The temporal dynamics of field-line reconnexion is studied by numerical experiment in a compressible conducting fluid. It is shown that because of localized enhancement of resistivity the reconnexion takes place in an initially antiparallel magnetic field and that an X-type field configuration develops, occupying an extended region. There is also a remarkable release of magnetic energy into kinetic and thermal energies. The global flow pattern can spontaneously be set up through the field-line reconnexion under no specially imposed boundary conditions.

A model based on nonlinear mixing of dispersive waves is used to predict higher harmonic waves generated by weakly nonlinear electron plasma waves. The total harmonic wave is given by superposition of modes which lie at different points (with the same frequency) in the dispersion diagram. The model well explains the experimental results concerning the harmonic waves produced by externally excited electron plasma waves propagating along a collisionless plasma column.

The equations of motion for turbulent two-dimensional magnetohydrodynamic flows are solved in the presence of finite viscosity and resistivity, for the case in which external forces (mechanical and/or magnetic) act on the fluid. The goal is to verify the existence of a magnetohydrodynamic dynamo effect which is represented mathematically by a substantial back-transfer of mean square vector potential to the longest allowed Fourier wavelengths. External forces consisting of a random part plus a fraction of the value at the previous time step are employed, after the manner of Lilly for the Navier–Stokes case. The regime explored is that for which the mechanical and magnetic Reynolds numbers are in the region of 100 to 1000. The conclusions are that mechanical forcing terms alone cannot lead to dynamo action, but that dynamo action can result from either magnetic forcing terms or from both mechanical and magnetic forcing terms simultaneously. Most real physical cases seem most accurately modelled by the third situation. The spatial resolution of the 32 × 32 calculation is not adequate to test accurately the predictions of the spectral power laws previously arrived at on the basis of the assumption of simultaneous cascades of energy and vector potential. Some speculations are offered concerning possible relations between turbulent cascades and the ‘disruptive instability’.

The mixing of two parallel or antiparallel beams of circularly polarized microwaves propagating in the extraordinary mode along a uniform, static magnetic field is examined. Resonant excitation of longitudinal electron plasma waves at the beat frequency is found to enhance the microwave absorption. An analysis is based on Maxwell's equations and the continuity and momentum equations for the electron gas with both collision and temperature effects included. Formulae for the average power absorption density and the absorption efficiency are derived. The results of a numerical study of the coupling constant and the efficiency are presented.

Necessary and sufficient conditions for the exponential stability of an N-component, warm or cold, rotating cylindrical plasma to axisymmetric electrostatic perturbations are obtained. The plasma is immersed in an axial magnetic field B0(r), where r is the radial co-ordinate, and the equilibrium quantities are permitted to be arbitrary functions of r consistent with the 0-order equations. The maximal growth rate of an unstable system is shown to be determined by a maximum principle.

The basic conservation equations for a perfectly conducting anisotropic plasma are used to derive curves relating physical quantities in uniform regions on either side of a shock. These curves are independent of the shock mechanism and for any specific mechanism only small segments of the curves would be allowable. Comparison is made with shocks in isotropic magnetohydrodynamics.

In this paper the nonlinear behaviour of the m = 0 torsional hydromagnetic wave is analyzed. Two cases have been considered: the nonlinear self-interaction of a single torsional wave and the nonlinear interaction of two identical, oppositely propagating torsional waves. In the first case the nonlinear terms in Ohm's law and the equation of motion generate a second order perturbation which accompanies the primary wave and has two components: a steady component and an oscillatory component having twice the frequency of the primary torsional wave. In the second case studied the self and cross-interactions of the two waves again generate a second order perturbation field. The existence of certain critical wavelengths, at which geometric resonances of the perturbation occur, is established.

The dispersion relation for an electron plasma in a magnetic field is investigated for a bi-Maxwellian distribution function. A new set of solutions for non-perpendicular propagation is found. The linear growth rates are computed and the instability regions in the (k, cos θ) plane are determined. An approximate analytical treatment of the problem is also given for certain ranges of the parameters.

