The hydrodynamic theory of drift Kelvin-Helmholtz instabilities is discussed. It is shown that the hydrodynamic approach gives, in the region of its applicability, the same results as the kinetic one. Previous studies on the hydrodynamic theory of drift Kelvin-Helmholtz instabilities are analysed. It is shown that certain parts of these studies are incorrect. Reasons for this are discussed.

A uniformly-streaming compressible and infinitely-conducting plasma is confined by a magnetic field aligned with the stream. The system is disturbed by introducing magnetic dipoles into the field. A Fourier-transform method is used to determine the displacement of the interface between the streaming plasma and the magnetic field within the framework of a ‘shallow-water’ approximation. For the case of a subsonic plasma stream, stationary waves appear on the interface upstream of the dipoles, and it is found that (i) these stationary waves are possible only if the gravity effects on the plasma are weak enough; (ii) the effect of surface tension at the interface is to reduce the amplitude and increase the wavelength of these waves. For the case of a supersonic plasma stream, however, stationary waves at the interface are not possible.

The filamentation and collapse of Langmuir waves in a weak magnetic field are analysed in two particular cases of low-frequency acoustic perturbations: (i) adiabatic perturbations which correspond to subsonic collapse, and (ii) nonadiabatic perturbations which correspond to supersonic collapse. Here the existence of Langmuir filaments and Langmuir collapse in a weak magnetic field are due to nonlinear interaction of high-frequency Langmuir waves (which make small angle with the external magnetic field) with low-frequency acoustic perturbations along the magnetic field.

An analytical theory for the time evolution of the distribution function, energy and current of an assembly of electrons submitted to a quasi-sinusoidal stochastic field is given. To the first order, energy and current are obtained using Sturrock's stochastic acceleration theory. The calculation of the transition probability enables us to get the distortion of the distribution function, and to recover the preceding first-order results. To the second order, collisions are taken into account, in the framework of the two-dimensional theory. The turn-on time for the current is evaluated. The results obtained are compared with the numerical results of Karney & Fisch.

The generation, structure and propagation of one-dimensional ionizing MHD shock waves in helium under a pressure of 100 mTorr are investigated with the help of numerical simulation. The normal magnetic field varies within 3 to 10 kG and the longitudinal magnetic field varies up to 2·5 kG. The model includes the kinetics of ionization and photo-processes. If a solid conducting piston is a source of perturbation, it may give rise to generation and further development of an MHD switch-on wave. Its evolution at an advanced stage depends weakly on the source. The curves for the dependence of the shock speed on time and the driving magnetic field as well as the profiles for the main quantities are presented. A possibility of comparison with real experiments is discussed. Algorithms based on Godunov's sliding meshes and the imbedding methods are used for numerical simulation.

The heat conductivity of a laser-created plasma heated by inverse bremsstrahlung absorption is investigated in the vicinity of a self-similar state (SSS), taken as reference state. Under certain conditions, the slowly varying macroscopic quantities obey true, local hydrodynamical equations and a well-defined, positive, heat conductivity exists. The latter is strongly time-dependent through the unperturbed temperature. Its value, compared to the classical heat conductivity at the same temperature, shows a reduction of about 20%. It is shown that, for high intensities and/or long wavelengths, the linear heat conduction theory necessarily breaks down, even if the temperature gradient is very small.

Starting from the two-fluid model hydrodynamic equations, a dispersion relation is obtained for wave propagation through a two-temperature plasma perpendicular to the direction of the spatially uniform external magnetic field B0cosω0t and several excitation conditions are deduced.

Ballooning mode theory for finite toroidal mode number n is derived for shearfree and sheared axisymmetric toroidal plasmas. The resulting finite-n theory is applicable for both compressible and incompressible perturbations. The inclusion of finite compressibility changes the ballooning mode eigenfunctions and eigenvalues, but not the form of the finite-n correction.

Self-consistent infinitesimal perturbations of electron density and electric field are used to analyse the stability of the plasma. The axisymmetric perturbations are stable for any magnetic and electric field strengths. The non-axisymmetric perturbations with azimuthal modes m ≥ 1 and less than a certain integer are unstable for certain ranges of magnetic and electric fields. The mode m = 2 can be more unstable than the mode m = 1. Previous analysis by other authors was confined to the case m = 1 and the perturbations were not self-consistent. Our results differ significantly from the earlier results.

An exact nonlinear Alfvén wave in a low-β plasma is investigated. Super Alfvén solitons with a density depression are found to exist. The analytical result for the small-amplitude soliton is given.

Plasma effects on the emission of synchrotron radiation are investigated using a two-dimensional electromagnetic relativistic simulation code. Results are compared with those for a vacuum; it is found that the emission lies between the vacuum emission for nc and nc + 1 where nc is the critical harmonic for EM wave propagation (nc = ωp/Ω0).

The restrictions imposed are that the magnetic field is everywhere in the x direction, and that no quantity varies with x, but several interesting instabilities can still occur. After some discussion of objectives, a fluid-like formulation is pursued, in which the pressure anisotropy is retained, but higher moments neglected. It shows a resonance at twice the gyrofrequency, and for electrons the constraint on the time step would be unacceptable, so they should be treated more crudely. Then the dispersion equation shows only two modes, which appear sufficiently harmless for us to proceed to computations.

The electrostatic lower-hybrid wave is shown to decay parametrically into a whistler wave and a resonant ion cyclotron mode or an ion cyclotron quasi-mode or a reactive quasi-mode. The convective threshold powers for these decay instabilities are found to be much larger than presently available pump powers. These decay instabilities, however, are expected to play an important role in the saturation of the parametrically excited short-wavelength lower-hybrid waves having frequency close to ωlh.

The nonlinear transient evolution of a suddenly applied monochromatic wave in a homogeneous plasma is considered, with particular emphasis on the magnetized case, where ordinary and extraordinary electromagnetic waves travelling normal to B are treated. Two important features are described. First, the penetration of the wave front is shown to be accompanied by ‘radiation’ of low-frequency waves, of which ion cyclotron and lower-hybrid waves are considered here. Next, the presence of a nonlinear, second-harmonic precursor is predicted, containing two natural modes of oscillation, one with exactly twice the frequency of the fundamental, and the other a slightly frequency-shifted contribution. The analysis is readily generalized to waves other than those considered here.

The results of recent experimental measurements of the differential cross-section for elastic scattering of electrons on sodium atoms were used to evaluate the electron steady-state distribution function in a weakly ionized, uniform and non-magnetized sodium plasma placed in a d.c. electric field. The field was assumed to be of moderate intensity, so that the thermal motion of the neutrals had to be taken into account in the evaluation of the distribution function. The resulting ‘modified Druyvesteinian function’ was applied to study the non-potential instabilities arising from the presence of the field in this particular plasma. Threshold drifts for both very slow and slow modes were obtained and the conditions for the onset of instabilities were discussed. It is shown that the thermal motion of the neutrals affects both critical drifts and the angles of propagation.

Ohm's law for homogeneous warm plasmas not varying with time is generalized for plasmas with parameters slowly varying in space and time. The corresponding integral constitutive relation is derived.