Amplified short-wavelength light scattered by relativistic electrons in the laser-induced optical lattice

The scheme of the x-ray free electron laser based on the optical undulator created by two overlapped transverse laser beams is analyzed. A kinetic theoretical description and an ad hoc numerical model are developed to account for the finite energy spread, angular divergence, and the spectral properties of the electron beam in the optical lattice. The theoretical findings are compared to the results of the one- and three-dimensional numerical modeling with the spectral free electron laser code plares.