Analytic model of stable shock-like structures in laser interaction with underdense plasma for identifying of phase and polarization dependent regime of laser wakefield accelerators

We present an analytical model describing a stable shock-like structure that is formed when an ultra-intense laser propagates through an underdense plasma. It is shown that such structures exist in a wide range of laser-plasma parameters, with a unique sub-luminal shock front velocity for each parameter. Numerical methods to accurately describe such shock-front is developed. The formalism is applied to describe the parameter space in which the Carrier-Envelope-Phase (CEP) effect under which phase and polarization dependent super-ponderomotive effects becomes significant. The developed formalism will enable quick identification of regimes in which CEP effects become significant, expediting designing of Laser Wakefield Accelerators operating in the superponderomotive regime.