TOWARD A SHOCK-VAVE FUSIOH REACTOR
P. F. Browne
(Addenda completed 26th March, 1966, to patent application "Shock Wave Fusion Reactor", No. 9509982.6, priority date 17 May, 1995).
1. Technical Field and Background
The invention relates to generation of energy by fusion of light atomic nuclei to form a product nucleus with liberation of energy of order megaelectron volts (Mev) per fusion as compared to tens of electron volts per chemical reaction in fossil fuels.
The "fusion fuel" most commonly contemplated is hydrogen in the form of its heavy isotopes deuterium (D) and tritium (T). Preferred, although not the only, reactions are
where standard scientific notation is used, the energies in brackets being those of the particular reaction products. Reactions (1) are referred to as DD fusion, and reaction (2) as DT fusion. The two DD reactions occur with about equal probabilities.
The total energy released per DD fusion (an average of both branches) is 3.6 Mev, and the energy released per DT fusion is 17.6 Mev.
For the same energy of bombarding deuteron and for the same number of target nuclei (D or T) per unit volume, the probability per unit time for a DT reaction exceeds that for a DD reaction by a factor of order 100.
In order for a fusion to occur the fusing nuclei must
approach each other more closely than a critical distance, which is difficult to arrange because of the electrostatic repulsion of the charges of the nuclei. This leads to threshold value of the kinetic energies of the nuclei before fusion, which implies a threshold temperature if the particle motions are randomized. Conventional approaches to the realization of a fusion reactor have, as yet, not been able to provide a sufficient density of ions above the temperature threshold for a sufficient length of time.
WO-A-91/13531 discloses apparatus for effecting a fusion reaction comprising
a spherical energy store itself comprised of a stressed metal or metal allow in which the stress has been induced at a plurality of discrete regions by atoms or ions at interstitial sites of the lattice, the energy stored in the lattice being capable of at least partial release when a shock wavefront passes over said stressed regions,
means for stimulating release of strain potential energy in the form of shock waves, and
a fusion fuel element positioned so that a fusion reaction is initiated by the shock waves.
In operation of the apparatus disclosed in WO-A- 91/13531, a spherically symmetric trigger shock front is directed to the energy store. This shock front results in localised readjustment of the lattice strain required to release strain potential energy. The released strain potential energy takes the form of secondary shock waves (emanating from localized regions of stress which mutually interfere to provide a resultant shock wave with the same shape as the trigger shock wave which is thereby amplified coherently. The overall result is that a considerably amplified shock front is produced which is capable to effect fusion in the fuel.
There is however a disadvantage associated with the
proposal of WO-A-91/13531 in that the energy store repetitively required replacement (since the strain energy is released).
It is therefore an object of the present invention to obviate or mitigate the above-mentioned disadvantage.
According to a first aspect of the present invention there is provided apparatus for generating nuclear power comprising
(i) a solid or liquid medium, herein referred to as a converging medium, in which a converging shock wave will propagate toward a focus,
(ii) shock wave generation means for launching a converging shock wave into said medium so that the shock wave converges toward the focus, and
(iii) fusion fuel either distributed within the converging medium or confined to a focal cavity in said medium,
the converging medium being such as to be capable of reducing the volume of a shock wave wholly by convergence of the shock wave toward a focus so that the energy per particle in the converged shock wave exceeds the threshold value for effecting fusion in said fuel.
The volume of a shock wave is the product of surface area of the wavefront and thickness.
The term "energy per particle" refers to energy per particle of the medium in which the shock wave propagates. The wave is a disturbance which passes through the medium. At any time certain atoms of the medium are disturbed by the wave, and these atoms have increased energy - much increased energy when the shock wave concentrates its energy as it approaches a focus.
wave concentrates its energy as it approaches a focus. The particles are particles of the medium, and they include all particles of the medium which convey the disturbance at any particular time (i.e. all particles in the disturbed region of the medium). Fusion fuel particles may or may not be among these particles.
Therefore in the apparatus of the invention, the final energy per particle is attained from an initial energy per particle typical of conventional shock generators and the apparatus can operate repetitively by means of convergence of the shock wave front alone thereby avoiding the need to amplify the shock wave front by the mechanism of WO-A-91/13531 which had the disadvantage of being non-repetitive.
Subject to plausible assumptions, the energy per particle in a converging shock wave increases as the inverse square of the radius of the shock wavefront, so that after convergence from initial radius ro to final radius rp the energy per particle will have increased by a factor (ro /rf )2, and if the energy per particle in the shock wave initially (at launch) is for example 0.1 ev and the convergence ratio is ro /rf = 300 then the final energy will be ≃ 10 kev which is the preferred minimum for initiating a useful rate of fusion reactions.
Preferably the final energy per particle is at least 15 kev, or preferably at least 20 kev.
Preferably the convergence ratio ro /rf achieved in the apparatus of the invention is at least 100. more preferably at least 150, most preferably at least 300.
It will be appreciated that the energy for effecting the fusion reaction is, in effect, provided by two steps. In the first step a shock wave of large volume is generated to give as much initial energy per particle as possible. In the second step, the shock wave is converged so as to reduce its volume whereby the same energy is distributed among a smaller number of particles whereby
the energy per particle is increased. The convergence is such that the energy per particle exceeds the threshold value for a useful rate of fusion in the fuel.
2. Summary of Preferred Embodiment
A preferred apparatus according to the present invention utilises
(1) shock waves, hereafter termed "converging shock waves", whose wavefronts converge toward a focus, so that wavefront area decreases by a substantial factor during convergence,
(2) a solid or liquid medium, or a composite of more than one such medium, hereafter termed "converging medium", in which the shock waves propagate toward a focus, whether or not the focus is actually reached,
(3) means of launching repetitively converging shock waves into the converging medium,
(4) as an optional feature, a cavity in the converging medium whose boundary surface is encountered by a converging shock wave before the focus is reached.
(5) nuclei capable of undergoing exothermic fusion reactions, hereafter termed "fusion fuel", the said fusion fuel being either distributed throughout the converging medium or concentrated into a volume toward which the shock waves converge,
Provision of the above features introduces options among which are the following. Options may be chosen in
any combination.
Feature 1
With regard to feature (1), common examples of converging shock waves have a spherical shockfront which converges to a point focus, or a cylindrical shockfront which converges to a line focus. Less common exmamples create converging shock waves by reflection at a boundary surface between two media, examples being reflection of a plane shock wave by a conical or wedge-shaped boundary surface, reflection of a plane shock wave by a paraboloid shaped boundary surface toward a point focus, conversion of a shock wave which diverges from one focus of an ellipsoid into a shock wave which converges toward the other focus of the ellipsoid by reflection at the boundary surface of the ellipsoid. Plane shock waves can also be made to converge by propagation in a medium of non-uniform density, the variation with position of propagation velocity, creating a lense effect.
