In this paper, a generalized kinetic dispersion equation that supports various hydromagnetic waves and instabilities is derived. The general dispersion equation is derived under the usual assumption of hydromagnetic perturbations [i.e., 1 w 1 2 Q #, and (kzvA/ai) ' dpll i, where fii and VA are the ion gyrofrequency and Alfven speed, respectively, and PII i is the parallel ion beta], but for arbitrary values of the quantity ili= (k, pl i)'/2= (k, vA/fii)2 PJ. i/2 that appears in the dielectric tensor. Here, pL i refers to the mean ion gyroradius, and fil i is the perpendicular ion beta. Otherwise, the dispersion equation is fairly general with no additional approximation, such as ignoring certain off-diagonal dielectric tensor elements (Which is usually done in the literature) employed. In the subsequent numerical analysis, special attention is paid to the fire-hose instability in a high beta plasma. The numerical results reveal that the conventional treatment of the fire-hose instability (i.e., taking zero ion gyroradius limit at the outset) is not adequate, and that the effect of finite ion gyroradius results in a significant enhancement of the growth rate over a large range of wave numbers.

The local magnetic field is shown to oscillate at its Alfvén resonance frequency(ies) in response to a wide band source whose frequency range covers the resonance frequency(ies). The proposed mechanism explains certain observations of magnetic pulsations where the frequency is found to vary continuously as a function of latitude for a given event.

The relaxation of rarefied gases of particles with the power-law interaction potentials Uϭ␣/r s , where 1 рsϽ4, is considered. The formation and evolution of the distribution function tails are investigated on the basis of the one-dimensional kinetic Landau-Fokker-Planck equation. For long times, the constructed asymptotic solutions have a propagating-wave appearance in the high velocity region. The analytical solutions are expressed explicitly in terms of the error function. The analytical consideration is accomplished by numerical calculations. The obtained analytical results are in a good agreement with the numerical simulation results.

Analytical expressions for the wave permeability tensor are derived for a twodimensional plasma model of a straight axisymmetric mirror trap. The dielectric tensor components are found through a solution of the Vlasov equation, using the theory of Jacobian elliptic functions. The bounce-resonance effect of trapped particles on wave dissipation is analysed. It is shown that collisionless wave dissipation in the plasma with a mirror-trap configuration of a magnetic field can differ essentially from Landau damping in a plasma with straight uniform magnetic field lines. This dielectric tensor can be used in numerical calculations of Alfvén and ion cyclotron heating of mirror-trap plasmas.

The effect of radio frequency fields on a plasma rotation in the edge (collisional) region of slightly rippled tokamaks is considered. The expressions for poloidal and toroidal velocities and for quasistationary radial electric fields are obtained as a function of absorbed rf power. The estimations of these quantities for the Phaedrus-T tokamak [N. Hershkovitz et al., 15th International Atomic Energy Agency Conference on Plasma Physics and Controlled Fusion, Seville, 1994 (International Atomic Energy Agency, Vienna, in press)] are also presented. It is shown that Alfvén waves can strongly modify the rotation velocities and radial electric fields in collisional regions of tokamak plasmas.