Two-frequency undulator in a short SASE FEL for angstrom wavelengths

Abstract

We perform a theoretical study and modeling of harmonic evolution in an x-ray single-pass free-electron laser (FEL) with a two-frequency undulator and phase shifters. For this purpose a phenomenological FEL model is developed and validated; it accounts for all losses individually for each harmonic. The model was tested with FEL experiments, covering radiation wavelengths ranging from 0.15–500 nm. An example of the LCLS experiment modeling with 1.5 angstrom radiation is presented. The phenomenological description is based on a few main FEL parameters: electron beam current, energy and its spread, and emittance. The results match well with measurements and numerical simulations in various conditions. We model the harmonic bunching and power evolution in an x-ray FEL with a two-frequency undulator, in which the first and third harmonics are suppressed between the undulator sections by phase shifts of kπ/5, k = 2, 4,… of the electrons with respect to the photons. The advantages of the two-frequency undulator in such phase-shifted FELs are highlighted. The possibility to produce intense x-ray radiation by the dominant fifth harmonic in the linear regime is demonstrated. The radiation at subnanometric wavelength λ5 = 0.15 nm from electrons with E = 5.47 GeV energy and I ∼ 3.66 kA current already reaches ∼14 GW power at 30 m. This is shorter than the saturation length of the common undulator FEL with its fundamental harmonic at the same wavelength. The power boost and the reduction of the saturation length are complemented by 2.5 times lower electron energy and 3 times lower FEL-induced energy spread. The harmonic power increase can be up to 104 times greater than that in a common planar undulator FEL.