Nonlinear Thomson scattering of two electromagnetic waves on the relativistic electron

The characteristics of Thomson scattering radiation of two weak electromagnetic (EM) waves forming a standing wave are calculated. It is shown that the effective mass of the electron in the field of the two EM-waves can be measured experimentally; the radiation can be used for microbunch diagnostics; the existence of a new type of radiation is predicted. The two EM-wave mechanism of vacuum laser acceleration of electrons is proposed, parameters of both waves (the first one is accelerating and the second ejecting the electron from the laser focus) are estimated and the limits of applicability are presented.