The method of matched asymptotic expansions is applied to the fluid model of the low-pressure positive column. The expansion of the eigenvalue in the plasma balance equation is obtained to second order in plane and in cylindrical geometry, and uniformly valid expressions for charged particle densities and fluid velocity in two separate regions are indicated.

The free-fall model is also examined and the scales of the transition layer and sheath layer found. Comparison is made with the results of direct numerical integration of the equations involved for both models.

The effect of finite ion-Larmor radius is considered on the Rayleigh–Taylor instability of a plasma. The macroscopic equations of motion are used where the finite ion-Larmor radius effects are incorporated in the stress tensor. The finite ion-Larmor radius stabilization of the interchange mode is demonstrated. For disturbances propagating along the magnetic field, it is found that the inclusion of gyro-viscosity has a stabilizing effect; it increases the critical wavenumber (compared to its value in the absence of gyro-viscosity) beyond which all modes are unstable.

A plasma in a time-dependent external electric field is considered. Collisions are described by means of Fokker—Planck and BGK models. Longitudinal and transverse wave propagation is treated by means of exact analytical solutions of the linearized Boltzmann equation. The results generalize previous calculations on dispersion relations and density fluctuation spectra.

An isotropic Vlasov plasma occupies an infinite space, the upper half of which (y > 0) is a dielectric. A transverse disturbance is incident normally on the face of the dielectric. The waves that are excited in each half of the space are obtained. It is shown that this result can be extended to cover the refiexion problem of any normally incident disturbance in a plasma defined by a dispersion relation Di(w, k). A few examples are considered; in particular transverse waves in a plasma streaming normal to the boundary where Čerenkov instability can occur.

In this note we comment and extend the results of a previous analysis in which the non-linear behaviour of one-dimensional electrostatic oscillations in a homogeneous, unbounded, collisionless and fully ionized plasma was considered. The evolution of a monochromatic wave of small, but finite amplitude is studied by expanding the dependent variables as well as the independent variable tin the form of asymptotic series; an ordering parameter e proportional to the initial amplitude of the electric field is introduced. The expansion of the independent variable in such a series allows us to eliminate secular terms from the part of the distribution function which does not depend on the free-streaming terms. This, in turn, allows us to determine corrections to the complex frequency a. Results of a previous note on non-linear Landau damping for an initially Maxwellian. distribution function are confirmed, but it is indicated that they apply to values of time up to a value τ1 rather than for all times. One can proceed to larger values of time in the manner of the multiple time-scale method. In particular it is found that the Landau damping is increased with respect to the linear value only initially during the first time scale.

The suppression of runaway electrons in a Lorentz plasma is demonstrated for a two-component, fully ionized plasma in the presence of a high frequency, weak, uniform electric field. The time for runaway to occur for electric field frequencies high compared to the collision frequency is longer than the runaway time for low electric field frequencies or zero frequency, by the ratio of the frequency of the electric field to the collision frequency squared. Both the resolvant method developed by Prigogine and co-workers and the double perturbation scheme of the Poincaré—Lighthill method are employed to derive the diffusion equation for the modified one-particle distribution function in the collision-dominated region of velocity space.

A laser produced plasma expanding in a uniform magnetic field emits far infrared radiation. The time-dependent radiation history is calculated assuming spherical symmetry and compared with experiment. General features of the radiation history agree well with experimental observation. However, a detailed comparison is difficult because of the oversimplified theoretical model employed.

A theoretical model is proposed for the process of re-connexion of frozen-in magnetic-field lines at an X-type null point in the field. The model involves a diffusion region, immediately adjacent to the null point and an outer wave- dominated region. For the latter an exact solution to the magneto-hydrodynamic equations is obtained; for the former an approximate relationship is derived between the field-re-connexion rate, measured by the Alfvén number of the incident flow, and the magnetic Reynolds number, based on the width of the diffusion region. The maximum field-re-connexion rate is determined entirely by conditions near the null point and may under suitable conditions become large. A condition for maximum conversion of magnetic energy is derived.

Two expressions for the power radiated by a charged particle in a homogeneous magnetoplasma are derived, using a method similar to that of Kolomenskii, Eidman and Liemohn. The first expression is identical with that of Eidman. The reason for the correctness of Eidman's result for dispersive media, in spite of his complete neglect of dispersion in the derivation, is explained. Liemohn, by taking dispersion into account at only one stage of the derivation, obtains a result which disagrees with the present one, often by many orders of magnitude, as illustrated by computations.

The second expression is derived by several authors by different methods; it is more suitable for computations than the first one. The radiation bands and their limiting frequencies are discussed systematically.

This paper considers the non-linear resonant interaction between three waves, which propagate in the direction of a constant magnetic field in a homogeneous plasma. A coupled-mode theory, which makes it possible to derive the coupling coefficients within a kinetic description, is developed.

The Chew—Goldberger—Low theory of a collisionless plasma, modified to include the effect of finite Larmor radius of the ion and the electron, is applied to a linearized problem of two-dimensional steady flow. The zeroth-order terms in the Larmor radius expansions of the velocity distribution functions of the ion and the electron are assumed to be anisotropic Maxwellian. The spatial development of a given velocity profile is investigated for flows with either crossed or aligned magnetic fields, and for various values of Mach number, Alfvén Mach number, and anisotropic pressure ratios in the main flow.

It is shown that in a dense magnetoactive plasma c/cA ≫ 1 with cold electrons and ions with an anisotropic temperature the ion cyclotron waves propagating along the magnetostatic field are excited with a maximum increment. The dynamics of the quasilinear stage of this instability is investigated. It turns out that, at any moment, the ion distribution function is of the form of a step with the steep front. The speed of the front in the velocity space and the characteristic time of the relaxation process are found. It is ascertained that the distribution function arising in the course of the relaxation is stable with respect to the ion cyclotron waves propagating obliquely to the magnetostatic field.

A new derivation of quasilinear theory for plasma oscillations is given, subject to the neglect of wave-wave interactions. The theory, which applies equally to damping and growing waves, requires that the individual wave resonances be narrow and the electric field spectrum sufficiently broad.

In the case of a free-particle plasma with no self-consistent field and with collisions described by the LenardBernstein operator we give an exact solution of the temporal echo problem.

A theory is given of an ion rarefaction wave in a low pressure plasma under conditions where ionization processes are unimportant.

One-dimensional ion-acoustic normal modes of bounded plasmas are theoretically investigated in plane, cylindrical and spherical geometries. The characteristic frequencies, damping constants and spatial structure of the oscillatory modes are obtained.

When a sheath grows into a plasma at a slower speed than the local ion speed of sound, an ion rarefaction wave propagates into the plasma ahead of the sheath. It is shown that, in the frame of reference of the sheath edge, the speed of ions arriving at the sheath edge cannot exceed (kTe/M)½.