Kinematical relations at nonlinear laser field: Free electron interactions

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Abstract
Kinematical relations of nonlinear interaction of laser beams with free charged particles are analyzed. General expressions are found for the number of scattered photons as a function of the number of simultaneously absorbed and/or emitted photons and the kinetic parameters of the charged particle-photon system. The results are applied to the processes of particle acceleration by lasers, frequency conversion, solitonic propagation, and others.