The phase velocity surface for waves propagating in a uniform cold plasma is sometimes misinterpreted as having the shape of a wave-front. A summary is presented of the correct interpretations of the phase velocity, ray velocity, and group velocity surfaces. A full set of computer generated plots of such surfaces are presented. These are intended as an aid to visualization of wave propagation in such a medium.

The modulational instability of the ion wave is observed experimentally. Two kinds of wave packets are launched in the plasma by means of a grid. One is a broad-band wave packet excited by a positive step voltage. The other is a quasi-monochromatic wave packet modulated by a pulse. For the step voltage response, we observe a large oscillation in the wave front which evolves to Korteveg–de Vries solitons and a small amplitude wave packet in the tail. The wave packet becomes modulationally unstable and divides into smaller wave packets. Whenever the wave packet is modulated, the spread of the packet is suppressed and is much smaller than is expected from linear dispersion. For the quasi-monochromatic wave packet, we also observe the modulational instability if the carrier frequency is high. The frequency of the carrier is shifted by the instability. The result of the quasi-monochromatic wave packet is qualitatively explained by the modified nonlinear Schrödinger equation taking account of the wave-particle interaction at the group velocity.

This paper complements an earlier one in which we considered the diffusion and drift across a magnetic field induced by a turbulent spectrum of fluctuations. We examine here the effects of these on the propagation of an unstable spectrum of modes. In the first paper a nonlinear dispersion relation is derived in a general closed form. This is then examined in the limint of short wavelengths (i.e.wavelengths much less than the gyroradii) and results of other authors are retrieved. In particular it is found that modes supported by the magnetic field are quashed whenever a particle may diffuse a wavelength per gyroperiod. For instance, in the context of current-driven instabilities (current across the magnetic field), electron cyclotron instabilities are quashed but not the ion-acoustic. The dispersion characteristics of the latter are unchanged except in that the drift which sustains the instability is altered by the presence of a turbulent (E × B) type drift. Depending on the level of fluctuations and magnetic field strength, this may amount simply to a rotation of the cone of unstable modes or may form a countercurrent which in turn suppresses the original current driving the instability.

In the second half of the paper the problem of calculating the fluctuation spectrum of the electric field is addressed since this is essential for a self-consistent computation of the diffusion tensor and turbulent drift appearing in the nonlinear dispersion relation.

An orbit perturbation procedure is applied to the description of monochromatic, large-amplitude, electrostatic plasma wave propagation. In the lowest-order approximation, untrapped electrons are assumed to follow constant-velocity orbits and trapped electrons are assumed to execute simple harmonic motion. The deviations of these orbits from the actual orbits are regarded as perturbations. The nonlinear damping rate and frequency shift are then obtained in terms of simple functions. The results are in good agreement with previous less approximate analyses. A significant feature of the analysis is that it treats a single wave by techniques previously applied to turbulent spectra. The analysis can consequently be extended to the case of a large-amplitude wave interacting with a lower-amplitude spectrum of waves.

It is shown that, in the case of incidence of p−olarized waves onto a plane- parallel plasma layer, the wave field pressure can cause the electromagnetic field to penetrate into the plasma, which is opaque in the linear approximation for the given waves. The plasma density average over the region of the electromagnetic field does not change.

The theory of quasi-linear diffusion of runaway electrons in the field of electromagnetic waves (HF field) excited by external sources is given. The frequency of the waves is somewhat less than the electron cyclotron frequency. The time-averaged distribution function of resonant electrons is derived. The presence of the toroidal electric field changes the process of quasi-linear relaxation considerably. It also leads to a continuous absorption of energy and momentum from the HF field. On the other hand, the HF field increases the number of high-energy electrons. As a consequence, beam instabilities can arise. A comparison with experimental results is given.

A statistical description of the Vlasov equation is made possible by truncation of phase space in the velocity co-ordinates and writing the equation in terms of Fourier components in configuration and velocity space. Invariants of the resulting nonlinear turbulence equations are discussed. Expectation values and in particular an electric field spectrum of the form (β+ ακ2)-1 are derived. α and β are constants; α is always positive; β may be negative, depending on the initial conditions of the plasma. The spectrum is in reasonable agreement with available experiments and simulations.