Dielectric Tensor of Weakly Relativistic Electron Distributions Separable in Momentum and Pitch Angle

Abstract

The dielectric tensor of a weakly relativistic, magnetized plasma is derived for distributions separable in momentum and pitch angle by using an expansion in powers of the Larmor radius. The results are initially expressed in terms of an integral over the electron pitch angle distribution which is itself unrestricted apart from a single symmetry condition. These results include relativistic and finite Larmor radius effects contributed by harmonics s with - 2 .;;; s .;;; 2 for all propagation angles and thus provide a useful framework for both numerical and analytical investigation of electron cyclotron phenomena (propagation and absorption of waves, maser action, current drive etc.) in a wide variety of isotropic and anisotropic plasmas. Explicit results are presented for the dielectric properties of isotropic, loss cone, anti-loss cone and hollow beam distributions, and for wave propagation perpendicular to the magnetic field. In these cases the pitch angle integrals are performed in terms of functions related to the standard plasma dispersion function.