The nonlinear coupling between collisional drift waves and a lower-hybrid pump is studied in a cylindrical geometry. A dispersion relation for the collisional drift wave is derived incorporating both ponderomotive and Ohmic-heating effects. It is found that Ohmic heating of electrons enhances the frequency as well as the growth rate of the drift waves. Effects due to the ponderomotive force are insignificant.

A family of models for fast steady-state reconnection has recently been presented by Priest and Forbes, of which the Petschek-like and Sonnerup-like solutions are special cases. This essentially linear treatment involves expanding about a uniform flow and field in powers of the external Alfvén Mach number Me, and hence is valid for small values of that parameter. To lowest order, the discrete slow-mode compressions attached to the diffusion region are straight, while downstream of them the plasma flows at simply the external Alfvén speed vAe and the field lines are straight. Here we present an extension of these solutions to the next order, which not only reveals that the wave itself is curved (as are the downstream magnetic field lines), but also that the downstream solution is sensitive to changes in the upstream boundary conditions. In the downstream solution there is a free parameter, which may be specified as a downstream boundary condition. Thus the boundary conditions at both the inflow and the outflow boundaries are crucial in determining the nature of the reconnection.

Starting from the particle continuity equation and the guiding-centre model for the particle velocity, using an equation of state in the form of the conservation of the ion magnetic moment, as well as Ohm's and Ampère's laws, a set of four coupled nonlinear equations has been derived to investigate the properties of magnetic turbulence in plasmas with hot ions and cold electrons. It is shown that finite-β effects can cause a linear coupling between the Alfvén and Varma modes in a weakly non-uniform plasma immersed in an inhomogeneous magnetic field. In the nonlinear regime the stationary solutions of the four field equations are found to be double vortices. Implications of our results for enhanced magnetic fluctuation and anomalous transport in a mirror reactor are pointed out.

The DNLS equation for parallel nonlinear and weakly dispersive MHD waves is extended to finite beta values as well as to three spatial dimensions, by means of the reductive perturbation method. Kinetic effects are included by means of the hybrid fluid and kinetic guiding-centre model of Grad (1961). The resulting equation contains a nonlinear and non-local term representing the effect of resonant particles.

A general investigation of linear drift-wave phenomena in cylindrically bounded plasmas, immersed in a magnetic field without shear and curvature, is performed within the two-fluid hydrodynamical approximation, taking into account electron-temperature oscillations and inhomogeneous radial distributions of the undisturbed electron density and temperature. For plasmas in which the electron temperature strongly exceeds the ion temperature the problem is reduced to an ordinary complex second-order differential equation describing the radial distribution of the oscillating electric potential. It is shown that the presence of electron-temperature oscillations (which must always exist in order to satisfy electron-energy conservation) and of radial gradients in the undisturbed electron temperature (which must always exist owing to cooling of the plasma at the boundary) leads to an important modification of the theory of drift waves in cylindrical plasmas (with regard to their stability and the radial distribution of the oscillating quantities) compared with previous papers in which these phenomena were disregarded. A numerical program for solving the corresponding complex-eigenvalue problem has been derived that allows a realistic calculation of all the quantities pertaining to drift-wave phenomena. It has been applied, in particular, to the calculation of the radial distribution of the oscillating coherent magnetic fields accompanying the coherent drift waves. The numerical results prove to be in good agreement with experiments performed with a helium plasma.

Large- and small-amplitude rarefactive ion-acoustic double layers have recently been studied in a fluid plasma with double Maxwellian electrons and a single cold ion species. Here the stationary large-amplitude theory is generalized to include two warm ion species. A technique for numerically solving the full nonlinear problem is presented. With it, useful predictions of the effect of ion temperatures and of light-ion contamination on the double-layer structure are made. A generalization to an arbitrary number of similar fluid components is pointed out. The small-amplitude perturbation theory is also extended to such a plasma, and in its restricted regime good qualitative agreement is obtained with the results of the large-amplitude theory.

