Linear wave dispersion laws in unmagnetized relativistic plasma : analytical and numerical results

In this paper dispersion laws for electrostatic and electromagnetic waves in a homogeneous and unmagnetized relativistic Vlasov plasma are derived. From the dispersion laws the relativistic plasma frequency, which is temperature dependent is derived. Using the standard technique of successive approximations, simple but powerful approximate relativistic dispersion laws are derived, resembling the electromagnetic dispersion law and the electrostatic Bohm–Gross dispersion law in the nonrelativistic case. The relation between the relativistic plasma frequency omega_pe, Debye wave number k_D and the thermal velocity v_th,e is established. The approximate dispersion laws are compared with numerical solutions of the full dispersion laws. The full dispersion equations are transformed so that they are well suited for numerical evaluation in the temperature range where a fully relativistic treatment is needed