Covariant kinetic dispersion theory of linear waves in anisotropic plasmas. I. General dispersion relations, bi-Maxwellian distributions and nonrelativistic limits

Abstract

The properties of longitudinal and transverse oscillations in unmagnetized anisotropic plasmas of arbitrary composition are investigated on the basis of Maxwell equations and the relativistic Vlasov equation. The longitudinal and transverse dispersion relations for plasmas with arbitrary distribution functions are derived. These dispersion relations describe the linear response of the system to the initial perturbations and thus define all existing linear plasma modes in the system. By analytic continuation the dispersion relations in the whole complex frequency plane are constructed. The further analysis is restricted to the important case of anisotropic bi-Maxwellian equilibrium plasma distribution functions. Explicit forms of the relativistically correct longitudinal and transverse dispersion relations are derived that hold for any values of the plasma temperatures and the temperature anisotropy. In the limit of nonrelativistic plasma temperatures the longitudinal and transverse dispersion relations can be expressed in terms of the Fried and Conte plasma dispersion function, however, the dependence on frequency and wave numbers is markedly different from the standard noncovariant nonrelativistic analysis. Only in the strictly unphysical formal limit of an infinitely large speed of light c→∞ the nonrelativistic dispersion relations reduce to the standard noncovariant nonrelativistic dispersion relations.