The effects of neutral gas friction, on the Rayleigh–Taylor instability of an infinitely conducting plasma of variable density, with ion viscosity and Hall currents, are investigated. For an ambient horizontal magnetic field, it is shown that the solution is characterized by a variational principle. Making use of the existence of this, proper solutions are obtained for a semi-infinite plasma, in which the density is stratified exponentially along the vertical, confined between two planes. In the simultaneous presence of the effects of ion viscosity and Hall currents, it is found that the potentially unstable stratification is unstable for all wavenumber perturbations, irrespective of whether or not the effects of neutral gas friction are included. Further, it is found that the growth rate increases with both Hall currents and neutral gas friction, and decreases with ion viscosity. The influence of the Hall currents and the neutral gas friction, therefore, is destabilizing, while that of ion viscosity is stabilizing. In the absence of Hall currents, it is found that the viscous plasma is stable, even for a potentially unstable stratification, for perturbations confined to a cone about the magnetic field vector. The angle of the cone of stable propagation of an inviscid plasma,. however, decreases with both Hall currents and effects of neutral gas friction.

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.

The problem of confinement and stability of a plasma enveloped by the magnetic field of a line multipole is considered. An energy method is used to find the increment in potential energy when the configuration is given a small displacement. The frequency and modes of oscillation are found in a particular example.

A generalization of the Appleton–Hartree equation is made to include the effects of energy-dependent electron-neutron collisions, Coulomb encounters and spatial dispersion. The frequency of electromagnetic waves propagating in a magneto-plasma is sufficiently high that the ion motion may be neglected compared with the electron motion. The present analysis extends Dougherty (1963, 1964) to include the simultaneous effect on wave propagation of Coulomb forces, spatial dispersion and energy-dependent electron-neutral collisions, where one or more of these effects can have a significant influence on circularly polarized waves propagating at frequencies near electron cyclotron resonance. The electrical conductivity tensor is expressible in terms of appropriate velocity moments of the electron distribution function. The electron velocity distribution function is determined by expanding the inverse of the differential operator of the linearized kinetic equation in a small parameter ε2', where in one case ε2 is the ratio of Coulomb collision frequency to signal frequency, and in the second case ε2 is the ratio of electron-neutral collision frequency to signal frequency. For wave propagation along the magnetic field, the dispersion relations for right-hand and left-hand circularly polarized waves, and also the dispersion relation for longitudinal waves, are solved numerically, and graphs are presented to show the effects of collisionless damping, velocity dependent electron-neutral collisions and Coulomb collisions.

It is shown that the concept of subdynamics introduced by Prigogine, George & Henin, and extended by Balescu & Wallenborn, can be generalized nontrivially to systems submitted to time-dependent external fields. The distribution vector of the system is split into two components by means of a time- dependent projection operator. Each of these obeys an independent equation of evolution. The description of the evolution of one of these components (the superkinetic component) can be reduced to a kinetic equation for a one-particle distribution function. It is shown that, when the external field vanishes for all times t ≤ t0, and if the system has reached a (field-free) equilibrium (or a ‘kinetic state’) at time t0, then for t ≥ t0 the kinetic equation derived here provides an exact and complete description of the evolution. A general expression for the nonlinear response of the system to the external field is derived.

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.

There are several practical situations in partially ionized plasmas when both collisionless (Landau) damping and electron-neutral collisions contribute to the attenuation of longitudinal waves. The longitudinal-wave dispersion relation is derived from Maxwell's equations and the linearized Boltzmann equation, in which electron-neutral collisions are represented by a Bhatnagar–Gross–Krook model that conserves particles locally. (The dispersion relation predicts that, for a given signal frequency ώ), an infinite number of complex wavenumbers kn can exist. Using Fourier–Laplace transform techniques, an integral representation for the electric field of the longitudinal waves is readily derived. Then, using theorems from complex variable theory, a modal expansion of the electric field can be made in terms of an infinite sum of confluent hypergeometric functions, whose arguments are proportional to the complex wavenumbers kn. It is demonstrated numerically that the spatial integral of the square of the electric field amplitude decreases as the electron-neutral collision frequency increases. Also, the amount of energy contained in the first few (lowest) modes, and the coupling between the modes, is examined as a function of plasma frequency, signal frequency and collision frequency.

