The paper presents a paraxial-ray theory of self-defocusing of obliquely propagating Trivelpiece-Gould (TG) modes in a homogeneous plasma. The TG mode with Gaussian distribution of intensity, in a direction perpendicular to its phase velocity, creates a ponderomotive force on electrons. The electrons are redistributed through ambipolar diffusion. The redistributed electrons are responsible for defocusing of the TG mode. The importance of our study is pointed out.

We consider effects of inhomogeneity on the absorption of high-frequency electromagnetic waves, propagating at arbitrary angles relative to the magnetic field, by current-carrying plasmas. An inhomogeneous current is assumed to be immersed in an otherwise homogeneous background, and the absorption of fundamental electron-cyclotron waves is discussed, with emphasis on the dependence of the inhomogeneity effect on wave frequency and angle of propagation.

It is shown that, although the mathematical analysis of the Alfvén-wave equation does not show any variation at non-zero or zero singular points, the role of surface waves in the physical mechanism of resonant absorption of Alfvén waves is very different at these points. This difference becomes even greater when resistivity is taken into account. At the neutral point the zero-frequency surface waves that are symmetric surface modes of the structured neutral layer couple to the tearing mode instability of the layer. The importance of this study for the energy balance in tearing modes and the association of surface waves with driven magnetic reconnection is also pointed out.

The hydromagnetic Kelvin–Helmholtz instability is relevant in many complex situations in astrophysical and laboratory plasmas. Many cases of interest are very complicated, since they involve the combined role of velocity shear, of density and magnetic field stratification, and of various geometries in compressible plasmas. In the present work we continue investigating the influence of various physical and geometrical parameters of the plasma on the Kelvin–Helmholtz modes. We use the general dispersion relation for the ideal compressible MHD modes localized near a velocity discontinuity between two uniform plasmas. We study analytically the existence and properties of the modes and their stability, for a velocity jump combined with a density jump, and for any relative orientation of B, u and k (B is continuous). Stability is analysed by means of a general procedure that allows discussion of any configuration and all kinds of perturbations. The boundaries between modes of different kinds are discussed. In contrast to the case of uniform density, for a density jump there are no monotonically unstable modes, only overstabilities. The unstable modes belong to two types. Those with the largest growth rates tend to monotonically unstable modes in the limit of uniform density, and are related to the torsional Alfvén mode. The other overstable modes have no analogue among the purely incompressible modes, and occur in a range of U that is stable in the incompressible limit. We derive bounds for the growth rate of the instability. The present results may serve as a guide to interpret results in more complicated and realistic situations as those occurring in laboratory and natural plasmas.

Oscillations in inhomogeneous cold plasmas or inhomogeneous magnetofluids are interpreted in terms of the dynamics of their spectra in wavenumber space. By Fourier transforming the basic integro-differential equation of the problem, a generalized wave equation in wavenumber space is derived, thus converting the oscillation and phase-mixing processes in the original χ space into processes of dispersive propagation and scattering of the spectrum in wavenumber space. The Barston singular continuum eigenmodes correspond to stationary scattering states of a monochromatic wave in wavenumber space, whereas the damping phenomena in χ space correspond to transient ‘leaking’ phenomena accompanying scattering and dispersive propagation of a wave packet in wavenumber space.

The process of phase mixing in inhomogeneous MHD or cold plasmas is interpreted as one of energy propagation in discrete Fourier space. Three instructive scenarios are examined: (i) an isolated inhomogeneity with zero boundary conditions; (ii) a periodic inhomogeneity; and (iii) a monotonic inhomogeneity sandwiched between two semi-infinite uniform regions. In each case the coefficients of the associated wave equation in Fourier space for an appropriately chosen dependent variable are very nearly constant almost everywhere, so the propagation is like that of a free unreflected wave. An exception may arise in the coupling of the lowest modes, which can be highly reflective. It is argued that Fourier space is the simplest and most natural context in which to discuss the development of fine-scale oscillations.

In this paper the characteristics for a single- and a bi-ion plasma in the presence of Alfvén waves are given. In the single-ion case, the analysis is extended to the situation where Alfvén waves saturate and dissipatively heat the plasma. When there is no dissipation, there are three sound waves and one entropy wave in the single-ion plasma. Each sound wave is associated with two Riemann invariants relating the changes in density and wave pressure to changes in the flow. In the case when the Alfvén waves saturate and heat the plasma, there are two sound waves and one modified entropy sound wave. Each wave is associated with two Riemann invariants relating changes in density and entropy to changes in the flow. The analysis for the bi-ion plasma is simplified to very sub-Alfvénic flows. In this case the Alfvén waves behave like another plasma component, and both the electric and Alfvén wave forces have the same structure. The system possesses two entropy waves and four sound waves. Each sound wave is associated with two Riemann invariants relating changes in density and flow velocity along the characteristic curves.

Transport coefficients for electric current and heat flux have been calculated for a two-temperature equal-mass plasma for several values of the temperature ratio R in the range 1 < R ≤ 100. Transport coefficients have been obtained using the linearized Fokker—Planck equations.

The influence of absorption of wave energy in regions of local plasma resonances in inhomogeneous (in the transverse direction) plasmas on the axial structure of discharges sustained by surface waves is studied analytically. The two regimes of charged-particle loss, namely diffusion- and recombinationcontrolled regimes, are considered. First, to extract the basic features of the phenomena, the discharge is modelled by a slab configuration and the case of slow surface-wave propagation is investigated. It is shown that it is resonant absorption that determines the properties of the discharge in the region towards its end. In the case of a cylindrical waveguide, which is the real configuration in experiments, the influence of the mechanism of resonant absorption is studied in both regions of fast and slow surface-wave propagation. With respect to the discharge behaviour, these cases correspond respectively to the regions at the beginning of the discharge close to the surface-wave launcher and at the discharge end.

The fundamental process of acceleration of charged particles by large-amplitude electromagnetic waves is investigated. Exact analytical solutions can be derived from the nonlinear equations that govern the motion of charged particles in wave fields. It is found that circularly polarized electromagnetic waves can act on the charged particles via α d.c. Lorentz force imposed by the wave fields. This process can effectively energize charged particles that may initially have low energies.