Clean fusion concepts and efforts — A survey

NUCLEAR INSTRUMENTS AND METHODS 144 (1977)

1-7 ; ©

NORTH-HOLLAND PUBLISHING CO.

1. Invited papers on advanced ./uel Jusion ./easibility studies CLEAN FUSION C O N C E P T S AND E F F O R T S - A SURVEY ROBERT W. B. BEST

Association Euratom-FOM, FOM-lnstituut voor Plasmqlj~sica, R(/nhuizen, Jutphaas, The Netherlands

Fusion reactors as presently conceived are breeders of tritium and, possibly, plutonium as well; a single reactor produces hundreds of tons of radioactive waste per year. Comparatively clean fusion fuels which avoid the production of radioactive matter are reviewed, together with the physical concepts how these fuels can be burnt. The main problems are bremsstrahlung and ion cooling in the presence of electrons, and low power density in the absence of electronJ. Laser compression of pellets of a mixture of protons and boron-ll may be a solution when lasers in the megajoule range become awfilable. Other valuable R&D efforts are clamped beam-plasma devices, the migma cell, and direct converters.

1. Introduction: why not dt-fuel? The challenge to fusion ~ research is to tap the nearly inexhaustible energy source represented by the light elements. A quarter of a century of research has convinced many scientists that controlled thermonuclear transmutation of deuterium and lit h i u m into helium is feasible on earth. This would make a very clean energy source if not neutrons and tritium were involved in intermediate steps in the transmutation process. The burning dt-plasma acts as a 14 MeV neutron source of 8 Ci per thermal watt. Most of these neutrons produce tritium in the lithium blanket surrounding the plasma. The circulating tritium inventory a m o u n t s to tritium recycling time 8 x Ci/W(th). tritium decay time Assuming optimistically that the recycling time can be reduced to about a day the circulating tritium inventory of a large plant [1 GW(e)] will be a few MCi which in the form of tritiated water vapour represents a biological hazard potential (BHP) of 104 km 3 airt). Tritium handling is a technical and economic drawback for a fusion system: the tritium flow must be separated from the heat flow with extreme perfection and reliability. Not all neutrons will be absorbed in lithium. It appears to be very difficult to capture less than about ten per cent of the neutrons in structural materials, leading to radiation damage and a structural activity of the order of 1 Ci/W(th). The

Reactions between light nuclei are conventionally referred to as fusion in this paper though many are fission-like.

14 MeV neutrons necessitate large expensive reactor structures. Firstly, because about a metre of blanket and shielding is needed to absorb t h e m , and secondly, because they limit the wall-loading to about 1 M W / m 2, and even then the first-wall life-time is only a few years. The maintenance of these large radioactive structures and their treatment after use (hundreds of tons per year), present economic and safety problems. The structural activity represents, depending on the materials used in a 1 GW(e) reactor, a BHP between 107 and 10 ~° km 3 air~). The latter figure corresponds to the total atmosphere of the earth. T h o u g h this BHP is at least an order of magnitude below that of a fission reactor and the radioactivity is tied to solids, the risk may be considered unacceptable. There is no conclusive guarantee that the radioactive inventory and waste can be isolated from the biosphere to a sufficient extent during sufficiently long times. E n o u g h chemical and magnetic energy is present to disperse tons of metal. H u m a n failure and malice cannot be excluded convincingly2). Creating the possibility of catastrophic poisoning of the biosphere and controlling the corresponding technology seems to be compatible with military organization only. It will be irresistible from an economic or a military point of view to exploit the copious neutron flux from a dt-plasma to breed fissile material in addition to tritium3). Thus the risks involved in dt-fusion are really not much different from those of nuclear fission and probably equally uninsurable. Therefore, alternative fusion cycles should be considered seriously, with particular attention to low neutron production, if fusion is to be an attractive energy source for this world. 1. A D V A N C E D FUEL FUSION FEASIBILITY

