Dielectric characteristics of axisymmetric low aspect ratio tokamak plasmas

In this paper the transverse and longitudinal dielectric tensor elements ar e evaluated for radio-frequency waves in an axisymmetric tokamak with circu lar magnetic surfaces, without the smallness assumption of the inverse aspe ct ratio and poloidal magnetic field. A collisionless plasma model is consi dered. The Vlasov equation is solved separately for untrapped and trapped p articles as a boundary-value problem. The cyclotron and bounce resonances a re accounted. The coordinate system with the 'straight' magnetic field line s was used. The separate contributions of untrapped and trapped particles t o the dielectric tensor components are expressed by the summation of bounce resonant terms, which include the double integration in velocity space, th e resonant denominators, the phase coefficients, the standard elementary an d 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 a nd current drive generation) in the frequency range of Alfven, fast magneto sonic, ion-cyclotron and lower hybrid waves, for both the low and large asp ect ratio tokamaks.