Short Intense Laser Pulse Depletion and Scattering in Under-Dense Plasma

Nonlinear evolutions of an ultra-intense, short laser pulse due to the wake excitation inside the plasma are studied by means of detailed particle-in-cell simulations and comprehensive analyses. Pulse lengths both longer and shorter than the plasma wavelength are considered. A new adiabatic regime of the interaction is identified in connection with the quasi-static being of the plasma in the pulse commoving frame. This situation occurs when radiation back-reactions are ignorable in the commoving frame against the measured high plasma momentum. By formulating this regime in terms of the local conservation laws, we calculate the overall pulse depletion and more importantly the global pulse group velocity. The outcome for the group velocity shows non-explicit density dependency and, strangely, remains above the linear value over a long time period. Further, we examine the model adequacy at different applied parameters via comparison with simulations. It is turned out that for pulse lengths larger than the plasma wavelength the modulation is developed by declination of the pulse-front group velocity, resulting in violation of the adiabatic description. The mechanism is the production of effective radiation back-reactions due to the pulse steepening at the unstable equilibrium points of the electrostatic potential. A detailed analysis of the anomalous plasma dispersion and scatterings confirms our adiabatic and beyond the adiabatic descriptions, especially in the case of the pulse modulation.