Two-dimensional s-polarized solitary waves in relativistic plasmas. I. The fluid plasma model

The properties of two-dimensional linearly s-polarized solitary waves are investigated by fluid-Maxwell equations and particle-in-cell (PIC) simulations. These self-trapped electromagnetic waves appear during laser-plasma interactions, and they have a dominant electric field component E(z), normal to the plane of the wave, that oscillates at a frequency below the electron plasma frequency ω(pe). A set of equations that describe the waves are derived from the plasma fluid model in the case of cold or warm plasma and then solved numerically. The main features, including the maximum value of the vector potential amplitude, the total energy, the width, and the cavitation radius are presented as a function of the frequency. The amplitude of the vector potential increases monotonically as the frequency of the wave decreases, whereas the width reaches a minimum value at a frequency of the order of 0.82 ω(pe). The results are compared with a set of PIC simulations where the solitary waves are excited by a high-intensity laser pulse.