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

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Abstract
The propagation of a relativistically 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 solutions correspond to the conversion of the pulse electromagnetic energy to an electron plasma wave in the narrow region of the considered stationary front. Our theoretical analysis is supported by the PIC simulations, which demonstrate the formation and existence of the shock-like structure of the pulse leading front and extremely fast pulse depletion.