A simplified analytic description is used to understand recent results of large-scale numerical simulations of resonant absorption and to disentangle the basic physics. It is shown that very efficient absorption takes place at frequencies where a discrete external kink and an Alfvén continuum mode merge into a modified external kink mode. The relation between this ‘hybrid’ mode and ‘pure’ continuum or discrete spectrum modes is discussed.

Plasma heating at the electron-cyclotron frequency by an ordinary wave propagating at right-angles to a unidirectional magnetic field is considered. The injected microwave power is assumed to be sufficiently large that the relativistic change in electron gyrofrequency during one flight through the wave beam is much greater than inverse time of flight. The electron motion in the wave field is described using the Hamiltonian formalism in the adiabatic approximation. It is shown that energy coupling from the wave to electrons is due to a bifurcation of the electron trajectory, which results in a jump in the adiabatic invariant. The probability of a bifurcational transition from one trajectory to another is calculated analytically and used for the estimation of the beam power absorbed in the plasma.

The time evolution to a steady state of the interaction of an obliquely incident P-polarized wave with an inhomogeneous collisional cold plasma is investigated. The two-dimensional numerical solutions presented show that the rate of energy absorption and the amplitude of the magnetic field do not depend on time during this evolution (after a short transient period). Using this important result, a simple analytical two-dimensional model solution for this evolution has been constructed. It is shown that this solution fuliils the energy conservation law and thus describes the transformation of wave energy into oscillatory and thermal energy during this process. An interesting analogy between this process and that of Landau damping follows from the analytic solution.

We investigate the effect of a weak ambipolar field on non-local heat transport by solving the reduced Fokker-Planck equation in the non-diffusive approximation for the electron distribution function. It turns out that for a moderately high-Z plasma with steep gradients the maximum-heat-flow expression is modified and the ensuing results compare favourably with the experimental values. However, in the gentle-gradient limit the classical Spitzer-Härm heat flux expression is unaltered.

The purpose of this paper is to derive the asymptotic solutions to a class of inhomogeneous integral equations that reduce to algebraic equations when a parameter ε goes to zero (the kernel becoming proportional to a Dirac δ function). This class includes the integral equations obtained from the system of Vlasov and Poisson equations for the Fourier transform in space and the Laplace transform in time of the electrostatic potential, when the equilibrium magnetic field is uniform and the equilibrium plasma density depends on εx, with the co-ordinate z being the direction of the magnetic field. In this case the inhomogeneous term is given by the initial conditions and possibly by sources, and the Laplace-transform variable ω is the eigenvalue parameter.

The storage of magnetic energy in many natural systems is driven by localized convection. Since the initial state can often be described as a potential field, the stress arising from subsequent magnetic twisting is characterized by vanishing net-current flow. Such a layering scheme provides the lowest global energy excess for a given local field twist. In this paper we investigate the nonlinear release of this stored energy by the resistive magnetic-tearing instability. Our aim is to discover whether the evolution of this dynamic reconnection process is modified by the finite width and restoring force of the energizing field reversal. We use a force-free magnetic-field model with the sheared reversing component varying as tanh y sech Ky. We study the unstable nonlinear evolution by a 2·5-dimensional resistive magnetohydrodynamic simulation in a slab geometry. Almost all of the perpendicular (with respect to the ignorable coordinate) stored magnetic energy is released for some cases in this model. Although the magnetic reconnection is due to resistivity, the resulting closed flux surfaces evolve to a lower-energy state, i.e. to a nearly circular one, by mostly ideal MHD. Thus an elongated flux surface drives the plasma flow, and the flow speed is comparable to the Alfvén speed. The excess or stored magnetic energy is thereby released. In general, however, these processes take place only after reconnection occurs, and thus the release of energy is limited by the reconnection rate. The evolution of our new current/field system, which is more realistic as a model of a solar flare, exhibits an energy-release rate similar to that of more conventional field configurations. This rate can be increased, however, by the effects of an assumed anomalous resistivity enhancement.

The nonlinear behaviour of azimuthally symmetric Alfvén waves propagating along the axis of a cylindrical ideally conducting compressible fluid-filled waveguide is investigated. It is shown that the nonlinear evolution of such waves is governed by the nonlinear Schrödinger equation. Modulational instability for fundamental (m = 1) radial mode is discussed for α2 = 0·1,0·2, 0·3 and different values of k. The amplitude-dependent frequency and wavenumber shifts are calculated and their variations with wavenumber are shown graphically.

The velocity-space diffusion equation describing distortion of the velocity distribution function due to resonant wave-wave scattering of electromagnetic and electrostatic waves in an unmagnetized plasma is derived from the Vlasov-Maxwell equations by perturbation theory. The conservation laws for total energy and momentum densities of waves and particles are verified, and the time evolutions of the energy and momentum densities of particles are given in terms of the nonlinear wave-wave coupling coefficient in the kinetic wave equation.

A large-amplitude whistler wave excited at the difference frequency of two high-frequency electromagnetic pump waves is shown to decay parametrically into a lower-hybrid wave (LHW) and a low-frequency ion–Bernstein wave (IBW) in a collisionless magnetized multi-ion-species plasma,. A nonlinear dispersion relation describing this parametric interaction process is derived. The low-frequency ponderomotive force along the direction of the external magnetic field leads to the dominant coupling. Possible applications to ion heating in the ionosphere, in the earth's magnetosphere and in laboratory plasmas are discussed.

The permittivity tensor Є¸(K, ω) of an electron–ion plasma with paramagnetic atoms as neutral component (a paramagnetic plasma) is obtained. Based on this tensor, new types of slow electromagnetic waves in the paramagnetic plasma are predicted.