station.

This pulse may be more conveniently provided by the explosion of one or more targets for inertial confinement fusion, imploded by a pulse of electromagnetic energy from a large number of starters. Each starter may have a large number of explosive lenses initiated by flying plate detonators. But the time variation, or jitter, in their detonation must be at least an order of magnitude smaller than the implosion time of such a target.

The temperature of high explosive after detonation is at most 0.5 eV. The ideal temperature of a source of electromagnetic energy for starting a burn in these devices is 1 eV. Any device providing hot gas for this purpose would be positioned in the converging annular shock tube, described in Section 6.27.7.1 of those applications, to maintain its output for as long as possible. A thorough explanation of the subject of inertial confinement fusion can be found in a book entitled “The Physics of Inertial Fusion” (S. Atzeni & J. Meyer-Ter-Vehn (2004)). Further useful information may be found in a book entitled “Laser Plasma Interactions 5: Inertial Confinement Fusion (Ed. M.B. Hooper (1995)) and a book entitled “Nuclear

Fusion by Inertial Confinement: A Comprehensive Treatise” (Ed. G. Velarde, Y. Ronen &; J.M. Martinez-Val (1993)). 3.0 Objects of the invention.

It is an object of the present invention to provide a method for, and an apparatus capable of, supplying pulses of electromagnetic energy through fibre-optic cables to a large number of flying plate detonators with minimum jitter. 4.0 Summary of the invention.

In view of the foregoing, a first aspect of the present invention provides an apparatus for supplying pulses of electromagnetic energy through fibre-optic cables comprising a shock cavity filled with a gas at a very high pressure, an apparatus for directing electromagnetic energy from an area or volume source enclosing that gas, and an array of fibre-optic cables with a common cladding at their input ends which seals the exit aperture of the apparatus for directing electromagnetic energy from an area or volume source, all of which are axially symmetric about a common axis of symmetry, and a circular array of axially symmetric explosive lenses, each with their own axis of symmetry and a detonator, which are cut where they would overlap the explosive lenses on either of their sides to cover and seal the input aperture of the apparatus for directing electromagnetic energy from an area or volume source.

According to a second aspect of the present invention there is provided a method using the apparatus of the first aspect. 5.0 Description of drawings.

Figure 1 is a schematic diagram showing three different types of starter.

Figure 2 shows the geometry of an explosive lens utilizing a cartesian oval.

Figure 3 shows a section of such an axially symmetric explosive lens through its axis of symmetry.

Figure 4 shows an icosahedron with one of its faces overlaid by a geodesated regular tesselation of order 2.

Figure 5 is a wire diagram showing an explosive lens trimmed to fit into a spherical array of explosive lenses.

Figure 6 is a schematic diagram showing a circular array of explosive lenses which are cut where they would overlap the explosive lenses on either of their sides to cover and seal the input aperture of an eye mirror.

Figure 7 is a schematic diagram in the form of a section through the axis of symmetry of an eye mirror showing a choice of defining rays for its final stage defined mirror.

Figure 8 shows an alternative choice for some of the defining rays.

Figure 9 shows the cut-off sphere, at which the critical density for the lowest wavelength in the beam from an eye mirror, occurs.

Figure 10 shows a geodesated regular tesselation of order 2 of a regular icosahedron in which the spherical array of eye mirrors is represented schematically.

Figure 11 shows a geodesated regular tesselation of order 3 of a regular icosahedron in which the spherical array of eye mirrors is represented schematically.

Figure 12 shows a hollow wall connected by a highly conductive support wire to a cold spot on a spherical target.

Figure 13 is a schematic diagram illustrating various positions at which a neutron target may be positioned.

Figure 14 is a schematic diagram showing an overlapping pair of nuclear explosive devices and a central neutron target. 6.0 Description of embodiments of the invention. 6.1 Starters.

Figure 1 is a schematic diagram showing three different types of starter. The top left-hand side of Figure 1 is in the form of a section through a starter 7, which section generates that starter. The starter may have any shape at a right-angle to the plane 19 of the paper. It may be linear, on an arc about a remote axis, such as the axis of symmetry of a very large eye mirror, or axially symmetric about an axis of symmetry 18 of its own.

The starter 7 comprises an explosive lens 51 with a detonator 52, a shock cavity 53 filled with gas 54 at a very high pressure, an apparatus for directing electromagnetic energy from an area or volume source enclosing the gas 54, which apparatus may be an eye mirror 8 if the starter 7 is axially symmetric, and a diaphragm 55 which seals the exit aperture of the apparatus for directing electromagnetic energy from the area or volume source.

The detonator 52 is either linear or along an arc. A paper entitled “Los Alamos Experimental Capabilities: Ancho Canyon High Explosives and Pulse Power Facilities” (Charles E. Moss, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (Feb. 11, 1993) LA-UR-93-222) shows a linear detonation system using a slapper/cable with discrete detonator points comprising PETN pellets, at Figure 4. However, a linear strip of explosive could be substituted for those pellets. An exploding bridgewire detonator may also be linear or along an arc. The time variation of exploding bridgewire detonators fired using an electric current is at least 25 ns, so that they are only suitable for applications where such detonation precision is acceptable.

The apparatus for directing electromagnetic energy comprises a defining unit 20 with first, second and third stage defining mirrors 30, 32 and 34 respectively and a defined unit 40 with first, second and third stage defined mirrors 31, 33 and 35 respectively.

Figure 1 also shows a pair of defining rays 5 and 6 respectively, which intersect at a point on the first stage defined mirror 31. The angular input aperture for such a point of intersection, as defined in Section 6.14.4 of GB 2,305,516 B, is the angle between the pair of defining rays which intersect at that point.

The shock cavity 53 is sealed, for instance, by two side plates 56 and 57 respectively, as shown. These side plates axe flat in the case of a linear starter. Equally, the side plates may lie on the same arc as the starter, or be axially symmetric about the same axis of symmetry 18 as the starter. That surface on the interior side of each side plate is reflective.

However, an edge of the explosive lens 51 may be contiguous with the leading edge of the first stage defined mirror 31, therebye eliminating the side plate 57. Moreover, the other edge of the explosive lens may be contiguous with the leading edge of the first stage defining mirror 30, therebye eliminating the side plate 56.

The explosive lens 51 may not be sufficiently strong to withstand the pressure of the gas 54 in its interior. In which case, the exterior of that explosive lens is supported by a case (not shown) which also serves to connect the defining unit 20 with the defined unit 40.

The top right-hand side of Figure 1 is similar to a mirror image of the top left-hand side of that figure, but the diaphragm 55 has been replaced by an array of fibre-optic cables 58 with a common cladding at their starts, which both receive electromagnetic energy from the apparatus for directing electromagnetic energy from an area or volume source and seal the exit aperture of that apparatus, which is generally an eye mirror 8. This embodiment is the master starter described in Section 6.2.1 . It is not necessarily axially symmetric.

The axis of each fibre is aligned with a defining ray for the defined mirror of a final stage of the apparatus for directing electromagnetic energy from an area or volume source, and its face is perpendicular to both, as well as being smooth and polished, in order to minimise transmission loss into that fibre. The input ends of the fibres are assembled into an array with a common cladding and no coating to maximise the area over which that transmission occurs. The output end of each fibre is attached to a flying plate detonator 59.

An axis of symmetry for a figure is a line such that every line which cuts that axis at a right-angle cuts that figure in pairs of points equidistant from that axis. An axially symmetric figure is not necessarily generated by rotation about an axis of symmetry. So that an array of fibre-optic cables, and thus the holes in a common cladding for those cables, may be axially symmetric. In practice, the array of fibre-optic cables need only populate that cladding and may be irregular.

The bottom of Figure 1 is similar to the top left-hand side of that figure when axially symmetric together with its mirror image, but the detonator 52 has been replaced by a number of flying plate detonators 59 of the type described in Section 6.2.1 each connected to at least three fibre-optic cables 58. 6.2 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 v\, on the incident side and a slow explosive, whose detonation velocity is V2, on the transmitted side of eccentricity vi/v? > 1 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 2 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 2 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 φ to the transverse axis 581 intersects the boundary 582 after a distance, Z, 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, G.

The coordinates of the point, P, from an origin at C are r, Θ. Those from an origin at G are g, 7. The ratio v\fv^ — n.

The boundary 582 meets the transverse aids 581 at a point, A, a distance a from F. Any deflagration-to-detonation run having a starting velocity less than t>i must take place entirely within the fast explosive 583 and thus over a distance less than a.

By the Law of Sines:-

so g sin 7 = Z sin φ — r sin Θ

Equating the optical path length through P with that along the transverse axis:- l + rn = a + (c — a)n or g sin 7(csc φ + ncsctf) = 0 + (c — a)n (1)

Equating the horizontal components of the path through P with the length of the transverse axis:- Z cos φ + r cos Θ — c or g sin 7(cot φ + cot Θ) = c (2)

By Snell’s Law:- sin(7 + φ) = n sin(7 — θ) or sin7cos0 + cos 7 sin </> = n sin 7 cos Θ — n cos 7 sin Θ sin 7(cos φ — n cos Θ) 4- cos 7(sin φ + η sin Θ) — 0 (3)

We therefore have two coordinate variables (g, 7) plus two parameters (θ, φ) connected by three equations with three constants (a,c,n). This system represents a line and may be solved numerically.

This line is the boundary 582 in Figure 2. 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 3 is a section of an axially symmetric explosive lens 591 with the geometry of Figure 2 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 m by splitting each edge into m equal edges to give 3(m — 1) new vertices on those edges. If m = 3 there is also a new vertex in the centre of that face, while if m — 4 there are three new vertices. All these new vertices are triangulated to give m2 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 m — 2, and 180 faces for m = 3. A larger number of smaller faces reduces the volume of explosive required.

Figure 4 shows an icosahedron 599, one erf 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 axe isosceles triangles.

In Figure 5 the edges of this inner triangle 600 are shown as dashed lines, and an explosive lens 604, similar to the one in Figures 2 and 3 but with smaller maximum values for Θ and φ, 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 5 is a wire diagram.

The detonator 593 is shown protruding from the face 606 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 equilateral inner triangle 600. But the cuts for its other two sides are closer to its point of detonation which is not therefore on a line through its incentre. So that the point of detonation does not lie on a line through its centroid with associated numbers corresponding to the lengths of its sides.

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, or by a slapper as described in Section 6.1 . Alternatively, each detonation may be achieved by direct laser ignition via respective fibre-optic cables all of the same length for all of the detonators, 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.

The rise time of a pulsed laser diode array is 10 ns with a timing variance, or jitter, of less than 0.5 ns, provided a suitable driver is provided.

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. A paper entitled “Laser Deflagration-to-Detonation in Keto-RDX doped with Resonant Hollow Gold Nano-shells” (RR. Wilkins, High Explosives Applications Facility Mailstop L-281, Lawrence Livermore National Laboratory, Livermore, CA 94550 (LLNL- CONF-656673)) described a method of initiating detonation in high explosive using a 20 W laser diode focussed onto an 800/zm spot at 2kW/cm2 for 12.1ms. However, the jitter in the detonations amounted to several millesconds. A laser-driven metal flyer plate accelerated by ablation from its surface by a laser can reliably shock detonate insensitive high explosive. Laser-driven flyer plates achieve 90% of their peak velocity in about 20 ns, at which point it may be arranged that they impact the high explosive in order to minimise timing errors. Clearly any error in the time over which they accelerate and reach the high explosive must then be some fraction of that period. The duration of the shock produced by such an impact is less than Ins. So that any variation in the onset of the detonation process must be some fraction of that duration.

The flyer plate velocity may be a significant fraction of the detonation velocity of the explosive, so that any deflagration-to-detonation run, and thus the minimum length of the distance a in the fast explosive 583, are both short.

The jitter between any deflagration-to-detonation runs may be reduced to less than 10 ns by careful preparation of the respective explosive lenses. But it is preferable to make the detonations nearly instantaneous.

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 plano-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.

The power needed to accelerate an aluminium flyer plate using a laser with a wavelength of 1.06/xm is high. The ablation pressure scales with (II / λχ,)2^3 where Ιχ, is the intensity and Xl is the wavelength of the illumination. So that 1.32 GW / cm2 is adequate for a waveband starting at 0.2μιη.

The time to onset of detonation, td, as a function of initial shock pressure, P, has been give as td — 17.9 Ρ~5/3μs. So that td oc (1^ / λχ,)-10^9. If the deflagration-to-detonation jitter is proportional to td then 10.45 GW / cm2 would reduce a jitter of 10 ns to 1 ns. The gas 54 in the master starter must not breakdown at such a level of illumination during the acceleration of the flyer plate, a period of about 20 ns. 6.2.1 Master starter.

