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The beam energy spread at the entrance of undulator system is of paramountimportance for efficient density modulation in high-gain seeded free-electronlasers (FELs). In this paper, the dependences of high harmonic micro-bunchingin the high-gain harmonic generation (HGHG), echo-enabled harmonic generation(EEHG) and phase-merging enhanced harmonic generation (PEHG) schemes on theelectron energy spread distribution are studied. Theoretical investigations andmulti-dimensional numerical simulations are applied to the cases of uniform andsaddle beam energy distributions and compared to a traditional Gaussiandistribution. It shows that the uniform and saddle electron energydistributions significantly enhance the performance of HGHG-FELs, while theyalmost have no influence on EEHG and PEHG schemes. A numerical exampledemonstrates that, with about 84keV RMS uniform and/or saddle slice energyspread, the 30th harmonic radiation can be directly generated by a single-stageseeding scheme for a soft x-ray FEL facility.

Beam energy distribution influences on density modulation efficiency in seeded free-electron lasers