Study of nonlinear wave processes in plasmas using the formalism of a special Lorntz transformation for a space-independent fram

Abstract

A study is made of nonlinear waves in plasmas using the formalism of a special Lorentz transformation for a space-independent frame, S′. This special transformation is used to transform the space-time dependent equations in a cold, relativistic, magnetized plasma to the S′ frame. Then the transformed equations are employed to derive the expressions for the Lagrangian and the Hamiltonian in the S′ frame. The Lagrengian and the Hamiltonian for a strong circularly polarized laser beam have also been obtained in the S′ frame. The exact form of the nonlinear dispersion relation is derived for circularly polarized waves. Then the results for the frequency and the wave number shifts of these waves in a cold, magnetized relativistic plasma are obtained with some Discussion on the nature of the frequency shifts. Finally, numerical results are presented for the radiation of Nd-glass laser in dense plasmas.

Keywords

• nonlinear waves in plasmas
• relativistic plasma
• Lorentz transformation.