A linear accelerator of lanthanum hexaboride particles for impact fusion

Nuclear Instruments and Methods in Physics Research A 334 (1993) 569-572 North-Holland

NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH Section A

A linear accelerator of lanthanum hexaboride particles for impact fusion Alexandre E. Pozwolski

Education Nationale, 6 rue de la Plaine, 75020 Paris, France

Received 12 October 1992 and in revised form 30 April 1993

A linear accelerator of dust charged particles is described. Because of the low charge over mass ratio of these particles the frequencies involved are smaller by two orders of magnitude compared to proton accelerators . So the device is excited by a sinusoidal voltage applied between grids, their spacing being adjusted so that the transit time between adjacent grids is always equal to a half-period, thereby suppressing the need of drift tubes. With lanthanum hexaboride particles the final velocity is above 400 km/s for an acceleration up to 30 MV . The impact temperatures resulting from the collision of such beam with a relatively slow beam of barium hydride BaDT particles are well in the fusion range. 1. Introduction The transformation of the kinetic energy of a projectile into heat in order to reach temperatures in the fusion range has been first suggested by Winterberg [1]. Maisonnier [2] also has considered fusion induced by macroprojectiles accelerated up to 2 x 10 6 m/s. A linear accelerator at least 100 m long looks necessary. We have shown [3] that the association of deuterium and tritium with a heavy metal like uranium would allow the reduction of the accelerating voltage by a factor about 100 because of the superheating effect of the heavy metal [4]. A general review of the problems associated with impact fusion was given lately [5]. In this paper we consider the acceleration of charged lanthanum hexaboride (LaB b) particles using a linear accelerator . The reason of this choice will be justified in the next section. Such accelerator would have several distinctive features that will be investigated . 2. Choice of the material It can be shown that the impact temperature T of a projectile of atomic mass M and velocity v is T=Mu e/3R, where R is the perfect gas constant. Classically, a projectile of mass m and charge q, accelerated by a potential difference U, will get a velocity v = (2qU/m) t/2 .

(2 )

Now, for a spherical particle of radius r the charge over mass ratio is q/m = 3e 0 E5/pr,

(3)

where p is the density (kg/m3), eo = 10 -9 /36ar (F/m) and ES = 10 1° V/m is the maximum electric field at the surface for positively charged particles (limitation due to the tensile strength of the material). For negatively charged particles ES is about one order of magnitude smaller, limited by auto-electronic emission . Combining eqs. (1), (2) and (3) we find easily that the impact temperature is T = 2ME OESU/Rpr = 0 .02125 UM/rp

(4)

for positively charged particles. Eq . (1) shows that for a given velocity the highest temperature is obtained for the material having the highest atomic mass (uranium) but from eq . (4), for a given accelerating potential, the highest temperature is got for the material having the highest M/p ratio. Cerium (M = 0.14 kg, p = 6700 kg/m 3) and barium (M = 0.138 kg, p = 3800 kg/m 3) are of special interest . These metals give with deuterium the stable combinations CeD 2 and BaD2. The maximum values of q/m for cerium and barium particles of radius r = 10 -7 m are respectively 393 and 693 C/kg . But the above results are just theoretical . However, it was experimentally proved that lanthanum hexaboride microparticles have an amazing charge over mass ratio, reaching 3000 C/kg for particles of radius 0.05 Rm . As a matter of fact such microparticles have been successfully accelerated over 110 km/s using a 2 MV Van de Graaff accelerator [6]. We have recently considered the

0168-9002/93/$06 .00 © 1993 - Elsevier Science Publishers B.V. All rights reserved

