Structure of the spontaneous emission spectra of high-γ free electron lasers as measured at the Darmstadt (S-DALINAC) FEL

Recent spontaneous emission measurements obtained from the Darmstadt infrared FEL indicate a relatively broad and down-shifted spectrum with several intensity maxima. The typical features of the spectrum can be well reproduced by a numerical simulation comprising the 3-D electron dynamics in a realizable planar undulator field, the spontaneous radiation according to the well-known Jackson formula, as well as the detection of the radiation with a finite aperture detector. An analytical consideration attributes the frequency down-shift to the reduced Doppler up-shift of the radiation as observed under a finite angle. The intensity peaks formally appear as a consequence of a phase modulation of the radiation of the electrons due to the betatron oscillation. The spectral spacing of these sidebands is roughly given by the Doppler up-shifted betatron frequency. For instance, weak misalignment of the undulator (finite angle with respect to the optical resonator axis) leads to the phenomenon of sidebands in the spectrum of spontaneous emission, and the possible subsequent amplification, at least in the small-signal gain regime of the FEL.