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.

Analysis of the influence of an injected monochromatic wave on a turbulent spectrum shows that the resulting nonlinear dispersion relation for the stochastic modes displays a real frequency shift and a corrected growth rate when contrasted with the classical quasi-linear dispersion equation.

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.

Using a Van Kampen treatment, we study the longitudinal electron oscillations for a plasma with a cut-off Maxwellian velocity distribution. Having defined and computed excitation coefficients in the real w, k plane, we represent this ‘wave density’ through the greyness of this plane. This representation should be useful as a help to the experimenter. Moreover we show the appearance of a slightly damped pole with a phase velocity slightly smaller than the cut-off velocity Vc if this velocity is in the interval 2 to 4VT and a modification of the Landau mode which propagates for higher and higher frequencies when Vc decreases.

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’.

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.

The recent Plum Brook—NASA experiments on counterstreaming plasma instabilities in which electric field emissions at frequencies [(n + ½) ±α]ωe (n = 1, 2, 3,…, 9, α < 0·5) have been observed, raised the theoretical problem of the non-symmetric two-stream instability. This is the case in which the counterstreaming beams have different velocities in the directions parallel and perpendicular to the static magnetic fields as well as different particle density.

We investigate theoretically this problem. The instability of quasi-electrostatic waves at shifted half odd integer multiples of the cyclotron frequency, due to two non-symmetric counterstreaming electron beams, is considered. The beam velocities parallel and perpendicular to the static magnetic field are represented by different double Dirac delta functions; no parameter limitation is imposed. A systematic investigation of (i) the coupling between plasma modes and cyclotron modes and (ii) the coupling between cyclotron modes (beam 1) and cyclotron modes (beam 2) resulting in shifted half odd integer multiples of the cyclotron frequency is carried out.

The results include approximate but simple analytical expressions for maximum growth rates and for marginal stability as well as exact numerical solutions for the detailed unstable spectra (1 ≤ m ≤ 20) in both ωτ- and kr-space. The relative weakening or suppression of certain modes is also predicted.

We investigate the influence of a lower hybrid pump field on the dispersion characteristics of various trapped particle modes and delineate the conditions for their excitation or suppression. Our calculations also reveal the existence of certain new instabilities driven by the pump.

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 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.

In this paper we consider the resonant interaction between three modified ordinary electromagnetic waves, which propagate perpendicular to a constant magnetic field. We show that for the modified mode to be a normal mode we must have the unperturbed current equal to zero. Using the averaged Lagrangian method, we calculate the coupling coefficient for the resonant interaction between three of these modes. It is proportional only to the cube of the drift velocity, as expected from the vanishing of the unperturbed current.

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.

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.

This paper investigates the general problem of stability of Bernstein—Greene— Kruskal type waves. By investigating perturbations perpendicular to the wave, we obtain a general sufficient condition for instability. This is then extended to the case of magnetized plasmas with a uniform magnetic field in the direction of the BGK wave. New perturbed modes, having no counterpart in linear theory, are also found. Various special cases are considered and previous, more particular results confirmed.

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.

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.

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.