Abstract
The complete solution, for all temperatures and wavenumbers, of the longitudinal and transverse dispersion equations of a relativistic Maxwellian plasma, is presented. It is assumed that the ions are immobile and that there is no zero-order magnetic field. Analytical methods are used for the very small and very large wavenumber cases, and in the intractable intermediate wavenumber regions numerical results are displayed graphically. The existence at all temperatures of very slightly damped longitudinal plasma waves and slightly damped nonoscillatory transverse excitations is established and the damping constants are evaluated. Necessary and sufficient conditions for the existence of slight Landau damping of longitudinal plasma waves in any general isotropic relativistic Vlasov plasma are also derived. Several new dispersion relations for undamped oscillations, which have phase velocity greater than c, are recorded. One of these, which describes transverse oscillations for large wavenumbers, corresponds to the propagation of light waves in the plasma.
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