A consistent drift-kinetic theory is developed for the interaction of resonant particles in a relativistic magnetized plasma with HF (high-frequency) wave packets for arbitrary ratio of the gyroradius to the wavelength. Gyrokinetic equations for the plasma particles are obtained for Čerenkov and cyclotron resonances as well as for those at the harmonics of the gyrofrequency, the half-integer cyclotron resonances and those with the beats of two wave packets. The periodic parts of the distribution function for the relativistic non-uniform and non-stationary plasma are calculated.

The problem of ion cyclotron wave structure in EBT has been analyzed using the smallness of the inverse aspect ratio ε = a/R0 and of the inverse cavity number ε' = 1/N. The procedure is to expand in these two parameters, reducing the complete toroidal problem to a system of equations to be solved in sequence. To second order in ε and ε', this system contains two ordinary differential equations of second order and one partial differential equation with periodic coefficients in a magnetically adapted system of co-ordinates. The smallness of the mean bumpiness parameter εB reduces the problem to a single second-order differential equation which, for a parabolic density profile, is a Whittaker equation. The EM wave structure corresponds to a simple mode with only a few wavelengths across the plasma radius, permitting multi-harmonic ion cyclotron heating with interesting efficiency, as observed in experiments.

Polarization of whistler-mode waves in a hot anisotropic plasma is considered in the two limiting cases of quasi-longitudinal and quasi-electrostatic propagation. It is pointed out that electron thermal motion never influences the phase of the propagating waves; the polarization of whistler-mode waves propagating along the magnetic field is totally independent of electron thermal motion. The deformation of polarization (in both electric and magnetic fields), of obliquely propagating whistler-mode waves could be, in principle, observed in magnetospheric conditions and thus could be used to estimate electron temperature and anisotropy. This deformation seems to be especially pronounced for the electric field polarization of quasi-electrostatic waves.

MHD theory with the Hall term has been used to analyse the Alfvén resonance heating of cylindrical plasmas using axisymmetric waves excited by an antenna. An analytic expression for the antenna impedance has been derived for a simple plasma model and this is used to help interpret the computational results for small, medium and large plasmas. Compressional wave eigenmodes give large antenna resistances; however, the energy is deposited near the plasma surface. At a frequency just above each eigenfrequency, the Alfvén resonance damping is zero. Below the first eigenfrequency, the energy can be deposited near the plasma centre; however, the antenna resistance is fairly low except for medium size plasmas with a nearly constant central density. Ion cyclotron wave resonances are briefly discussed. Some general concepts relevant to the penetration of wave energy into large plasmas are presented.

A systematic and comprehensive study of linear and nonlinear analyses of the propagation of low-frequency modes in two-ion-species plasma has been made. Two new non-propagating modes on different ion time-scales are reported. These modes are excited by nonlinear coupling with the external pump. The threshold field of the pump and the growth rates of the various modes above the threshold are also calculated. A comparison of the results with those of single-ion-species plasma shows that the non-propagating mode on the fast ion time-scale excites the oscillating two-stream instability. In addition, the mode corresponding to ωr = 0 on the slow ion time-scale becomes important nonlinearly and excites a new type of instability. It is interesting to note that the threshold electric fields excitation of these instabilities are the same.

Resistive normal-mode solutions of the MHD equations are found numerically in a smooth, non-uniform, magnetic field. The (α, S) boundary within which normal-mode solutions exist is explicitly computed, where α is the normalized wavenumber and Sthe Lundquist number. As an extension of our previous analytic results (Mok & Einaudi 1985), the damping rate of these modes is computed to a higher accuracy, and is found to have an a + bS−1/3 dependence, where a and b are independent of S.

By numerical simulations, the dynamical behaviour of the electrons in one-dimensional double layers is studied. The simulation results show that at least one third of the electrons emitted at the low-potential boundary of the simulation system are reflected back before passing through the double layers. Such reflexion is due to (i) quasi-linear or nonlinear scattering by plasma oscillations and (ii) ambipolar potentials observed around the potential front of the localized double layer. The whole temporal evolution of the localized double layers are also presented. In particular, we attempt to explain the steepening and collapsing of the localized double layers in terms of the formula for the double-layer thickness.

Whitham's averaged Lagrangian principle, and the Low Lagrangian are used to derive the averaged Lagrangian for slowly varying electrostatic and electromagnetic wave packets in dispersive Vlasov plasmas. From the averaged Lagrangian, the stress tensor and wave-momentum densities are derived for the total wave-particle system. For a specific division of these total quantities into wave and background parts, time-dependent ponderomotive forces in Vlasov plasmas are derived from a momentum conservation theorem. We also show that the wave-induced magnetization current can be derived by the averaged Lagrangian method.

It is shown that the combined effect of resistivity and thermal conductivity leads to convection in a cylindrical current-carrying plasma, under the action of a shearless magnetic field. In contrast to the case of part 1, these modes occur for large wavenumbers and Bθ≫ Bz The conditions, however, are the same as before. From this fact it is then conjectured that convection takes place for any wavenumber, determined only by the actual value of B0/Bz.

A new kind of surface oscillation, which can exist when the usual surface waves are absent because of resonant absorption, has been studied for a non-uniform plasma slab. Special attention is paid to the influence of the boundaries on the eigenfrequency spectrum.

A closed set of CGL equations, modified to include heat flux correction, is used to study the firehose and mirror instabilities in a rarefied plasma. A significant feature which has been noticed is that some of the terms contributed by the higher-order moments are of the same order as the terms in the unmodified CGL equations. We study the effect on the firehose and mirror instabilities of those terms which persist in the limit of vanishing heat flux vector. It is found that these terms lead to a new criterion for mirror instability. The criterion for hose instability, however, remains unaffected.

A relativistic treatment of the plasma dispersion functions and of the dielectric tensor for electron cyclotron electromagnetic waves is given for non-thermal plasmas where the electron distribution function can be represented as a combination of Maxwellians with arbitrary drifts along the magnetic field.

A new stellarator ripple-transport mechanism is predicted at the low collision frequencies characteristic of ions in a reactor plasma. A heuristic argument is used to derive an approximate diffusion coefficient whose magnitude, scaling and range of applicability agree well with the results of Monte Carlo calculations. The proposed diffusion coefficient is independent of collision frequency within its range of validity, which encompasses the parameters of most ions in a reactor. Its magnitude is smaller than previous estimates for the diffusion coefficient in this range, but larger than the diffusion coefficients in all other low-collision-frequency regimes. An explanation of the form of the diffusion coefficient is given in terms of analytic theory of ripple transport.