Stationary shock-front of a relativisticaily strong electromagnetic radiation in an underdense plasma

The propagation of a relativisticaily strong electromagnetic pulse in an underdense homogeneous plasma is considered with the focus on the possible existence of stationary structure of a pulse front. The analytical stationary shock-like solutions are obtained and analyzed. These solutionscorrespond to the conversion of the pulse electromagnetic energy to anelectron plasma wave in the narrow region of the considered stationaryfront. Our theoretical analysis is supported by the PIC simulations, whichdemonstrate the formation and existence of the shock-like structure of thepulse leading front and extremely fast pulse depletion.