High-repetition rate and coherent free-electron laser in the tender x rays based on the echo-enabled harmonic generation of an ultraviolet oscillator pulse

Fine time-resolved analysis of matter - i.e., spectroscopy and photon scattering - in the linear response regime requires a fs-scale pulsed, high repetition rate, fully coherent x-ray source. A seeded free-electron laser (FEL) driven by a super-conducting linac, generating 108-1010 coherent photons at 2-5 keV with about 0.5 MHz of repetition rate, can address this need. The seeding scheme proposed is the echo-enabled harmonic generation, alimented by a FEL oscillator working at 13.6 nm with a cavity based on Mo-Si mirrors. The whole chain of the x-ray generation is here described by means of start-to-end simulations. Comparisons with the self-amplified spontaneous emission and a fresh-bunch harmonic cascade performed with similar electron beams show the validity of this scheme.