The gravitational instability of a two-component plasma has been studied here to include simultaneously the effects of neutral gas friction, finite ion Larmor radius, magnetic resistivity and Hall currents. The viscosities of the two components of the plasma have also been taken into account. The mode of the transverse as well as the longitudinal wave propagation have been discussed. The dispersion relations have been obtained for both these cases and numerical calculations have been performed to obtain the dependence of the growth rate of the gravitationally unstable mode on the various physical parameters involved. For the transverse mode of propagation, it is found that the growth rate of the unstable mode increases with magnetic resistivity and with the ratio of the densities of two components. The influence of the magnetic resistivity is, therefore, destabilizing on this mode of wave propagation. The viscosities of the two components are found to have a stabilizing influence on the growth rate in this case since it is found that the increase of hte viscosity effects reduces the growth rate. For the longitudinal mode also it is found that the effects of viscosities as well as that of neutral gas friction are stabilizing. The magnetic resistivity does not affect the growth rate since the equation determining the growth rate is found to be independent of this effect.

Kinetic theory, including ion Larmor radius effects, is used to analyse the Alfvén wave heating of cylindrical plasmas using axisymmetric waves excited by an antenna at frequencies up to the ion cyclotron frequency. At the Alfvén resonance position, the compressional wave is mode converted to a quasi-electrostatic wave (QEW) which propagates towards the plasma centre or edge depending on whether the plasma is hot or warm. The energy absorbed by the plasma agrees with the MHD theory predictions provided the QEW is heavily damped before reaching the plasma centre or edge; if it is not, then QEW resonances may occur with a consequent increase in antenna resistance. The relation between ion cyclotron wave resonances and QEW resonances in a hot plasma is shown. The behaviour described above is demonstrated by numerical solution of the wave equations for small and large tokamak-like plasmas. WKB theory has been used to derive useful expressions which quantify the QEW behaviour.

The turbulent diffusion of plasma across a magnetic field is studied theoretically using a three-dimensional model which includes the full dynamics of the diffusing particles and which is valid for arbitrary magnetic field strengths. The theory is confined to perpendicular turbulence, i.e. where the build-up of the fluctuations lies primarily in the plane perpendicular to the magnetic field (although it is more generally applicable). A single expression for the diffusion is derived in terms of the fluctuation spectrum, particle energy, the dispersion characteristics of the excited modes and the magnetic field. Earlier results for equilibrium plasmas are confirmed. We demonstrate the continuous transition from anomalous (1/B) diffusion in regimes of low fluctuation levels (or strong magnetic fields) to classical (1/B2) diffusion in regimes where the fluctuation level destroys the coherence sustained by the magnetic field. In this latter regime, the particles behave as if unmagnetized except for a turbulent drift which appears in the presence of anisotropic spectra.

The first critical fast Mach number is rigorously defined to be the one at which the downstream flow speed in the shock frame equals the ordinary downstream sound speed. Above the first critical Mach number, resistivity alone is unable to provide all the dissipation needed for the required Rankine-Hugoniot shock jump. A survey of the dependence of the first critical Mach number upon upstream plasma parameters is needed to guide studies of the structure of collisionless shocks in space. We vary the upstream plasma beta, the upstream shock normal angle, and the ratio of specific heats for the plasma. The first critical Mach number depends sensitively upon upstream plasma parameters, and is between 1 and 2 for typical solar wind parameters, rather than the often quoted value of 2·7, which is valid for perpendicular shocks propagating into a cold plasma. We introduce the suggestion that the flux of superthermal and energetic ions upstream at quasi-parallel shocks might increase suddenly at the first critical Mach number. Our parametric survey indicates that this hypothesis might be most conveniently tested using interplanetary shocks.

‘Propagation along the magnetic field of a pulse current originated dlisturbance in a cold two-fluid plasma’, by G. J. Lewak, J. Plasma Physics, vol. 1, 1967 p. 435.

On page 449, the sixth of the list of references should read

Davis, L., Lust, R. & Schluter, A. 1958 Z. Naturforsch. 13a, 916.