STUI)IES

2

R. W. B. BEST

2. Clean fuels A search of the scores of possible reactions 4) of the more abundant light elements (i.e., the stable isotopes except 3He) indicates p~B as the most promising fuel with low neutron productionS). The reaction P + 11B ~ 3~,+8.7 McV has a 0.7 b high and 0.3 MeV wide maximum in the cross-section at 0.675 MeV proton energy, and another 0.2 b high very wide maximum at Ep = 1.4 MeV. The inevitable side reaction p+

11B ~

12C+7+

16MeV

has a cross-section of only 50/~b at E p - 0.7 MeV. The neutron-producing reactions p+llB

~ ~IC+n-2.8MeV,

c~+l~B __, l " t N + n + 0 . 2 M e V can be suppressed if the concentration of fast protons (Ep>3 MeV) and ~'s can be kept low. The cross-section of the (:zn) reaction on I~B is below 10 mb for E~
3He + ~He + 4 M c V

has a lower cross-section than pt~B: about 0.3b maximum at E p - 1.8 MeV with half-width 0.5 MeV 7). Since the loss rate in fusion burners tends to be proportional to Z 2, Li might still be competitive with B. An interesting feature of p6Li is that it produces 3He in a clean way, and 3He is itself a potentially clean fuelS): 23He ~ 4 H e + 2 p + I3MeV. The cross-section for this reaction is about 0.2 b at the neutron threshold (8 MeV, the binding energy of 3He). Also the reaction d + 3He =, " * H e + p +

3He, together with the half-width F of the maximum and the reaction energy Q, are listed for clean fuels; for comparison also tit-parameters are given in table 1. The quantity OMS is the 90° multiple Coulomb scattering cross-section; aMs = 2.6 Z2Z'2E 2, where Z and Z' refer to beam and target nuclei respectively. Other advanced fuels, such as dd and d6Li, are not considered in this paper since they produce a number of neutrons per unit of energy of the same order of magnitude as dtg).

18 M e V ,

which has 0.7 b maximum cross-section at E d = 0.4 MeV with half-width 0.5 MeV, could be quite useful if 3He could be produced without neutrons and if dd-reactions could be avoided (in a "two-component" burner with hot 3He and cold d, e.g.). The maximum cross-section ~ and the corresponding energy E of the incoming particle p or

3. Advanced fusion concepts 3.1. PLASMA The current fusion concept is to heat magnetically confined fuel above its ignition temperature at which fusion power exceeds bremsstrahlung loss. Then the reactor is kept burning by adjusting the cold fuel input and the ash removal rate. Heating and confinement of thermonuclear plasma have proved to be a formidable task, but it is plausible now that in a 10 billion dollar apparatus about l g of dt can be ignited and contained to produce 10 GW (all these are very rough numbers). Is it not plausible now that such an apparatus will produce net energy at a competitive price. Certainly, this fusion concept is even more difficult to realize for dSHe, and impossible for pltB and p6Li because of bremsstrahlung lossesS). The ignition temperature of d3He is an order of magnitude higher than that of dt, and p l l B and p6Li c a n n o t be ignited at all if the electron temperature is anywhere near the ion temperature. An advanced fusion concept is to compress fuel pellets or hollow spheres adiabatically, by the ablation pressure induced by laser irradiation, to 10 4 times solid density. It is then possible to reach pR-~ alues (density times radius) which exceed the mean flee path of bremsstrahlung photons 5) TABL 1 Fuel parameters.

plIB p6Li 3He dSttc dt

o(b)

E(MeV)

l(MeV)

Q(MeV)

oMs(b)