The master starter supplies this power to flying plate detonators 59 in all the explosive lenses in all the eye mirrors in any device through fibre-optic cables 58 all of the same length whose input ends are connected to the output aperture of that master starter as shown at the top right-hand side of Figure 1.

An eye mirror spreads the output from any point in or on its source around a portion of that output aperture. In the master starter, that source generally consists of η > 1 explosive lenses, as will be described in Section 6.3, so that the master starter smooths the power from a number smaller than n of those explosive lenses. Moreover, the metal flyer plate in each flying plate detonator 59 is illuminated by n fibre-optic cables whose input ends are equally spaced around the output aperture of the master starter in positions such that each of those fibre-optic cables receives electromagnetic energy originating from a different explosive lens in the master starter. So that variations in the amount of the radiation from different portions of that output aperture are smoothed out. And a number, equal to the total number of detonators in the device, of fibre-optic cables receive electromagnetic energy from each explosive lens in the master starter.

If those fibre-optic cables receiving only that electromagnetic energy, which originates from the explosion of only one explosive lens, each supplies sufficient electromagnetic energy to a respective one of a number of detonators, then their detonations will be initiated at the same time, irrespective of the timing of that explosion, and the speed of the detonator for that explosion.

If the starter at the top left-hand side of Figure 1 is axially symmetric and a shock wave reflector is provided inside the leading edge of the first stage defined mirror 31 to seal the shock cavity 53, then a single explosive lens may supply that electromagnetic energy. But that explosive lens will be large and massive. Similarly for the master starter at the top right-hand side of Figure 1.

However, neither an apparatus for directing electromagnetic energy from an area or volume source, nor its detonator, need be axially symmetric. So that the explosive lens for an asymmetric apparatus may be small and light. But axially symmetric mirrors are easier to machine.

So that in the preferred embodiment for the master starter, the shock cavity 53, the apparatus for directing electromagnetic energy from an area or volume source, and the array of fibre-optic cables 58 with a common cladding at their input ends, which seals the exit aperture of that apparatus, are axially symmetric about a common axis of symmetry.

If each detonator receives electromagnetic energy originating from all the explosions of all of the explosive lenses in the master starter through fibre-optic cables, in equal amounts at each point in time, then all of those detonators will receive the same amount of energy over the same period, and be initiated simultaneously as soon as sufficient energy has been supplied to them. Imwhich case, the circular array of explosive lenses, described in Section 6.3, with slow detonators may be used in the master starter.

So that the timing variation, or jitter, of the detonation of multiple explosive lenses in the master starter is also averaged out or eliminated. And the detonators 55 in those explosive lenses for the master starter can be conventional exploding bridge wires with a jitter of 25 ns and yet produce a much smaller jitter at the explosive lenses in the eye mirrors of the starter(s).

If there are a number of master starters at different locations, and it is required to make their explosions simultaneous, a further master starter may initiate those explosions. This further master starter may be sufficiently small to conveniently have a single explosive lens.

High-Power-Density Fibers have a pure silica core and a silica cladding, providing an ultra-high damage threshold. The fibre’s low OH- content makes them most suitable for wavelengths in the range 500-2100 nm. The largest core diameter available is 600/zm. High-temperature all-silica high OH- fibres have a polymide buffer coating extending their operating temperature range to 375°C. Newport’s F-MCC-T fibre, which is of this type, has a wavelength range of 250-1100 nm. High grade fused silica transmits down to 260 nm. Solarization resistant high grade fused silica fibres treated by infusion of hydrogen into the core at very high temperatures transmit down to 180 nm.

As the axis of each fibre-optic cable 58 is aligned with a defining ray, as stipulated in Section 6.1, the light entering each cable is substantially parallel to its axis. And the input to each fibre is uniform across its core. So that hot-spots cannot form and damage the fibre.

That input is temporally incoherent, so that interference effects, such as Stimulated Raman Scattering (SRS) and Stimulated Brillouin Scattering (SBS), cannot occur and reduce the transmission efficiency of that fibre. Moreover, the fibres are only a few metres long.

Lasers are generally focussed onto a spot, centred on or before the end face of an optical fibre, whose diameter approximates to 90% of the diameter of that fibre’s core. It is possible to prevent light entering the common cladding by means of a barrier.

However, the damage mechanism of a fibre optic cable is not failure of its cladding, which is generally made of a very similar material to its core, and is used as a waveguide in a double-clad fibre, but of the polymer cable surrounding the cladding.

Moreover, the fibres in their common cladding comprise a homogeneous block which is only constricted at its inner and outer circumference. Silica step index fibre ends permanently fixed into SMA fibre connectors using adhesive are known to fail at lower damage thresholds than free-standing fibre ends.

The fibres and their common cladding are assembled, ground flat, and polished. Both the fibres and their common cladding are then annealed by CO2 laser pulses of 10/zs duration to melt a very thin surface layer and thus remove surface cracks and scratches. This may increase their damage threshold to that of a polished fused-silica window, sometimes given as 10 GW/cm2.

However, for a pulse of 7.5 ns at a wavelength of 1.064μιη, the damage threshold for fused silica, either in bulk or both inside and on a properly polished window, is 475 GW /cm2. So that, as an alternative to annealing, both the fibres and their common cladding may be super polished to a surface roughness of less than lA as described in Sections lib and lie of a paper entitled “How to Polish Fused Silica to Obtain the Surface Damage Threshold Equals to the Bulk Damage Threshold” (T. Alley et al, Proc. of SPIE Vol. 7842, 784226, (2010)).

As the light entering each fibre has a uniform intensity across its end face, rather than a Gaussian profile, there is no reason to apply a safety factor for the latter profile.

Ultrarviolet light is unlikely to damage such fibres in the extremely short timescales required. And while ultra-violet light will accelerate a flyer plate at lower power levels, as mentioned in Section 6.2, light of higher wavelengths will do so at the expense of higher power levels.

The fibre-optic cables 58 are all of the same length, as aforesaid. So that, provided they are not affected differently in some way, such as excessive bending or significantly disparate temperatures, any pulse spreading will be the same for each of those cables, and the detonators will still be initiated simultaneously despite any pulse broadening as soon as they have received sufficient energy. Moreover, the various different types of dispersions have very little effect over such short fibre-optic cables.

Modal dispersion in a step-index fibre with a large number of modes is a fraction of the delay time approximately equal to:-

where NA is the Numerical Aperture of that fibre and ηχ is the refractive index of its core.

The Numerical Aperture of a typical High-Power-Density Fiber is 0.22, while the refractive index of pure silica is 1.46 at a wavelength of Ο.δμιη, giving that fraction as 0.0057 .

As the axis of each fibre-optic cable 58 is aligned with a defining ray, as stipulated in Section 6.1, the light entering each cable is substantially parallel to its axis. So that the actual aperture used is much smaller than the Numerical Aperture, and the delay time fraction is, in consequence, much lower.

Material dispersion is of the order of 0.004 ns / m. There may also be nonlinear dispersion (which can compensate material dispersion under certain conditions).

The area covered by the ends of that small number of fibres which corresponds to the number of different positions selected around the output aperture of the master starter must be approximately equal to that of a flyer plate, whose area must itself be greater than or equal to the minimum spot size necessary for detonation. Said number is preferably equal to the number of explosive lenses in the circular array of explosive lenses, as aforesaid.

The face of the truncated cone of fast explosive 594 must, of course, be larger than the flyer plate. The fibre-optic cables are assembled, and their ends are then ground and polished together to avoid any surface variation. The flyer plate is coated on the end of those fibre-optic cables together with their common cladding parallel to the surface of the high explosive. 6.3 Shock waves.

If the gas ahead of a plane shock wave is initially at rest, and a frame of reference moving with that shock wave is used, then the velocity of the gas in front of that shock wave into that shock wave may be denoted by u\ (which is equal to minus the velocity of that shock wave in the inertial frame of reference) while the velocity of the gas behind that shock wave out of that shock wave may be denoted by u^·

Similarly the speed of sound, density, pressure and enthalpy of a unit mass of the gas in front of that shock wave may be denoted by ai, pi, Pi and Hi respectively, while those quantities behind that shock wave may be denoted by 02, P2, P2 and #2 respectively.

If AE is the energy involved in the ionization and excitation of a monotomic gas plus that involved in the dissociation of a polyatomic gas then the equations for the conservation of mass, momentum and energy respectively may be written:- P1U1 = P2U2 (1)

Pi + Pl^l = P2 + P2^2 (2)

Hi + ±u2i=H2 + ±ul + AE (3)

It will be appreciated that AE is usually included in H2·

The adiabatic exponent, 7, is the ratio of the specific heat at constant pressure, cp, to the specific heat at constant volume, cy. Since the energy involved in the ionization and excitation of a monatomic gas and the dissociation of a polyatomic gas have already been accounted for by AE, the value of 7 in the plasma behind the shock wave will only be affected by changes in the number of particles in that plasma. As H2 f?i, the same value of 7 may be used for the gas ahead of the shock wave. For a gas having a constant specific heat ratio, 7:-

(4)

So that equation (3) may be written:-

(5) P2

Putting tti = —u2 in (2) gives:-Pi

Putting U2 = —ωχ in (2) gives:-P2

If AE — /#2 where 0 < / < 1:-

Multiplying both sides by pi/»2(7 — l)(p2 — Pi):- 2ρ2(Ρ2 - P\)lP\ ~ p\{7 - 1)(¾ - P2) = 2(1 + /)ρχ(ρ2 - PibPz + p\{l ~ 1)(-¾ - Pi) Pa ((7 - 1 ){pl ~ Pi) - 2(1 + f)pi(pi ~ Pi)l)) = Pi ((7 - 1)(P2 - Pi) ~ 2p2(p2 - Pi )7)

Eliminating P2 — pi:-

Pa ((7 - l)(pa + Pi) - 2(1 + /)pi7) = Pi ((7 - l)(pa + Pi) - 2p27)

Dividing both sides by pi :-

(6)

Combining equations (1) and (2) gives:-

The Mach number in the moving frame of reference of the gas in front of the shock wave may be denoted by Mi. It is given by:-

(7)

Solving equations (6) and (7) together and rejecting negative square roots gives:-

(8) (9)

If the temperatures of the gas in front of and behind the shock wave are denoted by Tj and T2 respectively, the two ideal gas relations give:-

When / = 0:-

When Mi 1:-

From equation (1):-

As the velocity of the gas in front of the shock wave in a stationary frame of reference is zero, the velocity of the gas behind the shock wave in that stationary frame of reference, and the change in the velocity of the gas across that shock wave, are both:-

The shock wave may be incident to a shock wave reflector perpendicular to its velocity, and be reflected as a planar reflected shock wave. Since the velocity of the gas behind the reflected shock wave in a stationary frame of reference is zero, the change in the velocity of the gas across the reflected shock wave is also equal to the velocity of the gas behind the shock wave in that stationary frame of reference.

If the Mach number in a frame of reference moving with the reflected shock wave is denoted by Mr and the further energy involved in the further ionization and excitation of the gas is denoted by AEr — frHr where Hr is the enthalpy of the gas behind the reflected shock wave and 0 < /# < 1, we may write this velocity as approximately:-

Hence

When Μχ 1 and Mr 1:-

The fraction of the atoms which are ionized, a, may be found from the temperature and pressure using Saha’s equation and the ionization potential for the gas together with the statistical weights of the particles taking part in the ionization reaction. The energy involved in the ionization may then be found and compared with AE. The entire procedure is repeated until correct choices of / and are found.

The detonation velocity of cyclotrimethylenetrinitramine (RDX) whose initial density is 1.77 gm/ cm3 is 8.64 km/s. The gas 54 is above its critical temperature (by definition of a gas). It is chosen to be xenon whose critical temperature is 289.75°K. The initial pressure, Pi, in that xenon gas is chosen to be 100 bars. 7% ^ 2

Now cp — cy — R, the gas constant, and cp — ——R where rif is the number £t of degrees of freedom per molecule, if the internal energy is partitioned equally amongst 71 ")" 2 those degrees of freedom. So that 7 = —-. For singly ionized xenon atoms and their ns 4 g electrons, rif = 6 giving 7 = -. The following calculations have been made with 7 = -. o 7

The shock wave has a pressure of 305.408 kbars, a density of 6.31944 gm / cm3 and a temperature of 76,320°K with / = 0.328 and the fraction of the xenon atoms which are ionized, a, at 0.873955 . It radiates as a blackbody giving an intensity of 192.383 MW / cm2.

