On the physics of generation of even and odd harmonics in the undulators of free electron lasers

Abstract

We theoretically explore the physics of even and odd harmonics generation and radiation in undulators of single pass free electron lasers (FELs). Planar undulators are studied as a most common design. The results are obtained analytically and some of them also numerically. In the analytical form the contributions of various factors to the harmonic generation are distinguished and their effect is analyzed. The results are verified with numerical simulations and compared with reported experimental data; the data for best documented FELs in terms of harmonic generation, LEUTL and LCLS, is analyzed. The reasons for even harmonic generation are identified; we show that they differ for the spontaneous undulator radiation and for the stimulated FEL radiation. Comparative analysis is performed with various theoretical models for the FEL harmonic powers. The advantages and possibilities of amplification and radiation the second FEL harmonic in the LCLS-II FEL with variable deflection parameter is demonstrated for the harmonic lasing self-seed (HLSS) FEL design. The possibility to suppress the radiated second harmonic in a FEL by a guiding field of a weak second harmonic of the main undulator field with negative phase is shown. This can be used to reduce the reflected signal of the second harmonic generation (SHG) when the nonlinear harmonic response of the mater is investigated.