Patent Number: 043280706
Section: description

DETAILED DESCRIPTION OF THE INVENTION The invention proposed, in comparison to previously proposed inertial confinement fusion drivers, promises to reduce greatly the driver power, and also substantially to relax the focusing requirement. The concept is explained in FIG. 1. The thermonuclear pellet T is placed in the center of a spherical cavity with the initial radius r=r.sub.o and which is several times larger than the pellet radius r.sub.p. The cavity is formed by a pusher P consisting of dense material, preferably uranium. Inside the cavity is a low density gas of a sufficiently high atomic weight, for example krypton. The pusher of the spherical cavity is surrounded by an ablator A. If beams B are projected onto the ablator A the pusher will be imploded with the velocity v. The fact that the outer ablator radius is larger than the pellet radius greatly relaxes the focusing requirements compared to direct pellet fusion. Because the beams are here only of modest power and because the outer ablator radius of the cavity is larger than the pellet radius the implosion velocity too will be here smaller than required for direct pellet fusion. The imploding pusher upon its impact on the krypton gas generates a shock wave, provided the gas density is sufficiently high to make the collision mean free path small compared to the cavity radius. Because of the many atomic transitions in the krypton gas and which are excited at the high temperature behind the shock front, the kinetic energy in the shock front will be rapidly converted into photons with the result that the cavity will be filled with black body radiation. If the density of the krypton gas is sufficiently low, but still sufficiently high to make a shock wave, one can ensure that the cavity itself is optically transparent. Then, if the implosion velocity of the cavity is sufficiently high the losses of radiation through the cavity wall can be made sufficiently low and the thusly formed black body radiation is highly compressed. The imploded black body radiation confined by the dense pusher wall will thereby expose the pellet surface to a power flux rising in proportion to T.sup.4. Furthermore, since the opacity of the pellet surface rises in proportion to T.sup.-3.5 the total power absorbed by it will rise in proportion to T.sup.7.5. The temperature of the black body radiation, if perfectly confined by the walls of the cavity, rises insentropically according to VT.sup.3 =const., where V is the cavity volume. For r.sub.p &lt;&lt;r one has Tr .perspectiveto. const. and the photon power flux transmitted to the pellet rises in proportion of r.sup.-7.5. By the absorption of the black body radiation in the pellet surface, the pellet is then itself ablatively imploded. If the implosion velocity V is constant one has for the time dependence of the cavity radius r=r.sub.o (1-t/t.sub.o), with t.sub.o =r.sub.o /v. Therefore, the total radiation power delivered to the pellet surface rises as EQU P(t)=4.pi.r.sup.2.sub.p .sigma.T.sub.o .sup.4 (1-t/t.sub.o).sup.-4 (1) where .sigma.=5.75.times.10.sup.-5 erg/cm.sup.2 sec .degree.K..sup.4 is the Stefan-Boltzmann constant. The total power absorbed rises as EQU P.sub.a (t).varies.(1-t/t.sub.o).sup.-7.5 (2) It thus follows that the power absorbed is strongly peaked at the end of the implosion process near t=t.sub.o. This simply means that during the implosion process the kinetic implosion energy of the pusher is first converted and intermediately stored in the form of black body radiation and only at the end of the implosion process delivered at high peak power to the pellet. This intermediate storage of the available energy into black body radiation makes it possible to work with a greatly reduced initial driver power. Furthermore, since unlike in laser fusion, the wave length is here much shorter and in the soft X-ray region, much larger pellet compression should be possible. The reason for this is that the plasma frequency of the target must be well matched to the frequency of the incoming radiation to assure good energy deposition in the target surface and hence high ablation implosion efficiencies. The minimum required velocity for the cavity implosion can be estimated from the requirement that the power of the black body radiation shall be .about.10.sup.14 Watt onto a pellet surface of .about.10.sup.