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.

In this paper the transverse and longitudinal dielectric tensor elements are evaluated for radio-frequency waves in an axisymmetric tokamak with circular magnetic surfaces, without the smallness assumption of the inverse aspect ratio and poloidal magnetic field. A collisionless plasma model is considered. The Vlasov equation is solved separately for untrapped and trapped particles as a boundary-value problem. The cyclotron and bounce resonances are accounted. The coordinate system with the 'straight' magnetic field lines was used. The separate contributions of untrapped and trapped particles to the dielectric tensor components are expressed by the summation of bounce resonant terms, which include the double integration in velocity space, the resonant denominators, the phase coefficients, the standard elementary and elliptic functions. The permittivity elements presented in the paper are suitable to analyse the spatial structure of the electromagnetic fields and their interaction with charged particles (e.g. during the plasma heating and current drive generation) in the frequency range of Alfvén, fast magnetosonic, ion-cyclotron and lower hybrid waves, for both the low and large aspect ratio tokamaks.

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.

The contributions of untrapped and three groups of trapped particles to the longitudinal permittivity of a tokamak plasma with elliptic magnetic surfaces are derived for radio frequency waves in a wide range of frequencies, mode number, and plasma parameters. The analytical expressions of the longitudinal permittivity elements are obtained by using the kinetic theory of dielectric tensor elements, where the drift kinetic equation is solved as a boundary-value problem. Considered is a collisionless plasma model of an axisymmetric tokamak with small ellipticity and a large aspect ratio. The limit to the known results for toroidal plasmas with the circular cross-section of the magnetic surfaces is shown.