The mean electromotive force generated by random Alfvén waves in a collision-less plasma is evaluated taking into account mean magnetic field gradients. It is shown that the mean electromotive force associated with a magnetic shear of the mean field and the helicity spectrum function of the random velocity field exists and has a component parallel to the mean magnetic field when it is generated by random waves propagating along the mean magnetic field and by statistically anisotropic random waves propagating in arbitrary directions. The results are applied to the magnetospheric substorms.

Ballooning mode theory for finite toroidal mode number n is derived for shearfree and sheared axisymmetric toroidal plasmas. The resulting finite-n theory is applicable for both compressible and incompressible perturbations. The inclusion of finite compressibility changes the ballooning mode eigenfunctions and eigenvalues, but not the form of the finite-n correction.

The mean electromotive force generated by random hydromagnetic waves is calculated by using Fourier analysis methods for the cases of an incompressible Hall plasma and a compressible plasma with finite β. It is shown that in the case of a Hall plasma the α effect can exist in the interaction between two waves which propagate in opposite directions and have different phase velocities and several new β–terms are produced by the Hall effect, while in the case of a compressible plasma the α–effect can exist only in the interaction between the Alfvén mode and the fast or slow magneto-acoustic mode, and not between the fast and slow magneto-acoustic modes. The results are discussed in the context of the substorms in the earth's magnetosphere.

The interaction of an electron with two electromagnetic waves propagating in an isotropic plasma is studied. It is shown, by numerical calculations, that the electron behaves stochastically, above a given threshold of the wave field amplitudes. The numerical threshold is compared with those given by analytical criteria. The results might be relevant to the laser-plasma interaction problem.

Linear stability of doublets against axisymmetric modes in the approximation of resistive MHD was studied earlier; two modes were identified as those most likely to be unstable, namely the ‘up-down’ mode, which tends to move the plasma up or down and the ‘droplet-ellipse’ mode which tends to deform the doublet into either a droplet or an ellipse. In the treatment described in this paper, quadratic terms in the perturbation are retained. For an equilibrium which is symmetric about the midplane it is easy to see that the quadratic terms vanish for the ‘up-down’ mode. For the ‘droplet-ellipse’ mode this is not the case. This mode allows two different deformations according to linear theory; the effect of the quadratic terms is found always to be stabilizing for one of these deformations, and destabilizing for the other. Thus, owing to the effects of such nonlinear terms, one may expect in experiments to observe unstable developments in a preferred direction, namely that of destabilization, and one expects to observe a faster deterioration of an equilibrium than that predicted from linear theory. These tendencies have been observed in doublet experiments. In this paper the formalism for including quadratic terms in the perturbation is discussed and results from numerical examples are given.

Self-consistent infinitesimal perturbations of electron density and electric field are used to analyse the stability of the plasma. The axisymmetric perturbations are stable for any magnetic and electric field strengths. The non-axisymmetric perturbations with azimuthal modes m ≥ 1 and less than a certain integer are unstable for certain ranges of magnetic and electric fields. The mode m = 2 can be more unstable than the mode m = 1. Previous analysis by other authors was confined to the case m = 1 and the perturbations were not self-consistent. Our results differ significantly from the earlier results.

The mean electromotive force produced by random hydromagnetic waves in a collisionless plasma is investigated taking into account non-uniformities in the mean magnetic field, fluid velocity and plasma density. It is shown that the mean electromotive force associated with gradients in mean quantities and the helicity spectrum function of the random velocity field exists and has a component parallel to the mean magnetic field which is associated with field-aligned gradients in mean quantities and density gradients parallel to the mean flow. The results are discussed in the context of the field-aligned currents in the earth's magnetosphere.

In this paper we develop similarity solutions for the problem of nonlinear Landau damping of Alfvén waves. These solutions which are applicable to power-law wave spectra illustrate not only the basic feature of the damping process, namely that short-wavelength waves decay more rapidly than long-wavelength waves, but also how the damping depends on the initial strength of the power spectrum and its distribution in wavenumber.

An exact nonlinear Alfvén wave in a low-β plasma is investigated. Super Alfvén solitons with a density depression are found to exist. The analytical result for the small-amplitude soliton is given.

