This paper contains an analysis of pulse shapes produced by a delta-function disturbance of the equilibrium state of a relativistic electron beam propagating through a constant-amplitude, helical magnetic wiggler field. Pulse shapes are determined by using the relativistic pinch-point techniques developed by Bers, Ram and Francis. Two pulses are produced corresponding to a convective upshifted pulse (representing the production of the high-frequency radiation desired in a free electron laser) and a downshifted pulse. The downshifted instability may be convective or absolute, depending upon the beam density and momentum spread. Parameter regimes in which the downshifted instability is convective are investigated. It is found that momentum spreads sufficiently large to suppress the absolute instability reduce the growth rate of the upshifted pulse to negligible values. Pulse shapes computed by using the Raman and Compton approximations are compared with exact pulse shapes. It is found that the Raman approximation should be applied to the downshifted regime for most systems of practical interest.

A previously described pseudospectral three-dimensional MHD code is used to compute the dynamical behaviour of a channel of magnetofluid carrying an axial current and magnetic flux. This situation contains the essential MHD behaviour of the reversed-field-pinch (RFP). An externally imposed electric field is applied to an initially current-free magnetofluid, and drives currents that rise and eventually fluctuate about values corresponding to pinch ratios Θ ≈ 1·3, 2·2 and 4·5. A period of violent turbulence leads to an approximately force-free core, surrounded by an active MHD boundary layer that is not force-free. A steady state is reached that can apparently be sustained indefinitely (≥several hundred Alfvén transit times). The turbulence level and time variability in the steady state increase with increasing Θ. The average toroidal magnetic field at the wall reverses for the Θ ≈ 2·2 and 4·5 runs, but not for the Θ ≈ 1·3 one. Negative toroidal current filaments are observed. The Lundquist numbers are of the order of a few hundred.

Explicit formulae for the refractive index describing oblique whistler-mode propagation at frequencies corresponding to ξ1 = −φ ≡ −0·924 (but |ξn| ≫ 1 when n ≠ 1), ξ0 = φ (but |ξn| ≫ 1 when n ≠ 0) and ξ0 = −ξ1 = φ (where ξn ≡ (ω − nΩ)/k‖w‖ are the arguments of the plasma dispersion function) are derived and analysed for two limiting cases of quasi-longitudinal and quasi-electrostatic propagation of the waves.

We obtain analytical expression for the interaction of obliquely propagating Bernstein waves with electrons by using the monochromatic wave approximation for quasi-linear theory in a weakly turbulent plasma. A numerical analysis is also carried out. The waves show initially strong damping and irregular amplitude oscillation, and the electron velocity distribution shows a variation corresponding to one of the waves. These are results of the energy exchange between waves and electrons. Despite the use of the monochromatic wave approximation, strongly scattering electrons with a broad velocity spread about the resonant velocity by the wave is seen.

Particle diffusion in phase space due to the crossing of multiple cyclotron resonances in an inhomogeneous magnetic field is investigated. The influence of the inhomogeneity is most significant for small wave amplitudes, when stochastic heating is absent in a homogeneous plasma. The diffusion depends on the relationship between the wave amplitude, the inhomogeneity parameter and the angle of wave propagation. The dependence of the diffusion coefficients upon the mentioned parameters is investigated by means of computer simulations for the case of constant inhomogeneity and for two models of variable inhomogeneity: a monotonic change typical of magnetospheric conditions, and a sinusoidal change typical of tokamaks.

The generation of steady currents by a rotating magnetic field (RMF) in a cylindrical plasma permeated by a steady azimuthal (or toroidal) magnetic field is studied analytically. Solutions are presented for the following limiting cases:

(1) high resistivity, when the penetration of the RMF and current drive are confined to a skin depth layer;

(2) low resistivity and weak toroidal field (small compared with the RMF), when the RMF fully penetrates the plasma and the toroidal current is that due to nearly synchronous rotation of the electron fluid with the RMF;

(3) low resistivity and intermediate toroidal field (comparable to the axial field associated with synchronous current), when the toroidal current is a significant fraction of its synchronous value, but large oscillating fields are generated; and

(4) strong toroidal field, when the RMF fully penetrates the plasma but current is only driven in a boundary layer at the plasma edge.

The applicability of these solutions is governed by the relative sizes of three dimensionless parameters.

Measurement of the RF (radio-frequency) magnetic field about the equatorial plane of the rotamak has enabled the distribution of the oscillating currents to be derived. The time-averaged forces, produced by the interaction of these currents with the oscillating field, have been estimated. In the standard field-reversed configuration there is a radial force, which helps to confine the plasma pressure, and a toroidal force, which drives the equilibrium current. In compact tokamak configurations there is an additional poloidal force, which produces a diamagnetic current. As the toroidal field increases, penetration of the RF fields improves owing to the excitation of a whistler wave mode. The connection between the rotating magnetic field technique and fast wave current drive is explained.

A family of models for fast steady-state reconnection has recently been presented by Priest and Forbes, of which the Petschek-like and Sonnerup-like solutions are special cases. This essentially linear treatment involves expanding about a uniform flow and field in powers of the external Alfvén Mach number Me, and hence is valid for small values of that parameter. To lowest order, the discrete slow-mode compressions attached to the diffusion region are straight, while downstream of them the plasma flows at simply the external Alfvén speed vAe and the field lines are straight. Here we present an extension of these solutions to the next order, which not only reveals that the wave itself is curved (as are the downstream magnetic field lines), but also that the downstream solution is sensitive to changes in the upstream boundary conditions. In the downstream solution there is a free parameter, which may be specified as a downstream boundary condition. Thus the boundary conditions at both the inflow and the outflow boundaries are crucial in determining the nature of the reconnection.

Large- and small-amplitude rarefactive ion-acoustic double layers have recently been studied in a fluid plasma with double Maxwellian electrons and a single cold ion species. Here the stationary large-amplitude theory is generalized to include two warm ion species. A technique for numerically solving the full nonlinear problem is presented. With it, useful predictions of the effect of ion temperatures and of light-ion contamination on the double-layer structure are made. A generalization to an arbitrary number of similar fluid components is pointed out. The small-amplitude perturbation theory is also extended to such a plasma, and in its restricted regime good qualitative agreement is obtained with the results of the large-amplitude theory.

The general equations describing the quasi-linear diffusion of charged particles from resonant interactions with a spectrum of electrostatic waves are given, assuming the wave and particle distributions to be azimuthally symmetric. These equations apply when a magnetic field organizes the wave and particle distributions in space, but when the local interaction between the waves and particles can be evaluated assuming that no magnetic field is present. Such diffusion is, in general, two-dimensional and is similar to magnetized diffusion. The connection between the two types of diffusion is presented. In order to apply the general quasi-linear diffusion coefficients in pitch angle and speed, a specific particle-distribution model is assumed. An expression for the unmagnetized dielectric function is derived and evaluated for the assumed particle distribution model. It is found that slow-mode ion-sound waves are unstable for the range of plasma parameters considered. A qualitative interpretation of unmagnetized diffusion is presented. The diffusion coefficients are then evaluated for resonant ion interactions with ion-sound waves. The results illustrate how resonant ion diffusion rates vary with pitch angle and speed, and how the diffusion rates depend upon the distribution of wave energy in k–space. The results of this study have relevance for ion beam heating in the plasma-sheet boundary layer and upstream of the earth's bow shock.