Abstract:
Depolarization mechanisms arising from the recycling of the polarized fuel at the limiter and the first-wall of a fusion reactor are greater than those mechanisms in the plasma. Rapid depolarization of the plasma is prevented by providing a first-wall or first-wall coating formed of a low-Z, non-metallic material having a depolarization rate greater than 1 sec -1 .

Description:
CONTRACTUAL ORIGIN OF THE INVENTION 
     The United States Government has rights in this invention under Contract No. DE-AC02-76CH03073 between the U.S. Department of Energy and Princeton University. 
    
    
     BACKGROUND OF THE INVENTION 
     This invention relates generally to polarized fusion reactors, i.e. reactors employing polarized fuel; and, more particularly, to reactor first-walls and first-wall coatings. 
     Kulsrud, Furth, Valeo, and Goldhaber have shown and described in U.S. patent application Ser. No. 492,924, filed May 9, 1983 how the performance of magnetic confinement fusion reactors can be improved by using deuterium and tritium plasmas that are polarized in certain preferred directions. They showed that polarizing the plasma fuel ions enhances the different nuclear fusion rates and controls the angular distribution of emitted reaction products. The feasiblity of using polarized plasmas depends on the absence of physical mechanisms that can depolarize the plasma rapidly on the timescale of particle confinement (˜1 sec) or fuel burnup (˜100 sec). Kulsrud et al demonstrated that the depolarization mechanisms in the plasma are too weak to be relevant. 
     There are, however, other depolarization mechanisms present which have not been considered carefully, and which are more important than those occurring in the plasma. These arise from the recycling of D and T at the limiter and the first wall of the reactor vessel. In all magnetic confinement scheme studies to date, the D-T fuel leaks out across the magnetic field lines about 10 to 20 times faster than the rate of fuel consumption. (Indeed, for a burning plasma, the ions must leak out at an appreciable rate in order for the helium ash to leave the plasma core.) As a consequence, most particles leave the plasma, strike the limiter (or first wall) and reenter the plasma about 20 times before fusing or before being pumped away. About half the flux of particles striking the first wall is reflected back into the plasma. The remaining particles have sufficient kinetic energy (20-100 eV) to penetrate about 100 Å into the wall. There the D and T ions come to equilibrium and eventually diffuse back to the surface where they recombine and desorb as molecules, or are desorbed directly by ion, electron, and photon bombardment. 
     The D and T nuclei in the crystal lattice and in the vicinity of the wall surface are subject to depolarization mechanisms that are not present in the plasma core. In the plasma edge and in cracks or voids of the wall material, D and T can exist as polyatomic molecules. For these species, tumbling caused by rotation and collision of the molecules can flip the nuclear spins. For absorbed D and T residing in the crystalline lattice, depolarization can occur by thermal diffusion and by photon and electron induced fluctuations of microscopic magnetic fields and electric field gradients (which couple to nuclear magnetic dipole and electrical quadrupole moments respectively). 
     These new mechanisms can greatly reduce the nuclear magnetization of D and T on timescales of 10 -3  and 10 1  seconds. Since the mean residence times of absorbed D and T in the wall are also comparable with these timescales, a careful choice of the composition and temperature of the first wall and limiter is crucial in preventing rapid depolarization of the plasma. 
     Therefore, it is an object of the present invention to provide a first-wall or first-wall coating which prevents rapid depolarization of a polarized plasma. 
     It is another object of the present invention to provide a method of preventing (or minimizing) rapid depolarization of a polarized plasma in a fusion reactor. 
     Additional objects, advantages, and novel features of the invention will be set forth in part in the description which follows, and in part will become apparent to those skilled in the art upon examination of the following or may be learned by practice of the invention. 
     SUMMARY OF THE INVENTION 
     To achieve the foregoing and other objects and in accordance with the purposes of the present invention, a first-wall or first-wall coating for use in a fusion reactor having polarized fuel may be formed of a low-Z non-metallic material having slow spin relaxation, i.e. a depolarization rate greater than 1 sec 1 . Materials having these properties include hydrogenated and deuterated amorphous semiconductors. 
