research and development activities must be performed in order to reach the required temporal quality. To the best of our knowledge, there is only one article[^1] reporting on the impact of temporal variations in seed laser pulses on EEHG FEL output radiation characteristics, [@EETOL3]. The analysis in [@EETOL3] is based on numerical simulations in the case of $1.2$ nm output radiation wavelength. According to results of the sensitivity study in [@EETOL3], the phase of the $202$ nm seed laser pulse (corresponding to the fourth harmonic of a Ti:Sa laser) must to be controlled to within $0.5$ degrees. Consequently, the phase of the Ti:Sa laser output must to be controlled to within roughly $0.1$ degrees. This result is consistent with our analysis, which is performed at a very elementary level.

We also evaluate the impact on the EEHG FEL output of wavefront errors in the seed laser. In the case of ideal performance, the seed (UV) laser beam must be characterized by a flat (i.e. diffraction-limited) wavefront in the waist plane in the middle of the modulator undulator. If the wavefront exhibits errors, errors in the microbuch wavefront follow, which are multiplied by the frequency multiplication factor. These microbunch wavefront errors 