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

In this paper dispersion laws for electrostatic and electromagnetic waves i n a homogeneous and unmagnetized relativistic Vlasov plasma are derived. Fr om the dispersion laws the relativistic plasma frequency, which is temperat ure dependent is derived. Using the standard technique of successive approx imations, simple but powerful approximate relativistic dispersion laws are derived, resembling the electromagnetic dispersion law and the electrostati c Bohm-Gross dispersion law in the nonrelativistic case. The relation betwe en the relativistic plasma frequency omega (pe), Debye wave number k(D) and the thermal velocity v(th,e) is established. The approximate dispersion la ws are compared with numerical solutions of the full dispersion laws. The f ull dispersion equations are transformed so that they are well suited for n umerical evaluation in the temperature range where a fully relativistic tre atment is needed. (C) 2001 American Institute of Physics.