The paper constitutes a review of the neoclassical theory of transport processes in the different types of toroidal magnetic configuration now being used to study the possibility of producing a controlled thermonuclear reaction. Owing to the abundance of the material that has accumulated in recent years and the large number of parameters involved in the problem, it has not been possible to present all the mathematical calculations in detail while confining the results to a few definitive expressions. The general approach to a solution of the problem and its key aspects have been discussed as fully as possible, and a number of definitive results are presented. In the review, a history of the subject and an account of its present status are given, the problem itself is formulated, the basic equations are discussed and analytical solution methods are described. Definitive expressions are given for cross-field particle and energy fluxes, the bootstrap current and conductivity, all of which are required to solve the particle and heat balance equations in magnetic confinement devices. The results are presented in a relatively simple form which is convenient for analysis of the experimental data and are accompanied by tables containing numerical values for the universal coefficients in the definitive expressions. The review is aimed at both theoreticians and experimenters working in high-temperature plasma physics and controlled thermonuclear fusion.

On the basis of neoclassical transport theory, approximate expressions are proposed for particle and energy fluxes which can be applied over the whole range of collision frequencies of interest for current experimental work and which allow for the contributions of both transit particles and toroidally and locally trapped particles. With the help of these expressions, an evaluation is made of the electron and ion energy confinement times for a number of stellarators (L-2, W-VIIA, Heliotron-E), and it is shown that the calculated confinement times coincide to within an order of magnitude with the experimentally determined values and do not as a rule require the introduction of additional anomalously high losses via the electron channel. Confinement times are calculated for two stellarators still at the design stage (ATF-1 and L-3) and also for a stellarator thermonuclear reactor. It is shown that, in the case of the reactor, the system would not have to be made unreasonably large in order to satisfy the Lawson criterion (N(0)τE> 1014).

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Illinois 601 15. USC M S . received 14th M a y 1970Ahtract. Starting from bare-ion pseudopotentials, net crystal potentials are evalutiied in direct space by (a) the usual linear screening technique and (b) the Thomas-Fermi method. For the metals considered (Na and AI), the potentials are quite similar, crossing outside the cores and never differing by more than 0.02 a.u. in the case of Na nor by more than 0.2 a.u. in the case of Al. The similarity of the results based on (a) and (b) suggest the use of the pseudopotential concept in conjunction with the rather general method (b) under conditions when (a) is questionable, that is whenever the zeroth order uniform electron gas solution is a poor physical approximation to the actual system under study (specific examples being molecules, insulating solids and interfaces).Methods (a) and (bj both yield shallower wells than those most often used as input information in band structure calculations and obtained by superposing atomic data.

A method is developed for studying MHD equilibrium and stability of plasmas confined in toroidal systems with a large constant magnetic field and a small field which varies rapidly in space. The method is used to obtain a system of magnetohydrodynamic equations averaged over the period of the rapidly varying field. In this form, the problem is greatly simplified, and the equations become similar to those used for axisymmetric tokamaks, for which methods have now been developed in some detail. -The problem of the limiting plasma pressure for equilibrium and stability in a stellarator is analysed, and it is shown that, within the framework of an ideal MHD model, 0 = 2P/B 2 can be larger than 10% in systems with large shear and partial compensation of the magnetic fields produced by the diamagnetic currents. Also the question of toroidal drift compensation and, as a result, of the decrease in the neoclassical diffusion coefficient is discussed.