The statistical mechanics of a spin-polarized plasma is investigated in detail. A rigorous quantum-mechanical description is constructed in terms of a generalized matrix Wigner function. In order to ensure the manifest gauge invariance of the theory, the non-canonical variables q (position) and π (mechanical momentum) are used for the particles. The evolution equation for the phase-space Wigner function, as well as the BBGKY hierarchy for the reduced distribution functions, are derived. A general expression is found for the quantum-mechanical realization of the Lie bracket of any pair of dynamical functions. In the quasi-classical limit, the equations of evolution and the Lie bracket reduce to a simple form. Our approach is compared with the previous semi-phenomenological theory of Cowley, Kulsrud and Valeo.

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.

This paper contains an analysis of pulse shapes produced by a delta-function disturbance of the equilibrium state of a relativistic electron beam propagating through a constant-amplitude, helical magnetic wiggler field. Pulse shapes are determined by using the relativistic pinch-point techniques developed by Bers, Ram and Francis. Two pulses are produced corresponding to a convective upshifted pulse (representing the production of the high-frequency radiation desired in a free electron laser) and a downshifted pulse. The downshifted instability may be convective or absolute, depending upon the beam density and momentum spread. Parameter regimes in which the downshifted instability is convective are investigated. It is found that momentum spreads sufficiently large to suppress the absolute instability reduce the growth rate of the upshifted pulse to negligible values. Pulse shapes computed by using the Raman and Compton approximations are compared with exact pulse shapes. It is found that the Raman approximation should be applied to the downshifted regime for most systems of practical interest.

On the basis of our previous work, a rigorous kinetic equation for a spin-polarized plasma is derived in the weak-coupling quasi-classical limit. The macroscopic polarization vector is defined in a unified form for spin-½ and spin-1 particles. Using the kinetic equation, an equation for the macroscopic polarization density is derived in the form of a ‘spin-hydrodynamical equation’. The depolarization rate for the spin–orbit interaction and the spin–spin interaction is estimated. Some difficulties for the spin–spin interaction are displayed and discussed.

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.

A previously described pseudospectral three-dimensional MHD code is used to compute the dynamical behaviour of a channel of magnetofluid carrying an axial current and magnetic flux. This situation contains the essential MHD behaviour of the reversed-field-pinch (RFP). An externally imposed electric field is applied to an initially current-free magnetofluid, and drives currents that rise and eventually fluctuate about values corresponding to pinch ratios Θ ≈ 1·3, 2·2 and 4·5. A period of violent turbulence leads to an approximately force-free core, surrounded by an active MHD boundary layer that is not force-free. A steady state is reached that can apparently be sustained indefinitely (≥several hundred Alfvén transit times). The turbulence level and time variability in the steady state increase with increasing Θ. The average toroidal magnetic field at the wall reverses for the Θ ≈ 2·2 and 4·5 runs, but not for the Θ ≈ 1·3 one. Negative toroidal current filaments are observed. The Lundquist numbers are of the order of a few hundred.

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.

Using nonlinear ideal MHD equations, we analyse the structure of the convection region within a Petschek-type model for reconnection. We show how, assuming that the normal field and flow components remain small and using simple wave analysis, the structure of the reconnection layer as well as the behaviour of the tangential field and plasma parameters can be specified in terms of the external parameters in the inflow regions. Equations for the normal field and flow components and the angular width of the reconnection layer (assuming planar symmetry and a steady state) are also given in terms of the value of the electric field along the reconnection line. The model is suited to application at the earth's magnetopause and in the distant magnetotail. In particular, it lends itself to an investigation of the requirements for reconnection to occur and the general validity of MHD reconnection models in practical applications.

Explicit formulae for the refractive index describing oblique whistler-mode propagation at frequencies corresponding to ξ1 = −φ ≡ −0·924 (but |ξn| ≫ 1 when n ≠ 1), ξ0 = φ (but |ξn| ≫ 1 when n ≠ 0) and ξ0 = −ξ1 = φ (where ξn ≡ (ω − nΩ)/k‖w‖ are the arguments of the plasma dispersion function) are derived and analysed for two limiting cases of quasi-longitudinal and quasi-electrostatic propagation of the waves.

