Some natures have been studied for the propagation process of very intense and very short laser pulse in underdense plasma.The wave equation is derived and solved using the method of 2-D Fast Fourier Transformation.The basic equations for relativistic self-focusing include the nonlinear source term and the effect of diffraction.As a result of ponderomotive forces and relativism,the plasma frequency is reduced and so the refractive index is changed.It affects the propagation of laser in plasma.When the incident laser power (p) exceeds the critical power (p_c),self-focusing appears during the propagation of laser.On the contrary,laser damps gradually and self-focusing doesn't appear.

Abstract] 2-D and 3-D numerical simulation methods of filamentation instability in laser-target interaction are presented.The Landau-fluid models are adopted with a simplified 3-D numerical method,it simulates filamentation process for laser beams in underdense plasma.Plasma background resulted by 1D simultaneously calculation of the laser-target coupling is used to investigate the filamentation process and several reasonable results have been obtained.Nonlinear and relativistic modification of transport coefficients,and nonlinear hydrodynamics computation prove to be needed for the case of intense laser beams.