Dispersion relation of longitudinal oscillation in relativistic plasmas with nonextensive distribution

The generalized dispersion equation for longitudinal oscillation in an unmagnetized, collisionless, isotropic and relativistic plasma is derived in the context of nonextensive q-distribution. The analytical expression for the dispersion relation is obtained in an ultra-relativistic regime, which is related to the q-parameter and temperature. In the limit q→1, the result based on the relativistic Maxwellian distribution is recovered. Using the numerical simulation method, we obtain the full dispersion curve which cannot be given by an analytic method. It is shown that the numerical solution is in good agreement with the analytical result in the long-wavelength, short-wavelength and near light wave region for ultra-relativistic plasmas.