Consequently, microbunch phase variations in time only lead to phase variations in the output radiation pulse, without suppression of the output power level.

\[sec:due\] Issues affecting the performance of EEHG FEL
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Phase control is an important aspect in the development of all FEL sources based on harmonic generation. Methods for dealing with issues concerning temporal phase variations in frequency multipliers are based on the same general principle [@ROBI]: the effect of frequency multiplication by a harmonic factor $N$, is to multiply the phase variation by $N$. The EEHG scheme is obviously based on harmonic generation, but is more complicated than other schemes, and consists of two modulators, two dispersion sections, and one radiator undulator. A unique feature of EEHG scheme is the utilization of two different seed laser pulses which can have different temporal and spatial quality. It is thus natural to investigate the question whether the general principle above can also be applied to EEHG. Analytical results [@EEHG2] refer to the specific model an of infinitely long, uniform electron bunch only. This steady state model proved to be very fruitful, allowing for simple analytical expressions describing the main characteristics of EEHG scheme. However, as discussed above, the seed 