Self-enhanced coherent harmonic amplification in seeded free-electron lasers.

High-intensity, ultrashort, fully coherent X-ray pulses hold great potential for advancing spectroscopic techniques to unprecedented levels. Here, we propose a novel scheme for generating high-brightness and femtosecond-scale soft X-ray radiation within a seeded free-electron laser (FEL) operating at MHz repetition rates. This scheme relies on the principles of self-modulation and superradiance. A relatively weak energy modulation of the pre-bunched electron beam is significantly amplified by the coherent radiation emitted in the self-modulator. Consequently, a coherent signal at ultra-high harmonics of the seed is achieved, and this signal is further amplified in the subsequent radiator through the fresh bunch and superradiant processes. Based on the parameters of the Shanghai soft X-ray FEL facility, three-dimensional simulations have been performed. The simulation results demonstrate that an electron beam with a laser-induced energy modulation as small as 2.3 times the slice energy spread can generate ultrashort coherent radiation pulses of around 2 GW within the water window spectral range. Moreover, the experimental results demonstrate that self-enhanced coherent energy modulation enables the production of coherent signals up to the 15th harmonic of a 266-nm seed laser. These findings indicate that the proposed scheme promises to generate ultrashort and coherent soft X-ray pulses at MHz repetition rates.