An intense relativistic electron beam propagating through a plasma creates a low-density plasma duct capable of guiding a free-electron laser mode. The beam dynamics plays an important role in the propagation of TM modes. For (where and are the beam and plasma densities respectively, and a and b are the x and y dimensions of the duct) and beam energy of about 2 MeV, the threshold current turns out to be about 20 kA. For marginal radiation guiding, the size of the plasma duct decreases with beam voltage. Application of a strong DC magnetic field shows that an even narrower duct can guide high-frequency radiation.

The propagation and stability of drift waves is examined, by means of a perturbation technique, in geometries where the magnitude of the magnetic field varies periodically along the field lines. Two sets of modes are found which can be driven unstable by resonant particles trapped in the magnetic field non-uniformity. One set of modes consists of standing waves with wavelength twice that of the magnetic field non-uniformity. The other set of modes consists of standing waves composed essentially of the sum of a component which does not vary along the line and a component which is a standing wave with wavelength equal to the wavelength of the magnetic field non-uniformity. The advantage of this method is that it predicts simply and pictorially the real frequency of oscillation for these modes.

The statistical mechanics of the weakly turbulent plasma is treated in an original manner by introducing the waves by means of the van Kampen modes. A system of coupled equations is derived which relates the correlations between waves and waves, waves and particles, particles and particles. The quasilinear theory is obtained at the first order, and the coupling wave equation at second order, under suitable assumptions.

The theory of electrostatic plasma turbulence is considered. The basic equations for the dynamics of the hierarchy of the moment equations are derived and the difficulty of the closure problem for strong plasma turbulence is discussed. The characteristic functional in phase space is introduced and its relations to the correlation functions are described. The Hopf functional equation for dynamics of the characteristic functional is derived, and its equivalence to the hierarchy of the moment equations is established. Similar formulations were carried out in velocity-wave vector space. characteristic functional are considered and their relationships are studied. An approximate solution for Hopf's equation for the nearly normal turbulence is obtained which is shown to predict diffusion of the mean distribution function in velocity space.

Stimulated Brillouin scattering of an electromagnetic wave is investigated analytically in a dissipative magnetized plasma in the presence of negative ions. With an increase in the number of negative ions (maintaining quasi-neutrality), it is found that the growth rate of ion-acoustic waves decreases very slowly up to 50% concentration (i.e. half of the total ionic contribution) of negative ions. Further increase in the number density of negative ions beyond 50% results in a sharp fall in growth rate.

The structure of transverse MHD shock waves in an initially partly ionized plasma is studied using a three-fluid model with collisional transport coefficients. This model includes the effects of non-equilibrium ionization and of ion velocity slip. A closed set of structure equations is obtained and it is shown that they have a saddle-point – saddle-point topology which prohibits direct integration. In distinction from previous MHD shock structure studies, it is not possible to reduce the number of variables in a realistic manner to allow direct integration, nor is it possible to use the method of matched asymptotic expansions. An iterative solution method is presented in this paper, based on a detailed analysis of the integral curve topology.

The stability of hydrodynamic longitudinal oscillations of an inhomogeneous magnetoactive plasma is analysed. If the non-uniformity of density is taken into account, it is shown to result in parametric-like instability at sub- and ultra- harmonics of natural plasma oscillation frequencies. The conditions for the development of unstable oscillations and their growth rates are determined.

We study the influence of a weak quasi-static parallel electric field on the stability of electromagnetic plasma waves. Using an operator calculus to solve the Boltzmann-Maxwell equations we derive a dispersion relation for the electromagnetic waves. Assuming that the electrons have a loss-cone distribution, the real frequency of waves in the whistler band is not changed by the presence of the electric field. Resonant interaction damps the HF waves for propagation parallel to the electric field. In the case of opposite propagation, a new HF excitation is found at frequencies ω ≲ ωce The width of the excitation region depends on the width of the loss cone, field strength and collision frequency. This result is applied to observations of the splitting of VLF emissions under natural conditions in the magnetosphere. It is found that the observed splitting could have been caused by the presence of the weak parallel electric field of a kinetic (shear) Alfvén wave in the emission region, which is quasi-stationary compared with the growth of the observed VLF emission.

Using the stationary equilibrium energy principle a sufficient condition is obtained for the stability of a compressible stratified fluid with a non-uniform horizontal magnetic field, with an aligned shear flow. The condition is used to provide a simple generalization of a known result for a specific atmospheric model.