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.
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