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A.E. Pozwolski / A linear accelerator of LaB6

achievement of high temperatures for fusion purpose using LaB6 projectiles in do accelerators [7]. Here we shall take advantage of the special properties of LaB6 using a moderate ac voltage in a linear accelerator . For a total accelerating voltage of 30 MV the velocity of the LaB6 particles would reach 425.7 km/s resulting in an impact temperature for lanthanum over 10 9 K. Fusion reactions are expected to occur when such fast beam crosses a relatively slow beam of BaDT particles accelerated at say 20 km/s ; this will be considered in section 7. 3. The design of the linear accelerator Lanthanum hexaboride particles are charged by contact. This may be carried out using needles arranged on a concave spherical surface, as suggested by Winterberg [1]. Alternatively the dust plasma generator designed by James and Vermeulen [8] looks specially useful for charging large masses . Such generator is sketched in fig. 1 : the LaB6 powder is deposited on plate A where the grains are negatively charged and then attracted by the grid B. These negative grains travel in the field free region between the grids B and C and then reach the plate D, 30 kV positive with respect to A. So between B and C there is a globally neutral cloud of particles of both signs. Now if the switch SW swings on position Q a 50 kV voltage will propel the positive grains to the right, inside the accelerator, whereas the negative grains are swept to the

left : this ensures current neutralization. The positive grains are first pre-accelerated by a do potential u = 500 kV applied between grids SS' (SS' = 3 m) and G1. These grids are concentrical and 0.5 m apart, The radius of SS' is R1 = OA' = 32 m and the area of SS' is 7 m2 . The beam of macroparticles enters the accelerator with the initial velocity r;o = 54 .7 km/s and its mass is m, = 121 mg . The voltage driving the accelerator is an ac potential u = Um sin wt . The rms voltage is 500 kV, the peak voltage is Um = 707 kV, and the average value of the voltage during a half-period is Ua = 2Um /ar = 450.15 kV . The frequency is f = 1 MHz, to = tar f and T = 1/f. The potential difference between grids G, and G2 is u = U, - U2 = Um sin wt . L, is the distance between G, and G2 and so the field is (Ut U2)/L, . If x is the distance covered by a particle entering G1 at t = 0, x = 0, with the velocity uo, then the acceleration of this particle is d2x/dt 2 (gUmlmL,) sin wt which integrates to dx/dt = (gUm/mL,w)(1 - cos cwt) + u, and x = (qUm /mL1w)(t - sin wt/w) + t,,,t. The particle is supposed to reach G2 (x=L l) when t = T,)12 so L 1 = gU.TO/2mLtw + voTo/2, which is equivalent to : L2 f2-UOLrfl2-gUml4arm=0 .

-15kV

Fig. 1. Schematic diagram of the accelerator : dust particles are first deposited on plate A and then a dust plasma is obtained between grids B and C. When the switch SW swings on position Q the positive grains are driven into the accelerator after pre-acceleration by the potential Uo. The ac potential u always accelerates the particles, first between grids Gl and G2, then between grids GZ and G3 etc. NN' is an exploding wire for neutralization . Actually all the grids are centered on 0, the focal point . There are 66 sections .

A . E. Pozwolski / A linear accelerator of LaB6

57 1

if such capacitance is associated with a shunt loading by an inductance L = 1/Cm 2 = 6 .33 x 10 -7 H . Let R i = 0 .001 fl be the resistance of such inductance . Then the total current is I = U,~, x R,/L20)2 = 31 .6 A. The corresponding power is P = U,ms x 1= 15 .8 MW . It could be reduced by lowering R i , using cryogenic techniques. The power needed to accelerate the beam (assuming one shot per second) is p = (1/2)m,u 2 = 10 .963 MW . The power efficiency is p/p + P) = 41% . Such value looks acceptable, however the previous figures clearly show, as expected, that a thermonuclear device is valid for a large output power only. We consider that each shot should release at least 1000 MJ and will discuss this point in section 7. 5 . Possibility of a compact version

Fig . 2 . The length L T of the accelerator (in m) and the velocity u (in km/s) as a function of the number N of sections . Curve (a) is for a normal version, driven by a voltage of frequency 1 MHz . Curve (b) depicts a compact version with a driving voltage at a frequency of 3 .5 MHz . The solution is : 4L, f = o o + (u 2+T2

