Multiphoton stimulated compton scattering

The processes of multiphoton Compton scattering of relativistic electrons are considered in a special one-dimensional geometry. The multiphoton parameter and the energy distribution of scattered electrons are found. The nonlinear behaviour of the gains of the two external electromagnetic waves is investigated in the saturation region. The multiphoton parameter is shown to be of order of one and the perturbation theory is shown to be inapplicable at very weak fields. For saturation of the gains much stronger fields are required which however are much weaker than those which are necessary for appearance of multiphoton processes in the spontaneous Compton scattering.