Feature 2
With regard to feature (2) a converging medium may be a composite of several media in contact with each other, so that the shock wave passes across boundary surfaces between media with some degree of reflection which can be minimized or adjusted to a desired value.
Feature 3
With regard to feature (3) a converging shock wave can be launched by impulsive pressure applied over the outer surface of the converging medium. Two preferred methods for providing simultaneous (or appropriately timed) impulsive pressure over a large surface area are, (i) by detonation waves in fluid (gaseous or liquid) explosive (Fig. 2a), and (ii) by mechanical impact (Fig. 2b). Apparatus for applying impulsive pressure to the surface
of a converging medium must do so repetitively. If chemical explosive is used, then gaseous or liquid form of explosive is required for rapid renewal. In more detail, these methods are as follows:
(i ) Production of Detonati on Wavefronts of Large Area and
Controlled Shape.
A preferred method for launching a shock wave is to apply pressure by a detonation wave with the same shape of wavefront as the Shockwave to be launched, the detonation wave being generated in gaseous or liquid chemical explosive in a combustion chamber surrounding the converging medium (Fig. 1a). If the converging medium is spherical, a spherical shock wave is launched by impact of a converging spherical detonation wave on the surface of the converging medium.
Creation of a detonation wave of large wavefront area and given geometry requires precise timing of the ignition (triggering) of different volume elements of the chemical explosive. The method for achieving this timing shown in Fig. la is to initiate a corona-type discharge at the tips of an array of pins protruding from one of two electrodes in the region where the explosive fuel is ignited ("combustion chamber"). The two electrodes are the concentric spherical walls of the combustion chamber in the example depicted in Fig. 1a. The pins are uniformly spaced (separation perhaps 5 mm) and of uniform length (perhaps 5 mm) for launching a spherical detonation wave of radius say 1 m. The smaller the separation and lengths of the pins, the shorter will be the distance propagated by the detonation wavefront before it acquires the desired uniform shape. The ignition of the explosive fluid occurs at the tips of the pins because a high electric field at the instant of application of a high voltage pulse (perhaps in the range 10 - 50 kV) between the electrodes initiates an
electrical discharge at the tips of the pins. The term "corona-discharge" often is reserved for one electrical polarity of the pins, but here either polarity can be employed. The ignition of explosive fluid in the localities of different pins should be simultaneous to within about 1 microsecond, unless timing delays are purposely introduced into the electrical feeds to the pins in order to control the shape or direction of the detonation wave. The pins may be fed through individual resistors, or through a common resistive medium.
A variant of the mechanism for launching a detonation wave of large wavefront area and desired shape is to replaces the pins by a wire mesh (or other perforated conductor) in contact with a slab of dielectric medium whose other surface is in contact with one electrode (the outer wall in the example of Fig. 1b). Mylar is a possible dielectric material; electrically glass is suitable, but lack of robustness to the explosion may- exclude glass. The high voltage pulse now is applied between the conducting sheets on either side of the dielectric layer, so that the dielectric polarizes. Neutralization of induced charges within the meshes on the mesh side of the dielectric occurs by microdischarges over the surface of the dielectric, thus igniting explosive fluid locally.
(ii ) Generation of Shock Waves by Mechanical Impact
A second method for launching a shock wave is to apply direct mechanical impact on the surface of the converging medium by solid projectiles, or pistons, which have been accelerated by explosive charges. A "hammer" driven by a single spherical detonation wave is shown in Fig. 1. By means of interleaving layers the effective surface area of the hammer head is able to decrease with decreasing radius.
In Fig. 2b an alternative method for delivering
mechanical impacts uniformly and simultaneously over the surface of a converging medium is depicted. Now independently accelerated projectiles are directed along radial cyclinders or "gun barrels" toward the surface of the converging medium. Acceleration may be by explosive charges introduced into each cylinder head and independently triggered, much like a multi-cylinder internal combustion engine. In this system there is the possibility of timing the independently delivered mechanical impacts in response to a feed-back signal. Acceleration of the projectiles in the radial gun barrels may be by other methods.
The facility to launch a pair of shock wavefronts in rapid succession is desirable in certain circumstances. Fig. 2d depicts a projectile which delivers double- impacts whose relative strengths and time separations are controllable.
Mechanical impacts combine high impulse strength with relatively low pressure because of the suddenness of the applied pressure. In every other respect the explosive detonation waves are preferred.
Feature 4
With regard to feature (4), there is provided the option of
I. a continuous solid or liquid converging medium or
II. a cavity in the converging medium toward which the shock waves converge, and at the boundary of which the converged shock waves are reflected.
Options I and II created by feature 4 lead to different types of shock wave reactor, termed respectively "uniform medium reactors" (UMRs), and "focal cavity reactors"
threshold conditions for useful fusion may be easier for the FCR reactor, the additional complexity of this system may be necessary.
The essential principle of operation of either type of reactor is conversion of energy in a Shockwave of large volume into energy in a shock wave of small volume without unacceptable loss of energy. Then energy distributed among a large number of particles becomes concentrated into energy in a small number of particles. This energy may be either kinetic energy or potential energy due to elastic compression, the one form of energy being convertable into the other provided that potential energy is not lost to a reflected wave.
Distinctions between the UMR and FCR variants of the reactor are clarified by the following more specific descriptions:
I. Uniform Medi um Reactors (UMRs) In "uniform medium reactors" (UMRs) fusion conditions are attained in localized volumes of the medium, of which the following are three types:
(A) a small volume surrounding the focus toward which the shock waves converge, termed "focal volume" (Fig. 3a);
(B) the volume of overlap of colliding shockfronts of the same shape and with opposite directions of propagation, so that at one instant of time the shockfronts are superimposed in their entirety (Fig. 3b);
(C) the volume of overlap of colliding shockfronts
with general shape and general direction of propagation which intersect along a curve (providing a tubular volume of intersection)
which moves as the shock fronts propagate
(Fig. 3c), causing the phenomenon of "jetting".
A preferred example of case (B) occurs when a spherical shock wave converging toward a focus meets, at a position close to the focus, a spherical shock wave diverging from the same focus (Fig. 3b). The diverging shock wave may be produced by reflection of a forerunning converging shock wave. Reflection near the focus may be natural or contrived, natural reflection being automatic and contrived
reflection being that due to introduction of a dense core medium, for example a ball bearing (which would require support in a liquid core). The very steep pressure gradient at the front of a strong (converged) shock wave
implies very sudden onset of thermalization which should eliminate radiative cooling during the inertial confinement time.