0.7 0.3 0.2 0.7 5

0.7 1.8 8 0.6 0.1

0.3 0.5 no max. 0.7 0.2

9 4 13 18 18

130 7 0.6 60 260

CLEAN

FUSION

(pl~ 5 g/cm2). The compression creates a temperature at which a significant part of the fuel fuses before it expands too much. For p~B a laser pulse in the megajoule range is needed~°), which is far beyond the realm of present technology and will require very large power plants to be economic. 3.2. BEAM PLASMA Another advanced fusion concept is the twocomponent or beam-plasma system, also called a wet-wood burner. Part of the fuel is contained at below-ignition temperature and another part is injected as a beam. The hot ions are injected at an energy above the maximum in the cross-section curve and slow down; the ion energy lSasses through the maximum, being transferred to the relatively cold electrons. The hot ions should be contained rather shortly (as compared with the above "dry-wood burner") and removed from the burner after slowing down to avoid quenching by inoperative ions. This means that rather simple confinement devices sufficel~). However, the wetwood burner is an energy multiplier with a multiplication factor which only slightly exceeds unity for the clean fuels. The multiplication factor equals 1 +F, where F is the ratio of fusion power and injection power; see table 2. Consequently, the energy of the particles leaving the burner must be converted very efficiently into electrical energy and largely recirculated to the ion injector. High efficiencies of converter and injector are feasible for ions in the MeV-range, but the resulting efficiency and economics of the whole system, consisting of injector, burner, and converter, tends to be poor, and for p6Li and 3He this concept cannot be realized at all. For details see the sections on these components. A concept to improve on the low value of the energy multiplier F is clamping. Magnetic adiabatic compression of the plasma pumps energy into

3

CONCEPTS

the particles, predominantly into the hot component, at a rate which compensates the energy loss rate of the hot ions to the cold electrons, thus clamping the ion energy at the maximum of the cross-section curve. The improvement is about a factor of 2; see the parameter G in table 2. In the decompression phase plasma expansion against the magnetic field pumps energy back into the field coils. The efficiency of this direct conversion of ~zparticle energy could be 60% 12). However, the price to be paid is a large, pulsed, and closed-line magnetic field configuration with high confinement time and difficult coupling to an expander and decelerator for direct conversion of the remaining plasma energy. 3.3.

COLLIDING BEAM

An advanced fusion concept which does away altogether with thermonuclear plasma is the concept of colliding beams. These beams should operate in the MeV-range where the multiple Coulomb scattering cross-section OMS is not much larger than the fusion cross-section for low-Z nuclei; see table 1. Essential for the colliding-beam concept is accurately prescribed ion motion with negligible electron-drag (contrary to the wet-wood burner) and less than 90 ° scattering from other ions (contrary to the collisional random motion of ions in I, thermonuclear plasma). The F-value for 3He can be estimated as (cr/CrMs)Q/E~0.5 from table 1. An already realized ion trajectory looks like a set of equally large circles which lie in a plane and pass through one central pointl3). In fact, the ~'circles" are not closed~ because of field inhomogeneity and scattering an ion precesses through many circles. An ion which scatters too much out of the plane leaves the " m i g m a cell". The problem with the colliding-beam device is that without neutralization it cannot contain more ions than a Debye sphere and, therefore, produces only milliwatts of

TABLE 2 Beam plasma parameters.

pl l B p6Li 3He d3He dt

0"O (× 10 15cm3s l)

nh rs (~ 1015cm 3s)

(

"[e IMe'v)

Pb/Pf

t"

(J

0.8 0.6 0.4 0.4 1

0.1 0.05 0.06 0.02 0.01

0.2 0.5 1 I 1

0.1 0,1 0. I 0.03 0.005

0.2 0.3 0.1 0.04 0.002

0.2 0.03 0.04 0.2 I

0.5 0.1 0.04 0.3 2

I. A D V A N C E D

FUEL

FITSION

FEASIBILITY

STUDIES

fusion power, while neutralization tends to violate the concept. An improved concept involves neutralization with non-Maxwellian electrons. Since ion-cooling is caused by electrons with less speed than the ions, i.e. with energies of about l keV and less, and bremsstrahlung is due mainly to electrons with energies around 100 keV and more, there is a strong incentive to taylor the electron-energy distribution so as to diminish the n u m b e r of electrons in both these low and high energy ranges. Instabilities caused by such tayloring can be suppressed in principle by feedback of unstable oscillations. The great virtue of the migma cell is its small dimension; this makes it possible to test the concept in inexpensive research, and it precludes the use of neutron-producing fuels for lack of room for magnet-shielding. If the colliding-beam concept turns out to work with 3He, then the problem is how to fuse p6Li to produce 3He. 4. Wet-wood b u r n e r

