Analysis of harmonic generation in planar and elliptic bi-harmonic undulators and FELs

Abstract

We present a phenomenological model for single-pass FEL radiation power and bunching evolution in planar and elliptic undulators with two polarizations of the emitted radiation; the models allows for the suppression of low harmonics in the spectrum. We study the harmonic generation in some planar and elliptic undulators with account for the off-axis effects and for the 3rd harmonics of the undulator magnetic field. Both spontaneous and stimulated types of radiation are studied. Spontaneous UR is studied with generalized Bessel functions formalism. The analytical FEL model, which employs these Bessel functions, is verified with FEL experiments in the range of radiation wavelengths 0.15–500 nm and confirmed by numerical simulations. The phenomenological description is based on the undulator parameters and FEL parameters, such as the electron beam current, energy, spread and emittance. The analytical formulation allows fast evaluation of the FEL performance with minimal resources. The effects of the 3rd harmonic of the undulator field and properties of the beam on the spontaneous UR and on the FEL radiation are explored. Generation of high even- and odd- harmonics due to the undulator field harmonic and finite beam size is studied. Their effects on the spontaneous and stimulated UR are compared with each other.