Radio-frequency wave dissipation by electron Landau damping in a low aspect ratio D-shaped tokamak

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 drift-kinetic equation is solved separately for untrapped (passing or circulating) and four groups of the trapped particles as a boundary-value problem. Periodicity of the perturbed distribution function over the poloidal angle is used for the untrapped particles, whereas the continuity of the perturbed distribution function at the reflection points (where the parallel velocity is equal to zero) is used for the trapped particles. The bounce resonances are taken into account. A coordinate system with the 'straight' magnetic field lines is used. The dielectric permittivity elements, evaluated in the paper, are suitable to estimate the wave dissipation by electron Landau damping (e.g. 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. Contributions of the trapped and untrapped electrons to the imaginary part of the parallel permittivity elements have been estimated numerically for typical low aspect ratio tokamak parameters.