Generation of wakefields and electromagnetic solitons in relativistic degenerate plasmas

The nonlinear interaction of intense linearly polarized electromagnetic waves (EMWs) with longitudinal electron density perturbations is revisited in relativistic degenerate plasmas. The nonlinear dynamics of the EMWs and the longitudinal field, driven by the EMW ponderomotive force, is governed by a coupled set of nonlinear partial differential equations. A numerical simulation of these coupled equations reveals that the generation of wakefields is possible in weakly relativistic degenerate plasmas with $R_0\equiv p_F/mc\ll1$ and $v_g/c\sim1$, where $p_F$ is the Fermi momentum, $m$ is the mass of electrons, $c$ is the speed of light in vacuum, and $v_g$ is the EMW group velocity. However, when the ratio $v_g/c$ is reduced to $\sim0.1$, the wakefield generation is suppressed, instead the longitudinal fields get localized to form soliton-like structures. On the other hand, in the regimes of moderate $(R_0\lesssim1)$ or strong relativistic degeneracy $(R_0>1)$ with $v_g/c\sim0.1$, only the EM solitons can be formed.