Requirements for a laser pumped FEL operating in the X-ray regime

A laser pumped free electron laser (FEL) can in principle generate coherent, polarized, high power X-rays using a much lower energy electron beam than would be required by a conventional FEL. This is due to the dramatic reduction in the wiggler period, which in the case of a laser pumped FEL is the laser wavelength. However, a number of practical obstacles could prevent the realization of a laser pumped FEL in the laboratory. Foremost amongst these is the requirement that the axial velocity spread on the electron beam be less than the difference between the average velocity of the beam and the velocity of the ponderomotive wave. This requirement places a severe limitation on both the beam emittance and energy spread. Conditions are given on the emittance, energy spread, current density, and laser intensity needed to achieve lasing in the X-ray regime.