Dispersion of waves in relativistic plasmas with isotropic particle distributions

The dispersion laws of Langmuir and transverse waves are calculated in the relativistic nonmagnetized formalism for several isotropic particle distributions: thermal, power law, relativistic Lorentzian κ , and hybrid β . For Langmuir waves the parameters of superluminal undamped, subluminal damped principal, and higher modes are determined for a range of distribution parameters. The undamped and principal damped modes are found to match smoothly. Principal damped and second damped modes are found not to match smoothly. The presence of maximum wavenumber is discovered above that no longitudinal modes formally exist. The higher damped modes are discovered to be qualitatively different for thermal and certain nonthermal distributions. Consistently with the known results, the Landau damping is calculated to be stronger for nonthermal power-law-like distributions. The dispersion law is obtained for the single undamped transverse mode. The analytic results for the simplest distributions are provided.