This paper presents a theoretical model of a plasma column sustained by an electromagnetic surface wave in the dipolar (m =1) mode for two different gas-discharge regimes: free-fall/diffusion and recombination respectively. The dispersion characteristics of the wave and the axial profiles of the plasma density, wave power, wavenumber and wave-field components for a given regime are specified by one numerical parameter σ = ωR/C, where ω is the angular wave frequency, R the plasma radius and c the speed of light, irrespective of the gas nature and pressure. It is established that there exists a ‘critical’ value of this parameter, σcr = 0·3726, below which a plasma is not likely to be sustained. A comparison between the axial structures of plasma columns sustained by electromagnetic waves in the dipolar and azimuthally symmetric modes is made. The model is in agreement with the available experimental results.

An investigation is made of wave generation and the radiation of third harmonics by an electrostatic wave in a narrow inhomogeneous layer of a warm plasma. The amplitudes of the third-harmonic wave are calculated. It is found that they depend both on the nonlinear interaction of the initial waves and on the interaction of second harmonics with the initial wave. The generation of third harmonics by interaction of the initial waves is a four-wave process, i.e. a higher-order nonlinearity.

The coupling of hydromagnetic Alfvén waves is studied numerically in a dipolc-field model of the magnetosphere. The two coupled hydromagnetic equations derived by Radoski are solved as an implicit boundary-value problem, namely the boundary conditions at the magnetopause are determined self-consistently. Thus the calculated wave-field distribution inside the magnetosphere can match all known linear characteristic features of the stormtime Pc5 waves observed on 14/15 November 1979 from satellites. A set of proper boundary conditions is found, excellent agreement between the numerical results and observations is demonstrated. Based on the very limited spatial coverage (L ≈ 6·6 and within a latitudinal region ( −10°, 10°)), of the data provided by the satellites, the theoretical model can successfully reconstruct the global micropulsations in the magnetosphere and identify the source regions of hydromagnetic waves.

The properties of electromagnetic wave propagation in a uniformly densitymodulated plasma are studied, starting from a unidimensional scalar wave (Hill) equation for the wave electric field. Introduction of the formalism of the spatial propagator Q(z2, z1), from the point z1 to the point z2 allows reduction of the problem to determination of the propagator relevant to a single plasma layer that constitutes the entire periodic structure. The transmission coefficient of a single layer can be computed for any kind of density profile by means of the Magnus approximation, satisfying energy flux conservation at each order in the relevant expansion. The appearance of ‘forbidden zones’ in parameter space leads to the possibility that the incident electromagnetic wave can be partially or completely reflected if a sufficient number of periods are present. The explicit computation of the transmission coefficient for a series of n successive layers confirms this effect as the result of a ‘resonant’ interaction of the incident wave and the ‘periodicity’ of the medium.

A self-consistent stability analysis of relativistic non-neutral cylindrical electron flows propagating along applied magnetic fields is considered within the framework of the macroscopic cold-fluid-Maxwell equations. The full influence of the equilibrium self-electric and self-magnetic fields is retained. Then the E x B drift (E being the radial electric field created by the uncompensated charge) generates a radial shear, vz(r) and v0(r). The effect of the shear in the axial velocity component, as reflected in the relative axial motion of adjacent concentric layers of beam particles, is investigated. The self-consistent treatment of the problem thus shows that the equilibrium state considered in this paper is unstable.

Nonlinear modulational instability and the evolution of a pulse that is initially non-solitonic for Langmuir waves described by the Zakharov equations are considered. The average Lagrangian method has been used to derive the nonlinear dispersion relation for Stokes waves. It is found that the region of instability increases with the amplitude of the perturbed Langmuir field. The propagation of the pulse is studied with the help of the Rayleigh-Ritz optimization method. It is noted that the width of the pulse oscillates rapidly for high initial pulse velocity.

Equations are derived for the kinetic-theory analysis of small-amplitude Alfvén waves in cylindrical plasmas carrying force-free currents. The equations, which include ion Larmor-radius effects to second order, are applicable to reversed-field pinches as well as to tokamaks. Fourier mode amplitudes are derived for model antennas with radial current feeds, and a quantitative analysis is made of the antenna resistance and the wave density fields in a small tokamak during Alfvén-wave heating. The effect of the plasma current on the wave thermal energy flux is discussed.

The possibility of a new set of thermonuclear cone instabilities in tokamaks is demonstrated. These instabilities are caused by an inherent anisotropy existing in the alpha-particle velocity distribution function owing to the finite width of the particle orbits in combination with a spatially varying particle source. The conditions for the excitation of shear Alfvén waves by well-trapped alpha particles are studied.

Subgrid-scale closures for magnetohydodynamic (MHD) turbulence are examined using the filtering technique. From the similarities between incompressible MHD turbulence and its hydrodynamic counterpart, as well as ideas from dynamo theory, a subgrid model is constructed from the large-eddy simulation (LES) of MHD turbulence. This model should find applicability in treating LES of the reversed-field pinch.

Computer simulations are used to investigate the basic three-dimensional structure of the fast reconnection mechanism spontaneously developing from a long current sheet. It is shown that if three-dimensional effects (∂sol;∂z ≠ 0) are not so strong, a locally enhanced resistivity results in current-sheet thinning, and a fast reconnection process, involving switch-off shocks, is eventually set up in a region limited in the z direction. The fast reconnection process near the z = 0 plane becomes quasi-steady and two-dimensional (∂/∂z = 0), so that the well-known Petschek mechanism is fully applicable. Distinct plasma rarefaction occurs inside the fast reconnection region, so that fast-mode expansion may propagate in the z direction, and the resulting inflow velocity uz takes the magnetic field into the fast reconnection region and contracts the latter. The global current system undergoes drastic changes during the fast-reconnection development. The current flow, initially directed in the z direction, first converges towards the neutral line, and is then largely deflected away from this line in the inner reconnection region.

The effect of a sheared equilibrium mass flow on the resistive tearing mode is studied numerically by calculating Δ′. Both stabilizing and destabilizing effects are found, depending on the velocity and magnetic field profiles. Specifically, when q0 ≈ 1, the flow is strongly stabilizing for centrally peaked current profiles, whereas the flow has a strongly destabilizing effect for flatter current profiles. While the extreme effects are more pronounced for larger flows, a smaller flow may have more influence on marginal stability. The case where the flow speed becomes comparable to the Alfvén speed is also examined. It is found that this may lead to the equations being singular at points other than a rational surface, drastically changing the behaviour of the mode.

Nonlinear propagation of acoustic-type waves in a partially ionized three-component collisional plasma consisting of electrons, ions and neutral particles is investigated. For bidirectional propagation, we show that the small- but finite-amplitude waves are governed by the Boussinesq equation, which for unidirectional propagation near the acoustic speed reduces to the usual Korteweg de Vries equation. For large-amplitude waves, we demonstrate that the relevant fluid equations are integrable in a stationary frame, and we explicitly obtain the parameter values for the existence of finite-amplitude solutions. In both cases, we take into account the different temperatures of the individual species. The relevance of the results to the earth's ionospheric plasma in the lower altitude ranges is pointed out.