Ultra-high harmonic conversion of a seeded free-electron laser via harmonic optical klystron

External seeded free-electron lasers (FELs) have proven to be compelling tools for generating fully coherent EUV and soft X-ray radiations. Echo-enabled harmonic generation (EEHG), as the most typical representative of external seeded FELs, has unparalleled harmonic conversion efficiency. However, due to the limitations of various collective effects, the harmonic conversion of a high-gain EEHG that has been proved in experiments does not exceed 50 times. This paper proposes a new EEHG technology with the help of harmonic optical klystron technology, which can effectively increase the number of harmonic conversion to about 100 times. Theoretical analysis and numerical simulations show that intense and almost fully coherent FEL pulses with a radiation wavelength of 3 nm can be generated. At the same time, the seed laser intensity required by this scheme is lower, compared to nominal EEHG, thus facilitating the generation of high repetition rate seeded FELs.