We propose a new scheme to generate high-brightness and temporal coherent soft x-ray radiation in a seeded free-electron laser. The proposed scheme is based the coherent harmonic generation (CHG) and superradiant principles. A CHG scheme is first used to generate coherent signal at ultra-high harmonics of the seed. This coherent signal is then amplified by a series of chicane-undulator modules via the fresh bunch and superradiant processes in the following radiator. Using a representative of realistic set of parameters, three-dimensional simulations have been carried out and the simulations results demonstrated that 10 GW-level ultra-short coherent radiation pulses in the water window can be achieved by using the proposed technique.
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