A preferred example of case (C) occurs when converging medium comprises two spherical caps on a common circular base, which is what remains of a sphere after removal of an equatorial slab from the sphere and closure of the gap so created. If the removed slab has thickness z, then spherical shock waves in the spherical caps converge toward different foci a distance z apart. Spherical shockfronts converging in the spherical caps intersect in a circular ring on the equatorial plane, this ring decreasing in radius as the shock waves converge toward their respective foci F1 and F2 in Fig. 3c. Particles in the collision ring are forced radially inward to form a sheet jet whose area reduces with
convergence of the shockfronts until the sheet collapses to the center.
The simplest case of "jetting" occurs during collision of plane shock waves propagating in directions which make angle 180º - α with each other. The curve of intersection now is a straight line which moves in the plane which bisects the wedge formed by the shockfront planes. The velocity of the motion is
D cosec α/2, where D is propagation velocity of the shockfronts and α is the wedge angle. This velocity exceeds D by a factor of 10 for α = 11º 24'.
It will be noted that all three fusion regions have similar volumes. In case A the focal volume V
f and radius r
f are related by V
f =
f /3, so that r
f = 0.3 cm
implies V
f = 0.11 cm . In case B the shell collision volume V
s is related to shell radius rs and shell thickness λ by V
S =
λ , so that r
S = 1 cm and λ = 1 mm implies V
s = 1.26 cm . In case C tubular collision volume
V
t is related to tube radius r
t and to tube length 2πa (for a ring tube of radius a) by V
t = (2πa) so that
rt = 1 mm and a = 1 cm leads to Vt = 0.2 cm3. Thus, in each case the energy of the shock wave is being shared among comparable numbers of particles.
Means of launching toward the same focus spherical shock waves which are closely separated in distance or time are shown in Fig. 2c and Fig. 2d.
II. Focal Cavi ty Reactors (FCRs) In the case of FCRs fusion conditions are achieved within the focal cavity after medium material has been injected into the cavity ("off-loaded") during reflection
of the converged Shockwaves. Off-loaded material is used in two ways which require different shapes of focal cavity:
(A) If the cavity boundary has the same shape as the converging shockfront, for example a spherical boundary concentric with the converging
shockfront (Fig. 4a), then at reflection a dense spherical shell of medium is off-loaded with velocity twice the velocity of particles carrying the wavefront in the medium. This off-loaded shell is an ideal driver for imploding fusion material frozen to the inside wall of a capsule which is in contact with the converging medium, so that both wall material and fusion fuel are driven toward the center of the cavity where the fusion fuel reaches very high density and temperature.
(B) If the cavity boundary has shape different to
that of the converging shock wave, then the shock wave meets different portions of the boundary at different times. For example, if the cavity has bi-cαnical shape (that of a pair of oppositely directed right circular cones on a common base - Fig. 4b) then injected particles will form a pair of oppositely directed jets which collide at the center of the cavity. If the cavity has multi- conical shape (circular cones projecting from a spherical surface in mutually orthogonal
directions - Fig. 4c), then there are three pairs of opposite jets along three mutually orthogonal directions, which is six jets directed toward the center of the cavity.
Feature 5
With regard to feature (5), there is provided the option of
(i) fusion fuel distributed uniformly throughout the converging medium,
or
(ii) fusion fuel (possibly encapsulated)
concentrated into a cavity within the
converging medium toward which the shock waves converge.
With regard to option (i), a preferred converging medium with distributed fusion fuel is the crystalline solid Li DT, or lithium hydride (LiH) with hydrogen isotopes deuterium (D) and tritium (T) in equal proportions instead of H. The crystal structure is cubic NaCl type. Some properties are:
(a) The mass density of Li2DT is ≃ 0.88 g cm-3, and the number density of Li atoms of atomic mass 7 is 6 x 10 22 cm-3 .
(b) The crystalline solid melts at about 700 °C, and latent heat of melting is ≃ 40 kJ mole-1 . Thus, a sphere of radius 1 m, containg 4 x 10 moles, requires energy
16 GJ for complete melting. The molten solid is corrosive to metals, restricting materials used for containment.
(c) Because the masses of Li, T and D are comparable (7, 3 and 2 atomic mass units respectively), thermalization time is short.
(d) The ionization of Li to Li3+ requires energy 5.4 + 75.8 + 122.6 = 203.8 ev, and ionization of D or T requires 13.6 ev, a total of 217.4 ev.
(e) A sphere of LiD with radius 2 m is capable of fully absorbing all products of fusions near the center. X-ray bremsstrahlung from the focal volume also will be largely absorbed, mean free path for 10 kev X-ray photons being
0.5 m. There is then little waste of input energy used in creating the conditions for fusion.
(f) LiD is a recognized breeder for T due to reactions 7Li + 1n → 4He + 3T + 1n - 2.47 Mev
6Li + 1n → 4He + 3T + 4.8 Mev
by the stable isotopes 7Li and 6Li present with abundances 92.5 % and 7.5 % respectively.
Option (ii) is to concentrate fusion fuel, possibly in encapsulated form, into a cavity in the converging medium toward which the shock waves converge. For example, DT fuel in a frozen state may be coated onto the inside of the wall of a spherical capsule of appropriate material (e.g. glass, plastic, metal), and the capsule then embedded in the converging medium in the appropriate position (centered on the focus).
3. Diagrams
Fig. 1 shows schematically the simplest variant of the shock wave fusion reactor. With reference to Fig. 1 converging medium 1, which has the density of a solid or liquid, is separated by wall 2 from chamber 3 for combustion of fluid chemical explosive ("combustion chamber") with substantial outermost wall 4. Pins 5 ensure that converging detonation wave 6 is spherical in shape, so that it launches spherical converging shock wave 7 in medium 1. Fluid explosive enters at port 8 and exits at port 9. Facility for heat extraction is not shown.
Fig. 1b and Fig. 1c illustrate schematically the method for generating detonation waves of large wavefront area and desired shape in fluid explosive. With reference to Fig. 1b, incipient corona-type discharges from the tips of the pins 1 ignite the fluid explosive at the tips of
the pins, thereby creating converging spherical detonation wave 2 which eventually launches a converging spherical shock wave in medium 3.
With reference to Fig. 1c microdischarges over the surface of dielectric plate 1 coverged by wire mesh ignite chemical explosive simultaneously over a spherical surface, thereby generating converging detonation wave 2 which later launches a converging shock wave in medium 3.
Fig. 1 d shows a standard circuit for generation of the high voltage pulse which is applied between the electrodes in Figs 1b and 1c. Capacitor C is charged through charging resistor R to high negative voltage - V with respect to earth, and triggering of spark gap S (or equivalently thyrotron S) by trigger pulse at T then discharges C through load resistor RL , providing output high voltage pulse + V. The voltages required are envisaged to be in the 10 - 50 kV range, and simultaneity or timing is controllable to within accuracy of order 1 μs or less.
Fig. 2a and Fig. 2b shows schematically two methods for launch of spherical shock waves by mechanical impact.
