Abstract
The theoretical study of the undulator radiation (UR) from electron beams in free electron laser (FEL) undulators is performed. We analytically account for the magnetic field harmonics and non-periodic field components, off-axis effects, divergence, energy spread and other losses in real installations. The expressions for the UR intensity and spectrum are obtained explicitly in terms of the generalized Bessel and Airy functions. The results are applied to high gain FELs, using the analytical FEL model. They are verified with experiments at SwissFEL, PAL-XFEL, LCLS, SACLA and LEUTL FELs. The spectrum, UR line shape and harmonic power evolution are theoretically analyzed and compared with the available experimental results. The spectral properties of the studied FELs are compared with each other; where the measured data is absent, the theoretical predictions are given.
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