Abstract
We give analytical description of the spontaneous and stimulated free electron laser (FEL) harmonic generation in multiperiodic fields, accounting for the off-axis effects and field harmonics in undulators. Exact analytical expressions for the Bessel coefficients involve generalized forms of Bessel- and Airy-type functions and describe also the effect of the non-periodic magnetic components in various elliptic and planar undulators with field harmonics. They allow clear identification of proper contributions in the UR harmonic intensities and polarizations. Advanced phenomenological model of the FELs harmonic powers provides analytical description of relevant effects in FEL harmonic radiation, verified with FEL experiments. The analysis of the off-axis effects for the odd and even harmonic generation is performed for LEUTL and LCLS FEL experiments. The modelled harmonic powers perfectly fit the experimentally measured data. High levels of the 2nd harmonic are explained by the wide beam in LEUTL experiment and by the off-axis beam deviation in LCLS experiment.
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