Generation of UR Harmonics in Undulators with Multiperiodic Fields

Abstract

Undulator radiation (UR) of some elliptical undulators with multiperiodic magnetic fields of sin-sin and sincos configuration is investigated, as is also UR of a planar and a spiral undulator in the presence of additional harmonics of the magnetic field. Exact analytical expressions for the UR spectrum and the intensity in terms of generalized special Bessel functions are obtained; the corresponding Bessel coefficients are derived. Comparison of the obtained results with the available experimental data for real devices along with numerical simulations confirms the accuracy of the analytical formulas. The possibility of generation of a strong fifth UR harmonic induced by the third harmonic of the undulator field is demonstrated. In free electron lasers (FELs) this effect leads to the generation of a strong fifth harmonic of coherent radiation against the background of a weak third harmonic. In a spiral undulator with a third harmonic of the field, large values of the Bessel coefficients are obtained for the fifth UR harmonic; this makes it possible to use such an undulator as a prebuncher, i.e., to bunch electrons, at the wavelength of the fifth harmonic in a cascade FEL with amplification of the higher harmonics. The corresponding FEL is modeled.