A s s u m e a two-component plasma consisting of hot ions with mass n u m b e r Ah, charge Zhe, and density nh, a cold ion c o m p o n e n t with parameters Zc and no, and electrons of temperature Te. The fusion power per unit v o l u m e is

Pf = nh n~ crvQ , where u is the hot ion velocity. The bremsstrahlung power in watt per cm 3 is Pb = 1.6× 10 -29 ( Z h n h -1- Zct7 c) (ZhH h -~ Z2~/c) Te~,

if Te is expressed in MeV and below 0.1 MeV: non-relativistic. T h e ratio between Pb and Pf is P__2 = 0.1 T¢I ( Z h + c Z ¢ ) ( Z ~ + c Z ~ )

Pf

crvQ

c

in which c = n¢/%. Te and Q are to be expressed in MeV and av in umts of 10-'~ cm3/S, as given in table 2. T h e last fraction in the expression for Pb/P,is m i n i m u m (Z~Zc+ZhZ~) 2 at c=(Zh/Z~) 3'2. It follows that a large difference in densities is required if there is a large difference in Z, to kee.o Pb/P~ low. The slowing-down time through the m a x i m u m of the cross-section is nh'Cs = 16

AhTel In Ei Z~(Zh +CZ~) E i - f '

in units of 10 ~5s / c m 3, where E~ is the injection energy and F the width of the resonance given in table 1. T~ should be expressed in MeV. In slow-

ing down an ion produces on the average F times its injection energy in fusion reactions:

F = CnhT~avQ/Ei. To answer the question whether the light or the heavy fuel ions should be injected, substitute nhrs and the optimum value for c in the expression for F, which then proves to be proportional to (73/273/2x_Z2Zc) 1 So the answer is that Z h < Z c ~h /~c ! maximizes F. But remember that in the case of d3He 3He has to be injected instead of d to avoid dd-reactions. In table 2 values are given for cry at the maximum of the cross-section curve, the slowingdown time r~, and some typical values for the densify ratio c = nc/nh, the electron temperature Te, and F = fusion power/injection power, consistent with tolerable bremsstrahlung power PbIn a clamped beam-plasma system the power fed into the hot ions, per unit volume, is nhE/r, where r is given by the above formula for the slowing-down time by electronic drag r~, but without the logarithmic factor. G, which is defined as the ratio o f fusion power and compression power, differs from F by the absence of this In-factor and the substitution of E for E~. Typical values are given in table 2. For more accurate calculations of F and G see ref. 14. 5. I n j e c t o r - c o n v e r t e r system A clean fuel burner can be viewed generally as a device which converts a mono-energetic and directed ion beam into another ion beam with more spread in ion energies and directions and more beam power. The usefulness of such a device depends on efficient ion acceleration and deceleration in injector and direct converter respectively. The pure acceleration or deceleration process in electric fields is very near to 100% efficient, but a variety of small losses occurs in the processes described below. The ion source consumes power which a m o u n t s to a few keV per ion produced. This is negligible for ions which are to be accelerated into the MeV range. As a rule the accelerated ions must be neutralized to be able to reach the centre of the magnetic field of the burner. The migma cell is an exception to this rule: single ionized He becomes doubly ionized in the centre. Neutralization is most efficient for negative ions, but still only 60% 15). The 40% non-neutralized ion loss can be recovered by direct conversion, to be considered

