Shock waves produced by magnetic compression are called transverse when the magnetic field contains no component in the direction of the shock wave normal. It is experimentally well known that very strong shocks of this type show classical MHD behaviour in terms of both jump conditions and structure. It is also known that relatively slow transverse shocks can be of an ionizing gasdynamic type with no jump in the imbedded transverse field. Since there are fundamental differences in both the structure and the jump relationships of these two types of shock waves, it is of interest to investigate the transition behaviour in the intermediate shock speed regime. A previously widely accepted model due to Kulikovskii & Lyubimov and Chu assumes no precursor ionization and requires significantly large values of the magnetic Prandtl number, Pm, within the shock structure. That model is shown to be physically inappropriate because experimentally observed transition speeds and corresponding post-shock temperatures imply negligibly small shock Pm values. Also in that model, MHD conditions are approached only asymptotically at large shock speeds. The present precursor ionization model assumes effectively zero Pm values throughout transition and into the low-speed MHD regime. As distinct from the previous theory, this model predicts the attainment of full MHD conditions at and above a well-defined finite shock speed. The assumption of a characteristic post-shock temperature model for the ionization mechanism allows unique jump relations to be formulated independently of other transport mechanisms. Results include computed values of various jump ratios and the electric field as functions of shock speed throughout gasdynamic, transition, and MHD regimes. The solutions form a one-parameter family depending on the relative combination of upstream magnetic field and density (e.g. the Alfvén velocity). Shock structure phase plane trajectories are computed at a number of typical shock speeds throughout transition.

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 equilibrium configurations of a one-species guiding centre plasma are circularly symmetric. Unlike results obtained for systems with artificial periodicity, the profiles depend uniquely on the energy and mean square radius. The random phase approximation is shown to be invalid.

A semi-infinite plasma slab with a density gradient and an externally applied electric field normal to an applied magnetic field is considered. Stable finite amplitude density and potential oscillations are investigated for parameters favourable for the E × B instability. Explicit expressions for the oscillation amplitudes, frequency, and wavelength are derived in the limit of a weak density gradient. The calculations are performed with a closed set of zero and first harmonic equations. It is shown that second harmonic contributions are small in the case considered.

The parametric excitation of slow, intermediate (Alfvén) and fast magneto-acoustic waves by a modulated spatially non-uniform magnetic field in a plasma with a finite ratio of gas pressure to magnetic pressure is considered. The waves are excited in pairs, either pairs of the same mode, or a pair of different modes. The growth rates of the instabilities are calculated and compared with the known result for the Alfvén wave in a zero gas pressure plasma. The only waves that are found not to be excited are the slow plus fast wave pair, and the intermediate plus slow or fast wave pair (unless the waves have a component of propagation direction perpendicular to both the background magnetic field and the direction of non-uniformity of the field).

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.

Propagation of electrostatic electron waves whose frequency is smaller than the electron plasma frequency in a large unmagnetized plasma is investigated both experimentally and theoretically. When a receiver is close to a transmitter, free-streaming electrons are detected owing to their large capacity for excitation. When the distance between the receiver and the transmitter becomes large, the third-order Landau mode is observed due to its smaller damping than that of free-streaming electrons. Finally, a dip in amplitude of the wave, caused by interference by the higher-order Landau modes, is seen. The results are in reasonable agreement with numerical calculation assuming a dipole excitation for the wave.

The marginal stability of a plasma carrying current along the static magnetic field with isotropic Maxwellian ions and isotropic Maxwellian electrons drifting relative to the ions is investigated. The complete electromagnetic dispersion relation is studied using numerical techniques; the electron sums are restricted to three terms which limits the analysis to frequencies much less than the electron gyro-frequency, but includes frequencies somewhat above the ion gyro-frequency. A ‘kink-like’ instability and an instability of the Alfvén mode are found to have the lowest threshold drift velocities in most cases. In fact the threshold drift for the kink-like instability can be significantly less than the ion thermal speed. Electrostatic and electromagnetic ion-cyclotron instabilities are also found as well as the electro-static ion-acoustic instability. No instability of the fast magnetosonic mode was found. The stability analysis provides only threshold drift velocities and gives no information about growth rates.