The general theory developed in part 1 is illustrated for a plasma described by the weak-coupling (Landau) approximation. The kinetic equation, valid for arbitrarily strong external fields, is written out explicitly.

The dispersion relation for a collisionless moving electron plasma, when the direction of motion is along the magnetic field, and that of the wave propagation normal to the magnetic field, is analysed. It is shown that in small magnetic fields the ordinary wave develops a new band of backward waves below the plasma frequency. When the frequency of the wave is higher than the plasma frequency, the effect of the motion of the plasma is identical to a deviation of the direction of propagation.

Within the range in which both electric field parameters are free, ionizing shock waves have a unique structure for each pair of chosen parameter values. In a relatively small shock speed range, however, conditions may exist for which at least one intermediate equilibrium region is imbedded within the overall transition. Non-unique structures consisting of different transitions between the same upstream and downstream equilibrium states may then occur. Steady trans-Alfvénic magnetohydrodynamic transitions (which are unacceptable in the pre-ionized case) may occur as part of an ionizing shock structure, because neigh bouring steady solutions always exist. This is due to the existence of skew ionizing shocks which are able to absorb rotational disturbances.

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.

In this paper, a method developed by Whitham for obtaining equations governing the slow variation of finite-amplitude wave trains, is slightly modified. The relevant equations describing wave-wave interaction, and self-action are derived. The stability of a finite-amplitude wave train is treated in two different ways. The possibility of having a ‘solitary modulation’ on a finite-amplitude wave train is pointed out.

The quasi-linear concept of plateau formation along resonant diffusion surfaces is compared with the time evolution of the electron distribution function during a computer simulation experiment of whistler-mode waves in unstable plasmas. It is found that, as the wave intensities grow, plateau formation does indeed occur, with the distribution function becoming constant along diffusion surfaces at the time when wave intensities maximize. Following the formation of the plateaus, both the wave intensities and the slope of the distribution function along diffusion surfaces oscillate in a manner suggesting msh;mode coupling. Tbe slope of the distribution function along diffusion surfaces, which controls the linear wave growth rate, also gives good predictions of the sign of the actual wave growth rate during the experiment.

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).

For a laser-driven fusion plasma dense enough to absorb the fusion particles, the slowing down of the reaction products and of their cascade of recoils is calculated (treating discrete energy loss in a collision correctly). The occurrence of reactions between the slowing-down particles and ambient ions is also calculated. The products of these reactions are in turn followed, through as many iterations as necessary. Illustrations are given.

Previous calculations of β = 1 cusp losses are extended to the case where there exists a third ‘adiabatic’ invariant of the particle motion, related to the magnetic moment, and additional to the particle energy and angular momentum. Simple analytic results are obtained for the particle and energy loss rate from a Maxwellian plasma in both plane and axisymmetric geometry, electric fields being assumed zero everywhere. The results are valid for a plasma radius large relative to the ion gyro-radius, in which case the adiabaticity in the sense used reduces the loss rate by a factor ⅔λ⅔ to give an overall scaling as λ–⅔ with external mirror ratio λ. The absolute value is about a factor two less than the previously accepted result (for λ = 1 only) for an axisymmetric cusp. cusp. The enhanced scaling with A arises from the absence of a certain class of particles in the sheath, which must be everywhere adiabatic; its applicability to a simple theta pinch is queried, however. The end loss rate of angular momentum is also obtained, and is non-zero at a point cusp. This is shown to lead to rapid rotational instability in a collisionless theta pinch.

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.

We present optical spectroscopic and magnetic probe observations of a laboratory discharge device, in which magnetic field line reconnexion occurs at an x−type neutral point. Time-resolved spectral-line profiles of the ionized argon line A II λ4348 are presented. These allow the determination of Doppler shifts and broadenings near the neutral point. Plasma heating occurs at the neutral point and downstream from it. Plasma is ejected from the downstream sides of the neutral point region at the local Alfvén speed at all times. This is equal to about one-tenth the upstream Alfvén speed at the one time it is known. The downstream magnetic Mach number or ‘local reconnexion rate’ is found to be nearly independent of the plasma conductivity and time. The rate of transfer of magnetic flux from the upstream to downstream regions is strongly dependent on conductivity and time.