Self-Consistent Electromagnetic Waves in Relativistic Vlasov Plasmas

Abstract

It is shown that the treatment of relativistic superluminous waves can be simplified by making a Lorentz transformation to a new frame in which the spatial variable no longer appears. Self-consistent solutions of the relativistic Vlasov-Maxwell equations can be constructed in the new frame. These solutions correspond to nonlinear traveling waves in a finite temperature plasma, and reduce to the usual linear results in the small-amplitude limit. A particular example is considered in which the nonlinear waves propagate through a relativistic Maxwellian plasma, and it is shown that pure transverse waves cannot exist in such a case, but that a coupled longitudinal field necessarily appears. For this case the nonlinear effects are evaluated correct to second order in the transverse field amplitude, thus obtaining a nonlinear dispersion relation and a measure of the coupling. In addition, solutions involving pure longitudinal waves can be found, and are also investigated. In limiting cases the results agree closely with previous calculations based on hydrodynamic models.