Spontaneous radiation from relativistic electrons in a tapered undulator

The spectrum, angular distribution, polarization, and coherence properties of the radiation emitted by relativistic electrons undulating through a quasiperiodic tapered magnetic field are studied. Tapering the wavelength and/or field strength along the undulator's axis has the effect of spreading the spectral line to higher frequencies; interference over this broader spectral range results in a more complex line shape. The angular dependence, on the other hand, is not affected by the amount of taper. The polarization of the radiation in the forward direction is determined by the transverse polarization of the undulator, but the polarization changes off axis. The radiation patterns predicted here are distinct from those of untapered undulators and their detection is now feasible. They will provide useful diagnostics of electron trajectories and threshold behavior in free-electron-laser oscillators using tapered undulators.