     A method for preventing the rapid depolarization of a polarized plasma in a fusion device may comprise the step of providing a first-wall or first-wall coating formed of a low-Z, non-metallic material having a depolarization rate greater than 1 sec -1 . 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The present invention is illustrated in the following drawing in which FIG. 1 is a schematic illustration of the plasma - wall interaction. The partially ionized cooler plasma near the wall is the plasma edge; diatomic and triatomic molecules in this region are the major source of edge depolarization. About 50% of incident ions (dark circles) are reflected by lattice atoms (open circles). Remaining nuclei enter the lattice and diffuse or become trapped. Nuclei on the surface desorb either by recombination or by collisions with incoming photons, electrons, and ions. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring to FIG. 1, the polarized nuclei in the walls constitute an ensemble of particles which are weakly coupled to external degrees of freedom (the &#34;lattice&#34;) and to each other. These two kinds of couplings introduce two different macroscopic timescales, called the spin-lattice and spin-spin relaxation times in the NMR (Nuclear Magnetic Resonance) literature. These are denoted by T 1  and T 2  respectively. 
     If the ensemble of nuclei is not in thermal equilibrium with the surrounding lattice, energy is exchanged with the lattice until the occupation of each nuclear state is proportional to its Boltzmann factor, exp(-E m  /kBT). Here E m  is the energy of a particular nuclear state, k B  is the Boltzmann constant, and T is the absolute temperature of the lattice. For typical nuclear magnetic dipole moments μ (of order 10 -  24 ergs gauss -  1), in the presence of typical reactor fields B=B o  z (B o  ˜10 5  gauss), the equilibrium nuclear magnetization, which is proportional to tanh (μB o  /k B  T), is vanishingly small for T≳μB o  /k B . Thus for typical wall temperatures (T≳300 K for the wall, 1000 K for the limiter) polarized nuclei will relax to a zero equilibrium magnetization by exchanging energy with the lattice. This decay of nuclear magnetization often occurs exponentially over a timescale which is defined to be T 1 , the spin-lattice relaxation time. The depolarization rate of nuclei is then simply T 1   -1 . 
     Spin diffusion and T 2  do not play a role in wall depolarization. Reactor wall temperatures are so high that atomic diffusion will always transport nuclear magnetization more rapidly than spin diffusion. Furthermore, in a wall containing equal concentrations of D and T, energy-conserving spin flips are inhibited since nearest neighbor nuclei are likely to have different nuclear magnetic dipole moments. 
     T 1  (and T 2 ) can be easily measured by numerous NMR techniques, and has been measured for many hydrogen and deuterium containing substances. The depolarization rate depends on T 2 , the spin-spin relaxation time, only at temperatures which are so low that atomic diffusion of the nuclei can be ignored. T 1  depends on two microscopic time-scales, the inverse Larmor frequency, ω o   -1 , and the correlation time, τ c . Transitions which repopulate the nuclear quantum levels and depolarize the nuclei are induced by nuclear motion which modulates the nuclear magnetic dipole moment. The deuteron can also depolarize by modulation of its electric quadrupole moment, which is usually its dominant relaxation process. 
     The plasma edge is a transition region near the walls, typically 10-20 cm in radial extent, where the large densities and temperatures of the plasma core decrease to their small values at the wall. The partially ionized plasma of the edge contains charged and neutral species (e.g., e - , D, D + , T, T + , D 2 , T 2 , DT, DT + , D 3   + , T 3   + , etc.) which interact with each other. The densities of these species are typically of order 10 10  to 10 13  cm -3 . Most depolarization mechanisms in the edge are the same as those discussed by Kulsrud et al. for depolarization in the plasma core. 
     We note that the spin-rotation process which dominates the depolarization mechanisms of the plasma edge can also occur in cracks or voids of the wall material. On the surfaces of such interior volumes, nuclei can recombine into diatomic forms, tumble, and depolarize. Unlike the plasma edge, there are no collisions, except with the surface, which can break up the molecule before depolarization will occur; the situation is potentially more serious. The contribution of this process to the total depolarization rate will depend on the rate of collisions, the fraction of D and T in such voids, and the rate at which bulk nuclei exchange with nuclei in the gas phase, a highly surface and material dependent number. Spin-rotation is therefore important in materials in which hydrogen or helium is weakly soluble, leading to blistering and cracking under high flux rates. This means that first wall and limiter materials have high H and He solubilities. 
     The relaxation mechanisms of the bulk and surface regions of the limiter and first wall are closely related and are best discussed together. There are three important mechanisms: hyperfine coupling of nuclei to unbound (conduction) electrons, dipole-dipole interactions modulated by atomic diffusion, and interactions with paramagnetic impurities (unpaired bound electrons). 
     The electron depolarization rate increases with increasing temperature. Because of the large velocity of electrons at the Fermi level [of order (2E F  /m e ) 1/2  ≃10 8  cm/sec)], the depolarization rate is also independent of the slow diffusive motion of nuclei at higher temperatures. Since a high temperature is needed to minimize the depolarization rates discussed below, the first wall materials must be nonmetallic to prevent significant plasma depolarization. More precisely, wall materials must have a small or vanishing density of s-electron states at the Fermi surface. A semimetal such as graphite has a small (lower-dimensional) Fermi surface and should give acceptable D and T electronic relaxation rates. 
