Relativistic Broadening Near Cyclotron Resonance.

Relativistic broadening of absorption or emission lines near cyclotron resonance in a warm plasma is investigated using the linearized relativistic Vlasov-Maxwell system. The unperturbed state is assumed to be isotropic, but not necessarily Maxwellian. The expansion parameter is eta v sub ec, v sub e being the electron thermal speed. It is assumed that the wave frequency, plasma frequency, and cyclotron frequency are all comparable in magnitude, and the refractive index n 01. The parameter alpha etan is of arbitrary order, thus the results are uniformly valid for all values of oblique propagation angles, although the relativistic effects are negligible for alpha 1. The dielectric tensor is reordered, and the dispersion relation appropriate for this problem is derived to the lowest significant order in eta. The results are expressed in terms of the readily calculable generalized plasma dispersion function Z. In the Maxwellian case the results are alegbraic in Z, and unlike the previously published results, they do not involve infinite integrals or series imposed on Z, thus leading to simple and efficient evaluations. The case of perpendicular propagation is obtained by taking the large alpha limit. Some inconsistencies in the literature dealing with the extraordinary mode are resolved. Author