Table of contents

Problems related to the definition of a target plasma for fast neutral injection into a mirror machine are discussed. Plasma parameters and magnetic configuration are first examined in the light of instability theory; the study is concerned with: the required neutral beam current; the beam energy modulation connected to the evolution of the ion distribution function; the evolution of the plasma geometry associated with the vacuum requirements; and the deduction of suitable plasma parameters. This ensemble leads to the conclusions that an experiment to study the stability of mirror machines in a quasi-steady state relevant to reactor regimes is possible starting from a reasonable extension of present laboratory plasmas.

The possibility of transferring a target plasma into a confinement region is considered. This method avoids the gas problem and reduction of access which are usually associated with the target production in situ. The transfer is shown to be feasible with good efficiency at the expense of a complicated set of pulsed magnets.

The formation and interaction of Langmuir solitons is governed by the Schrödinger equation with a self-consistent potential. Generally, two kinds of interaction - quasi-static and dynamic - are considered. In the former case, the problem reduces to solving the Schrödinger equation with a cubic term, while in the latter, the self-consistent potential satisfies the wave equation. It is maintained that in the quasi-static description, solitons do not asymptotically interact with each other if uninteresting shifts of the soliton phases are disregarded. In the dynamic approach - which is physically more consistent - solitons may interact with each other and with acoustic waves. The article considers the problem of the interaction of two identical solitons moving towards each other. Semi-quantitative estimates have been used in order to determine the region of parameters in which fusion of solitons is possible. The numerical modelling results which refine the analytical estimates are discussed. The analysis shows that there is practically no region where the quasi-static approximation can be applied, since this approximation disregards the low-frequency motions which are fundamentally important for the process of Langmuir turbulence instability. The process of soliton formation from a non-symmetrical Langmuir-wave packet is investigated. A study is made of the influence of the boundary conditions, especially the periodic ones, on the formation and interaction of solitons. Applying numerical modelling, the authors show that great caution must be exercised in using the periodic boundary conditions for unbounded systems. Wave boundary conditions have been suggested.

Fluid-numerical studies have been carried out to investigate the scaling of the stable magnetic sheath thickness ΔL_s with β, T_e/T_i, n₀, etc., in a collisionless finite-β plasma column. The system is initially close to a two-fluid equilibrium with sheath width ΔL sufficiently narrow for the azimuthal current to trigger various cross-field instabilities (ion acoustic, modified two-stream, Buneman). The enhanced field fluctuations in the sheath region, in addition to heating the plasma locally, leads to a decrease in azimuthal current and a corresponding increase in sheath width to some stable value ΔL_s, achieved as the system stabilizes and the field level saturates. The final sheath width in the numerical studies agrees well with the theoretical estimate.

The author derives the shape of the distribution function for the products of a thermonuclear reaction (α particles) that is brought about through Coulomb scattering of α particles by plasma electrons and ions. It is assumed that the thermonuclear reaction is stationary and that the energy of the reaction products is transmitted to the plasma. Consideration of the problem is based on a kinetic equation for the α-particle distribution function, in which the Coulomb collisions are taken into account by means of the Landau collision term.

A number of technological problems concerning the coils in internal conductor systems is investigated, with an efficient plasma confinement imposed as a working hypothesis: (i) At technically feasible power levels and linear dimensions, the Ohmic power losses can, under optimized conditions, be made much smaller than the thermonuclear reaction power, even with ordinary metal windings at temperatures of some hundred degrees centrigrade. Thus, superconducting coils should not become necessary in these systems, (ii) The mechanical stresses can be kept well below the limits of tensile strength of possible coil materials. In addition, both the internal coils and their magnetically shielded supports can be made magnetically force-free in certain cases, (iii) These results are due to the fact that high beta values are,in principle, available in systems with a main poloidal field, and that only a fraction of the total magnetic field energy originates from the internal conductors. This provides an important advantage over systems with a main toroidal field where, at a given plasma pressure, the Ohmic power losses and mechanical stresses become between one and two orders larger than those of poloidal field systems, (iv) The coil supports can be made large enough to provide cooling ducts for the internal conductor system.