CLEAN

FUSION

below. The principles of direct conversion are due to Post and Moir16), The ions may leave the burner in many different directions, but by guidance in a weakening magnetic field initially transverse energy components are converted into longitudinal energy due to invariance of magnetic moment. The strong increase in longitudinal velocities, yet enhanced by the plasma potential, decreases the ion density to a value at which the Debye length exceeds the ion gyro radius. The expanding magnetic field lines should take the shape of a fan which, at the end,is a few ion gyro radii thick. Then, by curving the magnetic field lines sharply out of the fan plane, the electrons, which have the same velocity as the ions and, therefore, carry negligible energy, are separated from the ions which lose their magnetic moment and form a well-directed beam of low density, suitable lor the decelerator. (It is interesting to consider the transformation of the phasespace volume occupied by the ion beam: the initial spread along two transverse velocity coordinates is transformed into a spread along the longitudinal velocity coordinate and the space coordinate along the fan circumference.) The art of recovering the kinetic energy of an ion is to get it on an electrode just before it falls back in the decelerating field. A way to accomplish this is to add to the main E-field a spatially alternating transverse E-field which confines the beam by periodic focussing and extracts decelerated ions. It can be shown 17) that the optimum number of periods in which an ion of average energy is decelerated to rest is about 20; fewer electrodes imply poor matching of the continuous distribution of initial ion energies and the discrete set of electrode tensions, and more electrodes increase the number of ions which do not reach the electrode which matches best their initial energy. The finite number of electrodes, together with the initial energy spread in the ion beam, cause a loss of about 10%. The " i d e a l " efficiency of 90% is further reduced by space-charge effects. It has been shown analytically and computationally ~7) that these effects introduce a factor ( 1 - P / P 0 ) in the efficiency, where P is the initial beam power and P0 the saturation power:

CONCEPTS

5

pressed in MW per meter fan circumference. The smallness of P/Po is a matter of economics. Summing up, the main inefficiency in the injector-converter system is due to deficient collection of decelerated ions. Further losses, resulting from space-charge effects, residual electrons and neutrals in the decelerator, structural obstacles in the ion beam in the expander, etc., can be made negligible, though economics may prevent this. The heat dissipated at the collector electrodes can partly be recovered with the aid of a steam cycle. 6. Other effects A number of effects should be mentioned in this survey which, however, have little influence on the conclusions. When the electron temperature is raised to relativistic height the electronic drag on the ions is sharply reduced. The drag is due mainly to the slow electrons which have less velocity than the ions, so the drag is proportional to the height of the top of the electron distribution function, which goes like Te3j2 times a relativistic correction factor 18) (½ Tf~) ½ e - l/~ [ K 2 ( l / ~ ) ] - i

105 ~2 ..)-1 = (1 + '8~-~ + ~ x +. where ~z= kTe/rnec 2 and K2 is the modified Bessel function. This effect could enhance the F or G value of wet-wood burners very much if the relativistic regime were not inaccessible due to bremsstrahlung. Accurate formulae for the bremsstrahlung of a mildly relativistic electron gas are quite complicated, but a relativistic correction factor which fits quite well the data of Stickforth ~9) for ~_< 1 is [(1 + 2 ~ b + 6 ~ ~

.,z,/Y .,z~,].

where n; and Z; are ion-density and charge number and ~ denotes summation over ion species. It is seen that bremsstrahlung of a hydrogenic plasma is enhanced by a factor 9 for kTe = mec 2. [Stickforth is incorrect in the ultrarelativistic mode2°).] Synchrotron radiation of mildly relativistic electrons is very difficult to assess as it depends sentively on geometry, profiles of temperature, pressure and magnetic field strength, wall-reflection, etc. This effect may rule out low-/J devices (e.g. Tokamak) for clean fusion 21) and it provides further reason to cut off the high-energy tail of the electron distribution in a migma. Another effect which seems advantageous is, in its simplest form, the fact that a relative velocity

Po "~ I O O A - I Z - Z E ~ d - 1 .

A, Z, and E are the mass number, charge number, and average initial energy of the beam ions in MeV, d is the beam thickness in m, and Po is exI.

