Spontaneous electromagnetic fluctuations in unmagnetized plasmas. V. Relativistic form factors of weakly damped/amplified thermal modes

Closed analytical expressions for the spontaneously emitted fluctuation spectra of weakly damped/amplified fluctuations in unmagnetized plasmas are derived using fully relativistic dispersion functions and form factors for the important class of isotropic thermal plasmas. Especially, an electron-proton plasma is investigated in the limits of nonrelativistic and ultrarelativistic plasma temperatures. The results confirm the earlier nonrelativistic approach for positive values of the imaginary frequency γ and complete the nonrelativistic treatment for negative values of γ<0. The well known electrostatic, collective Langmuir mode also occurs within the relativistic theory of spontaneously emitted fluctuations and is analytically and graphically identified. For the first time, the ultrarelativistic temperature limit is analyzed for subluminal phase speeds, which leads to the identification of an additional, so far unknown, longitudinal subluminal collective mode