The reflected shock wave has a pressure of 3.52426 Mbars, a density of 36.3641 gm / cm3 and a temperature of 153,050°K with /r = 0.1676 and the fraction of the xenon atoms which are ionized, ajj, at 0.894963 . It radiates as a blackbody giving an intensity of 3,111.3 MW/ cm2.

The speed of sound in the explosion products is some 0.77 of the detonation velocity, or 6.65 km/s. It exceeds the sound velocity in the reflected shock of some 3.52996 km/s. So that no further shock reflections are generated when the reflected shock wave collides with the explosion products.

Instead, the reflected wave is a rarefaction wave in which the pressure and temperature of the xenon fall. This may result in a population inversion between states of the ionized xenon atoms. The contact surface of the explosion products and the xenon is slowed, and may be reversed, by the collision.

The detonation velocity of octogen (HMX) whose initial density is 1.91 gm/cm3 is 9.38km/s. If the initial pressure in the xenon gas is 200bars, the shock wave has a pressure of 716.093 kbars, a density of 12.0099 gm / cm3 and a temperature of 94,160.6°K with / = 0.267 and the fraction of the xenon atoms which are ionized, a, at 0.876263 . It radiates as a blackbody giving an intensity of 445.741 MW/ cm2.

The reflected shock wave has a pressure of 7.85566 Mbars, a density of 65.7153gm/cm3 and a temperature of 188,780°K with fp — 0.1345 and the fraction of the xenon atoms which are ionized, or, at 0.885462 . It radiates as a blackbody giving an intensity of 7,201.56 MW/ cm2.

The sound velocity in the reflected shock wave is 3.9204 km / s.

The detonation velocity of octanitrocubane (ONC) whose initial density is 2.0gm/cm3 is 10.1 km/s. If the initial pressure in the xenon gas is 200 bars, the shock wave has a pressure of 827.798 kbars, a density of 11.6912 gm / cm3 and a temperature of 111,816°K with / = 0.236 and the fraction of the xenon atoms which are ionized, a, at 0.920723 . It radiates as a blackbody giving an intensity of 886.377 MW /cm2.

The reflected shock wave has a pressure of 8.84168 Mbars, a density of 62.2971 gm / cm3 and a temperature of 224,133°K with — 0.1177 and the fraction of the xenon atoms which are ionized, qa, at 0.920794 . It radiates as a blackbody giving an intensity of 14,309.7 MW/cm2.

The sound velocity in the reflected shock wave is 4.27175 km/ s. A typical target for inertial confinement fusion must be imploded in less than 30 ns. At the detonation velocity for RDX of 8.64km / s, a shock wave would only travel 0.2592mm in that time. So that the shock wave reflectors 60 and 61 respectively, shown in Figure 12, would have to be even closer to the explosive for any radiation from the reflected shock wave to become available. Moreover, only light from that annulus of the reflected shock wave adjacent to and inside the leading edge of the first stage defined mirror of one of the eye mirrors would easily enter the input aperture of that eye mirror.

Figure 6 is a schematic diagram showing a circular array 62 of axially symmetric explosive lenses 591, which are cut where they would overlap the explosive lenses on either of their sides to cover and seal the input aperture 64 of an eye mirror 8.

As shown, the axes of symmetry of the explosive lenses 591 lie on a cylindrical surface. If the leading edge of the first stage defining mirror 30 does not extend as far as the leading edge of the first stage defined mirror 31, the seal for the input aperture 64 will include at least the side plate 56. In an alternative embodiment, one edge of the circular array 62 of axially symmetric explosive lenses 591 is contiguous with the leading edge of the first stage defining mirror 30, while the other edge is contiguous with the leading edge of the first stage defined mirror 31, and the axes of symmetry of the explosive lenses 591 lie on a conical surface. Each of these embodiments, and any other variation thereof, will hereinafter be referred to as a circular array.

The focus 65 of each explosive lens 591 lies within many of the angular input apertures of that eye mirror. Upon detonation, the explosive lens 591 generates a shock wave converging on that focus, which may be a cumulative implosion.

Figure 6.15(c) at page 187 of “The Physics of Inertial Fusion” shows the density profile of a solution for such a cumulative implosion. The temperature becomes infinite upon convergence at the centre. Figure 6.17 at page 189 of that work shows Guderley’s imploding shock solution, which is not cumulative. The temperature is divergent at the centre. The insert to that figure shows the ratio of temperature to initial temperature, T/To, as a function of the ratio of radius to initial radius, t/tq, behind the reflected shock. It will be seen that the temperature has been increased asymptotically at lower radii. The increase in temperature due to the convergence of the shock wave is much greater than any loss in temperature due to radiation, which may therefore be neglected. But these types of self-similar solutions do not take account of energy loss from ionization.

As the total power of all wavelengths radiated per unit area rises with the fourth power of the temperature, while the surface area of the shock wave reduces merely with r2, the power radiated by the shock wave rapidly rises. A rapidly rising intensity on a target for inertial confinement fusion produces a sequence of shocks on it and compresses its cold fuel isentropically. This advantage is, however, considerably reduced if lower wavelengths are absorbed by the xenon gas.

As the eye mirror spreads the output from each shock wave around its exit aperture, and thus smooths that output, the intensity on the taxget for inertial confinement fusion will be sufficiently uniform.

Since the explosive lenses do not extend over an entire sphere, this arrangement requires less explosive.

If the converging shock wave is to reach its focus in time for the electromagnetic energy radiated at that focus to reach the taxget for inertial confinement fusion before the end of its implosion, the inner radius of the explosive lens, rjn, is constrained by:-

Tin (tdia "1“ timp)Vdet where tdia is the time between the initiation of the shock wave and the rupture of the diaphragm, timp is the implosion time of the taxget for inertial confinement fusion, and Vdet is the detonation velocity of the inner shell of explosive in the explosive lens.

There is no other constraint on the value of r»n. If Γ*η is smaller, the explosive lens will be thicker, and its mass larger. While its detonation velocity, Vdet·, may be increased by convergence.

The shock wave in a master starter may be either planar or converging. 6.4 Xenon absorption and emission.

The xenon gas 54 must allow light to pass through the apparatus for directing electromagnetic energy from an area or volume source in order for that light to be directed. It may, however, usefully protect the mirrors in that apparatus from the damaging effects of very low wavelengths.

The xenon gas ahead of the shock wave may be heated, excited and/or ionized by the radiation from that shock wave and reradiate either spontaneously or after stimulation.

Measurements of the photo-absorption coefficient of xenon gas at high pressures over the wavelength region 150 nm to 175 nm at pressures ranging up to 48 atm and temperatures between 298°K and 423°K were described in a paper entitled “Xenon photoabsorption in the vacuum ultraviolet” (Donald A. Emmons, Optics Communications, Vol. 11, no. 3, 257-260, July 1974).

The absorption coefficient of xenon, k, varies as the square of the atom density, n, as shown in Figure 1 of that paper; so that :-

where ko and n0 are the absorption coefficient and atom density respectively at 298°K and 1 atm pressure.

The absorption coefficient rises with temperature by a factor of 14 from 298°K to 423°K, as shown by Figure 1 of that paper.

The absorption coefficient rapidly decreases with longer wavelengths, before starting to level off near 163 nm, as shown by Figure 2 of that paper.

Similar temperature and wavelength relationships are evident when comparing a continuous-wave xenon arc-lamp with a much hotter pulsed xenon arc-lamp. The emission of a pulsed xenon arc-lamp, which is not optically thick, was described in a paper entitled “Xenon: The Full Spectrum vs. Deuterium Plus Tungsten” (Robert A. Capobianco, PerkinElmer). A pulsed xenon arc-lamp exhibits abundant atomic line structure from the far UV to the near IR. Figures 3 and 4 of that paper illustrate the difference between the emission of a pulsed and a continuous-wave xenon arc-lamp. These figures show that the emission of xenon rises rapidly with its temperature, particularly below 260 nm.

An investigation of the absorption spectrum of atomic xenon at very low pressure in the wavelength region 922-1296 A was reported in a paper entitled “Absorption spectrum of xenon in the vacuum-ultraviolet region” (K. Yoshino &amp; D.E. Freeman, J. Opt. Soc. Am. B/Vol. 2, No. 8/1268/August 1985). This wavelength region contains lines from all five Rydberg series of xenon.

An earlier investigation of the absorption spectrum of atomic xenon at very low pressure was reported in a paper entitled “The Absorption Spectra of Krypton and Xenon in the Wavelength Range 330-600 A” (K. Codling &amp; R.P. Madden, J. of Research of the National Bureau of Standards - A. Physics and Chemistry Vol. 76A, No. 1, 1-12, February 1972).

The spectrum of Xenon I from 3685.7 A to 15418.01 A is given in Table 7e-5 of the American Institute of Physics Handbook, Third Edition, 1982 Reissue.

According to another source, in the spectral region 460 to 1000 nm, there is low absorption in the range 670-690 nm, moderate absorption in the ranges 500-540 nm, 565-600 nm and 865-895 nm, high absorption in the ranges 730-760 nm and 790-820 nm, and also at 587 nm.

Since the frequency of a bound-bound absorption of a photon and that of a bound-bound emission of a photon are both dependent on the energy difference between two states of an electron in an atom, the existence of an absorption line at a particular frequency implies the existence of an emission line at that frequency, and vice versa.

The absorption of a photon may be followed by the re-emission of a photon of the same frequency in a random direction a fraction of a second later. But this second photon is likely to undergo further absorption, which may cause an electron to be ejected from an atom or ion, and this is unlikely to result in the emission of a photon of the original frequency.

Hence energy is extracted at a discrete frequency and deposited into a continuous distribution, or continuum. Thus a dark line is formed in the continuous background.

The presence of free electrons from the ionization of xenon in the shock wave may allow the formation of excited dimers, or excimers, as follows:-

Xe + e —* Xe* + e Xe* + Xe + Xe -c Xe*2 + Xe where the extra xenon atom is necessary to carry away the excess energy. High pressure increases the concentration of atoms and thus the probability of such a three body collision.

The xenon excimer returns to its ground state within 10 ns radiating spontaneously at 172 or 175 nm:-

Xe^ —^ Xe + Xe + hu

There is, however, insufficient path length for stimulated emission, despite the high gain of excimers, except perhaps behind the reflected shock, where the gas is at rest.

The conditions in which the thresholds for laser induced plasma formation and subsequent breakdown in a gas are generally measured are very different from those envisaged in the master starter and starter. There is a focal volume for the laser beam from which electrons may diffuse. The repetition rate of the laser is often 10 Hz so that each of its pulses may leave free electrons to seed an electron avalanche. And aerosols, hydrocarbons and material ablated from the quartz cell used to contain the gas are not removed from that cell and may be thermally ionized.

In contrast, both the master starter and the starter are intended to be used only once. And the output beam within an eye mirror is a nearly cylindrical annulus from which little electron diffusion may take place. The xenon is exposed to broadband temporally incoherent electromagnetic radiation, rather than monochrome coherent radiation. In the starter, and optionally in the master starter, this radiation has a rapidly rising intensity (which is unquantifiable, for reasons given in Sections 6.3 and 6.7). The master starter has a shorter pulse length, and can be designed to avoid breakdown of the xenon. The starter has a longer pulse, which rises to such a high intensity that breakdown is inevitable. A paper entitled “Experimental Investigation of 193 nm Laser Breakdown in Air” (M. Thiyagarajan h J. Scharer, 2008 IEEE Plasma Sciences Special Issue on Pulsed Power) reported that a significant fraction of the intensity of a laser beam can be transmitted even for very high intensities which have produced a plasma in the focal region. An ArF excimer laser with a wavelength of 193 nm and a pulse length of 20 ns was focussed on clean dry air at a pressure of 5 atm to give a peak incidence of 750 GW/ cm2, and 44% of the incident energy was transmitted through the resulting plasma. Multiphoton ionization was only responsible for 6% of the ionization. As multiphoton ionization was responsible for 24% of the ionization at a pressure of 1 atm, it is unlikely that it will be significant at pressures of 100 atm and above. So that breakdown at such pressures will be caused entirely by collisional cascade ionization and at a threshold value which is generally higher. 6.5 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 Xl — 0.35/xm at normal incidence, the admissable intensity to avoid excessive laser plasma instabilities is close to II « 1015 W/ cm2, where II is the intensity due to that laser. These figures give a typical radial implosion velocity of 3.5 x 107cm/s, which is sufficient for the hot-spot ignition of a spherical target comprising an outer shell of ablative material surrounding an inner shell of solid or liquid Deuterium-Tritium (DT) fuel at a cryogenic temperature, that is filled with DT gas. The threshold for the onset of such instabilities in a uniform plasma is IlX\ < 1015 (W/cm2) μιη2. 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:-

for both normal and grazing incidence.

