Are relativistic effects significant for the analysis of whistler-mode waves in the earth's magnetosphere?

Abstract

It is pointed out that relativistic effects lead to an increase in whistler-mode refractive index and to a decrease in the range of frequencies for which instability of these waves occurs. The latter effect is particularly important in a rarefied plasma in a strong magnetic field where the electron plasma frequency (IT) is of the order of or smaller than the electron gyrofrequency (Ω). The condition II ≲ Ω is satisfied in some regions of the Earth’s magnetosphere (e.g. outside the plasmasphere near the magnetospheric equator) and in these regions the analysis of whistler-mode waves requires the weakly relativistic rather than the nonrelativistic approach even if the thermal velocities of magnetospheric particles are well below the velocity of light.