Obliquely propagating unstable electron cyclotron electromagnetic (whistler) waves have been studied with the aid of an especially designed computer simulation experiment. The plasma–wave system considered is homogeneous and infinite, and the plasma is taken to be a mixture of warm (bi-maxwellian) and cold populations. With no cold plasma, the rates of growth of the low k modes maximize for the case of parallel propagation (¸ = 0°;) and decrease as ¸ increases; for higher k modes, the opposite occurs. Changing from k space to ω space the above results indicate that off-angle propagation tends to stabilize the low-frequency whistlers but to destabilize the higher-frequency ones. These results are consistent with linear predictions. In all cases, however, the total electromagnetic energy generated in the system decreases with increasing θ. When cold plasma is added to the system, the total generated electromagnetic energy can maximize for a non-zero propagation angle.

This paper is a computational study of nonlinear resonant particle trajectories in wave fields consisting of an array of narrow-band waves of closely spaced frequencies and wavenumbers. It looks at two analogous systems, cyclotron resonance with a whistler wavefield and Landau resonance with an electrostatic wave field. It is found that the wave array is able to trap particles in much the same way as a single mode. Inhomogeneity plays a vital role by causing the energy of trapped particles to change.

The nonlinear resonant particle current is such as to preserve the modal structure of the wave field, and it does not change the frequency of an individual mode. Power distribution amongst the modes is far from even. Most of the energy goes into the mode at one end of the array, depending on the direction of the inhomogeneity. Also, nonlinear resonant particle excitation of a broad band signal was found to cause spectral structuring to develop automatically.

The theory was applied to one of Coroniti's FTRS analyses of banded chorus elements. The observed spectral behaviour closely accorded with the computational results. The numbers involved fitted the theory very well, and strongly suggested that nonlinear cyclotron resonant particle excitation is the mechanism for banded chorus.

A numerical simulation concerning the spatial evolution of electron plasma waves and electron distributions in collisionless plasmas is performed. Only those particles in and around the resonant region are followed numerically, while the bulk plasma is treated analytically. Our results are in good agreement with existing theoretical results as well as experimental observations. The method introduced here is valid for waves with arbitrary amplitude. It does not depend on either a large-amplitude asymptotic expansion or a small-amplitude perturbation scheme.

The potential created by an alternating dipole in a warm magnetoplasma is calculated analytically, in the approximation of the full adiabatic theory, for excitation frequencies ω close either to the upper hybrid frequency ωT or to the plasma frequency ωp The potential is finite at these frequencies. For ω ˜ ωp, the equipotential surfaces can be considered roughly as planes perpendicular to the static magnetic field B. For ω ˜ ωT and ω2p ≪3ω2b (where ωb is the electron gyrofrequency), the equipotential surfaces are cylinders of axis B. On the other hand, if ω2p ≪3ω2b, the potential is the sum of a cylindrical wave and of a wave for which the equipotential surfaces are paraboloids of axis B. These results are used to calculate the mutual impedance ζ of a quadrupole probe, and it is shown that the measurement of Zγ atω = ωT provides a new method for determining the electron temperature.

Until now, a theoretical derivation to obtain an expression for the logarithmic derivative Δ(Q) of the ‘inner’ or resistivity region has not been attempted for the resistive tearing instability where ‘parallel’ viscosity has been included, although similar derivations have been done using ‘perpendicular’ viscosity type terms. Such a derivation is presented in this paper, along with a numerical procedure for evaluating Δ(Q). Numerical results have been obtained for a hard-core pinch configuration. The resultant graphs show branch-point behaviour that suggests inter alia stabilization due to ‘parallel’ viscosity at high temperature.

The signal and phase velocities of the possible waves (eigenwaves) in a dissipative binary plasma have been studied on the basis of the linearized thirteenmoment theory. The complete set of eigenmodes for the given system is formed using approximations in the range of frequencies high compared with typical collision or plasma frequencies. There are twenty non-trivial propagation modes. Four of them are modes with signal-front speed c associated with the induced electromagnetic wave. Eight modes belong to each of the gas constituents, among them two longitudinal diffusion modes (±WI), four transverse viscosity modespolarized respectively along two transverse axes ±W⊥ in the direction x1 and ±W⊥ in the direction x2) and two longitudinal thermal modes (±WII). The signalfront speed of all eigenwaves is lower than the speed of light, so that the system is hyperbolic. The ultra-relativistic plasma is also briefly discussed. In this case, all the mixture constituents will have the same set of signal-front speeds as a single gas, irrespective of the bulk viscosity. Comparison is made of the present theory and results with other theories (for some special cases).

The excitation of a relativistic electron beam, by means of a fast waveguide structure, is examined. Here the beam is injected into a modified waveguide, and interacts with the modes of the guide in such a way as to transform some of its energy into microwave radiation. This microwave generation device, called the Ubitron, is based upon a fast-wave excitation of a magnetically modulated relativistic electron beam. The beam is modulated by injecting it into a small spatially periodic magnetic field region within the guide. Analysis of this interaction shows that the slow space charge beam mode couples actively to the fast transverse electric guide mode. The result is parametric instability of the coupled modes. Synchronism between the doppler-shifted transverse travelling wave and the undulating electron beam results in a transfer of energy from the beam to the transverse field. The parametrically growing field can be a source of microwave radiation. The period magnetic field, together with the beam density, provide the coupling media between the unstable waves. The growth rate of the instability is shown to depend, in a nonlinear manner, on the product of the beam plasma frequency and the strength of the applied rippled magnetic field. The growth rate is obtained as a function of the system parameters.

The spectra of low-frequency surface waves propagating along a warm magneto- plasma layer bounded by dielectric are investigated, using a two-fluid hydrodynamic plasma model. It is shown that such propagation is possible only for some definite directions of the external magnetic field B0, with respect to the plasma-dielectric interfaces. The spectra obtained for a thick plasma layer correspond to the well-known results for a magneto-active plasma, bounded on one side by a vacuum, derived in the limit of one-fluid hydrodynamics.

The most common approach to the study of plasma nonlinearities is by a form of perturbation theory which first studies the linearized equations, then evaluates effects of nonlinearities in terms of these linear solutions. Such an approach is probably justifiable for the effect of weak nonlinearities, but will almost certainly miss features that are exclusively nonlinear in nature (i.e. effects which cannot be described by modifying linear theory, or effects which are present only when e.g. a source of disturbances in a plasma reaches a certain threshold amplitude). It is the object of this paper to investigate one possible such nonlinear effect.

Most of this paper is concerned with the construction of suitable Lagrangian functions for the dynamics of a cold plasma, in such a way as to retain the relativistically covariant formalism. In one method, this is achieved by the introduction of a set of three variables which label the world lines of the particles. A second method results in a Clebsch type of representation. Sturrock's relativistic Lagrangian and Low's hot plasma Lagrangian are also briefly discussed in the context of the present work. The behaviour of the canonical stress tensor is considered. The applicability of many of the general results of part 1 is ensured by establishing the existence of the Lagrangian function.