Hence doubling the implosion velocity for the hot-spot ignition of fuels other than DT requires an increase in /χ/λχ by a factor of about 180. This may be achieved in principle if λχ = 0.2μπι and 7χ — 1017 W / cm2. The corresponding value of the expression /χλ2 = 4 x 1015 (W/ cm2) μιη2 is above the threshold for the onset of laser plasma instabilities, but considerably less than the threshold of 1.37 x 1018 (W / cm2) μιη2 beyond which relativistic effects occur. So that the latter threshold does not limit 1χ. But the absorption coefficient for a laser would be reduced by a factor of up to 7 at II — 1017 W/cm2 necessitating a further and counterproductive increase in Τχ/λχ. 6.6 Comparison between lasers and eye mirrors. 6.6.1 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 hohlraum.

The principal instabilities are Stimulated Brillouin Scattering (SBS), Stimulated Raman Scattering (SRS), and filamentation. SRS produces hot electrons, as does resonance absorption. 6.6.1.1 Stimulated Brillouin 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 (ISI), temporal smoothing by spectral dispersion (SSD), and random phase plates (RPP) have been used to reduce SBS. 6.6.1.2 Stimulated Raman Scattering. SRS 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 hohlraum are limited to short wavelengths to avoid SRS.

The hot electrons generated by SRS in the plasma ablated from the inner wall of the hohlraum by light with a wavelength of Ι.Οδμιη degraded the implosion of a target by preheating it. 6.6.1.3 Filamentation.

Filamentation 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. 6.6.1.4 Resonance absorption.

The angle of incidence of meridional rays on the limb of a spherical target may cause significant resonance absorption of p-polarized light. At the critical surface, a Langmuir 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. 6.6.2 Advantages of eye mirrors. 6.6.2.1 Absence of interference effects.

Section 6.19.2 of GB 2,305,516B 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 2,305,516B described how the output may be split into part waves. Section 6.19.4 of GB 2,305,516B 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 filamentation 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. This spread also smooths variations in the power and timing of the output of electromagnetic energy from individual explosive lenses (which affects the entire pulse therefrom).

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 spherical ablator. 6.6.2.2 Short wavelengths.

As mentioned in Section 6.19.7 of GB 2,305,516B, 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 0.12μιη at normal incidence, when coated with Magnesium Fluoride, and of 0.035/xm 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 maximises the absorption coefficient by enhancing collisional absorption in regions of higher plasma density. It further reduces any SRS.

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, λχ,. 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 its annular exit aperture, as explained in Section 6.10.2.1 . 6.6.2.3 Wide waveband.

It was pointed out in Section 6.19.8 of GB 2,305,516B that if the electromagnetic energy is distributed over a number of component wavelengths which cannot interact coherently, SRS 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, 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 processes.

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. 6.6.2.4 Resonance absorption.

At oblique angles of incidence in the density gradient of the plasma blowing off from that spherical 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 100 fs 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 reflectivities 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 electromagnetic energy in their output beams may be reduced by the choices of the surfaces of the eye mirrors. 6.7 Effect of radiation on an eye mirror.

The irradiation of a mirror initially gives rise to a thermal wave running into that mirror. This wave is then quickly overtaken by a shock wave in the material of that mirror, which has a rarefaction expansion wave of ablated plasma extending from its trailing edge, giving rise to an ablative heating wave.

At a pressure of 100 atm and a temperature of 100,000°K, each of the atoms of a gold plasma will have undergone 10 ionizations on average. The plasma frequency at the resulting electron density corresponds to a critical wavelength, Xcrit, much larger than the wavelengths radiated by the shock wave in the xenon gas. The plasma is transparent for wavelengths below that critical wavelength. It follows that most of the energy radiated by that shock wave reaches the solid surface of the mirror despite the ablation from that surface.

It was shown in Section 6.18.5 of GB 2,305,516 B that “any error in the path of a ray due to any error in either of the mirrors of a stage other than the final stage in a series of stages is of no consequence if, at the point at which said ray is incident to the defined mirror of the succeeding stage, said ray lies within the cone of well directed rays which are incident at said point. Thus the tolerances for such mirrors are high.”

This section also pointed out that “in so far as the rays” in a set of rays rotated by an angular error in the surface of a defined mirror “remain within the circular cone” for well directed rays “they merely replace” those rays and “axe well directed by the defined mirror of that stage as before” and that “an angular error in the surface of a defined mirror which is small in relation to the angular input aperture at the point on that defined mirror at which said angular error occurs has little effect on the direction of the output beam as a whole.”

Section 6.18.6 of that patent further pointed out that “as the tolerances for the size and shape of any mirror other than that of a final stage in any series of stages are high, the surfaces of such mirrors may be sacrificial, or consist of a liquid which is sacrificial.”

The loaded areas of the defining and defined mirrors of any stage axe larger than those of the respective mirrors of the preceding stage. And the angles of incidence of the rays on the mirrors of any stage are larger than those on the respective mirrors of the preceding stage. So that the mirrors of any stage are loaded less than the respective mirrors of the preceding stage.

As plasma is ablated from the surface of a mirror, that surface may not only become less reflective, but may also become uneven or irregular in shape. However, such irregularities in the mirrors of stages other than the final stage in a series of stages will not degrade the performance of an eye mirror significantly, as aforesaid. And some irregularity may be tolerated in the defined mirror of a final stage. Reflection from the plasma will generally be non-specular. But some of that non-specular reflection will consist of well directed rays. Thus the effect of ablation will be to degrade the performance of an eye mirror gradually, rather than catastrophically.

Table 1

Time (ns) ma (gm cm-2 s_1) Ablation thickness (/xm) 1 3538.02 0.00183317 2 2975.11 0.00337468 3 2688.31 0.00476758 4 2501.76 0.00606383 5 2366.01 0.00728974 6 2260.59 0.00846104 7 2175.13 0.00958805 8 2103.72 0.0106781 9 2042.68 0.0117364 10 1989.57 0.0127673 11 1942.73 0.0137739 12 1900.92 0.0147588 13 1863.26 0.0157243 14 1829.06 0.016672 15 1797.78 0.0176034 16 1769.01 0.018520 17 1742.40 0.0194228 18 1717.68 0.0203128 19 1694.62 0.0211909 20 1673.03 0.0220577 21 1652.74 0.0229141 22 1633.63 0.0237605 23 1615.58 0.0245976 24 1598.48 0.0254258 25 1582.25 0.0262456 26 1566.81 0.0270574 27 1522.10 0.0278616 28 1538.05 0.0286586 50 1330.51 0.0448124 75 1202.25 0.0611131 100 1118.82 0.0760921 125 1058.11 0.0901574 150 1010.97 0.103534 175 972.748 0.116364 200 940.811 0.128744 225 913.512 0.140742 250 889.764 0.152412 275 868.814 0.163794

The intensity of radiation from the shock wave reported in Section 6.3 at those wavelengths emitted by a blackbody at a temperature of 75,947°K for which the xenon gas is transparent results in ablation of a gold surface at the ablation rates, ma, given as a function of time in Table 1 above, together with the cumulative ablation thickness. It will be seen that the cumulative ablation thickness after 28 ns is still only a fraction of the lowest of those wavelengths. Clearly any irregularity in the shape of a first stage defined mirror could only be a fraction of that thickness anyway. And even after 275 ns, the cumulative ablation thickness is less than the lowest of those wavelengths.

At a pressure of 200 atm and a temperature of 110,000°K, each of the atoms of a gold plasma will have undergone 11 ionizations on average.

The intensity of radiation from the shock wave reported in Section 6.3 at those wavelengths emitted by a blackbody at a temperature of 110,693°K for which the xenon gas is transparent results in ablation of a gold surface at the ablation rates, ma, given as a function of time in Table 2 below, together with the cumulative ablation thickness. It will be seen that the cumulative ablation thickness after 28 ns is still only a fraction of the lowest of those wavelengths. Clearly any irregularity in the shape of a first stage defined mirror could only be a fraction of that thickness anyway. And even after 275 ns, the cumulative ablation thickness is only slightly more than the lowest of those wavelengths.

Table 2

Time (ns) ma (gm cm-2 s_1) Ablation thickness (μιη) 1 4496.77 0.00232993 2 3781.32 0.00428917 3 3416.81 0.00605953 4 3179.70 0.0770704 5 3007.17 0.00926516 6 2873.18 0.0107539 7 2764.56 0.0121863 8 2673.80 0.0135717 9 2596.21 0.0149168 10 2528.72 0.0162271 11 2469.18 0.0175064 12 2416.05 0.0187583 13 2368.18 0.0199853 14 2324.71 0.0211898 15 2284.96 0.0223737 16 2248.39 0.0235387 17 2214.57 0.0246861 18 2183.15 0.0258173 19 2153.83 0.0269333 20 2126.39 0.028035 21 2100.61 0.0291234 22 2076.32 0.0301993 23 2053.38 0.0312632 24 2031.65 0.0323159 25 2011.02 0.0333578 26 1991.40 0.0343896 27 1972.69 0.0354118 28 1954.84 0.0364246 50 1691.06 0.0569559 75 1528.04 0.077674 100 1422.00 0.096712 125 1344.85 0.114589 150 1284.93 0.131591 175 1236.35 0.147898 200 1195.76 0.163632 225 1161.06 0.178882 250 1130.88 0.193714 275 1104.25 0.20818

It should be noted that the gold plasma never reaches the critical density for any portion of the relevant waveband, so that an ablative heating wave without critical surfaces develops, rather than an ablative heat wave with critical surfaces.

It is clear that the surface of a mirror will not become too irregular due to constant illumination even after a considerable time, therebye enabling the implosion to take place over a longer period. For the required implosion velocity, the acceleration would be slower, the distance travelled larger and the radius of the shell of cold fuel correspondingly higher. But, for a given mass of cold fuel, the aspect ratio would therefore also be higher.

It will be appreciated that it is very difficult to predict the effect on the mirrors of radiation from the converging shocks detailed in Section 6.3 . Firstly, they are local and vary in time. Secondly, each converging shock only exists over part of a sphere, and will spread from its edge as its implosion proceeds at some fraction of the speed of sound at the temperature of that shock, which speed is initially much lower than the velocity of that shock. Moreover, a bridge of hot gas from such outflows will form between adjacent shocks. So that each shock wave is non-stationary, non-uniform and aspheric. Furthermore, as the radiation rises, an ablative heat wave with critical surfaces may replace the ablative heating wave without critical surfaces over hot spots on the mirrors.

As the temperature of such a converging shock will not therefore be uniform across its surface, the illumination across the surface of the corresponding first stage defined mirror will also vary.

At a pressure of 200 atm and a temperature of 180,000°K, each of the atoms of a gold plasma will have undergone 18 ionizations on average.