)r/2

where v 2 = 4qU./m-rr = 2gUa /m. The final velocity of the particle leaving G 2 is

r

V f =u o +u 2 /lVO +(u

_ t/2 2 +i7,2 ) f/21=(uo+u2)

Numerically v = 51 .98 km/s, o f = 75 .5 km/s and L 1 = 3 .25 cm . Such length grows as the inverse of the chosen frequency . Now when the particle is leaving G 2 the potential difference between grids G2 and G 3 is U2 U3 = -u and after a half-period it is still an accelerating voltage. Similar calculations give the length of the subsequent sections . The curve (a) in fig . 2 gives the length of the accelerator viz . the number of accelerating sections . For an accelerator including 66 sections (67 grids) the length of the last section is L 66 = 21 .2 cm and the total length is L, = 9 .5 m . The lowest curve gives the velocity profile inside the accelerator . The final velocity is u = 425 .7 km/s corresponding to an acceleration by a potential u 2 /(2q/m) = 30 .2 MV = 66Ua + 0 .5 . All grids are centered on 0 and their sizes regularly decrease from 2 .95 m for Gf to 2 .06 m for G67 . 4. Power required to drive the accelerator The capacitance of the grids is of the order of C = 4 x 10 -s F . Resonance conditions will be reached

The length of the accelerator can be shortened merely by increasing the frequency of the applied voltage . But this introduces a danger of breakdown if the grids are too close . This can be avoided to some extent using magnetic insulation [9] . The magnetic field should be perpendicular to the electric field and for instance an induction of 0 .14 T would allow an electric field of 29 .4 MV/m . Such induction practically does not affect the motion of the considered macroparticles . If the frequency f increases to 3 .5 MHz, the other electrical parameters remaining unchanged, the length of the first section becomes L 1 = 0 .93 cm, and for the last section L 66 = 6 .06 cm . So now the total length of the accelerator is reduced to L t = 2.71 m . The curve (b) in fig . 2 gives the length as a function of the number of accelerating sections . The velocity profile is unchanged . 6. Focusing and space charge problems There are little space charge problems inside the accelerator because of the low value of the q/m ratio and the large section of the beam . However, outside the accelerator, as long as the beam converges toward 0, space charge problems will become more and more important . So the beam should be neutralized just at the exit of the accelerator . This may be readily achieved by a copper exploding wire NN' . Since the beam carries 0.363 C, 0 .241 mg of copper singly ionized would supply the needed electrons. Or, in a simpler way, a pulsed electron gun would serve the same purpose . In permanent conditions the space charge limit current density is given by the well known Langmuir Child equation : J=(4/9)(2q/m) f / 26 O U 3 / 2/L 2 . Taking U = 450, 150 V, the average voltage applied between two grids, an average spacing L = 0.1 m and q/m = 3000 C/kg we find J = 9 .19 A/m2 corresponding to a mass current Jm = 3 .06 g/(m 2 s) .

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A.E. Pozwolski / A linear accelerator of LaB6

