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Self Colliding Beams ("Migma") and Controlled Fusion

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Self Colliding Beams ( © 1975 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. IEEE TmactioMd on Nuc.kvc Science, VoLNS-22, No.3, June 1975 SELF COLLIDING BEAMS ("MIGMA") AND CONTROLLED FUSION B. Maglich, M. Mazarakis, R. A. Miller, J. Nering, S. Channon, and C. Powell Fusion Energy Corporation, Princeton, N.J. 08540 and J. Treglio* Stevens Institute of Technology, Hoboken, N.J. 07030 Khile much of the early work on colliding beams the lead in the development of THERW MIGMA was done in the U.S., NUCLEAR this technique is now held by Europe. The most spec- -a tular being the only colliding beams of nuclei in the /e.J !%;,,, BREE[XR Intersecting Storage Rings at CERN. It may be for this reason that the idea of using colliding beam technology as a means of achieving fusion has not reappeared until just recently. The idea of using colliding beams for fusion is nearly as old as is the interest in fusion as a source of power, but the problems of low reaction rate and high coulomb scattering initially seemed in- surmountable. This work describes recent work done at Fusion Energy Corporation which attempts to overcome these problems. Before turning to our own work, let us examine the well know facts about CERN ISR in a manner suggesting comparision with traditional plasma thermonuclear ma- chines. The confinement time of the ISR is 235 days, that is, a beam stored in the morning has decreased by less than a percent in intensity by evening. The pa- rameter, n7, density times confinement time can easily be found to be about 10" cmm3 set compared with pre- sent plasma values of no better than lO'","Lawson Cri- terion" (see below) values of 10'4, and values of 10" required when the Lawson Criterion is corrected by a IOkeV nlnnber of realistic considerations (see below). An- / IhJECTlCN ACHIEVED f, ~ ENB/IGYT,- other parameter of interest to plasma researchers is IONTEMP’s - t !i, = Sn nkT/??, which is the ratio of kinetic energy PLASMA MIltMA DEVICES MOOELI density to magnetic energy density. In magnetically -,--IQ-~~ I T710-3s confined plasmas, this ratio must be less than 1. At ! i ISR the ratio is 36 in the curved sections and as much DESlGPr PLASMA MIGMA i[ as 108 in the straight sections. The difference may ION TEMP’s + ~19801 (19761 he a:tributed to the high degree of order of the moticn in a beam compared with a plasma. Figure 1 shows another advantage of beam technol- oep simply in the higher energies attainable. In this Fig. 1. Reaction parameter <TV> for various figure we have plotted the reaction parameter <CW> as a losses and gains as a function of beam energy function of beam energy for several processes, assuming for head-on collisions. head-on collisions (which will be shown to be a good approximation in a migma). The processes shown are region. If, in addition, the field is given a shape of charge transfer (CT), multiple coulomb scattering (MS), the form: B, = BD(1 - kr'/R2 + kz2/R2), the particles elastic scattering, which includes synchrotron redia- will precess about the center in the horizontal plane tion dd - pt or nHe3, and the fusion reaction dHe' * and be focussed to the midplane vertically'y3 as shown pHe'. Also indicated are the equivalent energy ranges in the lower two diagrams in Fig. 2. This configura- of present and futur? plasma devices and present and tion is called "migma"from the Greek war2 for "mi~~rurc". future migma devices. A more detailed description of The migma configuration naturally results in a very this curve ,ippenrs in reference 1. It is possible to sharply peaked central density and consequently in a op?ratck .I net energy producing reactor in regions where very sharply peaked reaction rate. Fig. 3 shows the loss rates exceed gain rates, but this requires, for result of a Monte Carlo simulation of fusions in a cx.l-r!;>le, <,xtrewly good confinement, and the difficulty nigma; 95% of the fusions take place in 2.5% of the inT:olvrd probably plays d large part in the slow pro- radius. >:ress exp~~rienc~d by plasma research programs. 