High harmonics generation in underdense plasma from relativistic Thomson scattering

Summary form only given. A high intensity laser incident on a vacuum-plasma interface, insert an Intensive electromagnetic force on electrons and charged particles. Relativistic charged particle movements lead to the high order harmonics generation of the incident wave. Efficiency of high harmonics increases with the intensity laser incident. So that the non-relativistic velocities of the particles varies to the relativistic velocities of particles. Harmonics can be produced coherently by strong plasma waves or incoherently by nonlinear Thomson scattering process. The equations of the "charge conservation" and the "momentum conservation" and Maxwell equations are written for the electromagnetic fields. Then the high order harmonics equations are derived, six coupled equations. Theory for coherent emission in the direction of propagation of the laser beam indicates that-because of the mismatch between the phase velocities of the laser pulse the conversion efficiency should be low unless a means for phase matching or quasi phase matching, is implemented . We solved equations in phase matching and non phase matching conditions, Comparison between results of two conditions lead to incoherent radiation and relativistic Thomson scattering. One of considerable results in this paper is harmonics generation in direction of propagation of laser incident and normal to it. considering V.VV term in velocity equation and plasma as a fluid get this result. In previous works that has done in this field the researcher have reported-odd harmonics generated in direction of propagation of laser incident and even harmonics 9 generated in normal direction of propagation of laser incident but in experimental results we can see all harmonics in direction of propagation . The set of equations that are presented in other papers had been solved for SHG and THG while we have been presenting a set of equations and numerical analytic program do for any harmonics.