Modulated electromagnetic waves in relativistic plasmas: field and kinetic equations

Abstract

Modulated electromagnetic plane waves in relativistic collisionless, unmagnetized plasmas are investigated through expansion in a small parameter, corresponding to weak dispersion and weak nonlinearity. The oscillation-centre transformation is applied to construct a Hamiltonian action principle for the slow oscillation-centre variables. A description in terms of the relativistic Vlasov equation for oscillation-centre distribution functions is introduced. A system of coupled field and kinetic eequations is obtained order by order.The final result is a generalized vector nonlineat schrödinger equation, with resonant particle effects included through the coupling to the perturbed Vlasov equations.