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 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.