ADVANCED

FUEL

FUSION

FEASIBILITY

STUDIES

6

I,?,

~,~,

v between two ions of equal mass m can be established with only ~m~J2 instead of ½m~)2 injection energy when injecting both ions in opposite direction with speed ~t,. To exploit this effect in a wetwood burner, it is first of all necessary that ion-ion scattering is negligible during slowing down, in order that the beams keep their opposed directions (along the field lines of a toroidal magnetic field, e.g.). The condition is (n~aMsU)-l>r~, or in terms of quantities given in tables 1 and 2, c n hr~ ¢Tt'CrMS/~7 < 1 .

This condition is satisfied for all fuels except for plJB, while in the case of d3tte the injection of d strongly enhances dd-neutrons. The velocity difference t) can be obtained by injecting the " h o t " component with velocity uh < v and counter-injecting the other component with velocity ~)~= u - u h . The injection power is thus decreased, and F increased, by a factor Ahl)2/(A~2+cA~)~), which is maximized at zero total ion momentum Ah%=c'A~. So F can be increased by a factor (1 + Ah/CA~)at most. The above calculation ignores the slowingdown of the counter-streaming ions, but it shows that the power saving is only substantial for ~He (and dt). For ~He this effect raises F to about 0.1, which is still impractical. For the migma cell this effect on F is important, but roughly cancelled by the next effect. This effect relevant for a migma is nuclear elastic scattering. The distance of closest approach of 8 MeV 3He is of the same order as the radius of the nuclei, r ~ 10 13 cm. Trombello and Bacher 22) found differential cross-sections for single large-angle scattering which exceed the Mott value by about 0.03 b/sr (Mott refers to point charges). So 3He-3He collisions have a nuclear elastic crosssection of about 0.4b in addition to aMS. The main contribution to the multiple small-angle scattering cross-section aMS comes from angles of the order r/2D, where 2D is the Debye length and this small-angle scattering is governed by point-charge theory. The last effect to be mentioned is the heating of nuclear fuel by nuclear ash via nuclear elastic or Coulomb scattering. This effect is essential for the propagation of a burning shock front in laser-compressed or otherwise ignited fusion fuel. Being related to nuclear weapon research this is a classified subject. For clean fusion devices, not operating with laser ignition, the effect seems not particularly desirable for two reasons: the device should not confine fast ~z's which induce neutron-producing

B

B 1: 5, I

reactions, and energy transport from ~z's to fuel ions is not likely to be more efficient in the plasma than via converter and injector. 7. Clean fusion efforts - conclusions Potentially clean fuels (i.e. fuels which produce neutrons only in avoidable side reactions and which, as well as the ash, are nonradioactive) are p~B and p6Li, and 3He and d3He if 3He is produced in a p6Li-burner. Fusion burners are divided in plasma, beamplasma (or two-component) and colliding-beam devices. About 90% of the world's fusion effort goes into the plasma devices, and the remaining 10% mainly in a special beam-plasma device, the mirror with stabilizing cold plasma stream. A few tenths of a percent go into a colliding-beam device, the migma cell. Of the plasma devices only superdense laser plasmas can potentially confine the bremsstrahlung of clean fuels and, therefore, only such devices have distant prospects as large clean burners using ptlB. In the plasma devices d3He is not a clean fuel due to dd-neutrons. In the beam-plasma devices of the mirror-type pt~B or d3He can perhaps be burnt with UB or d in the cold plasma stream respectively, but the resuiting f-value (fusion power/beam powers0.2) is so small that at most break-even seems feasible with very efficient beam injectors and direct converters. In the case of plIB the mirror should be long to have sufficient proton confinement time, a few 90 ° scattering times. Clamping does not help in such open systems because of their short confinement time. Clamped beam-plasma devices could yield with p 1 1 B a rather high G-value (fusion power/clamping powers0.5) if a confinement time of the order of 1015 s/cm 3, corresponding to twenty 90 ° scattering times, could be realized for the protons in a closed system. Like the above-mentioned laser-plasma pllB-burner the clamped beam-plasma pUB-burner would be a very large device. A small part of the above-mentioned 90% of the fusion effort is useful for such a device, The migma cell is a small device in which fusion of 3He with a rather high F-value (about 0.5) may be demonstrated in the near future. The modest size inherent in a migma cell will prevent the use of neutron-producing fuels; this is a unique safety !~:~ture for a nuclear device. It is not clear, however, how -~tte can be produced cleanly

(I.l!,\N

l:t:S~()N

(~)N(I{P-IS

7

I19661 1, AI14(19681 1, A152(197/)) 1, AI66(197l) 1, A1911 (1972) 1.

by fusion of p6Li or otherwise, and much ingenuity will be required to increase the power of a migma to a useful level.

