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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.