Table 3

Time (ns) iha (gm cm-2 s_1) Ablation thickness (μιη)

Ionization 10 18 10 18 1 5982.12 3136.1 0.00309955 0.00162492 2 5030.35 2637.14 0.00570594 0.00299132 3 4545.43 2382.92 0.00806109 0.00422599 4 4230.00 2217.56 0.0102528 0.00537499 5 4000.49 2097.24 0.0123256 0.00646164 6 3822.24 2003.79 0.014306 0.00749988 7 3677.74 1928.04 0.0162116 0.00849886 8 3556.99 1864.74 0.0180546 0.00946505 9 3453.78 1810.63 0.0198441 0.0104032 10 3363.99 1763.56 0.0215871 0.011317 11 3284.79 1722.04 0.0232891 0.0122092 12 3214.10 1684.98 0.0249544 0.0130832 13 3150.43 1651.6 0.0265868 0.013938 14 3092.60 1621.28 0.0281891 0.014778 15 3039.71 1593.56 0.0297641 0.0156037 16 2991.06 1568.05 0.0313139 0.0164162 17 2946.07 1544.47 0.0328404 0.0172164 18 2904.27 1522.55 0.0343452 0.0180053 19 2865.28 1502.11 0.0358298 0.0187836 20 2828.77 1482.97 0.0372954 0.019552 21 2794.48 1464.99 0.0387434 0.0203111 22 2762.17 1448.05 0.0401745 0.0210613 23 2731.64 1432.05 0.0415899 0.0218033 24 2702.73 1416.9 0.0429903 0.0225375 25 2675.29 1402.51 0.0443764 0.0232642 26 2649.18 1388.82 0.0457491 0.0239838 27 2624.31 1375.78 0.0471088 0.0246966 28 2600.55 1363.33 0.0484562 0.025403 50 2249.64 1179.36 0.0757693 0.0397217 75 2032.78 1065.68 0.103331 0.0541708 100 1891.71 991.723 0.128657 0.0674481 125 1789.07 937.914 0.152439 0.0799157 150 1709.36 896.123 0.175057 0.0917731 175 1644.73 862.246 0.19675 0.103146 200 1590.73 833.937 0.217682 0.114119 225 1544.58 809.739 0.237969 0.124754 250 1504.42 788.689 0.2577 0.135098 275 1469.00 770.118 0.276945 0.145187

The intensity of radiation from a shock wave at those wavelengths emitted by a black-body at a temperature of 180,000° K for which the xenon gas is transparent results in ablation of a gold surface whose plasma is ionized 10 or 18 times at the ablation rates, ma, given as a function of time in Table 3 above, together with the cumulative ablation thickness. It will be seen that higher ionization results in lower ablation and that the cumulative ablation thickness after 28 ns is still only a fraction of the lowest of those wavelengths. Clearly any irregularity in the shape of a first stage defined mirror could only be a fraction of that thickness anyway. And even after 275 ns, the cumulative ablation thickness for 10 ionizations is not much more than the lowest of those wavelengths, while for 18 ionizations it is less than the lowest of those wavelengths.

At a pressure of 200 atm and a temperature of 180,000°K, each of the atoms of a rhodium plasma will have undergone 10 ionizations on average.

The intensity of radiation from a shock wave at those wavelengths emitted by a black-body at a temperature of 180,000°K for which the xenon gas is transparent results in ablation of a rhodium surface at the ablation rates, tha, given as a function of time in Table 4 below, together with the cumulative ablation thickness. It will be seen that the cumulative ablation thickness after 28 ns is still only a fraction of the lowest of those wavelengths. Clearly any irregularity in the shape of a first stage defined mirror could only be a fraction of that thickness anyway. And even after 275 ns, the cumulative ablation thickness is not much more than the lowest of those wavelengths.

Table 4

Time (ns) ma (gm cm-2 s-1) Ablation thickness (μιη) 1 3197.77 0.00257884 2 2688.99 0.00474738 3 2429.78 0.00670688 4 2261.16 0.00853040 5 2138.48 0.010255 6 2043.19 0.0119027 7 1965.95 0.0134882 8 1901.40 0.0150215 9 1846.23 0.0165104 10 1798.24 0.0179606 11 1755.89 0.0193767 12 1718.11 0.0207622 13 1684.07 0.0221204 14 1653.16 0.0234536 15 1624.89 0.024764 16 1598.88 0.0260534 17 1574.83 0.0273234 18 1552.49 0.0285754 19 1531.65 0.0298106 20 1512.13 0.0310301 21 1493.80 0.0322347 22 1476.53 0.0334255 23 1460.21 0.0346031 24 1444.75 0.0357682 25 1430.08 0.0369215 26 1416.13 0.0380635 27 1402.83 0.0391949 28 1390.14 0.0403159 50 1202.55 0.0630406 75 1086.63 0.085972 100 1011.22 0.107044 125 956.355 0.126831 150 913.74 0.145649 175 879.199 0.163698 200 850.333 0.181113 225 825.660 0.197992 250 804.196 0.234409 275 785.260 0.23042 6.8 Diaphragms.

If the pressure is P in a diaphragm of cylindrical section with radius a, thickness t and tensile strength T extending from # to π — #, then the condition for equilibrium is 2Pa cos Θ — 2Tt cos #, or Pa = Tt. So that the thickness required is independent of #. If the width spanned by the diaphragm is a constant, 2k, then a cos# = k. The volume of the diaphragm is:-

P k2P (π — 29)at = (π — 20) α2— — (π — 2Θ) sec2 #—— so that the volume of the diaphragm increases with #. The areal density at φ > # is 7Γ approximately tesc#, whose minimum is t occurring at φ — —. It should be noted that

A 7Γ a rupture at φ = — allows any part of the diaphragm remaining to be pushed out of the

Zt beam by the pressure of the xenon gas.

The diaphragms 55 consist of biaxiallv-oriented polyethylene terephthalate, metallized on the low pressure or vacuum side by vapour deposition of a thin film of evaporated aluminium, to make them less permeable to xenon.

As biaxially-oriented polyethylene terephthalate may be transparent, carbon particles are embedded in it to absorb electromagnetic energy, and minimise the time taken to flash pyrolyze the diaphragms. As this material becomes brittle and shatters at 235° C, the diaphragms may disintegrate before pyrolysis. In any event, their material is purged by the outflow of xenon gas 54 into a vacuum chamber, such as the hohlraum 120 shown in Figure 12. Any variation in the time at which a diaphragm ruptures only affects the time at which the beam from its respective eye mirror becomes available, and thus merely the initial part of a pulse of electromagnetic energy, which may be much less powerful than the later part of that pulse.

The time taken to rupture, and remove the residue of, the diaphragms, and thus make those beams available, must be added to the implosion time of a spherical target for inertial confinement fusion when calculating the distance travelled by the shock waves for the purpose of choosing the size of the explosive lenses.

Biaxially-oriented polyethylene terephthalate films may be much thinner than 254 μιη, which thickness would suffice to contain xenon at 100 bar in a cylinder or toroid of cross-sectional radius 2.54 mm. Double that thickness is necessary to contain xenon at 200 bar similarly. Films of 500//m are available.

Since each diaphragm will consist of a single sheet of material, which will be flat until xenon at high pressure gives it a circular section, it is desirable that its properties be made the same in the longitudinal (or machine) and transverse directions, so that its curvature is consistent around the exit aperture of its respective eye mirror. 6.9 Spherically symmetric illumination.

Figure 7 is a schematic diagram in the form of a section through the axis of symmetry 18 of an eye mirror 8. This axis of symmetry passes through the centre 70 of a spherical target 71. An enlarged schematic of that part of a final stage defining mirror 73 of that eye mirror, which actually lies in the upper half of that section and far to the left, is shown above those items, together with short lengths from its defining rays 81 to 100 respectively.

The innermost defining ray 81 meets the axis of symmetry 18 at its intersection 74 with the spherical target 71. The outermost defining ray 100 is tangent to the spherical target 71 at the point 75.

Each eye mirror not only smooths that power at its output aperture, coming from the explosive lenses in adjacent portions of its input aperture, but also their detonation jitter, rather as with the master starter without its fibre-optic cables 58 which make it possible to deliver power coming from the entire input aperture.

The intensity of electromagnetic energy on the final stage defining mirror 73 is a matter of choice, and may be uniform. The defining rays 82 to 99 respectively are chosen to make the intensity on the approximately hemispheric surface of the spherical target inside the circle generated by the rotation of the tangent point 75 around the axis of symmetry 18 uniform as their number becomes infinite.

Clearly a pair of identical diametrically opposed such eye mirrors, at equal distances from the centre of a sphere, will illuminate that sphere with spherical symmetry, except where their beams overlap, when provided with identical sources of electromagnetic energy of the chosen type.

As the spherical target implodes and reduces in size, some of the well-directed rays on the outside of a beam from a single eye mirror miss that target. This reduces the total illumination on that hemisphere. Moreover, rays further inside the beam and responsible for uniform illumination may be refracted by plasma emitted from the surface of the target away from the surface of the target, which will affect both the uniformity and amount of illumination. The angle of incidence of those rays on the target would, of course, change in the absence of refraction, as that target reduces in size, and affect the uniformity of illumination.

Figure 8 is similar to Figure 7, but shows an alternative choice for some of the defining rays. A spherical target 71 has been partially imploded to become the partially imploded spherical target 72 and is surrounded by plasma 76 whose density decreases with its radius from the centre 70. The spherical target 71 has been replaced as the target for the defining rays by a cut-off sphere 77 at which the critical density of that plasma, above which electromagnetic energy of a particular wavelength cannot propagate, occurs. The innermost defining ray 81 meets the axis of symmetry 18 at its intersection 78 with the cut-off sphere 77. The defining ray 98 is refracted by the plasma 76, but still reaches a tangent point 79. The outermost defining ray 100 misses the cut-off sphere 77. The original position of the spherical target 71 is shown for comparison.

The defining rays 82 to 97 respectively Eire chosen to make the intensity on the approximately hemispheric surface of the cut-off sphere 77 inside the circle generated by the rotation of the tangent point 79 around the axis of symmetry 18 uniform, taking into account the refraction of those defining rays, as their number becomes infinite.

However, as the target implodes further, both the uniformity and amount of illumination will be affected, as the cut-off sphere 77 will reduce in size and the region in which the defining rays are refracted will move inwards towards the axis of symmetry 18.

As the target in Figure 7, or the cut-off sphere in Figure 8, implodes and reduces in size, some of the well-directed rays on the inside of the beam from a single eye mirror cross over the axis of symmetry 18 and illuminate an area of the target 71, or the cut-off sphere 77, already illuminated by other rays, therebye creating an undesirable hot-spot.

Defining rays on the inside of a beam are therefore chosen to intersect the axis of symmetry 18 at or near its intersection 78 with the cut-off sphere 77, at which the critical density for the lowest wavelength in that beam, occurs. This, of course, results in an undesirable cold-spot at higher radii than that of the intersection 78.

Each vertex of a regular icosahedron has another such vertex diametrically opposed to it. A regular icosahedron has 12 vertices, 20 faces and 30 edges.

Each vertex of a geodesated regular tesselation of order m of a regular icosahedron has another such vertex diametrically opposed to it. Such a geodesation has 12 vertices, 3(m — 1) new vertices on those edges, and one or more new vertices on those faces if m > 2. If m = 3 there is one new vertex per face, while if m — 4 there are three new vertices per face.

All these new vertices are triangulated to give m2 new triangles. If m = 2, the inner triangle is equilateral while the three outer triangles are isosceles triangles.

The axes of symmetry of the eye mirrors for both the original and the new vertices lie on the respective lines joining each of those vertices to the common centre of the target, the regular icosahedron, and the imaginary sphere circumscribing it.

The axes of symmetry of the eye mirrors for the triangles forming the faces lie on the respective lines joining the incentre of each of those triangles to that common centre. The incentre of a triangle lies at the centroid g of its vertices a, b, c with associated numbers o, b, c equal to the length of the side opposite each of those vertices:-

If the triangle is equilateral, a — b — c and this reduces to the centroid of its vertices:-

Figure 10 is derived from a geodesated regular tesselation of order 2 of a regular icosahedron and shows a spherical array of eye mirrors representated schematically by a circle corresponding to the trailing edge of each of their final stage defining mirrors. These circles are all equidistant from the common centre of the target and the icosahedron.

The 20 inscribed circles 101 for the equilateral triangles, each of which is similar to the equilateral triangle 600 in Figure 4, have the largest common radius. The 12 circles 103 for the vertices of the icosahedron shown in Figure 4, which must clear those for the isosceles triangles, each of which is similar to any of the isosceles triangles 601, 602 or 603 respectively in Figure 4, have the smallest common radius. The common radius for the 60 inscribed circles 105 for the isosceles triangles and that for the 30 circles 107 for the new vertices geodesated from the midpoints of the sides, which nearly touch those for the equilateral triangles, are not only intermediate between the largest and smallest common radii, but nearly equal.

Figure 11 is similar to Figure 10 but is derived from a geodesated regular tesselation of order 3 of a regular icosahedron, which has 180 faces comprising two sizes of isosceles triangle.

The 120 inscribed circles 111 for the largest isosceles triangles have the largest common radius. The 60 circles 113 for the new vertices geodesated from the intermediate points of the sides together with the 20 circles 115 for the new vertices geodesated from the centre of the face of the regular icosahedron, which must all clear those for the largest isosceles triangles, have the next highest common radius. The 60 inscribed circles 117 for the smallest isosceles triangles have the next largest common radius. The 12 circles 119 for the vertices of the icosahedron shown in Figure 4, which must clear those for the smallest isosceles triangles, have the smallest common radius.

