Linearly polarized waves with constant phase velocity in relativistic plasmas

Abstract

The propagation of plane linearly polarized electromagnetic waves in cold plasmas at relativistic intensities is studied analytically under the assumption of a constant phase velocity. A system of coupled relativistic harmonic oscillators for the Lagrangian coordinates of the particles is derived. Based on this model, a perturbation expansion is carried out to solve the equations for small plasma densities on the one hand and nearly critical plasma densities on the other hand. In both cases fully relativistic expressions for the particle trajectories and the dispersion relations are derived. For small plasma densities the particle trajectory approaches the vacuum figure-eight orbit. For plasma densities close to the critical density a deformed circular orbit is found that differs from the commonly considered almost-transverse solution. Finally, the transition between the two classes of solutions at intermediate plasma densities is numerically investigated.