Free-electron lasers with electromagnetic standing wave wigglers

A detailed analysis of the electromagnetic standing wave wiggler for free-electron lasers (FEL's) is conducted for both circular and linear wiggler polarizations, following a single-particle approach. After determination of the unperturbed electron orbits in the wiggler field, the single-particle spontaneous emission spectrum and subsequently the gain in the low gain Compton regime (using the Einstein coefficient method) are explicitly calculated. This analysis results in a clear understanding of the resonance conditions and the coupling strength associated with each resonance of this type of FEL. In particular, a striking feature obtained from this investigation is that the electromagnetic standing wave wiggler FEL, under certain circumstances, exhibits a rich harmonic content. This harmonic content is caused by the presence of both the forward and backward wave components of the standing wave wiggler field. In addition, the nonlinear self-consistent equations for this type of FEL are also presented, permitting further investigation of it by the theoretical techniques and numerical codes developed for conventional FEL's.