Non-linear Compton scattering of laser pulses with strong temporal and spatial variations off relativistic electrons

Scattering experiments with high-intensity lasers and multi-MeV electron beams are gathering great interest as new light sources. Such experiments, especially with ultrashort laser pulses are prepared at Forschungszentrum Dresden-Rossendorf using the superconducting linac ELBE as brilliant source of monoenergetic electrons with energies of 10-40 MeV. We present simulations of the scattering spectra focusing on the effects of temporal and spatial variations of intensity in short optical laser pulses (Laser strength parameter significantly above 1) and the resulting shift of the non-linear Compton edge as well as higher and very high harmonic radiation.