Relativistic effects on parallel whistler-mode propagation and instability

Abstract

Abstract. Relativistic effects on parallel whistler-mode propagation and instability are considered analytically in some limiting cases relevant to magnetospheric and/or astrophysical conditions. The corresponding wave dispersion equation for a weakly relativistic anisotropic plasma is expressed in terms of generalized Shkarofsky functions. Asymptotic presentation of these functions is found in the limit of large wave refractive indices. Based on this presentation, a new analytical expression for whistler-mode refractive index is obtained and analysed. It is pointed out that relativistic effects increase the value of anisotropy above which the waves are unstable, in agreement with the results of the earlier numerical analysis. This increase is particularly important for whistler-mode propagation in a rarefied, hot plasma but could be potentially observed in the magnetosphere of the Earth in the region outside the plasmasphere.

Relativistic and non-relativistic analysis of whistler-mode waves in a hot anisotropic plasma

“…The dispersion equation for parallel whistler-mode waves in a weakly relativistic (with condition (1) valid) anisotropic plasma can be written as (Sazhin & Temme 1990) …”

“…It is this comparison that we make here. As in the papers by Sazhin (1987Sazhin ( b, 1989 and Sazhin & Temme (1990, 1991, we restrict ourselves to parallel whistler-mode waves. This paper can be considered as complementary to that of Sazhin (1988b), where a comparison between asymptotic nonrelativistic and weakly relativistic solutions was made, but different types of waves propagating almost parallel and almost perpendicular to the external magnetic field were considered.…”

“…In a series of papers (Sazhin 1987(Sazhin a, b, 1989Sazhin & Temme 1990, 1991 we have attempted to develop an asymptotic theory of whistler-mode propagation, instability or damping in a weakly relativistic plasma. Restricting ourselves to the limiting, but practically important, case of whistler-mode propagation strictly parallel to the magnetic field, we obtained some approximate solutions to the weakly relativistic dispersion equation.…”