The amplification of fast extraordinary mode waves with frequencies very close to the electron cyclotron frequency is investigated for a plasma which consists of a weakly relativistic electron component with a loss-cone type distribution and a cold background electron component. The basic mechanism of the amplification is attributed to a relativistic cyclotron resonance between the wave and the energetic electrons. The method employed in the present analysis enables us to solve the dispersion relation in a self-consistent manner for arbitrary ratio of the densities of the energetic and background electrons. It is found that the maximum growth rates occur at certain values of ω2pe/Ω2e and the angular dependence of the growth rate is sensitive to the ratios ω2pe/Ω2e and ne/nb. Here ωpe and Ωe are the electron plasma frequency and the electron cyclotron frequency, respectively, and ne and nb denote the number densities of the energetic and background electrons, respectively.

Plasma effects on the emission of synchrotron radiation are investigated using a two-dimensional electromagnetic relativistic simulation code. Results are compared with those for a vacuum; it is found that the emission lies between the vacuum emission for nc and nc + 1 where nc is the critical harmonic for EM wave propagation (nc = ωp/Ω0).

The stability of lower-hybrid waves in a collisional, fully ionized plasma carrying a field-aligned current is investigated. From the two-fluid equations in the cold-plasma approximation, a generalized dispersion relation and formulae for the real frequency ωI and growth rate ωR are derived. The results of a numerical study are presented showing the dependence of ωR and ωI on the angle between the direction of propagation and the magnetic field, the ratio of the electron drift velocity to the parallel phase velocity, and other plasma parameters. Lower-hybrid instability with electron drift velocity small compared with the parallel phase velocity is predicted.

Magneto-acoustic oscillations were excited in a non-uniform, current-carrying plasma column. Measurements of the oscillating axial magnetic flux at a number of excitation frequencies were used to determine the equilibrium plasma properties. In agreement with previous theoretical studies, the radial profile of the plasma density is shown to be accurately determined, while it is not possible to obtain detailed information on the radial profile of the equilibrium magnetic field.

The restrictions imposed are that the magnetic field is everywhere in the x direction, and that no quantity varies with x, but several interesting instabilities can still occur. After some discussion of objectives, a fluid-like formulation is pursued, in which the pressure anisotropy is retained, but higher moments neglected. It shows a resonance at twice the gyrofrequency, and for electrons the constraint on the time step would be unacceptable, so they should be treated more crudely. Then the dispersion equation shows only two modes, which appear sufficiently harmless for us to proceed to computations.

The Petschek model for incompressible reconnexion has been put on a firm mathematical foundation in an earlier paper by Soward & Priest, who discovered a ‘local’ similarity solution for the process. The present paper extends that analysis to compressible reconnexion, in which the previous Alfvén waves are replaced by slow magneto-acoustic shocks of switch-off type. By contrast with a previous suggestion, it is found unnecessary to include intermediate waves standing ahead of the slow shocks. The maximum reconnexion rate is typically half of Petschek's stated value, though faster rates are achieved when the external gas pressure is sufficiently low.

The nonlinear interaction of two HF electromagnetic spherical waves is studied in a homogeneous isotropic plasma. Due to space variations in the k vectors of the mother waves, the interaction is localized. The structure and the amplitude of the generated Langmuir wave are calculated and a possible experiment is discussed.

The linear Vlasov dispersion equation for electrostatic plasma instabilities driven by gravity and weak density gradients perpendicular to a uniform magnetic field is derived and solved numerically. Two interchange instabilities emerge: the well-known fluid mode at long wavelengths and a kinetic mode at wavelengths short compared with the ion gyroradius. The properties of both instabilities are studied, as well as the effects of gravity on the universal and lower-hybrid density drift instabilities. The results show that the kinetic interchange generally has a larger growth rate than the fluid interchange instability, indicating that, whenever the latter is present in a collisionless plasma, the former may also be found.

The electrostatic lower-hybrid wave is shown to decay parametrically into a whistler wave and a resonant ion cyclotron mode or an ion cyclotron quasi-mode or a reactive quasi-mode. The convective threshold powers for these decay instabilities are found to be much larger than presently available pump powers. These decay instabilities, however, are expected to play an important role in the saturation of the parametrically excited short-wavelength lower-hybrid waves having frequency close to ωlh.

The equilibrium of a plasma cylinder confined by means of a steady axial magnetic field, Bα, and a transverse magnetic field, Bω, which rotates about the axis of the cylinder is analysed using a two-fluid model. It is shown that the electron fluid is tied to the rotating field provided that

The rotating field does not impart a steady azimuthal motion to the ions provided that However, the ion fluid acquires a steady azimuthal velocity due to electron-ion collisions. A self-consistent radial electric field is produced; this field plays an important role in establishing the steady ion flow.