Abstract
On a basis of the relativistic Vlasov–Maxwell equations for an electron unmagnetized collisionless plasma, a three-dimensional analysis of the nonlinear mixing of electromagnetic and longitudinal waves is performed. Using a conducting relativistic plasma model two waves generate a nonlinear current which is the source of a longitudinal plasma wave described by a nonlinear differential equation and by a nonlinear conductivity tensor. A dielectric relativistic plasma model is used to explain the nonlinear excitation of a transverse wave, as an effect of the nonlinear polarization, and described by a nonlinear differential equation and by a nonlinear susceptibility tensor.
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