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Kinetic and fluid treatments of nonlinear wave interactions (wave mixing and electromagnetic wave scattering) in plasmas are considered and the difference between the two approaches is discussed. Solving the kinetic equation by the method of moments makes it possible to substantiate the validity and find the applicability range of the fluid approach to the study of nonlinear plasma processes. In particular, the detailed study of nonlinear processes in a plasma with external magnetic fields is performed. In the case of wave transformation, when mixed waves satisfy linear wave equations, both fluid and kinetic approaches yield similar expressions for the inducing current. In the case of electromagnetic wave scattering by thermal fluctuations, the results of the fluid and kinetic approaches are in accordance only in the limiting case of cold plasmas when thermal effects may be completely disregarded (these are thermal corrections to the wave dispersion equation and the additional Langevin source in the constitutive equation for fluctuations). Different expressions for the inducing current, obtained from various versions of hydrodynamic equations, reduce to the same form in the cold plasma limiting case

Wave Mixing and Electromagnetic Wave Scattering in Plasmas