With reference to Fig. 2a spherically shaped "hammer heads" 2 strike the spherical surface of converging medium 1, or the wall of converging medium 1, at all points simultaneously. The "hamnmer heads" are interconnected by interleaving plates so that the whole forms the inner of two concentric spherical walls of a "combustion chamber" for chemical explosive". A converging detonation wave 4 initiated at pin tips 3 accelerates the hammer assemby as a whole so that the "combustion chamber" expands until its inner wall 2 strikes the wall of medium 1.
Fig 2b shows simultaneous mechanical impacts over the surface of the converging medium 1 due to projectiles 2 which have been accelerated to high velocities by
explosive charges or chemical fuel burning in regions 3 triggered by individual independent sparks in plugs not shown. Timing of mechanical impacts may be controlled by timing spark ignitions in response to feed-back signals.
Facility to launch two or more shockfronts in rapid succession is desirable for arranging collisions between shockfronts in certain circumstances. Two methods for doing this are depicted in Fig. 2c and Fig. 2d. With reference to Fig. 2c, "delay medium" L has interfaces with the converging medium on the inside and some external medium on the outside with suitable transmission and reflection coefficients. Repeated reflections within L deliver waves 1, 2, 3 of progressively diminishing amplitude when wave W enters from the outside, and similarly deliver waves 1', 2' and 3' of progressively diminishing amplitudes when wave W' enters from the inside. Successive shock waves are separated in time by the time to propagate twice the thickness of the delay plate.
Fig. 2d depicts a spiring-loaded projectile which delivers a double-impact to a target. With reference to Fig. 2d the first impact occurs when part 1 of the projectile hits the target, and the second impact ocurs when part 2 of the projectile hits part 1, closing gap 4 by compression of the spring 3.
Fig. 3 shows three types of volume in a uniform medium reactor (UMR) where particle energies can exceed the threshold energy for useful fusion power production.
Fig. 3a shows a spherical focal volume.
Fig. 3b shows a shell volume where concentric spherical shockfronts collide, one converging and one diverging.
Fig 3c shows a tubulax-ring volume where non-concentric spherical shockfronts, both converging, collide. The spherical shockfronts 1 and 2 converge respectively toward the foci F1 and F2 without ever reaching these
foci. The heavy arrows indicate "jetting" of particles toward the center of the ring whose radius shrinks to zero.
Fig. 4 shows three shapes of focal cavity toward which spherical shock waves converge in a solid or liquid medium, a non-melted cavity wall being required if the converging medium is liquid. In each case material of the converging medium is "off-loaded" into the cavity when the converging shockfront is reflected at the cavity wall.
In Fig. 4a off-loaded material forms a dense spherical shell which implodes toward the center of the focal cavity, which is the focus of the original converging shock wave. Fusion fuel within the cavity, which may be a frozen layer on the inside of a cavity wall material, is compressed to high density by the implosion, so that fusion threshold is exceeded.
In Fig. 4b a bi-conical focal cavity is depicted, which has the shape of a pair of right circular cones positioned back-to-back on the same circular base. The converging spherical shockfront encounters first the tips of the bi-cone, where injection of medium material releases pressure in the converging shockfront. As the shockfront continues to converge injection occurs closer and closer to the base of the bi-cone. The result is that particles injected into the focal cavity approach the center of the cavity in the form of oppositely directed jets.
In Fig. 4c a multiple bi-conical cavity is depicted. In its simplest form it comprises three bi-concical cavities protruding from a common spherical surface in three mutually orthogonal directions, so that three pairs of opposite jets (in total six jets) in mutually orthogonal directions collide at the center of the cavity.
Fig. 5 depicts a method for replacement of focal cavities. Prefabricated focal cavities 1 and 2 are embedded in a cylindrical column of converging medium material 3 which is fed through the sphere of converging medium 4 with outer boundary 6 so that each cavity can come into the focal position for spherical converging shock wave 5. A cylindrical column of solid converging medium is pushed through liquid converging medium so that each prefabricated focal cavity is positioned correctly for each fusion burst. If the sphere of converging medium is solid the column of converging medium would require to pass through a tight-fitting hole with suitable lubricant for shock wave impedance matching in order to avoid strong reflection at the sphere-column interface.
Fig. 6 depicts a pair of paraboloids of revolution which are coaxial and are positioned back-to-back. Between the paraboloids is a planar slab 3 of gaseous chemical explosive which is liquid or chemical for rapid renewal between fusion bursts. Plane shock waves are launched in opposite axial directions by the chemical explosive in response to appropriate detonation, Figs, lb and lc depicting possible detonation methods. After reflections at the paraboloid boundary surfaces the plane shock waves converge to foci 1 and 2. A cavity is shown to surround focus 2, and a similar cavity could also surround focus 1. The symmetrical conditions enable the relative performances with and without focal cavities to be compared. An important advantage of the bi-paraboloid system shown in Fig. 6 is the relative ease with which focal cavities can be renewed, because the generation of the shock waves is separated from the mechanism for cavity replacement. The same sort of advantages occur for heat fransfer from the converging medium.
Fig. 7 depicts a converging medium 4 with ellipsoidal boundary surface over which chemical explosive is distributed in a thin layer 3. Fluid chemical explosive is supplied also to a small cavity 2 surrounding one focus. A point chemical explosion in cavity 2 generates a spherical shock wave which diverges from the focus 2 until reflected at the ellipsoidal surface of medium 4. The reflection converts the spherical wave diverging from focus 2 into a spherical wave converging toward focus 1. Chemical explosive spread uniformly over the ellipsoidal surface of medium 4 (possibly fluid explosive contained by a thin surrounding chamber 3) is triggered by the reflection. A sheet of piezoelectric transducer may aid the triggering by providing accurately timed sparks at each surface element. Provided that local triggering is timed accurately in response to reflection at different surface elements, the sheet explosive will generate a shockfront of the same type as the reflected shock front, which thereby is amplified. When the reflected amplified shockfront reaches focus 1, it may be strong enough to create conditions for a useful rate of fusion reactions. Strong casing 7 contains the explosions. In order for repetition the chemical fluid supplied to focal cavity 2 and supplied also to the surface chamber 3 should be fluid. A feed tube with input at 5 and output at 6 is shown for the former supply, but that for the latter supply is not shown.
4. Sams Engineering Design Considerations
(i )Renewal of Focal Cavi ties
An unwelcome complication for the CFR variant of reactor is the need to renew the focal cavity after each fusion burst, or at best one per several fusion bursts. Continual replacement is posible by arranging to position
new prefabricated focal cavities at the focal position after each burst.
