Study On Dispersion Relations For Non-Maxwellian Distribution Plasmas

The relationship of angular frequency co and wave vector k can determine the dispersion relations of plasma. According to the dispersion relations, we can study the problems of instability, propagation, refraction and absorption of the plasma wave. The properties of the dispersion relation not only depend on the physical parameters (e.g., density, temperature, magnetic field, etc.) but also on the shape of the distribution function. Therefore, it is of significant importance to study the dispersion relations of plasma. In this paper, we considered the dispersion relation for the relativistic plasma with non-Maxwellian distributions. The major question consists of the following two parts:First, starting from the kinetic theory, the dispersion relations of electrostatic and electromagnetic waves of an isotropic relativistic plasma with fast electron distribution are presented. The Analytic formulas of dispersion relations under the long-wavelength and the short-wavelength approximation are derived. Using the numerical calculation method, the full dispersion curve is obtained. It is shown that analytical dispersion curves in the long-wavelength and short-wavelength regions are coinciding with the numerical ones. Furthermore, the approximate expressions of the dispersion relation for the different parameters are given by fitting numerical curves with the polynomial regression method. The dispersion relations of the relativistic plasma with fast electron distribution is significative to study the electromagnetic radiation of the galactic nucleus, the radio galaxy and the quasars.Second, the dispersion relation for electromagnetic oscillation in relativistic plasma with a modified kappa distribution is investigated. By an analytic study, we have derived the approximate expressions. Analytic results not only depend on the plasma temperature but also on the power-law exponent. Similarly, using the numerical method, we obtain the dispersion curve in the whole wave number range. Furthermore, the effect of the temperature and the power law exponent on the corrected plasma frequency is discussed. These results may be useful for discussing electron acceleration and electromagnetic radiation in the solar wind.