-1 cm.sup.2. According to the Stefan-Boltzmann law this power is reached at a temperature of T.perspectiveto.3.6.times.10.sup.6 .degree.K. However, to store an energy of .about.10.sup.7 Joule in the form of black body radiation this would require a cavity volume of V=75 cm.sup.3. This rather large volume suggests to go to higher temperatures which not only reduces the required cavity volume but also increses the radiation power which is inversely proportional to it. As a reasonable compromise we choose the initial temperature to be 5.times.10.sup.6 .degree.K. which during the cavity implosion shall rise to .about.10.sup.7 .degree.K., implying a reduction in the cavity radius by a factor two and representing a very modest implosion. At a temperature of 10.sup.7 .degree.K. the final cavity volume is just 1.3 cm.sup. 3. The maximum total power incident at the pellet inside the cavity and reached at T=10.sup.7 .degree.K. is then 5.75.times.10.sup.15 Watt. The intitial and final cavity radius are here 1.4 cm and 0.7 cm. Since the ablator radius is of the same order, the beam focusing requirements can be easily met using light ion beams, one of the cheapest drivers. If a solid wall, in our case the pusher wall, moves into a gas of atomic weight A a shock wave moves ahead of the wall with the temperature behind the shock front given by (1) ##EQU1## where R is the gas constant, and Z the degree of ionization approximately given by ##EQU2## From (3) and (4) one can compute v to reach a desired value of T. For T=5.times.10.sup.6 .degree.K. and A=200 one finds v=46 km/sec, and for krypton with A=83, v.perspectiveto.71 km/sec. In the considered temperature range the collision cross section is .about.10.sup.-16 cm.sup.2. This requires to make the atomic number density of the shock heated gas not less than .about.10.sup.18 cm.sup.-3. To make the gas optically transparent the photon path length .lambda..sub.p =(.rho..eta.).sup.-1 (.rho. gas density) has to be larger than the cavity radius r.about.1 cm. The opacity coefficient .eta. is here given by (2) ##EQU3## where g.perspectiveto.1 is the Gaunt and t the guillotine factor. In stellar atmospheres one puts t.perspectiveto.10 but because of the great level density in high atomic weight material one may probably put t.perspectiveto.1. It thus follows that at T.perspectiveto.10.sup.7 .degree.K. and for .rho..ltorsim.0.3 g/cm.sup.3, corresponding to an atomic number density of .ltorsim.10.sup.31 cm.sup.-3, the optical path length is larger than .about.1 cm. Therefore, at an atomic number density of .about.10.sup.18 cm.sup.-3, as required for shock heating, the gas is optically transparent. To make the gas pressure smaller than the radiation pressure requires to put the atomic number density less than 10.sup.21 cm.sup.-3. Therefore, after the gas, having an atomic number density of .about.10.sup.18 cm.sup.-3, has been shock heated the work done by the pusher is primarily against the radiation pressure. Of crucial importance for the feasibility of the concept is the confinement of the black body radiation in the imploding cavity. The velocity by which the radiation can escape through the cavity wall is given by the radiative heat flux (a=4.sigma./c) ##EQU4## where .lambda..sub.p =(.eta..rho.).sup.-1 is the photon path length in the dense pusher wall. Putting j=aT.sup.4 v.sub.d, where v.sub.d is the photon diffusion velocity and .differential.(aT.sup.4)/.differential.x.about.aT.sup.4 /x, where x is the distance travelled by the diffusion wave, one finds ##EQU5## For T.perspectiveto.10.sup.7 .degree.K. and .rho.=18 g/cm.sup.3 one has according to (5) .lambda..sub.p =(.rho..eta.).sup.-1 .perspectiveto.2.times.10.sup.-4 cm. Putting x.ltorsim.1 cm, setting an upper value for the photon permitted to diffuse out of the cavity, one finds that v.sub.d .gtorsim.20 km/sec. Therefore, if v&gt;v.sub.d, the photon gas in the cavity will be compressed. More detailed calculations show, that at an implosion velocity of .gtorsim.50 km/sec the photon losses through the pusher wall are not very significant. The high final temperature of .about.10.sup.7 .degree.K. implies that the typical radiation frequency, given by h.nu..about.kT and which is in the soft X-ray domain, is matched to a plasma frequency of .about.10.sup.4 times compressed hydrogen. The proposed target bombardment by black body radiation is therefore much better suited to reach high target densities than the much longer wave lengths of laser beams. Furthermore, unlike laser beams, no stimulated Brillouin back-scattering occurs and the radiation reflected from the target surface is here not lost since all the radiation is trapped inside the cavity. The required low implosion velocity of .about.50 km/sec makes the proposed concept also an interesting candidate for impact fusion since those velocities should be attainable with relative ease by magnetic propulsion techniques. How this could be incorporated into an impact fusion target is shown in FIG. 2, where an incoming hypervelocity projectile generates and compresses black body radiation inside a conical cavity. If light ion beams are used to implode the cavity, the reduction in the implosion velocity from .about.200 km/sec down to .about.50 km/sec reduces the required beam power down to 1.5.times.10.sup.12 Watt. Light ion beams at these power levels and at the relaxed focusing requirement down to .gtorsim.1 cm.sup.2 can be already produced and therefore make them an especially promising candidate for the realization of the proposed invention. REFERENCES (1) L. D. Landau and E. M. Lifshitz, Fluid Mechanics, Pergamon Press, London 1959, pp. 331, 358. (2) M. Schwarzschild, Structure and Evolution of Stars, Princeton University Press, 1958, p. 67 ff.