A simple class of static equilibria, in the ideally conducting magnetohydrodynamic approximation, is found to include linear systems having surfaces of constant hydrodynamic pressure with a cylindrical topology and elliptic transverse cross-section functionally dependent on an axial co-ordinate. These suggest a possible mode of behaviour for non-axisymmetric toroidal systems and might themselves be realized experimentally as free boundary configurations of a plasma in an applied quadrupole-like magnetic field.

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.

Some properties of perpendicular collisionless shocks are investigated, using a model in which the ion orbits in the shock are assumed to be determined by the average electric and magnetic fields in the shock. These fields are modelled, with the jump in magnetic field across the shock being determined by the conservation relations, and the potential jump determined self-consistently within the model, using the fact that the mean ion velocity downstream of the shock is determined by the conservation relations. Extensive numerical calculations of ion orbits show that effective ion heating can occur in the absence of any dissipative process, with the energy residing in non-Maxwellian velocity distributions in the downstream regions. Results on this and on a number of other features of shock waves, agree well with experiments.

The sensitivity of electromagnetic ion-cyclotron wave growth rates to the details of the shape of proton velocity distribution functions is explored. For this purpose two different forms of bi-Lorentzian for the proton distribution functions were adopted. The growth rates for the two types of bi-Lorentzians and the biMaxwellians for the beam (hot) protons are compared. Although the growth rates for the three shapes depend on the velocity moments of the different velocity distributions in a similar way, their magnitudes were found to vary considerably.

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.

The guided modes of Woods' magnetohydrodynamic waveguide for a uniform, cylindrical plasma are shown to satisfy a homogeneous wave equation whose differential operator is the product of eight Helmholtz operators. The propagation constants of the Helmholtz operators are the characteristic roots of an 8 × 8 matrix which is derived and written down explicitly. This reformulated theory is extended to include localized sources which excite the guided modes. For certain cases, the Green's functions for the differential operators can be represented by Dini expansions in terms of modal eigenfunctions, which manifestly satisfy the boundary conditions. For the case of MHD waves excited by an azimuthally symmetric current source in a resistive, pressureless, inviscid, fully ionized plasma, a detailed solution is obtained which is in good qualitative agreement with experiments.

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 exact theory of plane waves of fixed profile travelling with constant velocity cZ/n (0 ≤ n ≤ 1) through a uniform, cold, electron-ion plasma in a magneto-static field is examined in terms of the governing equations referred to the frame of reference in which there is no space dependence. Canonical periodic solutions are defined as those with zero average rate of flow of electrons (and a fortiori of ions) in the laboratory frame. It is shown that the equations lead to a second- order, nonlinear, ordinary vector differential equation for the reduced velocity u of the electrons. A scalar first integral is obtained, from which it is deduced that the path in u-space of any solution lies within a bounded domain. It is shown that, for propagation across the magnetic field, a polarization is possible in which the particle velocities and the electric field are orthogonal to the magnetic field. The simpler model of an electron Plasma is considered. Explicit canonical periodic solutions, with the stated polarization, are obtained for propagation across the magnetic field in the case n = 0 and the case n ≃ 1. These support the conjecture that, for any fixed value of n in [0, 1], there are two ‘modes’ of arbitrary amplitude which reduce to the familiar monochromatic waves of linear magneto-ionic theory in the small amplitude limit.

Two-dimensional magnetohydrodynamic turbulence is explored by means of numerical simulation. Previous analytical theory, based on non-dissipative constants of the motion in a truncated Fourier representation, is verified by following the evolution of highly non-equilibrium initial conditions numerically. Dynamo action (conversion of a significant fraction of turbulent kinetic energy into long-wavelength magnetic field energy) is observed. It is conjectured that in the presence of dissipation and external forcing; a dual cascade will be observed for zero-helicity situations. Energy will cascade to higher wavenumbers simultaneously with a cascade of mean square vector potential to lower wavenumbers, leading to an omni-directional magnetic energy spectrum which varies as k-⅓ at lower wavenumbers, simultaneously with a build-up of magnetic excitation at the lowest wavenumber of the system. Equipartition of kinetic and magnetic energies is expected at the highest wavenumbers in the system.