of FERMI@Elettra $\Delta\lambda$ is limited to about $3\,$nm. This information is important because it sets an effective limit to the spectral separation $\Delta\lambda _n$ of the two pulses generated by the FEL.\

Electron beam: energy chirp {#electron-beam-energy-chirp .unnumbered}
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As is now well known for CHG FEL’s in which the electron beam acts as an intermediary in carrying the coherent seed signal, temporal variations such as chirps in the energy profile may seriously impact the FEL output emission (see, e.g., [@Biedron_Milton_Freund; @Shaftan; @Fawley_Penn; @LutmanGreen; @Lutman]). A linear electron beam energy chirp, whose slope will be noted $\chi_{1}$, couples to the total chromatic dispersion of the dispersive section and downstream undulators resulting in a simple shift of the central wavelength of FEL emission [@Shaftan]. In principle, any corresponding gain reduction due to this shift can be compensated by either retuning the resonant wavelength of the undulators (see Eq. \[resonance\]) or by slightly adjusting the seed wavelength. However, a quadratic chirp component $\chi_{2}$ will result in spectral broadening of output emission [@Fawley_Penn; @Lutman] and, for sufficiently large magnitudes, can also reduce the FEL gain if the broadening becomes a significant fraction of the FEL’s gain bandwidth. In principle, here too the effect 