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.

American Geophysical Union
doi.org/10.1029/GM086p0139
Geophysical monograph
Computational Dynamics

Sazhin, S. S., Sumner, A. E., & Temme, N. (1995). Are relativistic effects significant for the analysis of whistler-mode waves in the earth's magnetosphere?. In Space Plasmas: Coupling Between Small and Medium Scale Processes (pp. 139–142). American Geophysical Union. doi:10.1029/GM086p0139