Radiation from Elliptical Undulators with Magnetic Field Harmonics

We analyze undulator radiation in some multiperiodic magnetic fields. We consider undulators with planar, helical, and elliptical axisymmetric magnetic fields with higher field harmonics. For these undulators, we obtain exact analytic expressions for generalized Bessel functions and Bessel coefficients. Analytic results are compared with the results of numerical simulation. We analyze the effect of additional third field harmonic on radiation emitted by these undulators. For a helical undulator with an additional asymmetric third harmonic field, it is found that the fifth harmonic of undulator radiation prevails over the third harmonic. We perform 3D simulation of radiation from free-electron laser with such an undulator using the specially developed numerical program that accounts for the electron energy spread in the beam as well as betatron oscillations. We analyze two-frequency undulator with a harmonic elliptically polarized magnetic field and simulate radiation of a free-electron laser with such an undulator.