X-ray emission from relativistic electrons in a transverse high intensity optical lattice

A new scheme of all-optical free electron laser (FEL), operating in the X-ray range and triggered by interaction of a moderately relativistic electron bunch with a transverse high intensity optical lattice is presented. The ponderomotive potential of the optical lattice forms guiding channels, where the electrons are trapped and oscillate transversely. The collective oscillations of the guided electron bunch scatter the laser beams and amplify the signal at the Stokes frequency, thereby yielding a coherent beam at the Doppler-shifted frequency in the XUV or X-ray domain. Analytic descriptions of a small signal amplification in such a system are presented, and the optimal resonance conditions are defined. The gain scaling laws are confirmed by numerical simulations using a simplified kinetic model in the co-propagating reference frame.