Short-pulse length effects of the seed laser in high-gain harmonic generation free-electron laser

In order to generate coherent hard x-ray free-electron laser ( FEL), cascading stages of high-gain harmonic generation ( HGHG) scheme usually employ seed pulse with longitudinal length down to tens of femtoseconds. Such a short pulse length ( SPL) seed laser, with broad bandwidth in the spectral domain, can no longer be characterized by monochromatic light in FEL equations. In this paper, a set of self-consistent, multifrequency FEL equations is derived to describe the interaction between the seed laser and the electrons in the modulator of HGHG. Moreover, the SPL effects of the seed laser on the electron beam's energy modulation, the output pulse length, the output peak power, and the output wavelength tuning in HGHG are theoretically and numerically investigated. Study demonstrates that the SPL seed laser seriously and significantly influences the HGHG performances, and these influences have to be taken into account in the design and optimization of the seeded FEL scheme.