Spontaneous emission in a free-electron laser with a discrete taper

Abstract
Spontaneous emission in a tapered free-electron laser is considered for the case where the magnetic field of the undulator is described by an expression that varies discretely from one half-period to the next. This geometry permits the utilization of the knowledge of the electron trajectories in untapered undulators. The method can be applied for any conceivable configuration of tapered undulators with electrons propagating either on or off axis and yields the spectrum of radiation at arbitrary angles including harmonics. The approach is developed for linear polarization; however, circular polarization may be treated as well.