In the case of spherical geometry for the converging medium, it may be possible to introduce focal cavities with thin walls of a material with high melting point into converging medium which is liquid at operating temperature. Indeed, in the case when the converging medium is Li2DT, in liquid form, it may be possible to feed through the liquid a column of solid Li2DT containing prefabricated focal cavities, these cavities coming into the focal position before the column melts. If the converging medium is solid Li2DT then the column must be pushed through a tight-fitting hole in the converging medium with suitable liquid lubricant to prevent reflections at the column-medium interface.
The ideal geometry for cavity replacement is cylindrical, but convergence factor is the difficulty. If a convergence factor of 100 is required for spherical geometry, then factor 10,000 is required for cylindrical geometry.
A compromise may be the bi-parabαloid geometry depicted in Fig. 6. Here the mechanism for renewal of focal cavities is separated from apparatus for generating shock waves.
(ii ) Heat Transfer
Both variants of reactor are efficient in that the energy of particles liberated in fusion reactions is absorbed by the converging medium. Moreover, unused shock wave energy also is absorbed in the converging medium, which amounts to recyling much of the input energy.
Transfer of heat from the converging medium to an external body is required in order to obtain useful power output. In the case of a liquid converging medium the simplest method for heat transfer may be a through-flow of liquid medium. Indeed outflow of medium in liquid form
might be balanced by inflow of medium in solid form, a particularly efficient extraction mechanism because of latent heat of melting.
In the case of the UMR variant of reactor with spherical geometry, continuous throughput of converging medium material may be impractical. There is always the option of alternating intervals of power generation with intervals of cooling during which the shock generation need not ocur. A sphere of Li2DT of radius 1 m requires some 16 GJ in order to change from solid to liquid state, and therefore has the capacity to store a substantial amount of heat. Moreover, the store of fusion fuel is enormous for a sphere of Li2DT with radius 1 m. Indeed Li2DT is a breeder of tritium (see discussion of feature 5).
(iii ) Choice of Reactor Type
In regard to the choice between the UMR and CFR variants of reactor, only the consideration of threshold attainment may favour the CFR variant. The much greater simplicity of the UMR variant due to absence of cavities strongly favours this type, provided that achieving threshold condition presents no severe problems.
The type of reactor contemplated is a small efficient and mobile installation, in contrast to conventional power stations which are large immobile installations.
5. Principle of Operation and Estimate for Pefomance
Let an impact at the surface of a solid medium displace atoms in a thickness λ of the medium, atoms deeper in the medium being unaffected. The displaced atoms pile up at the leading edge of a layer of thickness λ, producing rarefaction in the remainder of the layer. This structure, a compressed layer followed by a rarefied layer, propagates through the medium as a shock wave. The
density and pressure profile of a plane shock wave does not change during propagation, neglecting dissipation (i.e. loss of energy by heating or exciting the propagation medium). The number of particles which carry the wave at any instant continues to be the number of particles of undisturbed medium in volume Sλ, where S is the constant shock wavefront. However, the number changes during propagation of a converging shock wave due to decrease of S. Then conservation of energy requires that the energy per particle increases, being proportional to S-2 if λ remains constant . The energy per particle is partly kinetic energy of forward motion and partly potential energy of medium compression, both contributions increasing with convergence.
Adopting the rest frame of the shock wave, the medium enters the wave with velocity - v
1 , is compressed in the wave, and leaves the wave with velocity - v
2, rather as air enters a jet engine, is compressed, and is blown out again. The analogy with the jet engine is more exact for a detonation wave because energy is being continually fed into a detonation wave by combustion of the explosive gas, whereas in a passive shock wave there is no such fuel burning. Expulsion of fluid with mass density ρ
2 and velocity v
2 through area S
2 in a time δt represents loss of momentum (p
2 S
2 v
2 δt ) v
2 , which implies "jet-engine" force
2 on tne comP
ression layer. Incoming material
loses momentum (p
1 S
1 v
1 δt)v
1 in time δt , which implies stopping force The stopping force on the leading
edge of the compression layer and the jet reaction force on the trailing edge have a pincer action on the compression layer, maintaining the compression.
For a plane shock wave equilibrium between the stopping force applied to inflowing fluid and the jet force applied to expelled fluid causes a stable situation in the absence of dissipation. For a converging shock wave this stability is lost. The thickness λ of the layer of
undisturbed medium which conveys the shock wave clearly is constant in the case of the plane shock wave, and it may also remain constant in the case of the converging shock wave (at least for large radii r). However, the shape of the pressure wave now changes as the wave propagates; specifically, the pressure rise steepens and the peak pressure increases as r decreases for the converging shock wave (unlike the plane wave). If Δrc is the thickness of the leading compressed layer and Δrr is the thickness of the following rarefied layer, then in order to maintain constant the total thickness λ the latter must increase as the former decreases. We assume λ = Δrc (r) + Δrc (r) = constant (1) where r >> λ. A consequence of (Al) is that the number
N(r) of particles carrying the wave at radius decreases in proportion to r -2 because surface area S(r) decreases as r2 for a spherical wave. Thus
N(r) = no(4πr2λ) α r2 (2)
If we assume, further, that the energy W of the shock wave is approximatly conserved during convergence from initial radius ro to final radius rf , then the energy per particle w(r) must increase in proportion to r-2 . That is,
w(r) = mu 2/2 + V(r) = Ws/N(r) α r-2 (3) where u(r) is the velocity of the average particle with mass m and V(r) is the potential energy of the average particle due to compression of the medium. How the total energy is distributed between kinetic and potential forms is of little consequence, provided that the potential energy V(r) is not transfered into a reflected wave. Indeed there may be periodic conversion of particle energy from kinetic to potential form and back to kinetic form. The pressure p(r) of the shock wavefront at times of maximum potential energy may be expressed by
p(r) = n(r)w(r) (4)
where n(r) is the density of particles in the compressed layer.
In order to obtain a reasonable rate of fusion reactions, we requre to transfer to some particles energy as large as about 10 kev. If this energy is entirely in kinetic form, then a deuteron with mass twice the hydrogen mass has velocity vD ≃ 10 8 cm s-1. In principle, energy stored as potential energy due to elastic compression of the medium can always be converted into kinetic form, so the velocity vD. has a definite physical meaning. The deuteron partial pressure required for fusion is therefore given by
PD(r) = nD(r)wD(r) = 4.8 x 1014C dyne cm-2 (5) where we substitute
wD = 10 kev, nD(r)> = 3 x 1022 C cm-3 (6) in which C is a compression factor (the ratio of particle density in the compressed layer to particle density in the undisturbed fluid). Pressures of order several megabar (several times 10 12 dyne cm-2 ) have been measured in solids for nσn-focussed shock waves. The hope is that focussing will increase this pressure by a factor of about 100.