6.1 . Elimination of boron In a beam of LaB6 microparticles of velocity c = 425.7 km/s the kinetic energy of a lanthanum atom is 130.7 keV and for a boron atom such energy is 10 .34 keV. If such beam interacts with a DT fuel target the boron may have a cooling effect and its elimination may be desirable. It was experimentally proved [61 that in a rarefied air atmosphere (no numerical data) a thermal dissociation of LaB6 occurs, resulting in pure lanthanum projectiles. Incidentally such dissociation is inseparable of a strong ionization of the molecules of the background atmosphere, making possible auto-neutralization. The energies involved in the dissociation and ionization processes, a few eV, are quite negligible compared to the energy of a lanthanum atom . 7. Conditions at the focal point 0 At the focal point 0 the fast beam carrying 121 mg of LaB6 particles will meet, coming from the opposite direction, a slow beam of BaDT particles, q/m = 400 C/kg, accelerated by a do 500 kV voltage to a velocity v'= 20 km/s . In order to release 1000 MJ such beam should carry 2 .953 mg of DT or 84 .45 mg of BaDT . The chemical composition when the beams meet is BaDT, LaB6. The densities of LaB6 and BaDT are respectively 4610 and 4210 kg/m 3 so, neglecting compressibility the mixture occupies a volume of 0.0462 cm 3 corresponding to a sphere of radius R' = 0.0222 cm . The atomic density is of the order of ni = 5 X 10 22 cm -3 . The inertial confinement time is of the order of T = R'/1~ = 5.2 X 10 -9 s so the Lawson criteria is checked since ni T = 2.6 X 10 14 . 7.1 . Temperature resulting from the impact For a global composition LaB6 + y(BaDT) the equipartition of energy results in the following temperature, neglecting the electrons, as it will be shown in the next section: T= [(M,a+6MB)u2+Y(MBa+MD+MT)U,21 /3R(7 + 3y) .

(8)

If boron could be eliminated then the temperature would become : 2 T = 1MLaV +Y(MBa +M D+MT)tJ' 21 /3R(1 + 3y) .

For the above composition y = 1 and T= 149 X 10 6 K in presence of boron; without boron T= 252 X 10 6 K. These values are more than enough to ignite fusion

reactions and so it looks that the quantity of DT fuel could be increased. Taking y = 4 the temperatures are almost the same with or without boron and equal to T= 78 X 10 6 K resulting in the possible release of 4000

mi.

7.2. The superheating process The heating of deuterium by lanthanum is a kind of Fermi acceleration [10,111. When a deuterium atom of initial velocity = 0 undergoes a headon collision with a lanthanum atom of velocity u = 400 km/s it rebounces with a velocity 2u = 800 km/s (energy 6.64 keV) . A second headon collision will result in a velocity 4u = 1600 km/s (energy 26 .5 keV). Assuming an interatomic distance d = 2 .7 Á the collision time is tc = d/u = 6.8 X 10 -16 s. So deuterium will reach fusion conditions in the order of 10 -15 s. But on the contrary, for the electrons, the exchange of energy with the heavy atoms is a very slow process because of the huge difference of mass . Initially the electrons are cold degenerated fermions whose contribution to the specific heat is quite negligible . They are always colder than the ions, a very significant difference with plasmas obtained from strong electrical discharges . 8. Conclusion Impact fusion looks a quite feasible process. Velocities in the range of a few hundreds of km/s are necessary and a linear accelerator of reasonable length can achieve such performance. The main difficulty is to realize grids with large meshes and having a good transparency. This should be checked by experiment . The use of lanthanum hexaboride looks specially attractive because of its exceptionally high charge over mass ratio and the high atomic mass of lanthanum. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]

F. Winterberg, Z. Naturforsch . 19a (1964) 231. C. Maisonnier, Nuovo Cimento XL2B (2) (1966) 333. A. Pozwolski, Patent no . 2 081 241 Paris (1970) . A. Pozwolski, Phys . Lett. A44A (1973) 196. A. Pozwolski, Laser and Particle Beams 4 (1986) 157. J.F. Friichtenicht and D.G. Becker, Astrophys. J. 166 (1971) 717. A. Pozwolski, Laser and Particle Beams 11 (3) (1993) . C.R. James and F. Vermeulen, Can. J. Phys. 46 (1968) 855. F. Winterberg, Atomkernenergie-Kerntech . 44 (1984) 312. E. Fermi, Phys. Rev. 75 (1949) 1169 . A. Pozwolski, StatPhys 14, ed . H.J . Kreuzer, Edmonton, Canada, Book of Abstracts (1980) p. 129.