MODELS AND SIMULATIONS FOR THE LASER-PLASMA INTERACTION AND THE THREE-WAVE COUPLING PROBLEM

摘要

We are concerned here with the modelling of the laser propagation and its interaction with a plasma. In a first part, we recall first some features related to the paraxial approximation of the solution of the wave equation and the coupling model between the plasma hydrodynamics and the laser propagation. In a second part, we consider the coupling with the ion acoustic waves which has to be accounted to model the Brillouin instability. It leads to the three-wave coupling problem which is a crucial in plasma physics. We give some mathematical properties of this system specially in the case when the speed of light is assumed to be infinite. We also propose a numerical method based on a implicit time discretization. It is illustrated on test cases.