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 Super-Conducting Linac, generating $10^{8}$-$10^{10}$ photons at 2-5 keV with abou 0.5 MHz can address this need. The seeding scheme proposed is Echo-Enabled Harmonic Generation, alimented FEL Oscillator working 13.6 nm cavity based on Mo-Si mirrors. whole chain generation here described means start-to-end simulations. Comparisons Self Amplified Spontaneus Emission fresh-bunch harmonic cascade performed similar electron beams show validity scheme.