Dielectric characteristics of axisymmetric low aspect ratiotokamak plasmas

In this paper the transverse and longitudinal dielectric tensor elements areevaluated for radio-frequency waves in an axisymmetric tokamak with circularmagnetic surfaces, without the smallness assumption of the inverse aspectratio and poloidal magnetic field. A collisionless plasma model is considered.The Vlasov equation is solved separately for untrapped and trapped particlesas a boundary-value problem. The cyclotron and bounce resonances areaccounted. The coordinate system with the `straight' magnetic field lines wasused. The separate contributions of untrapped and trapped particles to thedielectric tensor components are expressed by the summation of bounce resonantterms, which include the double integration in velocity space, the resonantdenominators, the phase coefficients, the standard elementary and ellipticfunctions. The permittivity elements presented in the paper are suitable toanalyse the spatial structure of the electromagnetic fields and theirinteraction with charged particles (e.g. during the plasma heating andcurrent drive generation) in the frequency range of Alfvén, fastmagnetosonic, ion-cyclotron and lower hybrid waves, for both the low and largeaspect ratio tokamaks.