Large-aspect-ratio tokamak equilibrium is studied, including effects, such as ellipticity of the flux surfaces, of second order in the inverse aspect ratio. To facilitate the interpretation of experimental data, the analysis uses simple coordinates that are readily evaluated, rather than co-ordinates based on the exact flux surfaces. An explicit formula for the safety factor, including second-order terms, is presented, along with a brief discussion of rotational effects. The analysis assumes near-circularity of the outermost closed surface and low plasma pressure.

Propagation characteristics of hydromagnetic waves in a magnetic plasma are investigated using the two-plasma fluid equations including the effect of lower-hybrid waves propagating perpendicularly to the magnetic field. The effect of lower-hybrid waves on the propagation of hydromagnetic waves is analysed in terms of phase speed, growth rate, refractive index, polarization and the amplitude relation between the density perturbation and the magnetic-field perturbation for the cases when hydromagnetic waves propagate in the plane whose normal is perpendicular to both the magnetic field and the propagation direction of lower-hybrid waves and in the plane perpendicular to the propagation direction of lower-hybrid waves. It is shown that hydromagnetic waves propagating at small angles to the propagation direction of lower-hybrid waves can be excited by the effect of lower-hybrid waves and the energy of excited waves propagates nearly parallel to the propagation direction of lower-hybrid waves.

In this paper we investigate the linear generation of electrostatic waves in a homogeneous, collisionless, unmagnetized plasma with two Maxwellian electron components, one drifting with respect to the other. The ions are assumed to be infinitely massive. It is shown that such a system may be unstable to a beam mode rather than the well-known Langmuir mode, if the drifting electron component is sufficiently dense and has a sufficiently low temperature. This ‘electron-beam instability’ is driven by the free energy in the particle distribution, and the associated phase velocity is greater than the electron thermal speed. The dispersion characteristics of the electron-beam instability and the Langmuir instability at the critical drift velocity for wave growth are determined for a wide range of parameters. The results of our investigation are applied to electron beams producing hard X-ray emission in solar flares, and it is argued that such beams may be unstable to the generation of electrostatic waves at frequencies below the electron plasma frequency.

The general equations describing the quasi-linear diffusion of charged particles from resonant interactions with a spectrum of electrostatic waves are given, assuming the wave and particle distributions to be azimuthally symmetric. These equations apply when a magnetic field organizes the wave and particle distributions in space, but when the local interaction between the waves and particles can be evaluated assuming that no magnetic field is present. Such diffusion is, in general, two-dimensional and is similar to magnetized diffusion. The connection between the two types of diffusion is presented. In order to apply the general quasi-linear diffusion coefficients in pitch angle and speed, a specific particle-distribution model is assumed. An expression for the unmagnetized dielectric function is derived and evaluated for the assumed particle distribution model. It is found that slow-mode ion-sound waves are unstable for the range of plasma parameters considered. A qualitative interpretation of unmagnetized diffusion is presented. The diffusion coefficients are then evaluated for resonant ion interactions with ion-sound waves. The results illustrate how resonant ion diffusion rates vary with pitch angle and speed, and how the diffusion rates depend upon the distribution of wave energy in k–space. The results of this study have relevance for ion beam heating in the plasma-sheet boundary layer and upstream of the earth's bow shock.

We examine the global energetics of a recent weakly nonlinear theory of fast steady-state reconnection in an incompressible plasma (Jardine & Priest 1988). This is itself an extension to second order of the Priest & Forbes (1986) family of models, of which Petschek-like and Sonnerup-like solutions are special cases. While to first order we find that the energy conversion is insensitive to the type of solution (such as slow compression or flux pile-up), to second order not only does the total energy converted vary but so also does the ratio of the thermal to kinetic energies produced. For a slow compression with a strongly converging flow, the amount of energy converted is greatest and is dominated by the thermal contribution, while for a flux pile-up with a strongly diverging flow, the amount of energy converted is smallest and is dominated by the kinetic contribution. We also find that the total energy flowing out of the downstream region can be increased either by increasing the external magnetic Mach number Me or the external plasma beta βe Increasing Me also enhances the variations between different types of solutions.

