Laser-induced Compton scattering at relativistically high radiation powers

We reconsider nonlinear Compton scattering, induced by a linearly polarized laser field. The radiation power is assumed to be in the relativistic regime such that the ponderomotive energy of an electron in the field is of the order of magnitude of the electron's rest energy or even above it, i.e., ${U}_{p}>~{\mathrm{mc}}^{2}.$ We investigate in detail for several scattering configurations the angular dependences of the induced nonlinear Compton processes of the order N of absorbed laser photons $\ensuremath{\omega},$ assuming that in general the electron beam and laser beam can cross at an arbitrary angle.