Nonlinear effects in photon emission by an electron in the field of a circularly polarized electromagnetic wave

The authors consider the process of inverse Compton scattering of an intense circularly polarized laser wave focused on a beam of relativistic longitudinally polarized electrons. They investigated regions of nonlinear effects corresponding to values of the intensity parameter obeying not only x2 < 1 but also x2 ≥ 1 (x2 = -e2A2μ/m2, where Aμ is the vector potential of the wave). In each of these regions they construct for a neodymium laser the spectra and the energy dependence of the degree of circular polarization of the emitted photon for various values of the polarization of the electron and the wave. For x2 < 1, when the radiation is dominated by the first harmonic, they take into account the second, as well as the third, harmonic. They show that for x2 > 1 the process of emission of a hard photon is essentially nonlinear. The calculations are based on direct evaluation of QED matrix elements in the diagonal spin basis