If the outermost defining rays of each beam are tangent to the spherical target 71 before it has started to implode (without crossing the axis of symmetry 18 of their respective eye mirror) as in Figure 7, while the innermost defining rays of each beam meet that axis of symmetry at its intersection with that cut-off sphere, at which the critical density for the lowest wavelength in that beam occurs at the end of the implosion, as in Figure 8, then the remaining defining rays for each eye mirror may be chosen to illuminate a hemisphere of the target and then the cut-off sphere throughout the target’s implosion with near spherical symmetry except for a small cold spot on that axis of symmetry which reduces to zero at the end of the implosion.

If there are n pairs of identical eye mirrors equidistant from the centre 70 of the spherical target 71 with n different respective axes of symmetry, then each cold spot is overlaid by η — 1 uniform illuminations, and the initial hole-to-uniform deviation in illumination is 100/n%.

There are 122 eye mirrors for an order 2 regular tesselation in four different sizes giving 61 pairs, so that the initial hole-to-uniform deviation in illumination is of the order of 1.64%. There are 272 eye mirrors for an order 3 regular tesselation in four different sizes giving 136 pairs, so that the initial hole-to-uniform deviation in illumination is of the order of 0.74%.

For ignition of a typical target, two-dimensional simulations with a stationary deviation from sphericity show that a peak-to-valley deviation in illumination no larger than 0.7% is required.

The intersection of the cone, generated by the rotation of a defining ray about the axis of symmetry 18, with a sphere is a circle. As such a sphere reduces in size, the radius of such a circle for a defining ray near the inside of a beam reduces proportionaly much faster than the radius of such a circle for a defining ray near the outside of a beam. Moreover, the angle of incidence of the latter defining ray on the cut-off sphere increases significantly, spreading the energy near the limb over a larger area, and offsetting the reduction in radius. So that the variation in intensity as the cut-off sphere reduces in size is much higher near the axis of symmetry. The increase in intensity just outside the cold spot may compensate for the lack of intensity within it.

Such cold spots at their largest correspond to Legendre modes, Z, between 40 and 60. It is expected that ablation pressure non-uniformities for modes with l > 16 will be smoothed out by plasma transport processes.

The order of tesselation, m, may be higher than 3. Moreover, each eye mirror may be provided with one or more final stages in parallel, or have eye mirrors in parallel inside it. All these modifications reduce the initial extent of the cold spots, and average jitter.

The defining rays for each type of eye mirror may be chosen differently, for instance, to make the intensity they produce on a sphere of different radius uniform. Indeed, each pair of diametrically opposed identical eye mirrors may have its own unique choice of defining rays. Equally, the thickness of the diaphragms for any pair of eye mirrors or final stages may be varied.

If the defining ray on the outside of a beam is tangent after refraction to the outside of that cut-off sphere at which the critical density for the lowest wavelength in that beam occurs at the end of the implosion, all the energy in that beam reaches the target. Figure 9 shows such a cut-off sphere 77 together with the axis of symmetry 18, the original position of the spherical target 71, its centre 70, the imploded spherical target 72, the plasma 76, and the defining rays 81 to 100 respectively. The innermost defining ray 81 intersects the axis of symmetry 18 at its intersection 78 with that cut-off sphere. The enlarged schematic shown in Figure 7 is also included.

The outermost defining ray 100 in Figure 9 is tangent to the cut-off sphere 77 at which the critical density for the lowest wavelength in the beam occurs at the end of the implosion at the point 80. The remaining defining rays 82 to 99 respectively are chosen to make the intensity on the approximately hemispheric surface of the cut-off sphere inside the circle generated by the rotation of the point 80 around the axis of symmetry 18 uniform as their number becomes infinite. If this choice of defining rays is made for all the eye mirrors, the peaJk-to-valley deviation is 1.9% while the root mean square deviation is 0.98% when m — 3.

In this case, the limb of the target is not illuminated by the beam. It can be shown that this has neglible effect on the symmetry of the implosion for Legendre modes, l < 9. Moreover, the effect rapidly reduces as the target implodes for modes with 9 < l < 16. And one or more of the different types of eye mirror may be used to reduce that effect, at the expense of some wasted energy, by symmetrically illuminating the target or cut-off sphere at some point during its implosion.

The total area of the explosive lenses in a circular array of explosive lenses needed to cover the input aperture 64 does not vary significantly as the order of tesselation, and with it the number of eye mirrors, is increased. But the individual explosive lenses 591 become smaller, so that their total volume, and therefore their total mass, decrease despite their greater number. Moreover, their inner radius, Γϊ„, and thus the corresponding implosion time, timp, reduce. In addition, the greater number of explosive lenses improves the averaging of variations in their power output and the timing thereof. However, detonation will only propagate if the charge diameter around the detonator is greater than or equal to the thickness of the reaction zone, which is 2 mm for RDX. But there is no direct relation betweeen Γ{η and either that charge diameter or a minimum size for the explosive lenses.

It is also possible to provide more than one circular array of smaller explosive lenses, in a concentric arrangement, in order to cover the input aperture 64 of an eye mirror. But it is preferable to increase the number of eye mirrors, and thus improve the uniformity of the illumination of the spherical target 71 for inertial confinement fusion. This allows that spherical target to have a larger in-flight aspect ratio, and a correspondingly longer implosion time, over which it will receive more electromagnetic energy. Moreover, the longer implosion time allows the explosive lenses to be slightly larger, as may be convenient. It should be noted that the type of explosive lens in one such concentric circular array may be different from the type of explosive lens in another such circular array. This allows the profile of the pulse of electromagnetic energy from the eye mirror to be varied.

Converging shock waves may be provided by a spherical array of explosive lenses, as well as by a circular array of explosive lenses covering the input aperture of an eye mirror, as eye mirrors may equally have a source of electromagnetic energy on their axis of symmetry. In such a case, the axis of symmetry of each eye mirror is aligned with the axis of symmetry of a respective explosive lens. 6.10 Target for inertial confinement fusion.

The intensities on the critical surfaces are increased not only by the enhanced electromagnetic radiation, due to the higher temperatures generated as the shock waves converge and any shock wave is reflected, but also by the reduction in the radii of those critical surfaces, as the target implodes. Moreover, lower wavelengths will be emitted as those shock waves converge and rise in temperature, further reducing the radii of those critical surfaces. This provides the rapidly rising intensity, which produces a sequence of shocks, and compresses the cold fuel isentropically. A paper entitled “High-gain direct-drive target design for laser fusion” (S.E. Bodner et al, Phys. of Plasmas, Vol. 7, No. 6, June 2000, 2298) described a target for inertial confinement fusion in which a spherical shell of solid DT fuel is surrounded by an ablator of CH foam filled with frozen DT. The ablator is surrounded by a thin plastic shell to confine the DT, and then by a thinner high-Z overcoating, such as gold. The spherical shell is filled with DT gas. Such a target has to be kept at a cryogenic temperature and be surrounded by a vacuum to allow the electromagnetic energy to reach it.

This type of target was intended to be irradiated by a KrF excimer laser with a wavelength, Xl, of 0.248 μπι for 27.5 ns and a power rapidly rising to some 300 TW, as shown in Figure 1 (b) of that paper. During the first 10 ns of that pulse, with the laser power at some 1.5 TW, the gold overcoat would be heated to about 70 eV, producing broadband x-rays to preheat the ablator, but not the spherical shell of solid DT fuel, reducing its density and thus increasing its mass ablation velocity. This velocity flow would then convect Rayleigh-Taylor fluid instabilities away from the ablation surface, which should allow the target to have a higher in-flight aspect ratio. Moreover, the very uniform illumination produced by, and the absence of interference effects for, an eye mirror, mentioned in Section 6.6.2, together with the spherically symmetric illumination from a spherical array of eye mirrors, allow the target to have a higher in-flight aspect ratio than with a laser. So that the target can be larger and have a longer implosion time.

This paper also envisaged “zooming” the spot from the laser inwards to follow the target as it imploded and thus avoid energy missing the target. This reduced the laser energy requirement from 2.1 MJ to 1.3 MJ, and illustrates the advantage of the arrangement described in the previous section.

The predicted gain was 127, and the predicted yield was 160 MJ. As the gain scales with λ-0-7, a higher yield could be obtained with radiation of lower wavelengths. For a wavelength of 0.17/im, the yield would be 208 MJ. This, however, is obtained at the expense of a small increase in the in-flight aspect ratio, which scales with λ4/15.

In an embodiment with a circular array of explosive lenses for each eye mirror, the mass of the explosive is much smaller than the explosive equivalent of this yield. But the mass of the structure required to contain the high pressure xenon gas, even in that embodiment, is larger, unless made from materials with a very high specific strength like carbon fibre. So that such materials may be necessary to reach the ideal temperature of 1 eV for a source of electromagnetic energy for starting a burn.

The main effect of such a device would be neutron radiation, which would be lethal outside the main area of blast effects.

However, in order to provide an implosion time of 27.5 ns, the explosive lenses would have to be inconveniently small. A paper entitled “Shock ignition of thermonuclear fuel: principles and modelling” (S. Atzeni et al, Nucl. Fusion 54 (2014) 054008) discusses target scaling models in Section 3.4 . For a scaling factor, s, the implosion time scales with s, the required power of illumination as s2 and the energy of illumination as s3. Equation (17) in Section 5.2 thereof implies that the gain scales as s0-81. Section 5.1.1 describes various studies of DT-wicked foam ablator targets, similar to that mentioned above.

So as to provide higher power without increasing the overall dimensions of the device excessively, each eye mirror may be provided with one or more eye mirrors in parallel to it. This will not affect the mass of the structure. The type of explosive lens in the circular array of explosive lenses for one such eye mirror may be different from the type of explosive lens in the circular array of explosive lenses in an eye mirror parallel to it. 6.11 Temperature control and support of spherical target.

Figure 12 is a schematic diagram in the form of a section through the axis of symmetry 18 of an eye mirror 8 showing part of the hohlraum 120 and a spherical target 121. If the radius of the hohlraum 120 is r/» and the radius of the spherical target 121 is rt then the ratio of their surface areas is r^/r2.

If the reflectivity coefficient of the hohlraum is r then the re-emission number, N, is r/( 1 — r).

The fraction of the power emitted by the hohlraum which reaches the spherical target is:-

Clearly this fraction is low when N is low, and thus when r is low, as for a blackbody.

Figure 12 also shows a hollow wall 123 containing liquid helium 122 at 4.2°K inside an innermost defined unit 124 but only supported by at least three thermally insulating supports 125 equally spaced around it and thus in the vacuum of the hohlraum. An even number of such supports are shown in Figure 12. The hollow wall 123 is connected by a highly conductive support wire 126 to a cold spot 127 on the spherical target 121 which is at 18.3°K. That end of this wire which is nearest to the spherical target has a taper 130 to avoid impeding the inside of the beam.

Figure 1 of a paper entitled “Cryogenic Material Properties Database” (E.D. Marquardt et al, NIST, Boulder, CO 80303, 11th International Cryocooler Conference, June 20-22, 2000 p.3) shows the thermal conductivity of oxygen free copper. This rises from 2000 W m-1 K-1 at 4.2°K and is above 5000 W m-1 K_1 from 11 to 20°K. The taper 130 may be subject to the latter temperature range, being nearest to the spherical target 121.

If the diameter of the support wire 126 is ΙΟΟμιη, its length is 1 metre and its thermal conductivity is taken to be 4000 W m-1 K-1 then the heat flow through that wire from the spherical target is 443.022^W. If there are 272 such wires then the heat flow through them is 120,501.984^W. If there are more but smaller eye mirrors and thus more wires then that heat flow is larger, but the angle of the taper 130 at the inner end of the wire must be reduced to avoid impeding the inside of the smaller beam.

The thermal conduction can also be improved by the use of wires of larger diameter with a longer taper 130. Moreover, it may be increased by moving each hollow wall 123 nearer the spherical target 121 so that its respective highly conductive support wire 126 may be shorter.

The rate of thermal conduction depends on the temperature excess of the spherical target over the liquid helium in the hollow wall. If the temperature of the spherical target rises, then the support wires conduct more heat out of that spherical target. If it falls, then those wires conduct less heat out. So that the arrangement is self-regulating, as long as there is liquid helium in the hollow wall.

The hohlraum 120 is enclosed by the hohlraum wall 128, the diaphragm 55, the innermost defined unit 124 and a shock wave reflector 60 between the leading edges of that unit. A shock wave reflector 61 between the leading edges of outermost defining units 129 of adjacent eye mirrors is also shown. The shock wave reflector 61 is not, of course, required when a circular array 62 of explosive lenses is used.

In an embodiment with a circular array 62 of explosive lenses, a pipe 66 from the hollow wall 123 to the outside of the shock wave reflector 60 ending in a valve 67 is provided to vent helium gas from, and supply helium liquid to, that hollow wall.

