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ORNL-TM-3783 Contract No. W-7^05-Eng-26 Thermonuclear

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ORNL-TM-3783 Contract No. W-7^05-Eng-26 Thermonuclear ORNL-TM-3783 Contract No. W-7^05-eng-26 Thermonuclear Division PROSPECTS FOB ALTERNATE FUSION FUEL CYCLES AT ULTRA-HIGH TEMPERATURES J. Rand McNally, Jr. APRIL 1972 — NOTICE : — This report was prepared as an account of work sponsored by the United States Government. Neither the United States nor the United States Atomic Energy Commission, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, com- pleteness or usefulness of any information, apparatus, product or process disclosed, or represents that its use would not infringe privately owned rights. OAK RIDGE NATIONAL LABORATORY Oak Ridge, Tennessee 37830 operated by UNION CARBIDE CORPORATION for the U. S. ATOMIC ENERGY COMMISSION BlSTRiBUTi-r*' Of TP"S aOC'JraT UKL 1ITE0 'A 1 PROSPECTS FOR ALTERNATE FUSION FUEL CYCLES AT ULTRA-HIGH TEMPERATURES J. Rand McNally, Jr. ABSTRACT Recent experiments and theory give support to the idea of developing a closed magnetic mirror "by the self-field of a trapped ring current. Since the mirror reactor may he able to operate at much higher burning temperatures than toroidal reactors, the viability of charged particle fusion chain reactions is thereby increased and may permit the chain reaction burning of cheap Li or Be nuclear fuel. Reaction kinetics studies in partially closed mirrors show MeV energies for the light fusion reaction products which can act as cata- lysts or chain centers for the propagation of such reactions. The MeV particles may also permit sustainment of both the ring current configuration and the burning temperature. Numerous problem areas associated with this approach are tabulated and will require extensive research. I. INTRODUCTION Fusion chain reactions can occur with the elements, lithium (Z = 3) at least through neon (Z = 10), with very light particles such o as neutrons, protons, deuterons, tritons, light helium (He) and alpha particles (A He\) acting as chain centers or catalysts to speed up the reaction. Examples of uncontrolled fusion chain reaction systems may 1 2 be the superbomb and supernovae. Of particular interest to the CTR 3 program are charged particle fusion chain reactions involving the chain centers p, d, t, ^ He, ^ He and fuels like 6 Li, 'Li,7/ and/or9 ^Be. These energetic charged light products of the fusion reactions can propagate further reactions together with a net energy release and thus may sustain a controlled nuclear fire quite analogous to the k chemical chain reactior.s in controlled combustion processes, except for the energy scale of the system. A simple example of a multiplying fusion chain reaction is 6 f) a_fas t, + Li a' + Li* - 2.2 MeV + a' + dfas- t. + a" - 1-5 MeV d + Li 2 or ^ + 22.k MeV fast "fast + 2 6Li - 2 "slow + 2 "fast Here, a multi-MeV alpha particle catalyzes the burning of two ^Li nuclei to give two multi-MeV alpha particles for a multiplication factor of 2 in two generations. Consult Reference 3 for more details. There are several experimental and theoretical results which suggest the possible viability of such charged particle fusion chain reactions at very high temperatures for a CTR scientific feasibility experiment. They are: 1. The experimental demonstration of the onset of exponential build-up in the PHOENIX II device at Culham Laboratory. 2. The theoretical development of scaling laws for scatter- limited mirror build-up. 3. The experimental demonstration of an Astron-like E-layer •j (closed mirror) at Cornell University. 3 b. The Fokker-Planck reaction kinetics calculations of D*T and D* He fusioning plasmas which reveal mean energies of ^ 1 MeV for the trapped fusion reaction products, as evaluated at 8 9 Culham and Livermore. 6 7 5- The potentiality of alternate fusion fuels, Li, 'Li, and Be.10'3 II. EXPONENTIAL BUILD-UP IN MIRROR SYSTEMS 5 Culham results indicate the verification of an important scaling law which can, under proper conditions, lead to a large scale expo- nential build-up of the hot ion density in mirror devices b£ several orders of magnitude. The IjbZ fission experiment of Fermi, et al11 demonstrated an exponential scaling law of a process rate which per- mitted the design of the graphite reactor at ORNL and the Hanford reactors. Mirror devices have large T and T but are presently limited to low density regimes. The exponential build-up of the plasma density in magnetic mirrors can provide large TnT values which would demonstrate the scientific feasibility of CTR. Exponentiation can be obtained