A new expression for the second-order dielectric function є(2) (K1,ω1, K2,ω2) is derived from the Vlasov–Poisson equations. The formula is also suitable for the calculation of this quantity in general situations when it is essential to use kinetic theory and when the wave vectors K1 and K2 have arbitrary directions with respect to each other as well as to the external magnetic field. We also consider two earlier formulae for this response function and discuss advantages and disadvantages of the different expressions.

We investigate ion waves in a plasma in the presence of massive charged dust particles, a common space-plasma component now known to exist also in planetary rings and comets. We derive an equation describing low-frequency electrostatic perturbations on a non-homogeneous background, where the inhomogeneity is due to a distribution of charged grains, each surrounded by an equilibrium statistical distribution of plasma particles. This model is then applied to propose an interpretation of some recent data from the Vega and Giotto space probes to Halley's comet the increase of the low-frequency electrostatic noise (ion-acoustic waves) in the region of increased dust.

Electromagnetic fluctuations, induced by energetic charged particles, are calculated using correlation techniques for a uniform magnetized plasma. Power emission in the ion-cyclotron range of frequencies (ICRF) is calculated for a specific model of velocity distribution function. The emissive spectra are distinct from that of the black-body radiation and have features that are consistent with experimental observation.

This paper aims at determining the validity limits of a linear analysis for a resistive instability. To this purpose, the effects of mode-coupling on the magnetic field structure are investigated in the reconnecting layer. Given an equilibrium magnetic field and a perturbation field, the conditions are found under which the equations for the magnetic field lines of force can be expressed in Hamiltonian form. These conditions can be fulfilled by a resistive instability. Consequently, in a simple equilibrium magnetic field the resistive eigenmodes have been analytically derived. This result is used to give an explicit expression of the Hamiltonian for field-line equations when two resistive eigenmodes are taken into account. The analytical form of the resulting Hamiltonian coincides with the so-called paradigm Hamiltonian (1·5 degrees of freedom) for which the Escande–Doveil renormalization procedure leads to an explicit expression for the global stochasticity threshold. Thus it can be shown that any pair of modes – in a suitable range of parameters – yields spatial stochasticity of magnetic field lines when the perturbation amplitude is still very low. Hence a limit of validity of the linear theory can be found. The linear phase of the resistive instability turns out to be relevant only to describe the onset of the instability itself.

The perturbative Chapman-Enskog procedure for solving Boltzmann's equation, holding when f1 ≪ f0 (f = f0 + f1 + …), is replaced by a method that is free of such a limitation. This work represents an extension to the case of strongly anisotropic plasma systems and the spherical geometry of that of Campbell (1984, 1986). The solution obtained here is expressed in terms of prescribed ratios of mean free path for collisions, as well as electric and gravitational fields, to the temperature- and density-gradient lengths. This solution is also used to discuss the limitation of the conduction transport coefficients in electron plasmas.

Lower oblique resonance cones excited by a harmonic point source in a drifting plasma are studied in different approximations. It is shown that the electromagnetic correction to the dispersion, giving finite wave velocities, is necessary for a correct description of the drift effects.

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.

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.

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.

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.

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.

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.

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.

The dielectric properties of Maxwellian plasmas are approximated using both Padé approximants to the dispersion function and direct approximation of the distribution. Physical constraints on permissible approximations are discussed, and it is found that some previously published results can lead to predictions of qualitatively incorrect wave properties, including unphysical negative damping. Approximate dispersion functions for Maxwellian distributions are given explicitly, and some of the effects of these approximations on the resulting dispersion are discussed. The approximations discussed here are of use both in analytic work and in accelerating large-scale numerical computations.

The nonlinear dynamics of a low-frequency electrostatic dissipative inhomogeneous plasma in an external magnetic field is studied for conditions above the critical point. The diffusion flux and the saturation level are self-consistently calculated from first principles, i.e. from the Braginskii equation.

Despite extensive theoretical investigation of the problem of ion-acoustic solitary waves in an inhomogeneous plasma, a fully satisfactory account has so far not been given. This paper provides a critical account of the shortcomings of the previous theoretical approaches and then describes a fully self-consistent treatment of the problem.

From the analysis of the symmetries of the derivative nonlinear Schrödinger (DNLS) equation, we obtain a new constant of motion, which may be formally considered as a charge and which is related to the helicity of the physical System. From comparison of these symmetries and those of the soliton solutions, we draw conclusions about the number of constraints that must be imposed and the way a Liapunov functional must be constructed in order to study the solitons' stability. We also examine the relationship between the stability with respect to form and the symmetries that are broken by the soliton solutions. We complete the analysis with some numerical simulations: we solve the DNLS equation taking a slightly perturbed soliton as an initial condition and study its temporal evolution, finding that, as expected, they are stable with respect to form.

A minor correction, having no major influence on our results, is reported here. The coefficients in the equations of state (16) and (17) should read

The set of equations (13)–(20) now comprise the correct, linearized and Fourierdecomposed double adiabatic equations in cylindrical geometry. In addition, there is a printing error in (15): a factor bz should multiply the last term of the left-hand side. Our results are only slightly modified, and the discussion remains unchanged. We wish, however, to point out that the correct stability criterion for isotropic pressure, (26), should be

This is the double adiabatic counterpart to the m ╪ 0 Kadomtsev criterion of ideal MHD.