~] 113. Weaver et al,, kav, rence k i v e r m o r e Lab. Report U C R L 74938 (]973L

% R. L. ~ a l k e r . Phys. Re,,. 76 (1949) 246.

The author has taken much advantage of discussions with Drs. W. L. Barr, S. Channon, F. Engelmann, B. C. Maglich, R, A. Miller, J. R. Treglio, C. J. tt. Watson, and Th. A. Weaver. The author bears the sole responsibility for the evaluations and views expressed in this paper. This work was performed as part of the research programme of the association agreement of Euratom and the "~Stichting voor Fundamenteel Onderzoek tier Materie'" (FOM) with financial support from the "Nederlandse Organisatie voor Zuiver-Wetenschappelijk Onderzoek" (ZWO) and Euratom.

7) j. B. Marion et al., Phy';. Re,,. 104 (19561 1405.

~) J. R. Trcglio. Fusion Energy Corp. Reporl FEC-02-75, Princeton (19751. ';) J. Rand M c N a l b Jr. et al., Nucl. I-usion 14 (19741 579. l°l tt. ttora, A t o m k e r n e n e r g i e 24-3 (1974~ 187: l h . Weaver, private c o m m u n i c a t i o n .

II) l./. 1,' Post et a]., Phys. Rev. Lctt. 31 (19731 280. 12) T. A. Oliphant c t a l . , Nucl. Fusion 13 (19731 529, 131 B. C. Maglich c t a l . , IEEE Trans. Nucl. Sci. NS-22 (19751 1790. ~41 G. H. Mile~ and It. t1. T o w n e r , ('onf, on , \ m / e a r cross seclions and lc¢/mo/oXv, Washington. D.C. (March 19751.

15~ K. 11. Berkner et al., Nucl. Fusion 15 (19751 249. i(,j R. I~. Post, /:m'tTZv 70. Las Vegas, w)l. I, p. 19: R. W. Moir et al., Proc. IAEA Conf. Madison, vol. 3 (June 19711 p. 315. 17) F. B. Marcus and C. J. t1. Watson, Proc. E.P.S. Conf., Moscow ( J u l y - A u g 19731 p. 239. 18) C. J. 11. Watson, private communication. I~) j. Stickforth, Z. Physik 164 (1961) 1. 20) M. Alexanian, Phys. Rev. 165 (1968) 256. 21) W, ~. D r u m m o n d and M. Rosenbluth, Phys. Fluids 6 (1963) 276. 22) T. A. Trombel]o anti A. I). Bacher, Phys. Re','. IJll (19631

,'\ore added in prool: l w o papers 23,24) on pllB appeared since this article was written, which treat synchrotron radiation in s o m e detail. Day, son discusses a w e t - w o o d burner v, ith Pb/Pr - 1 and l, ~ 3,

References l) F. N. Flakus, At. En. Rev. 13 (19751 587.

1108.

2) A. B. Lovins and J. H. Price, N o n - m w l e a r l i a u r e s (Ballinger

PuN. Co., Cambridge, Mass., 1975). 3) L M. Lidsky, Nucl. Fusion 15 (1975) 151. 4) F. Ajzenberg-Selove and T. l.auritscn, Nucl.

Phys.

23) j. M. Dawson, UCLA Plasma Physics Group Report 273, Los Angeles (Aug. 1976) 24) D. C. Moreau, Nucl. Fus. 17 119771 13.

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