Abstract
The dispersion and collisional damping of small amplitude, electron waves in a plasma are calculated to first order in the collisions treating the electrons relativistically. The treatment is to lowest order in the relativistic corrections. The Beliaev-Budker equation to order (p/mc)2 is used, and the dispersion calculated using an approximate solution to evaluate the electron current density. For no external fields, the longitudinal plasma oscillation, and transverse electromagnetic mode are treated. For a uniform magnetic field, the longitudinal plasma oscillation, the linearly polarized, and circularly polarized modes are treated. At higher temperatures the over-all damping decreases. In the longitudinal mode, the relativistic correction term increases the damping. In the linearly polarized transverse modes, the relativistic correction increases (decreases) the damping for ωp2 > 3c2k2(ωp2 < 3c2k2). The relativistic correction to the collisional part of the current in all the modes is due to electron-ion collisions, and in all but the circularly polarized modes results from the relativistic normalization constant of the equilibrium electron distribution function.
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