  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.

Accelerator Physics;Optics