The power emitted from the interior of a blackbody whose radius, r/», is 1 metre, but only 3% of whose surface is at a temperature of 300°K, is 173.154 W. If the radius of the spherical target, r*, is 2 mm, then the power it receives is 692.616^W.

The heating from the β decay of iT3 to 2He3 in the target described in the previous section is 602.92μ\Υ averaged over the half-life of tritium. A significant fraction of this energy is absorbed in the shell of DT if it is above 20μπι thick. The thickness of the shell of DT ice in the target described in the previous section is 190μιη. A larger target with the same amount of DT but in a thinner shell will absorb less of the energy from β decay, at the expense of a higher initial aspect ratio. Some heating is, of course, necessary for the occurence of β layering, which smooths the inferior surface of a shell of DT ice. A larger target can accommodate more and/or thicker highly conductive support wires.

The burn of deuterium can be triggered by a small seed of DT, which may be tritium poor. DD reactions produce 1T3 and 2He3 which in turn can react with other deuterium nuclei. But the ignition temperature of deuterium is high at 35 keV.

Providing eye mirrors in parallel inside each eye mirror in a spherical array of eye mirrors in order to increase the energy delivered to a target with a high ignition temperature reduces the extent of each hollow wall, therebye increasing the percentage of the interior surface of the hohlraum which is at an ambient temperature of around 300°K, and thus the radiant power from that surface.

The heat flow through 272 wires 1 metre in length is two orders of magnitude higher than the sum of the power received by the spherical target plus its heating from β decay. Clearly the wires may therefore be much longer (and/or thinner) if necessary. Alternatively, the spherical target may be maintained at a much lower temperature. 6.11.1 Hot-spot volume ignition.

The DT gas inside the spherical shell of cold fuel is compressed and heated by the implosion of that shell to form part of the hot-spot.

For a typical target for hot-spot ignition, two-thirds of the energy is required to heat the hot-spot, while only one-third of the energy is required to heat the cold fuel. If such a target is scaled by a factor s, then both the mass of the hot-spot and that of the cold fuel are scaled by s3. But if the initial temperature of the target is reduced sufficiently, and with it the vapour pressure of the DT gas, the mass of that part of the hot-spot provided by the DT gas will not increase. There is no reason to increase the mass of the hot-spot to ignite the target. On the contrary, the pressure exerted by a less dense hot-spot will rise less quickly, and deaccelerate the incoming denser fuel shell more slowly, therebye reducing the onset of Rayleigh-Taylor instabilities. If the entire hot-spot is provided by the DT gas, the energy required for its ignition and the subsequent burn of the cold fuel scales as s3/3 + 2/3. (It should be mentioned that a larger, more massive, hot-spot would ignite at a lower temperature; so that the energy required for a target with such a hot-spot scales as s3/3 + 2s2/3.)

Provided the DT gas has been imploded so as to form a hot-spot with the conditions necessary for its own ignition, neutron energy redeposition and inverse bremsstrahlung in a scaled up shell of cold fuel will reduce the pre-ignition temperature needed in that cold fuel as s > 2 for the target in Section 6.10, much as in volume ignition. So that the energy required for ignition and burn will no longer scale with as much as s3/3 + 2/3.

Since the implosion time scales with s, the energy deposited in a larger shell at the same power level will also. The resulting implosion velocity of the shell of cold fuel therefore scales as s-1. There is a lower limit for this implosion velocity, which decreases as the mass of the target increases, as sufficient momentum is needed in that shell to overcome the pressure exerted by the hot-spot, which might otherwise slow it down prematurely. Numerical studies show that this lower limit of the implosion velocity is 2.5 x 107 cm / s for the ignition of a target with a large shell and 3.5 x 107 cm / s for the ignition of a target with a small shell. So that half the energy is required for a larger shell. But the conventional larger target, which would have been the subject of such studies, would have had a larger hot-spot more tolerant of irregularities, which may be partly responsible for the decrease.

Clearly scaling the implosion time by a factor of s = 10 in order to reach the minimum size of the explosive lenses for detonation will not require the power to be increased by a factor of a2. So that the size of the spherical array of eye mirrors need not be scaled by a factor as much as s, or at all if those eye mirrors are each provided with one or more eye mirrors in parallel to them. However, the eye mirrors must be sufficiently large to perform for the scaled implosion time. In any case, the cooling available is more than two orders of magnitude higher than is needed and allows a spherical array whose internal radius is much larger than one metre to be used as well as a larger spherical target.

The explosion of a number of these devices, positioned in the converging annular shock tube of a fusion power station, would suffice to ignite the full-size cylindrical targets described in Section 6.2 of patent applications GB 2,496,022, GB 2,496,250, GB 2,496,012 and GB 2,496,013 . So that the hohlraum target, described in Section 6.23.1.2 of those applications, and the short cylindrical target, mentioned in Section 6.23.1.3 thereof, would not be required to provide the recirculated energy to ignite any such full-size cylindrical target. 6.12 Burn of lithium deuteride tritide.

The deuterium ion, or deuteron, and the tritium ion, or triton, from lithium deuteride tritide can react:- iD2+ iT3-> 2He4(3.49MeV)+n(14.1MeV) (1) with a cross-section of up to 5 barns (which occurs at 64keV). One barn is 10-28 m2.

The resulting fast neutrons can then react not only with the deuterons and tritons, but also with the naturally occurring isotopes of lithium according to the cross-sections indicated:- η + ιΤ3 —> 2η + jD2 - 6.26 MeV (0.01 barns @ 12 MeV) (2) n + iD2 -> 2n + iH1 - 2.22 MeV (0.0105 barns @ 14 MeV) (3) n+ 3Li6 —> 2n + 2He4 + iH1 — 3.7 MeV (0.09 barns from 10 to 20 MeV) (4) n + 3Li6 —>· 2He4(2.08MeV) + aT3(2.7MeV) (0.02 barns @ 11.5 MeV) (5) n + 3Li7 -> 2n + 2He4 + jD2 - 8.73 MeV (0.025 barns @14.1 MeV) (6) n+ 3Li7 —> 2n+ 3Li6 — 7.25 MeV (0.04 barns from 11 to 20 MeV) (7) n + 3Li7 ->· 3n + 2He4 + iH1 - 10.95 MeV (neglible) (8) n + 3Li7 -> n+ 2He4 + iT3 - 2.47 MeV (0.4 barns @ 11.5 MeV) (9)

The protons produced by reactions (3), (4) and (8) can react with both 3Li6 and 3Li7. These reactions produce only charged particles:- !&amp;+ 3Li6-> 2He4+ 2He3 +4.02 MeV (10) iH1 + 3Li7 -> 2 2He4 + 17.35 MeV (11)

The following equiprobable deuterium reactions may also take place:- iD2 + jD2 2He3 (0.82 MeV) +n(2.45 MeV) (up to 0.11 barns at 1.75 MeV) (12) iD2 + iD2 -»· iT3(1.01MeV) + 1H1(3.02MeV) (up to 0.096barns at 1.25MeV)(13)

At a scaling factor of s = 10, pcTa^h — 18 g / cm2. The neutron cross-section for elastic collisions with deuterium at 14.1 MeV is 0.8 barns, while that for tritium at 14.1 MeV, and both 3Li6 and 3Li7 at all relevant neutron energies, is 1 barn. If the neutron mean free path is denoted by ln and the density by p then pln « 4.7 g/cm2 for a cross-section of 0.9 baxns, 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 four elastic collisions before escaping from the centre of 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 3L16 ion, 7/32 nds of its energy in such a collision with a 3L17 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 4.58 MeV by a collision with four successive 3L16 ions, or to 1.34 MeV by successive collisions with four deuterons. At the former energy, the cross-sections of reactions (5) and (9) are both approximately equal to 0.1 barns. At the latter energy the cross-section of reaction (5) is 0.6 barns while that of reaction (9) is neglible. 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 baxns 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, fn ~ PcKph / (PcTcph + Hn) where Hn — 20g/cm2; so that fn fa 9/19.

The deuteron 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 be maintained if more neutrons axe 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). The number of reactions of fast neutrons with lithium, and the number of slower neutrons escaping, will both be higher with 3Li7 fuel, because of the high cross-section of reaction (9). This may be advantageous 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 which 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 Li2DT than DT, more energy is required to compress it. If m.D is the mass of a deuterium nucleus, mr is the mass of a tritium nucleus and mu 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:-

if Pdt = 0,225 g/ cm3, pu^DT = 0.85 g/cm3 and mu = 7.

The energy required for hot-spot ignition is given by:-

where Γβ is the gas constant, 2¾ is the temperature required by the appropriate self-heating condition, and ph is the density of the hot-spot.

The gas constant is (ni+ne)kB/Amp where η* is the number of ions, ne is the number of electrons, A is the mass number of the reactants and mp is the mass of a proton, fee is the Boltzmann constant.

For equimolar DT, n* — ne — 2 so that its gas constant is where mo is the mass of a deuterium nucleus and mr is the mass of a tritium nucleus.

For Li2DT, ne = 2η% = 8 so that its gas constant is

where mu is the average nuclear mass for the combination of lithium isotopes used.

Hence

If Tfc(DT)=4keV for ignition with an isobaric hot-spot while T/j(Li2DT)=13.7keV on a similar basis then the energy required to ignite Li2DT in terms of that to ignite DT by unit volume for the same compression factor is:-

if Pjdt—0-225 g/ cm3, PLi2.DT=0.85g/cm3 and znLi=6.

If Th(Li2DT)=20keV to burn Li2DT in the Jetter cycle then:-

A calculation similar to that for the volume ignition of DT in Section 4.5 of “The Physics of Inertial Fusion” already referenced indicates that LijjDT compressed to 580g/cm3 may be ignited at Tc = 3keV for pcr^.ph = 18g/cm2 without reaction (5) and/or (9) producing tritium. That fuel is optically thick above pcr^1 = 13g/cm2. Ignition takes place over the entire volume of fuel, and does not involve mechanical work.

The temperatures required for the entire fuel for the volume ignition of Li2DT would require an increase in the size of the device of at least 250%. Alternatively, the source may be at a higher temperature provided by xenon at a higher pressure and thus a lower degree of ionization requiring less energy for that degree of ionization. Mirrors able to withstand such high illumination of low wavelengths would, of course, be required. But as a target which is solid at room temperature does not require cooling, no size limitation is imposed by any cooling system.

Fused Li2DT is a solid of density 0.85 g/cm3. The ultimate tensile strength of warm pressed polycrystalline lithium hydride ranges from 16.8 MPa to 54.9 MPa. A spherical target with an inner radius of 2 mm and a shell of Li2DT fuel 0.2 mm thick could tolerate a pressure up to one fifth of such an ultimate tensile strength, and thus at least thirty times atmospheric pressure. This is much higher than a similar plastic capsule. Equally a spherical target with an inner radius of 20 mm and a shell of Li2DT 2 mm thick could tolerate the same pressure.

The spherical shell of Li2DT fuel is filled with DT gas: so that the implosion of that shell will cause a hot-spot of DT gas to form. Since no inner shell of solid or liquid DT is needed as a seed for the Li2DT, the DT gas may be at any temperature.

Since α-particles, neutrons and electromagnetic energy from fusion in the DT hot-spot will progressively ignite the Li2DT cold fuel, such an arrangement will reduce the increase in size required.

However, the presence of lithium in the fuel, and the consequent reduction in the amount of DT available for fusion, will reduce the yield for the same burn-up fraction by a factor of

unless the hot-spot generates enough neutrons for reaction (5) to produce tritium and release energy in significant amounts. Moreover, the burn-up fraction for Li2DT in the absence of tritium production will be smaller than that for DT. 6.13 Excavation.

The Limited Test Ban Treaty prohibits underground nuclear explosions if they cause “radioactive debris to be present outside the territorial limits of the State under whose jurisdiction or control” the explosions were conducted.

Article VIII of the Comprehensive Nuclear-Test-Ban Treaty envisaged that in a review ten years after its entry into force, which did not take place, “the Review Conference shall consider the possibility of permitting the conduct of underground nuclear explosions for peaceful purposes.”

Other than any radioactivity caused by materials which can capture a thermalized neutron, are fissionable by a fast neutron, or undergo a (n,2n) reaction, the only radioactive product would be a small quantity of unburnt tritium in the locality of the explosion. As the half-life of tritium is 12.26 years, it emits an electron with only 0.018 MeV energy, and it passes through the body quickly, the risk associated with unburnt tritium is comparatively small.

