Spontaneous and Stimulated Undulator Radiation in Symmetric and Asymmetric Multi-Periodic Magnetic Fields

In this work, the radiation from electrons in multi-periodic undulator fields with symmetric and asymmetric harmonics was analyzed using generalized Bessel functions formalism. The asymmetric, symmetric, anti-symmetric periodic magnetic were studied order to get enhanced of high (UR). effect on spontaneous stimulated UR explored. exact integral forms for coefficients obtained undulators general field harmonics. Spectral properties several configurations compared each other. resulting spectrum harmonic intensities analytically form integrals respective results that numerically SPECTRA program. dimensionless scaling parameter a free electron laser (FEL)—the Pierce (ρ)—was computed different considered undulators. We differences behavior high-gain single pass FEL same variable deflection (k) considered. k (deflection common planar undulator) context, an experiment strength at FLASH 2 analyzed; shorter saturated length self-seeding (HHSS) regime vs. self-amplified emission (SASE) is explained.