We present two contrasting cases of the interaction of a high intensity laser beam with overdense plasma, namely the case of a circular polarization, and the case of a linear polarization of the laser beam. An Eulerian-Vlasov code is used for the numerical solution of the one-dimensional relativistic Vlasov-Maxwell set of equations, for both electrons and ions. The laser beam is incident normally on the plasma surface. We consider the case when the laser wave free space wavelength λ0 is greater than the scale length of the jump in the plasma density at the plasma edge Ledge (λ0 ≫ Ledge) and the ratio of the plasma density to the critical density is such that n/ncr ≫ 1. The incident high intensity laser radiation is pushing the electrons at the plasma surface through the ponderomotive pressure, producing a sharp density gradient at the plasma surface. There is a build-up of the electron density at this sharp edge that creates a space-charge, giving rise to a longitudinal electric field. The results obtained differ substantially in several aspects when circular or linear polarization for the incident laser wave is considered. In the case of a circular polarization, the radiation pressure is pushing the sharp edge in the forward direction, and the ions are accelerated and reach a free streaming expansion phase where they are neutralized by the electrons. For the case of a linear polarization, there is a standing structure with a sharp edge that forms at the wave front, and in this case, the electrons at the plasma edge oscillate nonlinearly in the field of the wave, which periodically goes to zero. This results in an important distorsion in the reflected electromagnetic wave that includes the generation of harmonics. We present two simulations to illustrate the differences between these two cases. The generation and propagation of collisionless shock waves in these systems are investigated. The results underline the importance of including the ion dynamics in the interaction of high intensity laser waves with overdense plasmas.