     A strong source of nuclear depolarization in metals and nonmetals is interactions between the nuclear magnetic dipole moments, of diffusion D and T with nearby magnetic dipole moments, such as those of other diffusing nuclei, lattice nuclei, or unpaired bound electrons (paramagnetic impurities). 
     For a given wall material, the diffusional depolarization rate can be minimized by operating at the highest possible temperature compared to T d  (T d  is the temperature at which depolarization due to diffusion is minimized) assuming that T d  is not larger than the melting or sublimation temperature. For transition metal hydrides, this means T≳500 K. For nonmetals, the choice is less clear; it depends on the density of various traps and the distribution of trap energies. Temperatures near the sublimation point of nonmetals (≳1400 K for graphite) may lead to unacceptable erosion rates and a large flux of wall impurities (e.g., carbon ions) into the plasma. 
     Another source of depolarization--perhaps the major source at high temperatures for nonmetals--is unpaired bound electrons such as dangling bonds, unfilled transition (3d) or rare earth (4f) valence shells of atoms, and electrons trapped by lattice defects. Since an external field causes such electronic magnetic moments to align on the average, they are called paramagnetic impurities. 
     A diffusing nucleus near such an impurity can rapidly depolarize for two reasons. First, the electron magnetic dipole moment is ˜10 3  times larger than any nuclear moment; local microscopic magnetic fields are large (˜10 4  gauss at a separation of 10 -8  cm). Second, unlike nuclear magnetic moments, paramagnetic impurities are strongly coupled to the lattice with spin-lattice relaxation times of order 10 -9  -10 -6  sec. A nucleus becomes strongly coupled to the lattice in the vicinity of such an impurity and can spin-flip. 
     A summary of the desirable properties for a suitable first-wall material is contained in Table 1. 
     Our analysis indicates that depolarization of the plasma by recycling in material walls is far more important than depolarization in the plasma core. Instead of depolarization rates ≲10 -5  sec -1  in the core, we can expect rates ≲1 sec -1  for nonmetallic walls at high temperatures. For some parameters, the mean residence time can be less than the spin-lattice relaxation time. 
     Hydrogenated (or deuterated) amorphous semiconductors satisfy most of the properties of Table 1 and are a suitable first-wall material. Hydrogenated amorphous semiconductors offer other advantages. First, a coating of a-Si:H over the limiter and walls would be easy to apply by introducing puffs of methane or silane under low discharges; the reactor need not be turned off and opened to apply new coatings. Second, because these materials have high concentrations of D and T already present, the flux of lattice nuclei into the plasma (a source of impurities) would be decreased compared to crystalline graphite or SiC (although graphite and SiC would also be suitable first-wall materials). Third, small amounts of dopants such as nitrogen could be used to tune the spin-lattice relaxation time, and perhaps the residence time. FinallY, the porosity of the coating could be varied by controlling the deposition rate. This can reduce the depolarization rate by providing a loose network of channels through which polarized nuclei can escape back to the surface. For a first wall coating, a thickness of at least 200 Å (or a range of 100-500 Å) would be sufficient. Although it is unlikely the polarized fuel components would diffuse any deeper than 200 Å, greater thicknesses may be used for other considerations such as structural stability. 
     Additional materials satisfying the properties of Table 1 include a-C:H, graphite, and SiC. 
     
                       TABLE 1______________________________________Desirable Properties of Wall and Limiter MaterialsPROPERTY         COMMENTS______________________________________High temperature reduces dipolar, quadrupole,            and paramagnetic relaxation;            decreases residence time.Nonmetallic materials            eliminates relaxation due to            inelastic spin-flip collisions            with conduction electrons.Lattice nuclei have small or            decrease diffusional relaxationzero magnetic dipole momentsHigh H and He solubilities            avoid blistering of wall which            can lead to internal sources of            diatomic molecules and spin-            rotation relaxation.Rapid surface desorption by            minimize residence time bymolecular recombination            allowing nuclei to escape            rapidly.Low-Z atomic composition            avoid high-Z impurities in            plasma that lead to high            radiation loss.Low surface and bulk            not easily controlled becauseconcentrations or para-            of constant erosion and re-magnetic impurities            deposition.Cubic lattice symmetry            noncubic lattice sites can            depolarize deuterons by            quadrupole relaxation.______________________________________