Transverse effects in the production of x rays with a free-electron laser based on an optical undulator

The interaction between high-brilliance electron beams and counterpropagating laser pulses produces x rays via Thomson backscattering. If the laser source is long and intense enough, the electrons of the beam can bunch on the scale of the emitted x-ray wavelength 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 nonuniformity of the laser energy are the principal quantities that limit the growth of the x-ray signal. In this work we analyze with a 3D 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 in violation of the Pellegrini criterion for static wigglers. A generalized form of this criterion is validated on the basis of the numerical evidence.