Slippage effect on energy modulation in seeded free-electron lasers with frequency chirped seed laser pulses

Free-electron lasers (FELs) seeded with external lasers hold great promise for generating high power radiation with nearly transform-limited bandwidth in the soft x-ray region. However, it has been pointed out that the initial seed laser phase error will be amplified by the frequency up-conversion process, which may degrade the quality of the output radiation produced by a harmonic generation scheme. In this paper, theoretical and simulation studies on frequency chirp amplification in seeded FEL schemes with slippage effect taken into account are presented. It is found that the seed laser imperfection experienced by the electron beam can be significantly smoothed by the slippage effect in the modulator when the slippage length is comparable to the seed laser pulse length. This smoothing effect allows one to preserve the excellent temporal coherence of seeded FELs in the presence of large frequency chirp in the seed laser. Our studies show that the tolerance on frequency chirp in the seed laser for generating nearly transform-limited soft x-ray pulses in seeded FELs is much looser than previously thought and fully coherent radiation at nanometer wavelength may be reached with current technologies.