Numerical study of an FEL based on lwfa electrons and a laser-plasma wiggler

Recent works [1] have suggested that laser-wakefield acceleration (LWFA) may be used to produce the electron beam of an FEL, thereby considerably reducing the size and cost of the device. However, when using conventional magnetic wigglers, the requirements on the beam quality are very stringent, and are still challenging with current LWFA beams. An interesting alternative may be to use a laser-plasma wiggler (e.g. a plasma wave or a laser beam). Compared to a conventional wiggler, a laser-plasma wiggler has a field amplitude several orders of magnitude higher, as well as a correspondingly shorter wavelength - which may place lower constraints on the beam quality and eliminate the need for transport. Taking into account beam quality, beam transport and wiggler inhomogeneity, we evaluate the range of wiggler properties (field, wavelength) that would make the FEL radiation possible. From this analysis, the counterpropagating laser wiggler [2] seems to be one of the most promising solutions. We therefore extend the widely-used Ming Xie formula [3] (which was derived for a static, magnetic wiggler) to a counterpropagating laser wiggler. We use this formula to evaluate the potential use of current state-of-the-art lasers.