Soft X-ray generation in cascade SASE FEL with two-frequency undulator

The generation of soft X-ray radiation in cascade self-amplified spontaneous emission free electron laser (SASE FEL) using harmonics of a two-frequency undulator is studied. An advanced phenomenological model of SASE FEL, accounting for the properties of the undulator and of the electron beam, including major losses, is employed. The account for the beam energy spread, divergence and diffraction is harmonic dependent, which is a step forward from the previous models and phenomenological approach, which consider all the losses independent of the harmonic number. The model is validated with the experimental measurements of the FEL harmonic generation and with relevant three-dimensional numerical simulations. The model is adopted for the description of cascading SASE FELs. With its help the dynamics of high-gain harmonic generation (HGHG) SASE FEL cascades is analyzed to obtain the maximum high harmonic power in the X-ray band with the lowest possible seed frequency and the shortest FEL length. The advantages of the two-frequency undulator for SASE FEL in this context are demonstrated and the possibility of its usage in cascading HGHG SASE FEL is shown. Several types of cascade FELs with two-frequency undulators are simulated. Frequency multiplication in two, three and four stage cascades is introduced to obtain soft X-ray radiation. The possibility of the generation of a powerful radiation, 75 MW at lambda similar to 2.5-4.5 nm and a lower intensity 3rd harmonic, 100 kW at lambda similar to 1 nm, is demonstrated in multi-cascade FELs at just 20-35 meters with the seed wavelengths lambda(seed) similar to 140nm, similar to 40 nm and similar to 11-13 nm. Copyright (C) EPLA, 2017