The permittivity tensor and bounce resonance effects on wave dissipation in toroidal plasmas

The asymptotic solution of Vlasov's equation in the drift approximation for a toroidal plasma geometry with circular magnetic surfaces is presented. The method of solution introduces Jacobi functions as variables, making it possible to obtain results in a relatively simple manner. The analytic evaluation of the parallel components of the dielectric permittivity tensor_3j is shown and the resulting strong influence of the bounce resonance of untrapped electrons on the wave dissipation is discussed. Additionally, a numerical calculation of₃₃, together with a comparison between the toroidal and the cylindrical (Landau damping) results, are presented.The authors wish to thank Katherina von Bülow, from the Mathematical Institute of UERJ, for fruitful comments and careful reading of this paper, and CNPq of Brazil for financial support.