'l%o se The central region of a migma is equivalent to an of us used to ordinary physics, where experiments nre infinite number of colliding beams at all crossing an- planned and t,xecrltod in some fraction of a professional gles. However, the flux is largest for beams meeting lifetime, arv naturally drawo to the region near 1 MeV, head-on, and, further, the fusion rate increases where losses iall below gains. The basis of the migmn strongly with relative collision energy. As 3 c*nsc- principle of controlled fusion can be explained by re- quence, the fusion rate is the same as if all col- ferring to Fig. 2. If the hypothetical two storage lisions were between deuterons with a relative crossing rinus of dcutcrons shown were constructed, multiple angle of about 165" or nearly head-on.' coIllomb scattering wollld drstroy the beam long before It is known that in focussing m.lchines the mean any sizniiicant fusion had occnrrcd. If instoad, the sqtlnred beam spread increases linearly with time rather sol1 idin): llC.lrns wrr pl,lcrd in the axially r;ymmetric th:in cubically with time as in n nonfocussed situation. h insle vi~lumt~ .IS shown, a particle scattered in the Y!ultiple coulomb scattering is similarly suppressed in horizontal pl.lne would lx returned to the central a migma. The exact calculation is given in reference 4. 1790 dd STORAGE dd COLLIDING RINGS ORBITS IN 1 no niw* 1 4-- -2.5% R 95:31 i’iicw L’ TM D-i:: ‘h Z.% oi RE WLILC Id‘-in~ RATE s Y 12‘ d + d -T + p-‘N MIGMA F?ii Td = I MeV SINGLE VOLUME 3, B(O,O) = 2.5T q,js >> ~fuson t BEAM SCATTERS OUT “AUTOMATIC” RETURN $ ’ I31015 R = 63cm 2 Il. t’+j = 10” MONTE CARLO WCH l,“.. 2 TTr j+ : 11 ./ yfi!@g$ p ii 1 iLh &- Fig. 2. Comparison of migma with a -; Y hypothetical pair of intersecting 11 storage rings. r w ,013i , I “1 dq ?r 1, / 0.41 4 h?lP 12 14 Fig. 3. Monte Carlo caiculation of relative fusion rate as a function of radius in a migma. For reasonable vertical confinement the scattering time is found to be longer than the fusion time. Migma has some superficial features in common with mirror-confined plasmas, including the DCX series which was an attempt to heat a mirror-confined plasma by a beam of up to 600 keV. The differences are actu- ally many and important. To begin with, migma is high- ly organized, resulting in the high central density and predominance of near head-on collisions already men- tioned. The gradient of the magnetic field is large across a migma orbit, while it is essentially zero across the lower energy plasma orbits. Among other things, this means that migma is focussed rather than confined by magnetic pressure. Because migma is fo- cussed, a ratio of kinetic to magnetic energy density, t?, greater than 1 can be achieved. Because ions are injected directly, MeV energies can be attained, com- pared with roughly 1 keV in present plasmas. In ad- dition to the advantages discussed in connection with -Izpp 11. Fig. 1, higher energies also allow the use of non- polluting advanced fuels. 5 A graphic demonstration of the difference between migma and plasma is shown in Fig. 4. The two sets of lines plotted are flux lines and migma energy envelopes Are obtained from the requirement of conservation of canonical angular momentum and are the boundaries of migma ions of given energy. Plasma, on the other hand will be bound to the flux lines. One consequence of this is that migma does not obey the Alfven mirror relation that plasma does. As mentioned earlier, Fig. 1 seems to indicate that around 1 MeV is the favorable energy region for dd fusion. However, dd plasma reactors were targeted for about LOO krV. This difference is puzzling and is rooted in the "Lawson Criterion"." The Lawson Cri- Fig. 4. Magnetic flux lines compared with the terion ~2s developed by J. D. Lawson almost 20 years more sharply curved migma energy envelopes for ago. It is derived from a simple energy balance equn- the SGme magnetic field. (See text). tion and includes a single conversion efficiency for 1791 all forms of energy emitted by the reacting medium. Lawson clearly stated that this criterion was "ideal- ized" and "by no means sufficient for the successful operation of a thermonuclear reactor.'16 Reference 1 includes 18 effects not in the original Lawson Cri- terion used to derive a more realistic criterion. Fig. 5 shows the resulting values of nr for energy break- even for a set of parameters representative of plasma ; /I t, SET-1 ,,I’ SETII('MIGMA") 11;’ mew - SEPTUM PIMW ’ 1rPLASMA”) i ;\ , , , I Ill 7c2= j ST4TlON j, ItI ~ I al IO” KCELERATOR -* Sub ‘1 ~ q 111 [\ ,/J/g f r c2 III ,.;~sG--qqpP~p3o’ 0.9999 i ;!i\ ,’ c 7 5 / i 10 A.! II ‘\ /!P”,,q.,:;;r ” E r 0.999. i/i!\ \ / ~T+;;;i> W1hm \; / 4 I 3 2 T!’ I 1 / ,&y-l”.* / g”p, tg ‘38 I I ;0’5 ,YIIIzJ Set I sca,e 1 -‘:ys~,;;o;;24:.i;p= / 1 b, \ 1 ,.,.
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