Often one is interested in the electrical conductivity of a plasma for frequencies of the applied electric field comparable to or greater than the effective collision frequency. For the purpose of obtaining an order of magnitude estimate of the conductivity a Lorentz gas model with a Fokker–Planck collision term is used. For this simple model a formula for the a.c. electrical conductivity for two limiting cases is derived in closed form. The first term of the expression for the conductivity in the case where w/k is very large agrees with that obtained by Bernstein & Trehan (1960) for the spatially homogeneous case, while the effect of the spatial gradients is indicated in the higher order terms. In the case where w and k are both equal to zero the expression for the d.c. electrical conductivity of Spitzer (1962) is recovered.

Starting from the Boltzmann equation, new boundary conditions are derived to be matched with the Navier—Stokes equations, that are supposed to hold in the main body of a gas. The idea upon which this method is based goes back to Maxwell and Langmuir. Since the distribution function is supposed to be completely determined by the Navier—Stokes equations, this new set of boundary conditions extends in some sense the validity of the macroscopic equations to the transition and free molecular régimes. In fact, it is shown that the free molecular and slip flow régimes are correctly described by this method; the latter is also supposed to give a reasonable approximation for the complete range of Knudsen numbers. The new procedure is applied to different problems such as plane Couette flow, plane and cylindrical Poiseuile flow, heat transfer between parallel plates and concentric cylinders. Results are obtained and compared with the exact numerical solutions for the above-mentioned problems.

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.

The propagation of nonlinear electromagnetic waves in a plasma is investigated by seeking travelling wave solutions to the macroscopic plasma equations. The model considered is that of a warm, anisotropic electron plasma in a magnetic field, in which the waves are allowed to propagate at any angle with respect to the magnetic field. A nonlinear dispersion relation is obtained which is valid for frequencies sufficiently close to the resonant frequencies. Travelling wave solutions are found for all amplitudes for which the local density remains positive. Also in sufficiently anisotropic plasmas the nature (i.e. propagating or cut-off) of one of the resonant waves can depend upon the amplitude.

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.

Solutions are obtained for cylindrical waves of the equations governing a magnetized self-gravitating collisionless plasma. Subject to certain conditions, we find two types of instability: (i) the hose instability which is related to the anisotropic pressure; and (ii) gravitational instability.

The diochotron instability of a thin, tenuous, cylindrical layer of charged particles, whose gyro-radius is of the order of the mean radius of the cylindrical layer, is investigated using the Vlasov equation. Two distribution functions are considered which give practically the same density in the physical space, but are quite different in the velocity space: in the first the velocity spread is practically zero; in the second the particles oscillate around the mean radius of the cylindrical layer. It is shown that the first distribution exhibits the usual diochotron instability, while the second one does not. It is also shown that, however small the velocity spread, the thickness of the cylindrical layer cannot go to zero. Its minimum value is roughly determined by equating the plasma frequency to the cyclotron frequency.

This paper examines analytically the transition domain between collisionless and collision dominated flows in the environment of a plasma sheath. The onset of collisions also brings into focus the concurrent effects due to ionization, which are retained in the theory. An integral method of iteration is established, and the dominant correction terms due to collision and ionization effects are obtained. Various limiting cases are examined.

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.

The admittance of a plane grid capacitor immersed in an ion beam plasma has been measured, and the results are in general agreement with the kinetic theory of the admittance (Buckley 1968). With a steady bias potential applied to the grids, the results showed a deviation from the theoretical behaviour that is attributable to plasma depletion by the grids. The effect of varying the background pressure showed that electron-neutral collisions had a negligible effect on the measured admittance. A significant change in the admittance was found for a measuring voltage applied to the grids of the order of the electron temperature.

Transport coefficients are given in tabular form for partially ionized helium in chemical equilibrium at several pressures and for temperatures up to 35000 °K. Simplified theoretical expressions, derived with the Chapman—Enskog—Burnett method, were used for the computations. The convergence of the approximations to the electrical conductivity was also studied. It was found that the first approximation was within 17% of the true value at low ionization in contrast to recent results for argon where it could not be determined if even the fourth approximation had converged to the true value.

A modification of the Penrose criterion is applied to the local dispersion relation for low-frequency, electrostatic instabilities in a low-density, slightly inhomogeneous magnetoplasma. The Nyquist diagrams obtained can be classified according to their behaviour near the origin; this is sufficient in some cases to conclude that the equilibrium is unstable. With this method, in the limit of negligible ion Larmor radius, we find that the Langmuir waves propagating in a direction orthogonal to the external magnetic field are driven unstable by a temperature gradient.

A pair of plane parallel grids is inserted in a hot plasma, and an oscillatory voltage is applied across them. The electric field excited in the plasma, and the complex admittance of the grid/plasma system, are computed for applied frequencies high enough to justify neglect of ion response. The grids are electrically, but not mechanically, coupled to the plasma, which is assumed to be in a spatially uniform collision free Maxwellian equilibrium state. The field is computed as a function of distance from the grid plates over a range of frequencies covering the plasma frequency, and the complex admittance of the system is computed as a function of frequency at various grid separation distances. The real component of the field and the capacitive component of the admittance are subject to three major effects: cold plasma dielectric behaviour, oscillatory Debye sheaths on the grids, and (above the plasma frequency), longitudinal plasma waves. The imaginary field component and the conductive admittance component are produced by spatial Landau damping. In an accompanying paper (Freeston 1968), the computed admittance is compared with laboratory measurements made in a situation approximating well to the idealized problem considered here.

A non-linear wave propagation mechanism is found for ionization fronts. The fronts propagate due to ionizing collisions between electrons and neutrals. A parameter is obtained which specifies the amount of electrical interaction. For small electrical interaction, charge separation may occur and the front can propagate at any speed greater than a critical value. For large electrical interaction, the number densities of ions and electrons are nearly equal and a lower bound on the propagation speed is also found.

A kinetic theory is presented which is valid for both weakly unstable and stable plasma. The theory corrects the conventional Balescu—Guernsey—Lenard description for the weakly stable portions of the fluctuation spectrum. The theory is no longer Markoffian in the distribution function F alone but is in the pair F and Ik the spectrum of fluctuations. Further the evolution in time from an initially weakly unstable distribution to the stable regime can be described. Even after passage into the stable state the fluctuations can be large nd lead to enhanced diffusion across a magnetic field. The coefficient of spatial diffusion is given in this weakly stable (or untable) state. A strong coupling is found between plasmons and the particles in the distribution with velocities near the phase velocities of the plasmons. There is only weak thermal contact between the plasmons and these particles with the main body of the distribution whenever certain nonlinear processes are of secondary importance.

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 collisionless relativistic Boltzmann equation is used to investigate the stability of a large-scale two-component plasma containing numerically small anisotropic relativistic populations. Although most permitted waves are stable, Alfvén type waves are found to be unstable whenever the anisotropy exceeds O(v A/c). Growth times are estimated as days for supernova remnants and millennia for cosmic ray protons.

This paper concerns the time-dependent motions of the cavity formed when a uniform corpuscular flux is incident on the magnetic field of a line current. The two-dimensional problem is formulated and solved with two particular classes of solutions being given; namely, the steady-state solutions and the time-history of the interaction with a cloud of flux.

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.

The non-linear induced scattering by plasma particles of right-hand and left- hand polarized electromagnetic waves propagating along the magnetic field, is studied. The non-linear Landau damping for frequencies near the ion cyclotron frequency in a weak turbulent inhomogeneous plasma is determined.