An electron thermal instability is proposed, which could explain the occurrence of the break-up of a plasma shell into separated current elements during the early history of a discharge. Inclusion of electron thermal conduction and Faraday's law leads to an optimum wavelength for growth, in good agreement with recent results on a θ pinch at NRL, Washington. Finally, the addition of ion motion leads to a modification of the stability criterion. The non-convective instability exists only at low temperature and high density; but a convective instability now appears, which persists at high temperature, and could be relevant to fusion conditions.

We investigate radiation of waves at double the frequency from an arbitrary inhomogeneous, isotropic plasma layer, when 8-polarized electromagnetic waves are obliquely incident on it and their lengths are considerably greater than the width of the layer. We calculate the amplitudes of the radiated waves. We show that, in general, the second harmonics are radiated in the direction of propagation of both the reflected and the transmitted wave being at the basic frequency. At small plasma densities, the second harmonics are emitted practically only in the direction of propagation of the reflected wave at the basic frequency. For normal incidence, there is no wave radiation at double the frequency of the incident wave.

A theory is presented for the rate of thermal relaxation of a two-dimensional plasma in a strong uniform d.c. magnetic field. The Vahala—Montgomery kinetic description is completed by providing a cut-off time for the time of interaction of two particles which contribute to the collision term. The kinetic equation preclicts that thermal relaxation occurs as a function of the dimensionless time (ωpt) (ωp/Ω) (n0λ2D)−½, where ωp, is the plasma frequency, Ω is the gyrofrequency, and n0 λ2D is the number of particles per Debye square. By contrast, in the absence of an external magnetic field, a two-dimensional plasma relaxes as a function of (ωpt) (n0λ2D)−1.

The thermal relaxation process for a spatially uniform two-dimensional plasma in a uniform d.c. magnetic field is simulated numerically. Thermal relaxation times are defined in terms of the time necessary for the numerically computed Boltzmann H function to decrease through a given part of the distance to its minimum value. Dependence of relaxation time on two parameters is studied: number of particles per Debye square n0 λ2D and ratio of gyrofrequency to plasma frequency Ω/ωp. When Ω2/ω2p becomes ≫[ln (L/2πλD)]−½, where L is the linear dimension of the system, it is found that the relaxation time varies to a good approximation as (n0 λ2D)½ and Ω/ωp.

The modified Chew—Goldberger—Low (CGL) equations are applied to the effect of Hall current on the instability of an incompressible plasma jet surrounded by non-conducting, compressible matter. The dispersion relation is obtained and discussed. The following is found. (i) When λ (the ratio of plasma density to the density of surrounding medium) is much greater than unity, the plasma jet is unstable for all wavenumbers for which k* = Küα < [(4R22 – 1)ü(1 + V2α)], where R2 = p∥/p⊥, V2α = H2/4αρ, K = (l2 + α2)½. Also, the jet is unstable for R2 > 1 + V2α. (ii) When λ ≪ 1, the critical wavenumber ratio for the instability to set in is k* < [(V2α + 3R2)ü(1 + V2α)½. Also, the jet becomes unstable for R2 < ⅓. (iii) When either l = 0 or α= 0, we must have R2 > 1 + V2α for instability. It is established that the Hall current has a destabilizing effect for certain wave- numbers. The dispersion relation for the incompressible plasma jet in cylindrical geometry is solved numerically on a computer.

By applying quasi-linear diffusion theory, general expressions are obtained for particle diffusion coefficients in both pitch angle and energy. The results are valid for resonant interactions with any mode of weak plasma turbulence, with wave energy distributed over any range of frequencies and wave normal angles. Simple relations are found between the diffusion coefficients, these relations reflecting the geometry of the diffusion surfaces for resonant particles.

The magnetoplasma dispersion function is defined as

It is found in all the dispersion relations for wave propagation perpendicular to the magnetic field in hot plasmas. We review the properties of fω(z), and present several new expansions, which may be of interest in the study of properties of waves in plasmas, or may suggest computational methods for calculating fω(z).

An effect of an axial current on the propagation of low-frequency axisymmetric magnetohydroclynamic waves in a radially non-uniform plasma column was investigated theoretically and experimentally. It was found that the axial current and the density gradient cause a coupling between the torsional and compressional waves.

Collision integrals of excited hydrogen atoms were calculated in the temperature range 10000–25 000 ˚K. These values were used for calculating the viscosity and έ the contribution of the heavy components λH to the translational thermal conductivity of a LTE hydrogen plasma. The results show a dependence of έ and λH on the calculated transport cross-sections.

