An analytic study is made of the electrostatic mode structures which exist between the upper-hybrid cut-off and the plasma resonance in a plasma in which the zero-order density gradient points along the magnetic field. In general the solutions consist of long-wavelength cold modes which are converted to short-wavelength Bohm-Gross modes near plasma resonance. However, there exist certain discrete angles of propagation at which finite solutions exist that can be described solely in terms of cold plasma theory. The relevance of these processes to resonant absorption experiments in the auroral ionosphere is considered. A brief study is made of the changes produced by a finite angle between the density gradient and the magnetic field. The possibility of finding analogous low-frequency structures is also investigated.

The theme of the paper is the relation between the so-called Z mode and the upper-hybrid wave in a magnetized plasma. First, certain problems as to reflexion and transmission of upper-hybrid waves at quasi cut-off (that is, cut-off predicted within electrostatic approximation) are stated and solved by singular perturbation technique. Then the theory is extended to a problem concerning generation and trapping of upper-hybrid waves in magnetic field aligned electron density irregularities. First a single density depression is considered, and then the formalism is further extended to a system of many parallel density depressions. The study was motivated by problems in the theory of artificial small-scale ionospheric irregularities occurring in radio wave experiments.

Parallel whistler-mode propagation in a hot anisotropic plasma at frequencies near the electron gyrofrequency is considered by using analytical methods and a simple graphical technique, without any special restrictions on the value of the imaginary part of the plasma dispersion function argument. An exact criterion for the possibility of whistler-mode propagation in the vicinity of the electron gyrofrequency is derived. In particular it is pointed out that whistlers in this frequency interval can propagate only in a very hot and rarefied plasma submerged in a strong magnetic field. These whistlers can only be damped, the modulus of the decrement of the damping cannot exceed 1·1 times the electron plasma frequency. The refractive index remains close to unity.

The propagation of the fast magnetosonic wave is studied, taking into account the effect of the two-ion hybrid layer. Using a one-dimensional model, which includes density and magnetic field gradients, the wave equation is solved in the cold plasma approximation. The existence of radial eigenmodes confined between the two-ion hybrid layer and the low field side wall is predicted. Comparison with experimental data obtained on the TFR tokamak confirms the theoretical conclusions. Toroidal eigenmodes are observed even in the mode conversion regime when the antenna is on the low magnetic field side.

The ponderomotive force generated by random Alfvén waves in a collisionless plasma is evaluated taking into account mean magnetic and velocity shear and is expressed as a series involving spatial derivatives of mean magnetic and velocity fields whose coefficients are associated with the helicity spectrum function of random velocity field. The effect of microscale random Alfvén waves through ponderomotive and mean electromotive forces generated by them on the propagation of large-scale Alfvén waves is also investigated.

We consider the nonlinear interaction of three high-frequency waves and lowfrequency density perturbations in a sharply bounded plasma. The coupled equations are presented in a general and convenient form. To demonstrate the usefulness of our method we derive explicit expressions for the threshold of a number of possible instabilities in semi-infinite and cylindrical plasmas.

Several conclusions regarding the stability of inhomogeneous Vlasov equilibria are drawn from earlier work. A technique is presented for generating first-order formulae for the change δω in the frequency of any normal mode, when a parameter λ characterizing the equilibrium is changed slightly. Several applications are given, including a first-order calculation of the growth rate or damping of an electromagnetic mode due to the presence of plasma. A condition is derived for the existence of a normal mode with real frequency. When there are ignorable co-ordinates, the normal modes can be written in the form of waves propagating in the ignorable directions. The character of the modes depends on certain symmetries in the dynamic spectral matrix. Special cases arise when the orbits can be approximated in certain ways.

The time-dependent behaviour of a homogeneous plasma in a weak electric field near the onset of runaway of electrons is studied for astrophysical applications. The relativistic Boltzmann equation is used to calculate the particle distribution function. It is shown that the plasma is stable against electric field fluctuations in the onset region for runaway, provided that the global behaviour of the System is determined by the magnetic field structure.

A general investigation of the electrical conductivity for radio-frequency (RF) fields in strongly magnetized plasmas with small-scale density fluctuations is performed within the cold plasma hydrodynamical approximation. It is shown that in such plasmas an RF phenomenon similar to the Bohm diffusion exists: the presence of stochastic RF electric field in a turbulent plasma can lead to a strong enhancement of the RF currents flowing in the direction of the applied electric field components transverse to the magnetic field. The appearance of these turbulent drift currents favours energy transfer from the RF fields to the plasma and thus leads to their stronger damping. This effect allows us to interpret quantitatively the enhanced damping of the magnetosonic waves observed in several experiments. The magnetized radially inhomogeneous cylindrical plasmas in these experiments are characterized by density fluctuations due to drift instabilities. The theory has also a number of other applications; an example is given of the whistlers damped by the ionospheric density fluctuations.

An investigation is made of the effect of RF-induced velocity diffusion on the distribution function, f(v), of the heated ion species in minority heating schemes using the fast Alfvén wave. The solution for the distorted distribution function is expressed in a Legendre series from which deviations from isotropy can be assessed. Solutions are found in the limits of high and low velocities and the elongation of the constant f(v) surfaces is also given.

The present series of papers is concerned with the problem of the thermal selffocusing of an electromagnetic wave in an underdense plasma which is examined within the context of ionospheric modification by high-power radio waves. We formulate this problem as a coherent four-wave interaction between a pump wave, Stokes side-band waves and a thermally driven density perturbation. Our treatment assumes that the heating of the electrons in the interference pattern of the pump and side-band waves is in equilibrium with longitudinal heat conduction and energy transfer to the ions and, in addition, that the density perturbation is subject to decay on account of longitudinal ambipolar diffusion, ambient plasma drift motion, recombination and the stabilizing influence of perturbations to the electrical conductivity.

After giving a higher-order solution of the equation describing the nonlinear equilibrium of rippled electron beams, in the second part of the paper we derived mathematical expressions for the growth rates of electrostatic perturbations for the resonant coupling of (i) fast and slow and (ii) fast—fast or slow—slow waves. Actually, viewed from a physical point of view, only type (i) of wave coupling may lead to the kind of instability considered in the paper.