Dispersion relations of nonlinearly coupled electromagnetic and electrostatic waves in relativistic plasmas

Abstract

In the present work large amplitude electromagnetic waves in cold plasmas at relativistic intensities are studied analytically in a plane wave geometry. Special attention is drawn to the nonlinear coupling of electromagnetic and electrostatic modes. In the framework of the Akhiezer–Polovin model, periodic and more general quasiperiodic waves are taken into account. For small densities a two-time-scale method is used to calculate an analytical solution up to the fourth order in the plasma density. Nonlinear dispersion relations are calculated for coupled waves, taking into account the full plasma response for linear as well as for circular polarization. In the presence of a large amplitude electrostatic wave, the results show a major difference from the commonly considered dispersion relation for electromagnetic waves. Finally, the solutions of the Akhiezer–Polovin model are compared with particle-in-cell simulations.