Ion and electron heating in the earth's bow shock region is studied in terms of the modified two stream instability by treating the electron's response to be electromagnetic and that of ions to be electrostatic. The modified two stream flute mode, driven unstable by the density and temperature gradients, can heat the ions to about 50 times their upstream temperature. However, the electrons are heated mainly by the non-flute mode and their temperature can be increased by a factor of 1·5 or more. Consequently the ions will be hotter than the electrons downstream of the shock, as observed by satellites.

The effect of finite geometry on the interaction of a hot low-density beam with a uniform plasma filling a circular waveguide is studied. An expression is derived for the growth rate of the instabilities developing at the harmonic of the beam gyrofrequency, taking the finite beam gyroradius into account. The calculations are done in the quasistatic approximation.

Parametric amplification of Alfvén waves in a plasma, subjected to a spatially uniform but temporally stochastic magnetic field, is investigated. The analysis is made using Bogoliubov and Mitropoisky's asymptotic method and Stratanovich's method for stochastic differential equations. This enables us to obtain the probability distribution function for the evolution of the wave, under Markovian approximation. Thus, a complete statistical characterization of the wave can be obtained, if needed. It is shown that Alfvén waves with wavelengths larger than the radius of the plasma column are amplified with probability unity, if the power spectral density of the fluctuating field at twice the wave frequency is non-zero.

We find a Lagrangian density from which the equations of motion for the Lang-muir solitons follow in the usual way. We show how this Lagrangian leads to the usual conservation laws. For the one-dimensional case we discuss how a consideration of these conservation laws can help us to understand some of the results obtained in numerical experiments on the behaviour of a strongly turbulent plasma. We point out that the situation in the three-dimensional case may be fundamentally different, and we discuss near-sonic perturbations and Karpman's treatment of these.

The problem of electromagnetic radiation from electric and magnetic line sources embedded in a moving bounded magrietoplasma sheath situated over a perfectly conducting plane is studied. The radiation fields due to the line sources consist of both E and H modes, excited simultaneously in the moving sheath. However, when the magnetic field lies parallel to the line source and is oriented normal to the direction of the sheath motion, the modes become decoupled. The far-zone radiation fields for both the electric and the magnetic line sources have been obtained, using the method of saddle-point approximation. The corresponding radiation patterns are also obtained and their variation studied as a function of the magnetic field, the location of the line source, the thickness and the velocity of the moving plasma sheath. It is found that the fields radiated by an electric line source remain unaffected by the presence of an ambient magnetic field and that, in the presence of a sufficiently intense magnetizing field, the magnetic line source over a perfectly conducting plane radiates as though surrounded by vacuum.

The nonlinear interaction of a high-frequency wave (transverse or longitudinal) and an ion-acoustic wave in a homogeneous plasma is investigated. The waves are assumed to be simultaneously excited by two localized external sinusoidal disturbances with frequencies ω0 and ωS in the plasma. From the coupled wave equations a system of ordinary differential equations for the spatial change of the amplitudes of the interacting waves (including the primary frequencies ω0, ωS and the mixed frequencies ω0±ωS) and a zero-frequency density disturbance is derived. The spatial development of the high-frequency amplitudes is characterized by localized regions of high intensities, coupled with local depressions of the plasma density. The influence of the initial amplitudes and the frequencies ω0, ωS on the maximum of the primary high-frequency amplitude and the ‘cavity’ depth is shown. The numerical results are compared with conclusions from a simplified model of three resonantly interacting normal modes.

We suggest that the electron density and temperature of a plasma could be determined by immersing two small dipole antennae in it, and by measuring, as a function of frequency, the cross-spectrum of the random signals that they receive. When the plasma is in thermal equilibrium, this spectrum is related simply, by Nyquist's theorem, to the real part of the mutual impedance of the two antennae. We have studied the case where, in addition, the plasma is collisionless and no magnetic field is present. The spectrum has a main resonance peak slightly above the plasma frequency, while for still higher frequencies it exhibits oscillations, the amplitudes of which decrease as one moves away from the plasma frequency. The main resonance peak becomes sharper, but smaller, as the distance between the antennae becomes large compared with the Debye length.

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.

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.

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.

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 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.

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.