  Free-electron lasers (FELs) seeded with external lasers hold great promise
for generating high power radiation with nearly transform-limited bandwidth in
soft x-ray region. However, it has been pointed out that the initial seed laser
noise 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 for laser phase error
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 laser pulse length.
This smoothing effect allows one to preserve the excellent temporal coherence
of seeded FELs in presence of large laser phase errors. For ultra-short UV seed
lasers with FWHM around 16 fs, the slippage length in a modulator with ~30
undulator periods is typically comparable to the laser width; for longer seed
laser pulses with FWHM around 80 fs, the slippage length can be made comparable
to the laser width using a modulator tuned at the sub-harmonic of the UV seed
laser. Three-dimensional simulations have been carried out for a soft x-ray
facility using seed laser pulses with large frequency chirp and the results
show that the sensitivity of the bandwidth of the seeded FEL to the initial
frequency chirp can be significantly reduced by a proper design of the
modulator such that the slippage length is comparable to the laser width. Our
studies show that the tolerance on laser phase error 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.
