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Study of nonlinear wave processes in plasmas using the formalism of a special Lorentz transformation for a space-independent frame. (English) Zbl 0585.76191
Summary: 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 Lagrangian 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.
MSC:
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
83A05 Special relativity
76Y05 Quantum hydrodynamics and relativistic hydrodynamics
70H05 Hamilton’s equations
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