High frequency electromagnetic modes in a weakly magnetized relativistic electron plasma

Using the linearized Vlasov–Maxwell model, the polarization tensor for a weakly magnetized electron plasma is derived. For isotropic relativistic Maxwellian velocity distribution function, dispersion relations are obtained for both parallel and perpendicular propagations. The integrals (called Meijer G functions) that arise due to relativistic effects are examined in various limits and dispersion relations are derived for the nonrelativistic, weakly, strongly, and ultrarelativistic Maxwellian velocity distributions. It is generally observed that the propagation domains of the modes are enlarged as one proceeds from the nonrelativistic to the highly relativistic regime. Resultantly, due to the relativistic effects, the Whistler mode is suppressed in the R-wave, the nonpropagation band of X-mode is reduced, and the X-mode itself approaches the O-mode. Further, the results derived in the ultra- and nonrelativistic limits found to be in agreement with the earlier calculations [G. Abbas et al. Phys. Scr. 76, 649 (2007); F. F. Chen, Introduction to Plasma Physics and Controlled Fusion (Plenum, New York, 1984), Vol. 1].