Longitudinal electrostatic waves in isotropic thermal plasmas: Ultrarelativistic pair plasmas

Abstract

The dispersion relation of longitudinal electrostatic waves in unmagnetized isotropic thermal plasmas is investigated in the collisionless limit using fully relativistic kinetic plasma theory. Specifically, an electron-positron plasma is studied in the limits of nonrelativistic and ultrarelativistic plasma temperatures. In the limit of nonrelativistic plasma temperatures, the earlier dispersion relation, based on nonrelativistic dispersion theory, is reproduced. In the limit of ultrarelativistic plasma temperatures, we analyze analytically and numerically the dispersion relation of the longitudinal electrostatic mode which occurs in the subluminal and superluminal frequency regime. We correct some earlier results in the literature on the subluminal dispersion relation.