It is shown that rotation of a periodic column of magnetohydrodynamic fluid can be stabilized against current-driven instabilities by rotation. The rotation is considered as resulting from a slight departure from overall charge neutrality, and is braked by wall friction (loss of angular momentum to the cylinder wall). Both effects are modelled phenomenologically in the equation of motion, and the emphasis is on their bulk dynamic effects rather their microscopic kinetic theory origins. Much as rotation is known to stabilize a Navier—Stokes fluid against transverse displacements, it is shown that sufficient rotation will suppress the helical vortices and helical deformations of the current channel that are known to result when the axial current in the column exceeds its stability threshold.

We define a new generalized symmetrical permittivity tensor of rank two, χαβ in order to characterize the inductions in Maxwell's formalism for an isotropic relativistic plasma. We then show that only the Lorentz gauge allows one to write the field potentials with a propagator inversely proportional to this tensor. In this sense, we may say that the Lorentz gauge is the only one suitable for Maxwell's formalism.

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.

A numerical technique, alternative to Grad's well-known ADM method has been proposed to deal with the slow adiabatic evolution of a toroidal plasma with flow. The equilibrium problem with prescribed adiabatic constraints may be solved by simultaneous calculations of flux surface geometry and original profile functions. Implications for the problem of bifurcation due to nonlinearity of the governing equations are discussed. In the case of field-aligned sub-Alfvénic flow the system is in the second elliptic regime if β <A2/(1 – A2) at the magnetic axis, where A is the Mach Alfvén number of the flow. Super-Alfvénic flows do not satisfy the local firehose stability criterion.

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 paper explores the interrelationship between the generalized Grad-Shafranov equation, or trans-field force balance equation, for steady MHD flows with an ingnorable co-ordinate, and work by Imai on field-aligned MHD flows. The development of Imai, assumes at the outset that the fluid velocity V is parallel to the magnetic field B, and exploits an analogy with steady compressible irrotational flow in ordinary fluid dynamics. In Imai's analysis the magnetic induction B is written in the form B = σb, where , and MA is the appropriate Alfvén Mach number. Gauss' law Δ. B = Δ. (σb) = 0 then plays a role analogous to the mass continuity equation in ordinary fluid dynamics, where σ corresponds to the density of the pseudo-fluid. Imai's analysis leads to a transonic equation for the field potential φ defined by b = Δφ. For a restricted class of flows the trans-field force balance equation formulation also leads to the transonic potential flow equation, but the assumption of an ignorable co-ordinate allows for the possibility of non-field-aligned flows with non-zero electric field potential ΦE The characteristics of the generalized Grad—Shafranov equation are related to the Mach cone and the group velocity surface for linear magnetosonic waves. The corresponding forms of the characteristics for the potential transonic flow equation in the (x, y) plane and in the (bx, by) hodograph plane are discussed. Sample solutions of the potential transonic flow equation for radial, helical and spiral flows are obtained by means of the hodograph transformation, and are used to illustrate the differences between hyperbolic and elliptic flows. The potential transonic flow equation is obtained for the case of an ignorable co-ordinate z of a rectangular Cartesian co-ordinate system (x, y, z), and also for the case of flows with an ignorable co-ordinate of a spherical polar co-ordinate system (r, θ, ω). Astrophysical applications are briefly discussed.

The reflection and transmission coefficients for an electromagnetic beam propagating in an inhomogeneous plasma are calculated analytically using the Magnus approximation in different physical configurations. The theoretical predictions for such coefficients are expressed in simple analytical form, and are compared with the exact results obtained by numerical solution of the wave propagation equations, using the Berreman 4 × 4 matrix method. It is shown that the theoretical approach is able to reproduce the correct results for reflection and transmission coefficients over a wide range of physical parameters. The accuracy of the theoretical analysis, at different orders of approximation, is also discussed.

An advanced two-chamber model for the main plasma scrape-off and the divertor chamber of a tokamak is constructed. It is studied in the framework of catastrophe theory. The model shows bifurcations in the topology of the equilibrium surfaces. The results are in qualitative agreement with some of the experimentally observed features of the H-mode transition.

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.

Helicon waves have been used for efficiently coupling radio-frequency power to plasmas, and are studied for their potential application for low-frequency current drive in tokamks. In this paper the electromagnetic field components and the dispersion relation for azimuthally independent helicon-wave oscillations in a cylindrical plasma column are derived. The coupling of transverse electric TE and transverse magnetic TM modes associated with these oscillations is discussed. The effect of the collisional damping on determining the nature of the TM mode (either surface wave or body wave) is analysed.

We derive the dielectric tensor of a hot plasma by including the smallgyroradius corrections up to the first harmonic (ω ≈ 2ωcα). We show that these corrections introduce radial wavenumbers associated with transverse electromagnetic modes (TEM). The special case of a cylindrical plasma column is discussed for a hydrogen plasma at the ion-cyclotron frequency and for an electron plasma at the electron-cyclotron frequency and its first harmonic.