Table of contents

A description is given of a general method of deriving dynamic equations for the amplitudes of interacting waves (both volume and surface waves) in a bounded plasma. The treatment is based on the study of the interaction of magnetohydrodynamic waves in a plasma cylinder confined by a strong magnetic field. Decay instabilities were studied in order to find the probabilities and evaluate the characteristic times of the corresponding three-plasmon processes. It is shown that the non-linearity of the boundary conditions can have a substantial effect on three-plasmon interactions involving surface waves.

The linear problem was solved in advance. It is shown, in particular, that in addition to the Alfvén surface waves, acoustic-type surface waves with frequencies approximately equal (ω_A being the Alfvén frequency) can propagate in the plasma cylinder.

The authors consider the possibility of a self-sustaining thermonuclear reaction in a dense plasma (n ≳ 10¹⁶ cm³). The pressure of the plasma is contained by walls and the magnetic field only serves to reduce thermal conductivity in a transverse direction. A solution is obtained for the plasma balance equation that makes allowance for radiation losses along the magnetic field, and it is shown that there is no satisfactory solution across a uniform magnetic field. The authors discuss the possibility of a steady-state thermonuclear reaction with a non-uniform magnetic field.

On the basis of Boltzmann's kinetic equations hydrodynamic equations have been obtained for the ions and electrons of a fully ionized collisional plasma in a strong inhomogeneous magnetic field under assumptions characteristic of works on "drift" instability. These equations are a generalization of the results of Mikhailovsky's work on an inhomogeneous magnetic field and make it possible to solve problems connected with the hydrodynamic drift instability of plasma in the presence of shear, curvature of the lines of force and inhomogeneity of the absolute value of the magnetic field.

An asymmetric arrangement of the conductors of a helical stellarator winding and currents passing through them unequal in absolute value cause the formation of a spatial magnetic axis. In the vicinity of this axis the useful volume bounded by a certain surface exhibits the principal properties needed to stabilize a number of plasma instabilities – shear and minimum . This paper is a detailed analytical study of asymmetric systems of this kind. It is demonstrated that the use of the second and third harmonics of a helical magnetic field in devices with a high aspect ratio makes it possible to obtain δV'/V' between 0.08 and 0.15 for shear S* =0.05 and 0.13 and a useful volume of sufficient size. The configurations considered can be used to create closed magnetic traps for the purpose of confining a high-temperature plasma and studying the stabilizing effect on it of shear and minimum , both together and separately.

The results of measurements made in a 40-eV plasma contained by a 500-Oe HF magnetic field travelling along a plasma column are compared with computed values for the penetration of such a field into a homogeneous solid cylinder with conductivity σ and free-electron concentration n. Very satisfactory agreement with theory is observed. In particular, the predicted dependence of the relative strength of the field due to the drift current on the parameter is confirmed. With increasing f the relative strength of this field reaches a maximum of 0.8 and then decreases, the skin layer remaining substantially less than the radius of the plasma column.

To obtain satisfactory agreement with theory, it was sufficient in the conductivity calculations to take into account the cross-section for Coulomb collisions and the total cross-section for electron-atom collisions.

It is shown, in addition, that for ionization coefficients higher than 5% the magnetic-field and plasma pressures balance.

The authors investigate the thermal insulation of plasmas in Tokamak-3, taking as thermal insulation parameter the energy confinement time ofthe plasma τ_E and relating it to the discharge parameters: the stabilizing magnetic field H_z, the charged particle density n_e and the discharge current I. It is found that for n_e ≥ 2 × l0¹³ cm⁻³ τ_E is virtually independent of H_z, for n_e = (l-5) × 10¹³ cm⁻³ τ_E increases somewhat with n_e and in proportion to I. The experimental results fit the empirical formula τ_E∼a²H_φ.

The interaction in a plasma between high-frequency and low-frequency waves with given phases is considered in a three-wave approximation. The number of interacting waves is arbitrary. Linear damping of the waves is taken into account. Approximate solutions are found of the equations for the amplitudes. A criterion is established for the decay instability of a strong high-frequency wave. The author finds the equilibrium distribution of energy among the waves and the criterion for its establishment. The results are illustrated by examples of the interaction between transverse electromagnetic and Langmuir waves in a homogeneous equilibrium plasma and of the interaction of space charge waves with ion-acoustic waves in a conducting cylinder situated in a longitudinal magnetic field. Comparisons are made with experiment.

The influence of ion-acoustic instability on the penetration of a high-frequency field into a plasma is investigated. The slowing-down of the plasma electrons as the instability develops is taken into account by means of a non-linear Ohm's law j_z = j₀ [1-exp(-αE)] which enables one to consider continuous variations of the depth to which the field penetrates the plasma as a function of the parameter α = E₀/E_k, where E₀ is the peak electric field value and E_k the field value at which ion-acoustic instability occurs in the plasma. The depth of penetration by the field into the plasma is determined as a function of α. For large α the penetration depth increases by a factor α^½ relative to the skin layer thickness of the linear theory (where α ≪ 1).

The authors consider the long-wave oscillations of a cold bounded plasma against a background of steady-state electron oscillations. The problem is solved in a non-linear approximation with respect to an external high-frequency field. It is found that, as in the case of a constant current, the surface waves are unstable.

The authors investigate surface waves excited in cold plasma by an oscillating current, considering cases where the plasma is bounded (plasma layer and plasma cylinder). It is physically clear that one has to take into account the actual geometry of the plasma configuration when the damping length of a surface wave is commensurate with the transverse dimensions of the plasma. The authors study the surface waves when the plasma is surrounded by a metallic sheath of infinite conductivity. The conditions are found for the build-up of three-dimensional surface waves and the corresponding expressions derived for their frequencies and growth rates.

A translation of the abstracts of all the articles for this issue into French, Russian and Spanish.