A kinetic model equation for an electron plasma is proposed. The principal new feature of the equation is an attempt to incorporate collision terms which model both short-range two-body scattering and many-body small-angle scattering. The equation is then used to study the time relaxation of a spatially uniform plasma. A simplified form of the model is finally used to analyse sound propagation in the plasma. Dispersion equations are derived and studied in several limiting cases. Landau damping in the small wave-number limit is shown to be less important than collisional damping for most plasmas.

Expressions for Alfvén waves, their Landau damping, and magnetosonic waves are derived in a homogeneous relativistic Vlasov plasma. Relativistic effects reduce the speed of both waves.

The ‘quantum electrodynamics’ of the scattering of radiation from a fully ionized, interacting plasma is to be considered.

The plasma particle interaction must properly be treated quantum mechanically when the electron plasma wave phonon energies are comparable to or greater than the mean random electron energies and/or when the phonon momenta are of the order of magnitude or greater than the average electron momenta in the plasma.

In these two circumstances or either one of them, the plasma particle inter action must be treated in a quantum mechanical manner. The ‘solid-state’ plasma recently discussed by D.E.McCumber is an example of a quantum plasma.

Whether a classical or a quantum plasma is considered, the collective properties, as well as the single-particle properties, need to be considered. The collective properties of the plasma become important when it interacts with a radiation field in the case where the electron plasma frequency, ωp, is of the same order of magnitude, or exceeds, the operating radiation frequency ω, i.e. ωp≥ω.

A criterion to distinguish the properties of a plasma as to whether it is classical or quantum mechanical in nature can be defined in terms of three fundamental lengths of the electron gas. These definitions hold for a one-component plasma. They are: the classical length βe2, the Debye screening length and the thermal de Broglie wavelength defined as 1/kT. From these three quantities, we can define two dimensionless parameters. They are the classical parameter and the quantum parameter δ=λ/λD which is a measure of the quantum effects. For a quantum plasma δ>1 and in the classical limit (h = 0),δ=0, Λ<1.

When we take into account the collective behaviour characterized by the plasma oscillations, screening effects are an automatic aspect of the electron plasma gas.

It is hoped that the present review article will provide the background material for general understanding of the field and easy access to the current literature. It is also hoped that the present discussion will establish greater interest in this subject.

As an example of a calculation of plasma properties, a calculation of the generalized dielectric constant for both a low-density plasma in the classical limit and a high-density plasma in the quantum mechanical limit is performed and compared in a suitable manner.

A perfect magnetofluid model is used, without viscosity or resistivity. The simpler velocity and magnetic profiles are classified into stable and unstable groups. The analysis takes account of exponential and non-exponential time dependence, and of rigid and free boundaries.

A variety of stability criteria are established, and related to similar results in non-conducting fluid mechanics. A constant magnetic field is shown to stabilize some velocity profiles but destabilize others.

The investigation of the high-frequency interaction of a relativistic electron beam and a plasma is extended to include arbitrary variation of the plasma density. Analysing the coupled linearized Vlasov—Maxwell equations by means of a low-temperature expansion of the orbit integrals, a general equation for the electric field accurate to first order in the plasma temperature, beam temperature, and betatron frequency is obtained. This equation is applied to the investigations of transverse and longitudinal modes. A new transverse mode with |ω − kV0| ∼ ωβ is found to be collisionally unstable. The electrostatic instability is found to be slowed down by both low plasma temperature and low beam temperature, but the betatron oscillations increase the growth rate. A new longitidinal mode with |ω − kV0| ∼ ωβ, is found to be unstable for nonzero beam temperatures. The lowest order correction to the electrostatic growth rate due to a small plasma nonuniformity is obtained. The sign of this correction is found to depend critically on the shape of the inhomogeneity.

A numerical iteration procedure has been used to obtain the solution of an integrodifferential (linear) equation which gives the energy distribution of the electrons of a low-temperature, diffusion-dominated discharge. The equation takes explicitly into account the effects of inelastic electron-neutral collisions. The results presented here have been obtained, as an instance, for helium and neon discharges, in presence of a static and uniform magnetic field.

Closed forms are found for the dispersion relations describing the propagation through a uniform anisotropic plasma of the three modes of electromagnetic waves whose wave vectors are perpendicular to a steady and uniform magnetic field. Such relations are found to be conveniently expressed in terms of hypergeometric functions of the second order.

The investigation deals with a collapsing, cylindrical, ionizing shock in an applied axial magnetic field. The magnetic field in the nonconducting gas ahead of the shock increases as the shock converges and the consequent increase in the Lorentz force behind the shock produces a retardation. It is shown that no accelerating self-similar solution exists and the governing equations are then solved numerically.

Recent calculations for hydromagnetic analogues of the classical Rayleigh– Taylor problem with Hall effect are compared. It is shown that an early calculation is the limiting situation of the work of Taiwar & Kaira, which confirms that the Hall effect introduces new instabilities.

Transport coefficients have been computed for partially ionized hydrogen at pressures of 0·01, 0·1, 1 and 10 atm and temperatures up to 50,000 °K. Theoretical expressions containing accurate collision integrals for charged particles were employed for the calculations. The electrical and thermal conductivities are compared with recent measurements in the wall-stabilized electric arc. Generally satisfactory agreement is noted for the electrical conductivity to 19,000 °K, but the computed thermal conductivity is considerably lower than that measured.

The jump conditions across a transverse ionizing MHD shock wave, where the magnetic field is in the plane of the shock, are examined. The conservation laws, in conjunction with Maxwell's laws and the equation of state, yield three jump equations in four unknowns. To uniquely describe jumps across an ionizing wave requires an additional descriptive relationship. The theory of Kulikovskii & Lyubimov and, later, Chu, in which the internal structure of the shock itself supplies the missing relationship, is examined. In particular, Kulikovskii & Lyubimov show, for appropriate ratios of thermal to magnetic diffusivities, that for low-speed waves the magnetic field compression across the shock is unity and the jump equations reduce to the ordinary Rankine—Hugoniot relations. For high-speed shock waves, the magnetic field compression, B2/B1, equals the gas compression across the wave, p2/p1, and the jump equations become the magnetohydrodynamic shock jump relations. Furthermore, intermediate speed shocks induce magnetic field compressions between 1 and p2/p1. An experiment was performed in an inverse pinch where E behind the shock, the shock and piston velocities, and the magnetic field compression across the shock, were measured over a wide range of initial conditions and shock velocities in hydrogen. The jump relations were written with B2/B1 as a parameter and programmed into a digital computer. The program was written for real, equilibrium hydrogen. The program provided easy access to a unique solution of the jump equations for any B2/B1. The experiment tends to confirm the Kulikovskii—Lyubimov—Chu theory. Ordinary shock waves were observed at low speeds and near-MilD shocks were observed at high speeds. Further, the relation was verified for the plasma behind the shock for low-speed shock waves, and was verified to within experimental accuracy for the intermediate class of shock waves.