The 14.1 MeV neutrons from DT fusion reactions give rise to (n,2n) reactions. Scattered neutrons with energies generally less than 1 MeV give rise to (n,7) neutron capture reactions. Because of the higher cross-sections for thermal neutrons, neutron capture predominates in hohlraums at the National Ignition Facility. The isotopes produced generally decay by 7 radiation.

Au198 from a (n,7) reaction has a half-life of 2.69 days. Au196 from a (n,2n) reaction has a half-life of 5.6 days, while its metastable state has a half-life of 14 horns.

Rh104 from a (n,2n) reaction has a half-life of 44 secs, while its metastable state has a half-life of 4.7 mins. Rh102 from a (n,7) reaction has a half-life of 207 days, while its stable state has a half-life of 2.9 years.

It is therefore preferable to use Au197 in devices intended for excavation, rather than Rh103.

There are 9 naturally occuring stable isotopes of xenon. Of the unstable isotopes of xenon, Xe127 has the highest half-life at 36 days.

The fast neutrons may be conveniently moderated by adding water to the ground to be excavated.

The low-level short-lived radioactivity would enable a wide, but shallow, canal to be constructed on flat ground, by excavating two parallel cuts, and using the excavated material to form two raised banks on the outsides of each cut respectively. Equally, a change in the level of that canal may be effected by a transverse cut with one of its banks raised. 6.14 Fissionable stage.

The fast neutrons released by fusion may induce fission in natural or depleted uranium. 1D2 + iT3 -> 2He4(3.49 MeV) + n (14.1 MeV) (1) n + 92U238 X+Y+n+n’ +180 MeV (2) where X and Y are different fragments and n and n’ axe neutrons with different energies. Such fissions induced by very energetic particles favour fragments of equal mass. The mean energy of neutrons from the fission of g2U235 is 2 MeV. 8 MeV is released as prompt 7 rays while the radioactive fragments release 19 MeV by β decays and 7 MeV by 7 decays. Neutrons which retain their initial energy of 14.1 MeV will release more than two neutrons. A beam of 15.057 MeV neutrons colliding with g2U238 atoms will give rise to an average of 4.5 neutrons per collision with an average energy of 1.979 MeV.

The cross section for neutron induced fission of g2U238 is only significant above 2 MeV. It is generally held that g2U238 cannot sustain a chain reaction because its own fission neutrons are not energetic enough to cause more g2U238 fission reactions. This is mainly because too many such neutrons would be slowed down by inelastic scattering into the energy region where they are strongly absorbed by g2U238 and below the energy region where their cross-section for neutron induced fission is high.

Thus a 6 cm thick blanket of g2U238 will increase the yield by a factor of five.

The main effects of such a device would be prompt 7 radiation, which would be lethal outside the main area of blast effects due to fusion and fission, and neutron radiation, which would be lethal further outside that area.

Figure 13 is a schematic diagram in the form of a section illustrating various positions at which a neutron target of 92U238 or other material may be positioned.

Neutron target 131 is inside the path of the beam from an eye mirror and outside the paths of the beams from all the other eye mirrors in the spherical array of eye mirrors. Neutron target 132 is inbetween the paths of the beams from three adjacent eye mirrors and outside the paths of the beams from all of the remaining eye mirrors in the spherical array of eye mirrors. The radii from the centre of the spherical array of eye mirrors to these targets are small, so that their volume is low for the required thickness of 92U238. But they cannot form a shell enclosing the neutron source, so that not all the neutrons emitted from that source will enter targets of these types. A neutron target 131 may be held by a support wire, such as the highly conductive support wire 126 attached to the spherical target 121.

Neutron target 133 lies inside the trailing edge of the defined mirror of the, or the innermost, final stage of the, or the innermost, eye mirror. Neutron target 134 lies between the trailing edges of the defining mirrors of the, or the outermost, final stages of three adjacent eye mirrors. These are, of course, the outermost eye mirrors of any eye mirrors in parallel. The radii from the centre of the spherical array of eye mirrors to these targets is larger, so that their volume is higher for the required thickness of 92U238. But they form a shell enclosing the neutron source which can be complete except for the exit apertures of the eye mirrors, or comprise a hollow wall 123 (as shown). And they provide part of the structure of the spherical array. Moreover, the neutron targets 134 may easily be extended along the reverse surfaces of their respective three adjacent defining mirrors to cover those exit apertures.

Neutron target 135 lies inside the leading edge of the defined mirror of the, or the innermost, first stage of the, or the innermost, eye mirror. Neutron target 136 lies between the leading edges of the defining mirrors of the, or the outermost, first stages of three adjacent eye mirrors. These axe, of course, the outermost eye mirrors of any eye mirrors in parallel. The radii from the centre of the spherical array of eye mirrors to these targets is even larger. But they may act as reflectors for the shock wave and provide part of the structure of the spherical array.

Neutron target 137 encloses an entire explosive lens 591 (not shown), except for its fibre-optic cables 58 (not shown). In an embodiment with a spherical array of such explosive lenses, the neutron targets 137 may be extended (as shown) to form a complete shell surrounding the neutron source. This acts as a case and pressure container for the device. But it is at the largest radius from the centre of the spherical array of eye mirrors. In such an embodiment, a separate structure, (not shown) to connect the defining unit 20 in each eye mirror to the defined unit 40 in that eye mirror is provided. If the space between the defining mirrors 129 contains gas 54, the hohlraum wall 128 must withstand its pressure, rather than those mirrors, therebye minimising the mass of the structure.

Any combination of these neutron targets may be used, with a combined thickness equal to that required in any given direction. In an embodiment with a circular array of such explosive lenses for each eye mirror, the neutron targets 135, 136 and/or 137 respectively may be extended to form a complete shell surrounding the neutron source. In order to minimise the mass of the device, the thickness of the neutron targets may be only sufficient for their structural role, shock wave reflection and pressure containment, as appropriate, except in some preferred directions, such as a plane which may be made horizontal.

Clearly the nearer the fissionable material is to the centre of the spherical target, the lower the mass of that material will be for a given areal density.

Figure 14 is a schematic diagram showing an overlapping pair of left and right nuclear explosive devices 140L and 140R respectively. A 92U238 central neutron target 148 lies between the centres 141L and 141R respectively of the corresponding partial spherical targets 145L and 145R respectively of those devices. Its conical ends 142L and 142R respectively act as guides for the two simultaneous implosions. Its cylindrical body 143 lies between those conical ends. The vertex of the conical end 142L lies at the centre 141L of the partial spherical target 145L, while the vertex of the conical end 142R lies at the centre 141R of the partial spherical target 145R. The conical ends 142L and 142R respectively and the cylindrical body 143 all have that line 144 which lies between the centres 141L and 141R respectively as their axis of symmetry.

The two nuclear explosive devices 140L and 140R respectively are detonated simultar neously by a master starter.

Further neutron targets may be incorporated in both these nuclear explosive devices as described above for a single such device.

It will be seen from Figures 10 and 11 that the eye mirrors for the left and right nuclear explosive devices 140L and 140R respectively fit together if one of those devices is rotated about the line 144 to enable each of the eye mirrors along its edge to lie between two of the eye mirrors along the edge of the other such device. For this reason, the arc of the circle representing each nuclear explosive device extends beyond its intersection with the arc of the circle representing the other nuclear explosive device.

The uniformity of the illumination of a partial spherical target by those of its respective eye mirrors which axe present is unaffected, but those parts of their beams, which would have illuminated the portion of the spherical target which is absent, are wasted. However, there can be no contribution to the uniformity of the illumination from the outside of the beams from eye mirrors which are absent. It is therefore advantageous to vary the illumination from each eye mirror near the edge of a nuclear explosive device, so that more of its beam is incident to the partial spherical target.

Claims (21)

CLAIMS.

1. An apparatus for supplying pulses of electromagnetic energy through fibre-optic cables comprising a shock cavity filled with a gas at a very high pressure, an apparatus for directing electromagnetic energy from an area or volume source enclosing that gas, and an array of fibre-optic cables with a common cladding at their input ends which seals the exit aperture of the apparatus for directing electromagnetic energy from an area or volume source, all of which are axially symmetric about a common axis of symmetry, and a circular array of axially symmetric explosive lenses, each with their own axis of symmetry and a detonator, which are cut where they would overlap the explosive lenses on either of their sides to cover and seal the input aperture of the apparatus for directing electromagnetic energy from an area or volume source.

2. An apparatus as claimed in claim 1 in which at least one fibre-optic cable receives electromagnetic energy originating from each different explosive lens.

3. An apparatus as claimed in either of claims 1 or 2 in which the gas is monatomic.

4. An apparatus as claimed in any of claims 1 to 3 in which the gas is xenon.

5. An apparatus as claimed in any of claims 1 to 4 in which the apparatus for directing electromagnetic energy from an area or volume source is an eye mirror.

6. An apparatus as claimed in any of claims 1 to 5 in which the seal for the input aperture of the apparatus includes at least one side plate.

7. An apparatus as claimed in claim 5 in which the seal for the input aperture of the apparatus includes at least one side plate.

8. An apparatus as claimed in either of claims 5 or 7 in which each explosive lens has a focus which lies within at least one of the angular input apertures of the eye mirror.

9. An apparatus as claimed in any of claims 5, 7 or 8 in which each detonator lies on the axis of symmetry of its respective explosive lens at one focus of a Cartesian oval whose other focus is the focus of the explosive lens a distance, c, away from that focus, with an outer truncated cone of fast explosive, whose detonation velocity is Vi, whose truncation is at right-angles to that axis of symmetry and passes through that detonator, and whose inner surface is the Cartesian oval at a distance, a, along the axis of symmetry from that focus, a slow explosive, whose detonation velocity is t>2, whose outer surface coincides with that Cartesian oval, and whose inner surface is a partial sphere concentric with the focus of the explosive lens, and an inner spherical shell of fast explosive whose outer surface coincides with that partial sphere and is concentric with the focus of the explosive lens, the geometry of the Cartesian oval being determined by the three constants (a, c, vi/v2) and any deflagration-to-detonation run in the outer truncated cone of fast explosive having a starting velocity less than v\ takes place over a distance less than a.

10. An apparatus as claimed in any of claims 1 to 9 in which each detonation is triggered by direct laser ignition, via a fibre-optic cable of the same length, an optical focussing lens system, and a detonator comprising a flyer plate coated on the inside of a window parallel to the surface of the high explosive.

11. An apparatus as claimed in claim 10 in which a return fibre-optic cable is provided for each detonator so that its function may be verified before use.

12. An apparatus as claimed in either of claims 10 or 11 in which each fibre-optic cable receives electromagnetic energy from a respective laser diode through its cylindrical microlens.

13. An apparatus as claimed in either of claims 10 or 11 in which each fibre-optic cable receives electromagnetic energy from a respective laser diode through its cylindrical microlens within a pulsed laser diode array which is electrically wired in parallel.

14. An apparatus as claimed in any of claims 1 to 9 in which each detonation is triggered by direct laser ignition, via a fibre-optic cable of the same length, and a detonator comprising a flyer plate coated on the end of that fibre-optic cable parallel to the surface of the high explosive.

15. An apparatus as claimed in any of claims 1 to 9 in which each detonator is an exploding bridgewire detonator.

16. An apparatus as claimed in any of claims 1 to 9 in which each detonator is a slapper detonator.

17. An apparatus as claimed in claim 1 in which the circular array of axially symmetric explosive lenses and their detonators are replaced by a single explosive lens, which is axially symmetric about the common axis of symmetry, together with a detonator for that single explosive lens, the apparatus for directing electromagnetic energy from an area or volume source has a first stage defined mirror, and a shock wave reflector is provided inside the leading edge of that first stage defined mirror to seal the shock cavity.

18. An apparatus as claimed in any of claims 1 to 17 in which the axis of each fibre-optic cable is aligned with a defining ray for the defined mirror of a final stage of the apparatus for directing electromagnetic energy from an area or volume source.

19. An apparatus as claimed in any of claims 1 to 18 in which the fibres and their common cladding are assembled, ground flat, polished and then annealed by CO2 laser pulses to melt a very thin surface layer.

20. An apparatus as claimed in any of claims 1 to 18 in which the fibres and their common cladding are assembled, ground flat and then polished to a surface roughness of less than 1 A.

21. A method of providing pulses of electromagnetic energy through fibre-optic cables comprising the steps of:- (a) providing an apparatus as in any of the preceding claims; and (b) detonating the explosive lenses therein using the respective detonators therein.