We obtain analytical expression for the interaction of obliquely propagating Bernstein waves with electrons by using the monochromatic wave approximation for quasi-linear theory in a weakly turbulent plasma. A numerical analysis is also carried out. The waves show initially strong damping and irregular amplitude oscillation, and the electron velocity distribution shows a variation corresponding to one of the waves. These are results of the energy exchange between waves and electrons. Despite the use of the monochromatic wave approximation, strongly scattering electrons with a broad velocity spread about the resonant velocity by the wave is seen.

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.

A nonlinear drift-mode equation including the effect of an electron-temperature gradient has been derived. To discuss modulational instability, we have obtained a nonlinear evolution equation for the drift mode from a third-order secularity-elimination condition using a multiple time- and space-scales technique. The effect of localized structure on the transport process has been investigated.

Particle diffusion in phase space due to the crossing of multiple cyclotron resonances in an inhomogeneous magnetic field is investigated. The influence of the inhomogeneity is most significant for small wave amplitudes, when stochastic heating is absent in a homogeneous plasma. The diffusion depends on the relationship between the wave amplitude, the inhomogeneity parameter and the angle of wave propagation. The dependence of the diffusion coefficients upon the mentioned parameters is investigated by means of computer simulations for the case of constant inhomogeneity and for two models of variable inhomogeneity: a monotonic change typical of magnetospheric conditions, and a sinusoidal change typical of tokamaks.

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.

A solar-coronal magnetic loop is rooted in the photosphere, where motions shuffle the footpoints of the field, generating currents in the corona. The dissipation of these currents provides a possible mechanism for heating the solar corona. A theory is described based on a generalization of Taylor's hypothesis, predicting that as the loop is twisted up, it relaxes towards a minimum-energy state V × B = μB. The footpoint motions inject helicity as well as energy, and the evolution is determined through a helicity-injection equation. The loop is modelled as a straight magnetic-flux tube, with twisting motions at the ends, confined by a constant external pressure at the curved surface, which is a free boundary. The problem of the loop evolution in response to given footpoint motions is solved, and an interesting example of multiple equilibria arises. The heating rate is calculated for an almost-potential loop. The model may also be regarded as representing a laboratory experiment: in particular, a simple idealization of a spheromak, with the footpoint motions replaced by an applied voltage.

The generation of steady currents by a rotating magnetic field (RMF) in a cylindrical plasma permeated by a steady azimuthal (or toroidal) magnetic field is studied analytically. Solutions are presented for the following limiting cases:

(1) high resistivity, when the penetration of the RMF and current drive are confined to a skin depth layer;

(2) low resistivity and weak toroidal field (small compared with the RMF), when the RMF fully penetrates the plasma and the toroidal current is that due to nearly synchronous rotation of the electron fluid with the RMF;

(3) low resistivity and intermediate toroidal field (comparable to the axial field associated with synchronous current), when the toroidal current is a significant fraction of its synchronous value, but large oscillating fields are generated; and

(4) strong toroidal field, when the RMF fully penetrates the plasma but current is only driven in a boundary layer at the plasma edge.

The applicability of these solutions is governed by the relative sizes of three dimensionless parameters.

Finite-amplitude circularly polarized Alfvén waves propagating along the ambient magnetic field are described by a derivative nonlinear Schrödinger-type equation. It leads to stationary, solitary and periodic solutions with phase modulations. The amplitude–width relation for these solitons is shown to be an inequality. The relevance of the results is briefly discussed for particular phenomena in the solar wind.

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 weakly nonlinear localization of obliquely modulated high-frequency electromagnetic waves in an electron-positron-ion plasma is considered. It is shown that the amplitude of the wave turns out to be a strongly dependent function of the angle between the slow modulations and the fast spatial variations and that the possibility appears of spontaneous generation of low-frequency magnetic fields. These magnetic fields are also functions of this angle and of the high-frequency wave polarization. The analysis of colinear modulation in electron-positron plasmas shows that some restriction must be made regarding the validity of previous calculations.

Measurement of the RF (radio-frequency) magnetic field about the equatorial plane of the rotamak has enabled the distribution of the oscillating currents to be derived. The time-averaged forces, produced by the interaction of these currents with the oscillating field, have been estimated. In the standard field-reversed configuration there is a radial force, which helps to confine the plasma pressure, and a toroidal force, which drives the equilibrium current. In compact tokamak configurations there is an additional poloidal force, which produces a diamagnetic current. As the toroidal field increases, penetration of the RF fields improves owing to the excitation of a whistler wave mode. The connection between the rotating magnetic field technique and fast wave current drive is explained.