Relativistic effects on parallel whistler-mode propagation and instability

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.