The stability of a general toroidal MHD equilibrium with a continuous pressure profile is investigated for the case where the fluid is surrounded by vacuum. It is found that a disturbance which is localized near the free boundary grows exponentially in time unless a certain necessary criterion is satisfied. Because of the weaker boundary condition, this criterion imposes a more stringent restriction on the configuration than does Mercier's criterion near the boundary. For the cylindrically symmetric case the criterion requires a decrease of the rotational transform and yields a critical relation between the shear and the pressure gradient.

A hybrid model treating electrons as a dissipative fluid and ions as particles is used to investigate numerically the properties of high-Mach-number magnetoacoustic shock waves propagating perpendicular to a magnetic field. Upon increasing the Alfvén Mach number MA, the electron pressure behind the shock becomes bounded for M_A ≳ 15. Ion reflectivity a increases but stays rather small even for M_A → ∞, B₀ → 0 (i.e. α = 30 – 40% for reasonable collision frequencies in the shock). Thermalization of the plasma by multiple bouncing in a cylindrical tube is studied for the case where the ion gyroradii are large compared to the tube radius. Strong damping is found to lead to equilibration after about two bounce oscillations. Ion reflection during the first implosion is found to be essential for non-adiabatic ion heating in the succeeding thermalization period.

The steady-state operating conditions and stability against temperature-density excursions are evaluated for tokamaks operating in the reactor regime on a D-T cycle. Global ion and alpha-particle balances and global ion and electron energy balances, together with MHD equilibrium and stability constraints, constitute the basic computational model. Constant, neoclassical, neoclassical-diffusion and trapped-ion instability scaling for particle and energy confinement times are considered.

Steady-state operating conditions tend to be unstable below about 30 keV for constant confinement time scaling, assuming equal particle and energy confinement times. These low-temperature conditions are somewhat more unstable with neoclassical scaling and somewhat less unstable with trapped-ion instability scaling. The unstable modes, at low temperatures, are identified as pure temperature fluctuations for constant and neoclassical diffusion scaling, but as mixed temperature density fluctuations for trapped ion instability scaling. At higher temperatures, the least stable mode is a pure density fluctuation, for all confinement time scaling laws considered.

Increasing the particle confinement time relative to the energy confinement time causes a build-up of alpha particles, with attendant bremsstrahlung enhancement, and a reduction in stability against temperature-density excursions.

A systematic study is made of the coupling of RF energy to a plasma column by means of an external set of current sources in the toroidal cavity constituted by the machine. The coil loading due to the absorption of RF power by the plasma and by the wall is discussed inside various frequency domains of interest for RF heating. The plasma is described by hot-fluid theory with effective collision frequencies; the latter are either particularized to describe analytically linear collision-less damping or used as parameters to simulate other loss mechanisms like the non-linear ones. Boundary conditions consistent with the magnetic confinement are taken at the plasma-vacuum interface.

Special emphasis is placed on the bounded-plasm a effects in the entire frequency range (from ω≪ω_ciup to ω>ω_LH). In particular, magnetoacoustic resonances may strongly increase the efficiency of RF energy transfer when the physical absorption mechanisms are electron TTMP or ion cyclotron resonance. At higher frequency, resonance modes of the coaxial type are found in which the plasma plays the role of the central conductor of a coaxial toroidal cavity.

The author obtains a general criterion for the stability of a toroidal plasma with respect to g-mode perturbations, which were first considered by Furth, Killeen and Rosenbluth for a plasma of finite conductivity in a magnetic field with shear and gravitational field g. The criterion is used to elucidate the stability of g-mode perturbations in an axially symmetric tokamak of circular cross-section. It is shown that, if aq'/q is positive and not too small, g-mode perturbations are stable for q² > 1 (where q is the safety factor, a is the radius and the prime denotes a derivative with respect to a). With negative values of aq'/q, instability is possible even if q² ≫ 1.