The mean electromotive force generated by nonlinear standing Alfvén waves propagating along the mean magnetic field is investigated. It is shown that the α-effect can exist owing to the interaction between oppositely propagating two waves, provided that the initial fields have non-zero helicity. The result is discussed in the context of field-aligned currents and periodic particle flux variations in the earth's magnetosphere.

As a continuation of our earlier work, we have analysed the higher-order perturbative corrections to the formation of (ion-acoustic) solitary waves in a relativistic plasma. It is found that the relativistic considerations affect the amplitude and width variation - as conjectured in our previous paper. Our analysis employs a higher-order singular perturbation technique, with the elimination of secular terms in stages. In this way we arrive at an inhomogeneous KdV-type equation, which is then solved exactly. At this point a new phenomena arises at a critical value of the phase velocity at which the coefficient of the nonlinear term in the KdV equation vanishes. A new set of stretched co-ordinate is then used to derive a modified KdV equation. In both cases we have numerically computed the specific physical profile of the new solitary wave and its width.

Biskamp and Welter (1983) have defined an anomalous resistivity due to shortwavelength turbulence. They reported that this resistivity can be of either sign, and that negative anomalous resistivity in particular can affect the growth of the tearing instability. We use a spectral numerical-simulation code and ancillary diagnostics to analyse the behaviour of resistive magnetic tearing in the presence of turbulence of the sort postulated by Biskamp and Welter. We find that, in general, the ‘anomalous resistivity’ tends to return quickly towards zero even when artificially supported away from zero, and that its effect on tearing-mode behaviour is not consistent with its interpretation as a resistivity. We investigate analytically the behaviour reported by Biskamp and Welter, and the behaviour we observe. We also argue that, while not meaningful as a true resistivity, the ‘anomalous-resistivity’ parameter is a useful diagnostic showing the energy balance of the System – a property we refer to as Alfvénicity – illustrating, for example, the onset of nonlinearity in the tearing process.

A simplified model is discussed that captures the basic physics of the phenomenon of oscillatory virtual cathodes in electron beams. A monoenergetic non-relativistic one-dimensional electron beam is injected through a conducting grid into a semi-infinite drift space. Attraction from image charges (and, possibly, an adverse externally applied electric field) cause particle reflection and the formation of a caustic where the charge density has an integrable singularity. The steady-state solution of the Vlasov equation describing the flow is known from numerical simulation to be unstable, but analytical demonstration of this instability has proved intractable. Here we derive an integral-delay equation describing the time-dependent evolution of the electron beam under the assumption that the caustic accelerates much more slowly than the electrons in its neighbourhood and thus at most two streams are present at each point. Under this assumption we show that the charge singularity is ~|x-xc|-½ the presence of an external field, exactly what it would be for non-interacting particles, but in the absence of applied field it is weaker, ~|x-xc|-⅓ Our methods can be used to estimate the charge singularity, and thus the collisionless ‘shock conditions’ for virtual cathodes in any geometry. The importance of delay effects for the onset of beam oscillations is demonstrated in an exactly solvable version of the model in which the interaction between the two streams is ignored. This solution, although unphysical, can provide a means for testing the performance of numerical schemes, which have difficulties in problems of this type due to the charge singularity.

It is shown that electrostatic Vlasov–Poisson perturbations that propagate parallel to the magnetic field in a planar magnetron are stable for both an isotropic and also for a particular anisotropic (Ty = 3Tx) temperature distribution. The inhomogeneity of the electron density is fully incorporated in the analysis. The proof makes use of only the dispersion relation of Trivelpiece–Gould type, without actually solving the eigenvalue equation. These results suggest, not unexpectedly, that these modes should be stable for all such anisotropic velocity distributions.

Using reductive perturbation theory and a planar waveguide geometry, the effects of higher-order nonlinearity and finite boundaries on the propagation of electron plasma and ion-acoustic KdV solitons are investigated by taking into account finite electron and ion temperatures. For an electron plasma wave, the higher-order nonlinearity is found to increase the amplitude of the soliton and slightly decrease the width of the soliton compared with that predicted by the first-order theory. For an ion-acoustic wave the higher-order-nonlinearity and finite-boundary effects give rise to a W-shaped soliton.