Parallel permittivity elements for radio frequency waves in elongated D-shaped tokamaks

Abstract

Parallel permittivity elements are derived for radio-frequency waves in an axisymmetric tokamak with D-shaped transverse cross-sections of the magnetic surfaces under arbitrary aspect ratio, arbitrary elongation and small triangularity. The bounce resonances are taken into account for untrapped (passing or circulating) and three groups of trapped particles. The corresponding limits for the simpler plasma models are considered. Our dielectric characteristics are suitable to estimate the wave dissipation by electron Landau damping during the plasma heating and current drive generation in the frequency range of Alfvén and fast magnetosonic waves, for both the large and low aspect ratio tokamaks with circular, elliptic and D-shaped magnetic surfaces. The dissipated wave power is expressed by the summation of terms including the imaginary parts of both the diagonal and non-diagonal elements of the parallel permittivity.