of the FEL emission.

![Comparison of the outputs of simulations carried out with the numerical code Perseo for different values of the quadratic chirp of the electrons (left: spectrum; right: temporal intensity), for the following parameters: seed bandwidth $\sigma_{\lambda} = 0.47\,$nm, duration $\sigma_t = 93\,$fs, energy $70\,\mu$J and central wavelength $261.1\,$nm; $R_{56}= 20\,\mu$m; undulators tuned to the $6^{th}$ harmonic of the seed ($43.5\,$nm); electron beam peak current $300\,$A, normalized transverse emittance $1\,$mm-mrad, relative energy spread $0.01\%$ and no linear chirp component. Solid line: $\chi_2=-10\,$MeV/ps$^2$; dashed line: $\chi_2=10\,$MeV/ps$^2$; dotted line: $\chi_2=50\,$Mev/ps$^2$ .[]{data-label="Figure_quadratic_energy_chirp_Perseo"}](Figure_quadratic_energy_chirp_Perseo){width="70.00000%"}

Conclusion {#conclusion .unnumbered}
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We studied the mechanism leading to the generation of two spectrally- and temporally-separated radiation pulses for a seeded, harmonic upshift free-electron laser operating in the extreme ultra-violet spectral region. This mechanism, discovered and studied in detail at the FERMI@Elettra FEL facility, relies on the use of a high-power chirped seed pulse to produce strong, coherent overbunching in an electron beam; the presence of the chirp is the key element to producing a spectral splitting between the two temporal pulses. By changing either the seed laser power or the strength of the dispersive section, we demonstrated excellent control of both the temporal distance and the spectral 