by attaining b s 0 in the build-up equation: dn+V 2 —rrdt- = la + bn+, - cn+ where a is the trapping fraction of the injection current I due to l) targets, 2) background gas and 3) Lorentz trapping; n+ is the ion density, V the plasma volume, and c the coefficient for scattering losses. The coefficient b is b = ICTL - NQ V k and is usually negative. The exponential build-up condition for the injection current becomes (b 2s 0): n ov V „ I s ° cx V TCTTL Thus, by obtaining long containment times, T = 1 , the required no cr vc x injection current can be grossly reduced. This can best be done by going to very high injection energy for which the charge exchange cross section (CT ) drops by a million-fold (see Fig. l). cx -15 2 The Culham experiment had IT ~ ^0 mA sec, a,p(exp.) = 2.8 x 10 cm (for ionization of excited H° atoms), and plasma trapping an5d the onset of exponentiation were claimed in their Madison IAEA paper. Two circumstances prevented any large scale exponential build-up of the plasma density in PHOENIX II: a) the exponentiatio/ o*\ n was based on the very low population of highly excited atoms (H ) which can not permit any large scale exponentiation (cascade effects were small) and b) the plasma became unstable because the maximum electron energy appears to be too low to provide adequate electron Landau damping (threshold n a max E ). Exponentiation at MeV energies would occur primarily on the large population1 2o f ground state H^ ions and would ensure a large It (^ 2000 mA sec ); however, CTt, the trapping cross section, is somewhat lower 1/1*0) than in PHOENIX II. Programmed 12 electron cyclotron heating (ECH) at MeV energies would provide a large maximum Eg and thus minimize plasma potential effects as well as provide adequate electron Landau damping. The velocity spread of 12 gradually increased. the ions (necessary to minimize the negative mass instability) is also ensured because of appropriate stepping power effects as ne and Te are 5 If PHOENIX II were provided with cw ECH, it might be possible to keep the plasma potential low by increasing the max E by a factor of e j. 80 (to the ion energy of 8 keV), thus permitting the exponentiation of the plasma density from 3 x Kr9 cm ^ to ~ 2 x 101 3 cm , assuming Landau damping continues to control the threshold density. However, 11 this would give an nT of only about 2 x 10 at 8 keV assuming T ~ 1 cx sec (compared to an instability driven loss time of only 0.2 sec, when Landau damping is limited by ecp ~ kT ~ 100 eV). If partial burnout e occurs in PHOENIX II, T becomes > 1 sec and nT is then limited as ' cx in the next section to about 7 x 10'.1 1 ion-sec/cm3 . III. SCALING LAWS FOR SCATTER-LIMITFD MIRRORS Should exponentiation persist, without instabilities, the equi- librium condition for the plasma throughput rate is nV 12 — — n av VP T 2 sc or 2 nT ~ av P sc where P is the mirror loss factor (2/P ~ 6 1°S10 R)• The multiple-small- a anc one angle Coulomb scattering parameter <JVSC * obtains 2 nT = C E^ log10 R . The coefficient C has been evaluated in terms of Fokker-Planck calcu- lations for plasma build-up in mirrors by including energy diffusion and slowing down as well as scattering into the loss cone and is of IT order 10 "" when the injection energy EQ is in keV (for deuterons in a 2/l mirror for which log1Q R ~ 0.3).^ Thus, one obtains the following table (neglecting mirror closure effects and nuclear elastic scattering) TABLE I. MAXIMUM nT IN SCATTER-LIMITED MIRRORS * Eo nTma x 10 ^ 1 keV 3 x 10 ion-sec/cm 10 keV 9 x 1011 100 keV 3 x 1013 1 MeV 9 x 10 2 MeV 3 x 1015 * Independent of injection current provided exponentiation exists. Thus, with stable exponential build-up, an injection-accumulation method is capable of attaining a mirror-confined Lawson criterion plasma (nT > 10 ) only for energies above about 200 keV. The ORNL DCX-1 experiment used E ~ 300 keV, but exponentiation could not be attained H because of the negative mass Instability (the threshold density of which is proportional to AE ). At MeV energies AE, the energy spread, 12 becomes very large (~ E) as a result of slowing down effects so that exponential build-up, once attained, should be sustained to much higher 12 densities." IV. THE IMPORTANCE OF CLOSING THE MIRROR Kammash has indicated that it may be essential to almost close the magnetic mirror in order to make fusion reactors competitive with Ik non-fusion power plants. At the time of his writing no closed magnetic mirror had been produced although the ELMO device had very 7 15 1 ft 17 high 0, ASTRON had a 15$ E-layer, and the 9-pinch had high p.
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