To summarise, subject to plausible assumptions, energy per particle in a converging spherical shock wave increases during convergence as the inverse square of the radius of the shock wave, so that after convergence from initial radius ro (at launch) to final radius rf (the radius of the "focal volume"), the energy per particle w(r) will have increased by factor (r /rf)2 . Finally, we have the value w(rf) = 10 kev. For a "convergence factor" ro/rf = 300, the initial particle energy must then have the value w(ro) = 0.1 ev. The smallest focal volume achievable for convergence factor 300 probably has a radius of a few millimeters (since we may expect rf ≃ λ).
Adopting r = 3 mm, it then follows that r0 = 90 cm.
The initial energy Ws of the shock wave is given by
Ws = n
ow(r
o) = 10 MJ (7) where we use the values
ro = 90 cm, λ = 1 mm,
no = 6 x 1022 cm-3 , w(ro) = 0.1 ev (8)
The value for no is that for LiH (or Li2DT), The value for w(ro) gives an atom of Li velocity 1.65 km s-1 and a deuteron velocity 3.1 km s-1 , which are reasonable for shock waves launched by chemical explosives.
There arises the question of how many particles can acquire energies of order 10 kev in the above manner. One obvious limit is the energy available in the shock wave,
Ws = 10 MJ. The maximum number of particles that can be given energy 6 kev is
N(6 kev) = Ws/w(ro) = 1022 (9)
The volume of undisturbed medium occupied by 10 22 particles is
V
N = p
o
= 0.1 cm
3 (10) where for Li
2DT we have the values ρ
o = 0.88 grm cm
-3 and m = 4.75m
H, where m
H is the mass of a hydrogen atom. The radius of a sphere with volume (10) is r
N = 3 mm.
We conclude that a sphere of Li2 DT of radius 90 cm can provide fusion conditions within a volume of radius 3 mm which contains some 10 22 particles, assuming that there is no loss of shock wave energy between launch and a focal volume of radius 3 mm. If there is such loss, so that a fraction f of shock wave energy reaches the focus, then the initial energy of the shock wave must be increased from Ws to Ws/f, which may well require that its radius is increased by the factor f- ½. If f is 10 %, then f- ½ = 3.16, and the required sphere must have radius ≃ 3 m.
There remains the question of how much fusion energy will be released per burst. If deuterons and tritons in the focal volume have kinetic energies
D* and *
respectively, then the relative kinetic energy of a deuteron (that in the rest frame of a triton) is
W
DT =
* + W
T* = 6 + 4 = 10 kev (11) where we assign the value = 6 kev, and hence * = 4
kev. The temperature θ appropriate for a Maxwellian distribution of relative velocities, is
θ = 2 WDT /3 = 6.67 kev (12)
The fusion rate for a single deutron of energy w DT interacting with tritons at rest with density nT is
Γ = <vD T δ DT>nT = 106C s-1 (13) where we use <vD T δDT > = 3.6 x 10-17 cm3s-1 (from Fig. B2, appendix B) and nD = 3 x 1022 C cm-3 (appropriate for
Li2DT), C being a compression factor. The total number of fusions is obtained by multiplying by the total number of deuterons in the focal volume, namely N/3 where N is given by (9). Energy relasaed per DT fusion is εDT = 17. 7 Mev = 2. 82 x 10 -12J, so fusion power is
PF = 1016 C watt (14)
If the fusion rate persists for time τ = C-1 ns, the energy released is 10 MJ, which equals the input energy
Ws , which is a gain factor of 2 since the input energy is not lost. The value for τ varies as C-1 if it is determined by cooling of the electrons by X-ray bremsstrahlung.
APPEITDIX A: COHVERGING SHOCK WAVES
(i) The Newton sphere model for converging shock waves
In the familiar exhibit known as Newton's spheres a line of touching identical steel spheres. S1 , S2.... Sn , are suspended so that they can swing in the direction of the line. A half-swing of S1 is brought to rest by the impact with S2, launching a shock wave which propagates along the line and eventually causes Sn to complete the other half swing. Then Sn falls back and launches a return shock wave which has the same effect on S1, and so on. The process continues many times because the shock propagates along the line of spheres with little dissipation.
Newton's spheres provide a vivid demonstration of conversion of kinetic energy of outside sphere S
1 into potential energy of elastic compression of the middle spheres S
2 .... S
n-1 , and then back again into kinetic energy of end sphere S
n . The question is what happens when Newton's spheres have progressively decreasing mass. The decreasing mass situation models progress of a converging spherical shock wave provided that the masses of undisturbed layers of converging medium of constant thickness λ decrease in proportion to their surface areas. For each propagation step λ the number of particles N(r) and the mass M(r) decrease by the factor
Correspondence between layers of medium which convey a segment of a converging shock wave and a line of Newton spheres whose masses decrase in proportion to the masses of the layers of medium is depicted in Fig, A1.
We may treat λ as a mean free path far the particles which contribute to the mass M. Then we consider, in
effect, a sequence of Newton spheres of progressively decreasing mass which now are equally spaced from each other by distance λ. A disturbance propagates down the line of spheres, the energy being kinetic in form over the distance λ, and then for the short duration of inter- sphere impact becoming potential energy of elastic compression. We have to consider an elastic collision between adjacent spheres along the line. Initially the more massive sphere has velocity v1 and the less massive sphere is at rest. After the collision the respective velocities, v'1 and v2, are found by conserving momentum and energy. Specifically 1
with solution
v2/v1 = 2μ/(1 + μ)
v'1/V1 = (μ - 1)/(μ + 1) (A3)
From (A1)
μ = (1 + λ/r)2 ≃ 1 + 2λ/r (A4) and from (A3)
v2/v1 - 1 = (μ - 1)/(μ + 1) (A5)
Assuming λ << r, so that μ << 1, we have
v2 = v1 - (dv/dr)λ, μ ≃ 1 + 2λ/r (A6) where we assume λ/r << 1. Hence (A5) becomes
- (dv/dr) (λ/v) = λ/r (A7) which integrates to
v(r)/vo = ro /r (A8) where initial velocity is v for initial radius r .
The small remnant velocity
1 possessed by the more
massive sphere represents energy transferred from the disturbance to the medium, which is energy lost by the shock wave. The amount lost per propagation distance λ is
ΔW = W(v'1/ v'1)2 (A9)
Since λ/r << 1,
ΔW = - λdW/dr , v'1/V1 ≃ λ/r (A10) and we write (A9) as
dW/W = - λdr/r2 (A11) which integrates to
W(r) = Wo exp (λ/ro - λ/r)
≃ Wo exp (- λ/r) (A12)
Whilst λ/r « 1 it follows that W(r) ≃ Wo, which means little loss of shack wave energy. Exponential loss occurs for r≃ λ.
