Dielectric constant of an ultrarelativistic plasma

An analytic expression is derived for the longitudinal dielectric constant _l of an isotropic collisionless high-temperature plasma which is valid for the entire range of phase velocities in which there is no Landau damping or it is exponentially small. This expression contains the formulas for _l given in the papers of Silin and Mikhailovskii as limiting cases. Numerical calculations for the temperatures 10 mc² and 100 mc² are illustrated graphically.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 57–60, September, 1982.