The interaction between high-brilliance electron beams and counter-propagating laser pulses produces X rays via Thomson back-scattering. If the laser source is long and intense enough, the electrons of the beam can bunch and a regime of collective effects can establish. In this case of dominating collective effects, the FEL instability can develop and the system behaves like a free-electron laser based on an optical undulator. Coherent X-rays can be irradiated, with a bandwidth very much thinner than that of the corresponding incoherent emission. The emittance of the electron beam and the distribution of the laser energy are the principal quantities that limit the growth of the X-ray signal. In this work we analyse with a 3-D code the transverse effects in the emission produced by a relativistic electron beam when it is under the action of an optical laser pulse and the X-ray spectra obtained. The scalings typical of the optical wiggler, characterized by very short gain lengths and overall time durations of the process make possible considerable emission also with emittance of the order of 1mm mrad.
Characterization of soft x-ray echo-enabled harmonic generation free-electron laser pulses in the presence of incoherent electron beam energy modulations