A method of plasma containment by means of spherical multipole (SM) magnetic fields has been developed. The analysis of the confining field geometry has proved that the high-order SM-configurations constitute minimum-B traps with a given number of point cusps instead of linear loss gaps which occur in a standard minimum-B geometry. Injection and trapping of a gun-produced plasma in the SM magnetic trap have been investigated and compared with those in a spindle-cusp trap.

The instability of electromagnetic waves propagating across a static magnetic field in the presence of a thermal anisotropy (T∥ > T⊥) is investigated. The marginal stabifity criterion as well as the rate of growth of the instability are derived. When compared with the fire hose instability (of electromagnetic waves propagating along the static magnetic field) it is found that higher electron pressures are required for this new instability to be set up; however, the maximal rate of growth is much larger than in the fire hose case.

The interplanetary plasma is stable to this thermal anisotropy instability; high β plasma devices may be unstable.

The T⊥ = 0 case treated by Hamasaki is recovered.

We study the quasifinear relaxation of an aperiodic instability, namely the instability caused by the temperature anisotropy of a collisionless electron plasma in the absence of an external magnetic field. We give a detailed description of the relaxation process and we examine the validity of the quasilinear theory (existence of separate time scales, quasilinearity of the particles' orbits).

We investigate the dispersion relation for travelling helicon waves in a uniform non-resistive plasma. We show that the effect of electron inertia for a cylindrical plasma bounded by conducting walls is qualitatively different from the plane wave case, leading to significant differences in the dispersion relation at all frequencies in the range 0 < ω < Ωe.

Kinetic equations are obtained which describe the variation in one spatial direction of a plasma whose average properties are independent of time and do not vary in the perpendicular direction.

These equations consist of a coupled set giving the variation of the electric field fluctuation spectrum and the particle distribution functions. They take into account particle discreteness effects and describe the plasma both when it is stable and weakly unstable. It is suggested that they may be used to describe an infinite plane shock wave in a plasma.

The problem of a monochromatic plane electromagnetic wave incident from vacuum on the plane boundary of a plasma half-space is considered. The method of solution is based on the representation of the disturbance in the plasma half- space as that generated by some current source in the complementary half-space into which, for the purpose of the representation, the plasma is conceived to extend. The specular reflexion boundary conditions and the diffuse scattering boundary conditions are treated in turn, first for normal incidence and then for oblique incidence.

The collective approach of Pines & Bohm has been applied to the problem of the thermodynamics of the N-particle electron gas including transverse radiation. Partitioning of the internal energy and certain of the other thermodynamic quantities is discussed generally. The system is seen to divide itself into three approximately independent subsystems: (1) an infinite set of free harmonic oscillators, corresponding to the transverse field, with an energy spectrum given by ωT(κ), where ωT(κ), is given by the dispersion relation for transverse electromagnetic waves in a plasma; (2) a set of 8 free harmonic oscillators corresponding to the longitudinal (plasma) oscillations, with an energy spectrum ωT(κ), given by the dispersion relation for plasma oscillations; and (3) a set of (N — 2s/3) quasi-particles of mass approximately equal to the electron mass, interacting via a short-range potential which is essentially screened Coulomb. Analytical expressions for the energy, pressure, and constant-volume specific heat of the transverse oscillators are given, together with approximate expressions applicable to the high-density—low-temperature and low-density—high-temperature limits. Detailed numerical calculations of the internal energy and pressure of the longitudinal modes are presented. In addition, the contributions to the energy and pressure from the particle portion are evaluated in the low-density—high-temperature limit as functions of the cut-off wave vector κc; κc is the maximum k-vector of the longitudinal oscillators.

The propagation of a packet of weakly non-linear dispersive cold plasma waves is studied by means of a two-time scale expansion. The effects of amplitude dispersion and the coupling to the mean plasma motion are taken into account. The governing equations are put into a conservation form. It is found that this system of equations is elliptic or hyperbolic depending on the wave-number of the dispersive waves. In the elliptic case modulations in the wave train grow exponentially in time and a periodic wave train will be unstable in this sense. In the hyperbolic case, slow variations in the wave train propagate and the characteristic velocities give a non-linear generalization of the linear group velocity. It is shown that except for waves which have their wave vectors nearly at right angle to the unperturbed magnetic field only fast waves with wave-number less than 0.585 (Ωi Ωe)½/Vα are stable; where Va is the Alfvén velocity and Ωι Ωε, are the ion and electron cyclotron frequencies respectively. A process of steepening of these waves into shocks with dissipation due to wave turbulence at the head of the wave packet is suggested.

A self-consistent solution of the Vlasov—Poisson equations is obtained for a low-temperature, bounded, Maxwellian plasma of arbitrary non-uniform density. An eigenvalue equation for the central frequencies and electric fields of the resonance oscillations is obtained, which agrees with the equation obtained by a low-temperature expansion of the orbital-integral solution. The Landau damping rate is given in a general, explicit form in terms of the central frequencies and fields of the resonances.

In a previous paper [Lewak (1969), see also Pflrsch (1966) for related treatment], it was shown that the Vlasov equation in the Semi-Lagrangian (S.L.) formulation, may be written in a form resembling the fluid equations.

plus Maxwell's equations with the source terms given by

where n is the determinant of the tensor Tij = ∂gi/∂ζj, and N is the constant mean number density of electrons. The averaging notation < > here is defined by

where f(σ) is the electron distribution function to be specified. The equations assume for simplicity a uniform fixed ion background, although this is not a necessary restriction and equations (1) and (2) need only an obvious modification to account for ions. The force fields in (1) are related to the electric field E and magnetic field B in the plasma by .

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.

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.

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 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.