Relativistic corrections to the nonlinear plasma permittivity: II. Coupling of longitudinal and transverse waves

Abstract

The resonant interaction between longitudinal and transverse plasma waves is investigated on the basis of a relativistic kinetic theory. The relativistic form of nonlinear plasma permittivity is derived assuming that initial plasma is at thermal equilibrium and described by a relativistic Maxwellian distribution. For low nonrelativistic plasma temperatures (kBT/mc2 ≪ 1), the nonlinear plasma permittivity is markedly different from the standard form provided by a classical nonrelativistic approach. The relativistic correction derived in this case is estimated to be of the order of thermal plasma parameter, μ−1 = kB T/mc2, and it will vanish only for an idealized cold plasma, T → 0.