On the relativistic damping of transverse waves propagating in magnetized Vlasov plasmas

The general relativistic dispersion relations of transverse waves parallel propagating in magnetized Vlasov plasmas, are reconsidered. In a previous paper [Lazar and Schlickeiser, Canadian J. Phys. 81, 1377 (2003)] we have derived these equations by a rigorous relativistic kinetic theory and by a correct analytical continuation for all complex frequencies. Detailed expressions are more explicitly presented here for residues to completely describe the damped waves-forward or backward moving waves, and left-handed or right-handed polarized waves. The cyclotron damping occurs when the circularly-polarized wave frequency nearly coincides with the gyrofrequency of plasma particle, modified by the relativistic Doppler effect in its own referential. The rigorous analysis of relativistically correct dispersion equations leads to an important correction of nonrelativistic theory: the superluminal EM waves undergo no cyclotron damping in magnetized equilibrium plasmas.