Hybrid echo-enabled harmonic generation scheme for seeding coherent soft x-ray free-electron lasers

A two-stage echo-enabled harmonic generation (EEHG) scheme is proposed to produce sub-nanometer coherent x-ray radiation. The proposed scheme is not a simple two-stage cascaded EEHG but consists of an EEHG as the first stage and a high-gain harmonic generation as the second stage. By using double seed laser pulses with independently tunable powers in the first stage, the second stage can also work in the EEHG principle. To study various effects on the energy bands when the electron beam is traveling through the first stage radiator, theoretical analysis and 3D simulations have been performed and the results show that the fine structure of EEHG can be well maintained. Simulations also indicate the possibility of generating fully coherent x-ray radiation around 1 nm directly from a conventional UV seed laser.