The above analysis neglects inelastic collisions in which energy is transferred from the shock wave into excitation of the atoms of the medium. Excitation is associated with any change of state, far example change from solid to liquid, from liquid to gas, or from gas tα plasma. Convergence from ro to a radius much less than ro implies ro /λ elastic collisions and ro /λ* inelastic collisions. If λ* > λ when particle energy becomes comparable to the energy of the excitation transition, neglect of inelastic processes may be justified. (ii ) Self-similar Hydrodynamical Solution
For a gas with specific heat ratio γ, the hydrodynamical shock equations expressing mass conservation, momentum conservation and entropy conservation take the form [11
δ (In ρ > /δt + uδ (ln ρ)/δr + δu/δr + (n - 1)u/r = 0 δu/δt + uδu/δr + ρ-1 δp/δr = 0
[ δ/δt + uδ/δr] ln (pp- α) = 0 (A13) where n = 1,2, or 3 for a plane, cylindrical or spherical wave respectively. The third equation expresses that the comoving derivative of entropy vanishes, specifically
dS/Dt = 0, S = cV In pV + const (A14) where cV is specific heat at constant volume.
The equations (A13) applied to a spherical imploding shock wave of radius R(r) in a medium which has constant undisturbed density ρo admit "self-similar" solutions which separates the time and special dependence of the
fluid parameters [2,3,13. Instead of u(r), p (r) and p(r) far the velocity, density and pressure of fluid behind
the shockfront, we introduce respectively v(ξ), g(ξ) and
π(ξ) , where ξ = r/R(t) and
A dot is used to denote d /dt. The implication is that
each of the spacial fields u(r), p(r) and p(r) at time t
can be obtained from those at time t by applying time- dependent scaling factors, different far each field.
Substitution of (Δ15) into (A13) yields
V )
where dash means d/dξ . Solution by separation of the
variables t and ξ now is possible. One puts
in which case it follows that
so that (A16) reduce to
(v - ξ)(ln g)' + v' + 2v/ξ = 0
kv + (v -ξ )v' + π'/g = 0
(v -ξ )[ln(πg
-α)]' + 2k = 0 (A19)
which are linear ordinary differential equations for
functions v(ξ ), g(ξ ) and π(ξ ). In solving (A19)
conservation laws at the shockfront impose one set of
boundary conditions, and conditions at launch impose
further boundary conditions, assuming that the self- similar solution describes the motion at all times and is
not merely an asymptotic approximation.
Integration of (A17) proceeds by writing
Then we obtain
where C and to are integration constants, and A = (C/α)α .
When k = 1,
m
where m and Ro are integration constants.
The choice for k amounts to imposing a boundary condition. We choose k = - 1, in which case a = 1/2 and the solution (A21) is
Then, by reference to (A15) we obtain
which is in agreement with (A8).
(iii) References
[1] Ya. B. Zel'dαvich and Yu. P. Raizer, Physics of shock waves and high-temperature hydrodynamical phenomena , eds. W. D. Hayes and R. F. Probstein, vol II, Academic Press, New York, 1967, pp. 794-806.
[2] G, Guderley, Luftfahrt-forsch. 19 (1942), 302.
[3] K. P. Stanyukovich, Unsteady motion of continuous
media, Engl. trans., ed. M. Holt, Academic Press, New York (1960).
APPENDIX B: ENERGY OF SHOCK-INDUCED FUSION BURSTS
(i ) Fusion Reactions and Cross Sections
In order to understand how the new invention differs from conventional ideas on fusion reactors it is necessary to outline the theoretical basis for nuclear fusion. We consider only the conventional D-D and D-T reactions, although others are possible. These reactions and the energies of the reaction products are
The two branches of the D-D reaction occur with about equal probability.
It is standard practice to express cross sections in terms of the kinetic energy of the bombarding particle
(deuteron) as observed in the rest frame of the target particle (deuteron or triton). The cross section σ is a function of the kinetic energy of the bombarding particle in the rest frame of the target particle. If μ is the reduced mass given by - is the
relative velocity in the rest frame of the target particle, then the relative kinetic energy is
where
μvDT = mDvD = mTvT = P* (B4)
(B3) expresses that the relative kinetic energy is the sum of the kinetic energies in the center of mass frame of reference with respect to which the particles have momenta ± p*. In the case of a collision between a deuteron and a triton we have reduced mass
μ = m
Dm
T / (m
D + m
T) = Sm
D/5 = 2m
T/5 (B5)
Because a cross section is a function of the energy of the bombarding particle in the rest frame σf the target particle, one brings all of the target particles (tritons) to rest in order to obtain the velocity distribution v
DT of the deuterons. Thermalization temperature θ (= kT) of this distribution is defined by
Cross sections are expressed as functions of relative kinetic energy w
DT = or an equivalent variable,
where m
D is the mass of the bombarding
particle. From (B6) the different energy variables are related by
For example , in the case of a deuteron with kinetic energy kev in the center of mass frame of
reference , we have = 4 kev, and hence
W
DT = 10 kev, so θ = 6. 67 kev and = 16. 67 kev. In
These cross sections as functions of w are given in Fig. B1, after ref. [13. The analytical ex
prssions are φ
where w is in kev and σ is in barns (1 barn = 10-24 cm2).
Because particles in the high energy tail of a
Maxwellian distribution of velocities make the major contribution to fusion rate which is proportional to
V
DTσ(v
DT), it is necessary to average this product over the distribution. The result, as a function of is
given in Fig. B2, after ref. [13. The analytical expressions are
<σ DDvDD> = 2.33 x 10-14 θ-⅔ exp(-18.76/θ⅓ ) cm3 s-1
<σ DTvDT> = 3. 68 x 10-1 2 θ- ⅔ exp (- 19. 94/θ⅓ ) cm3s -1 (B10 )
The unequal sharing of energy among the particles which results from thermalization boosts fusion rate by factor T 17 4
r
where values are given by (B8).
( ii ) Bremsstrahl ung Cooling Time
The question of the duration τ of power release raises the topic of cooling time . Cooling is caused primaily by X-ray bremsstrahlung (radiation due to acceleration of electrons by deflection in the Coulomb field of ions of charge Ze). The power Pb in watts radiated by Ne electrons in a plasma with charge-weighted ion density n and electron temperature θe is [1]
Pb
where θe in -3
with summation over different species s of ions, species s with charge Zse being present in density ni s
In the case of Li2DT we have particle densities
nLi = 6 x 10 22C cm-3, nD = DT = nLi /2 (B14) where C is the factor by which the medium is compessed relative to the undisturbed medium. In the case of full ionization we have
D D
e x D
so that
e = 160 n . For a pure DT pellet we would hav so that presence of Li
3+ increases radiativ
loss by a factor of 40.