A linear description of the temporal evolution of a localized wave packet in a weakly inhomogeneous plasma is derived by expanding the spatial variations in the plasma parameters up to second order. The solution applies to systems with or without unstable normal modes, and it can provide a quantitative measure of the correlation length of the fluctuations to be expected, as exhibited by the spreading and propagation speed of the wave packet. The general formalism is applied to the collisionless trapped-particle mode in tokamak geometry, the current-driven drift mode, and the negative-energy loss-cone mode in a magnetic-mirror geometry.

The eigenvalue equation for the interchange instability is derived from guiding-centre equations including finite-Larmor-radius corrections. Analytic solutions are found which are valid near the ⋅ = 0 surface and away from this surface. Matching these two solutions over their common range of validity determines the eigenvalue and hence the mode frequency. The growth rate and radial profile of the mode may readily be evaluated explicitly. The analysis is applicable to the high-β pinch, since cylindrical effects dominate over toroidal. For typical parameters, FLR stabilization is found to increase the marginally stable pressure gradient by a factor two over that given by the Suydam criterion.

Experiments with the first complete high-β stellarator torus with helical magnetic axis are reported. The Garching 2.6-MJ capacitor bank was used to feed a toroidal theta coil with a major.diameter of 2.7 m (ISAR T1), Toroidal equilibrium was achieved by superposing helical ℓ = 1 and ℓ = 2 (partly also ℓ = 0) fields on the slender (A = R_T/r₀ ≈ 150) toroidal pinch plasma such that the plasma surface facing the torus centre was more corrugated than the outer side (M-and-S effect). The toroidal equilibrium condition and the corresponding plasma distortions were consistent with sharp-boundary-model predictions. Effects in connection with initial dynamics, toroidal plasma currents and transverse magnetic fields could be explained by simple models. In agreement with sharp-boundary theory, short wavelength m = 1 and m = 2 modes were found to be stable and long wavelength m = 1 modes were unstable, limiting the plasma life-time by wall contact. Long-wavelength m ≥ 2 instabilities were not observed in contrast to sharp-boundary theory, i.e. this model is much too pessimistic for m ≥ 2 modes, even if the finite gyroradius is included. No significant difference in the stability behaviour was found, compared with previous linear and toroidal sector experiments.

Necessary and sufficient conditions are obtained for the description of particle motion by a "quasi-potential" in an inhomogeneous static magnetic field and an r.f. electric field. This analysis leads to a new concept of "critical energy", the height of the adiabatic barrier, which is proportional to , E₀ being the strength of the r.f. field in the plasma. The theoretical results are confirmed by numerical calculations. Although this concept holds in a general magnetic field, analysis is restricted to the cusped magnetic field.

The achievement of controlled fusion will make available excess neutrons which can be used in various ways in combined fission-fusion power cycles. The various schemes are here classified as hybrid–in which heavy-element fission occurs in the fusion blanket; symbiotic–in which fissile material is bred in the absence of fission events; and augean–in which the neutron surplus is used to transmute fission reactor waste products. The earliest work in this field, unpublished and originally classified secret, is reviewed. Recent studies of hybrid systems based on subcritical thermal and sub-critical fast-fission blankets are described in detail. An analysis of symbiosis based on the Th-U fuel cycle is summarized. The conditions required for high-level waste transmutation are presented; Augean systems seem best suited to actinide waste burning. It is concluded that basic physics of various fission-fusion systems has been surveyed but the engineering and economic aspects of combined systems have been largely ignored. It remains to be shown whether fission-fusion systems will prove superior to alternative methods of accomplishing the same ends.

The Second International Conference on Plasma Theory, organized by the Institute of Theoretical Physics of the Ukrainian SSR Academy of Sciences and the P.N. Lebedev Physics Institute of the USSR Academy of Sciences with the support of the Scientific Council for Plasma Physics of the USSR Academy of Sciences and the International Union of Pure and Applied Physics, took place in Kiev from 28 October to 1 November 1974. The Organizing Committee for the Conference was presided over by Academician N.N. Bogolyubov.