The purpose of the paper is to investigate, by means of kinetic theory, the wave—wave couplings that may occur in a magnetized and partially ionized plasma medium containing neutrals (or ions) with inverted population levels. We study the interaction of three monochromatic waves which propagate parallel to the direction of a magnetic field in the medium. Transverse as well as longitudinal waves are considered. The present paper, which represents a generalization of previous contributions to the subject, offers several new interesting processes of interaction, which may be basic to the description of phenomena occurring in astrophysics. Furthermore, it is of interest in connexion with laboratory plasma and laser experiments.

It is emphasized that the dispersion relation for surface waves at a vacuum—plasma interface can be obtained by setting the reflexion coefficient to zero The relations for warm, collisional and hot, collisionless plasmas are derived in this way, and shown to be inagreement with previous results. The former relation is expressed explicitly as a cubic equation for y = 2c2k12/ω2p, as a function of x = 2ω2/ω2p − 1, where k1 is thecomponent of the wave vector along the interface, a is the frequency and w the plasma frequency; and the nature of the three branches of the y(x) curve is analyzed in detail. The rotation of the vacuum wave vector as the frequency runs from 0 to ∞ is displayed, and it is established that one and only one branch corresponds, in the collisionlesscase, to pure surface waves.

The oblique echo model for the resonance near the local upper hybrid frequency fT observed by topside sounders involves the propagation of slow waves away from the sounder, which later return as echoes after refiexion due to an electron density gradient. The model is investigated by using ray tracing techniques. Use of Poeverlein constructions gives some idea as to the qualitative nature of the rays which contribute to the resonance. A quantitative description requires the use of ray-trajectory equations. By using a simple approximate warm electromagnetic dispersion relation (which, nevertheless, retains all the important features of the exact dispersion relation), the ray-trajectory equations are integrated analytically for the case of a stratified plasma with a linear density gradient. These equations are used to investigate the behaviour of the frequency of the received echoes as a function of delay time. The resonance exhibits strikingly different characteristics for fT<2fH and fT>2fH respectively, where fH is the electron gyrofrequency. For fT<2fH the resonance is ‘strong’, the receiver observing a continuous response consisting of two echoes which interfere to give a fringe pattern. Some typical ray paths are illustrated. For fT<2fH the resonance is ‘weak’ and without fringes. A condition is derived for the existence of intercepting ray paths and for the maximum time delay that occurs when they do exist.

The Charybdis apparatus is designed to produce parallel and oblique shock waves in a magnetized plasma. An initial hydrogen plasma (nel 7 × 1020 m-3, T1 ˜ 1.3 eV) is produced in a Pyrex chamber (0.46 m cia., 1 2 m long) containing an axial magnetic field (B1 up to 0.2 T). A diffuse current front is produced in a fast-rising radial discharge between a central electrode and an annular outer electrode at one end of the chamber. The Lorentz force on the current sheet causes axial motion, and a quasisteady shock proffle propagates ahead. A clear shock separation is achieved across almost the complete radial extent for a wide range of initial parameters. The shock propagation angle to the initial field ranges from 0Ú to 40Ú. The Alfvén Mach number MA of the flow is varied by changing the initial field strength. Switch-on shock behaviour is demonstrated at a point of parallel propagation for low MA. For higher MA cases, no separated point of parallel propagation occurs in the shock profile.

This paper presents an idealized, one-dimensional theoretical model of a novel method of launching a slow-mode hydromagnetic shock wave. The reduction of the transverse magnetic field component, at the boundary of a semi-infinite plasma containing a uniform oblique magnetic field, results in the propagation of a fast-mode expansion wave followed by a slow-mode shock. An experiment designed to test this launching method is described. An initial hydrogen plasma containing axial and azimuthal magnetic field components is set up in a large annular apparatus. The azimuthal field is then reversed at one end of the device, by a fast-rising radial discharge. Diagnosis of the resulting flow, with small magnetic and electric probes, shows the propagation of the fast expansion wave and the slow shock; but there also follows a third wave, having the properties of a ‚piston’. When the theory is extended to include a moving boundary (i.e. ‚piston’), good quantitative agreement is obtained with the experimental results. The annular geometry of the experiment leads to centrifugal effects not considered in the one-dimensional theory; but these are not sufficient to disrupt seriously the main flow pattern. Detailed measurements of the shock indicate a dispersive structure.

We consider the Raman back-scatter instability produced by an electromagnetic wave in a plasma whose density increases in the direction of propagation. It is shown that, when reflexion of the waves involved in the interaction is taken into account, it may be possible to obtain, in the linear approximation, normal modes that grow exponentially in time. This is in contrast to the theory that neglects refiexion, and focuses attention only on the region of resonant interaction, which predicts only spatial amplification.