Substituting into (B12) θe = 6.67 kev and
1
60 where n
D =
cm and V = 0.1 cm
3,
Pb = 8 x 1016 C watt (B16)
This radiative power loss exceeds the fusion power (14) by a factor of about 8, and it must not prevent the threshold temperature for release of fusion power from
being attained. The question becomes what is the radiative loss energy during the time for ions to thermalize with electrons. Note that both fusion power PF and X-ray bremsstrahlung power Pb are proportional to C, so that compression does not influence PF /Pb .
If thermal energy in the focal volume is Wth = 10 MJ, as previously estimated, bremsstrahlung cooling time is tb = wth /Pb ≃ 0.1 C-1 ns (B17)
Radiative loss of energy is delayed by two considerations. The full ionization of atoms may not be achieved before the ions thermalize to ≃ 6 kev, and secondly the time for ions to share their energy with electrons is longer than the time for the ions to share energy among themselves (see below).
(iii ) Energy Transfer Times
Two other time scales are of importance. One is thermalization time tT , which is the time for particles with an arbitrary distribution of velocities to come to the Maxwellian distribution. The other is the time teq for hot positive ions to share their heat with cool electrons. The time t T is important in order that the boost factor α due to ohermalization of deuteron energies can be realized quickly. The time teq is important because bremsstrahlung coals electrons, but not necessarily deuterons if the time for exchange of heat between deutrons and electrons exceeds cooling time for the electrons.
For t
T we use a formula derived by Spitzer [23 for particles of mass A
i (in atomic units) with charge Ze which are present in number density n.: )
Here factor ln
arises because multiple small angle deflections at long range statistically deviate a
particle through angle π/2 before a large deflection at small angle, and under the present conditions we may assume In
= 6.7. The values A = 2, Z = 1, T = 10
8 oK , and n
i = 6 x 10
22 cm
-3(for Li
2DT) yield t
T = 40 C
- 1 ns.
For cooling rate due to transfer of energy to relatively cold electrons, Spitzer [23 gives
dθ
i /dt = - (θ
i - θ
e )/t
eq (B19) where
For values, Ai = 2, Ae = 1/1836, ni = 6 x 1022 C, Z = 1 and ln = 6.7, we may reduce (B20) to
teq = 1.6 x 10-26C-1(Te/Ae + Ti/Ai)3/2 (B21)
Initially the term Ti /Ai is dominant, but after electron temperature exceeds about Ti /1000 the term Te /Ae becomes dominant. Up to Te ≃ 106 °K bremsstrahlung cooling rate is not a serious loss, so the question is how long does it require to heat electrons to 10 ºK. We put Te /Ae = 1836 x
106 ºK, and obtain from (B20) teq≃ C-1 ps.
We conclude that cooling by bremsstrahlung is not delayed significantly by either thermalization among ions or by thermalization between ions and electrons.
(i v) Conventional Approaches to Nucl ear Fusi on
The ratio of fusion energy to thermal energy is )
Noting that N / (
D + N
T) = 1/2 and ε
DT ≃ 3000 for kev, and again taking (σ
DT v
DT ) ≃ 4 x 10
-17 cm
3s
-1
for θ = 6.67 kev, it follows that
n T = 2 x 1013g cm-3s (B23) where ne = nn + nT = 2nD). The relation (B23) is the
Lawson criterion for DT fusion at θ ≃ 10 kev. It relates the time of confinement τ to the density ne of the
confined plasma without consideration of practical limitations an ne and τ in order to obtain a given gain factor, say g = 1.
In the two major approaches to fusion currently being researched the values of ne and τ in (B23) are vastly different. For magnetic confinement, ne ≃ 1013 cm-3 and τ ≃ 1 s. In the inertial confinement approach ne ≃ 1025 cm-3 and τ ≃ 1 ps.
(a) The approach of longest standing employs magnetic fields to confine plasmas, but it continues to be difficult to confine a plasma at temperature ≃ 10 kev with density ≃ 10 13 cm-3 for the required time τ ≃ 1 s.
Confinement times in tokamaks are 10 - 100 times shorter than predicted, and modifications are being suggested
[33, A variety of magnetic confinement systems have been considered [4].
(b) Inertial confinement, a more recent approach, is usually implemented by irradiating isotropically a pellet of fusion fuel by fαcussed high-power laser pulses. An absorber layer surrounds a driver layer which encloses DT fuel. Rapid ablation of the absorber layer launches, as a reaction, an imploding shock wave which compresses the pellet to very high densities. Laser pulses of energy
1 - 1.5 kJ and duration 0.6 - 0.7 ns have compressed a pellet of fusion fuel from radius 150 μm to radius 30 μm
(as revealed by X-ray bremsstrahlung images), the compressed densities being 20 - 40 g cm-3 implying ne ≃
(0.5 - 1) x 1025 cm-5 (100 - 200 times the density of liquid DT) [5]. The aim is to achieve the high particle density before heat arrives. The neutrons produced indicate that the Lawson criterion (B23) with g = 1 still has not been met.
The possibility of replacing laser beams by heavy ion beams in the "inertial confinement" approach has been considered, but not yet tested [6]. The aim is to implode a spherical hollow shell comprising an outer heavy tamper
layer, a middle absorbing layer, and an inner frozen DT layer. The sudden heating of the absorber layer by the charged particle beam generates an implosion as a reaction to expulsion of the tamper, as happens with the laser beam radiaion. A beam current of a few mega-amperes delivers energy of a few mega-joules to the target in a time of perhaps 100 ns. Heavy ions are preferred to light iαns as their kinetic energy is greater and their range in the target is smaller. In proposed devices, implosion velocity is calculated to reach 3 x 10 7 cm s-1. Ignition is supposed tσ occur at "spark radius" 75 μm when pressure is 0.2 Tbar (= 2 x 10 17 dyne cm-2).
The present proposed shock wave fusion generator, in type A form, can implode a hollow shell of fusion fuel more effectively than the charged beam technique, because the driver is a hollow shell of much greater particle density with better isαtropy.
(i v) References
[ 1] S. Glasstone and R. H. Lovberg, Controll ed
thermonuclear reactions, Van Nαstrand, Princeton, N.J. (1960) pp. 6-32.
[2] L. Spitzer, Physics of fully ionised gases,
Interscience Publ., New York (1956) pp 65-81.
[33 N. Rostαker et al., Magnetic fusion wi th high energy self-col liding ion beams, Phys. Rev. 70 (1993) pp. 1818-1821.
[4] F.F. Chen, Al ternate concepts in magnetic fusion , Phys. Today, May (1979) pp. 36-43
[5] R. L. McCrory et al., Laser compression and stabili ty in inertial confinement fusion, Plasma Phys.
Contolled Nucl. Fus., 31 (1989) pp, 1517-1533.
[6] R.C. Arnold and J. Meyer-ter-Vehn, Inertial
confinement fusion dri ven by heavy-ion beams,
Rep. Prog. Phys. 50, (1987), pp. 559-606.