find $\Delta t = 198\,$fs. This is close to the value found in the simulation (right panel of Fig. \[Figure\_output\_Perseo\]), that is $\Delta t = 186\,$fs. Therefore, we claim that the agreement between theoretical, experimental and numerical studies can be considered as very satisfactory.

![Predicted FEL spectral and temporal profiles obtained using the the numerical code Perseo, 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; electron beam peak current $300\,$A, normalized transverse emittance $1\,$mm-mrad and relative energy spread $0.01\%$; undulators tuned to the $6^{th}$ harmonic of the seed ($43.5\,$nm). The dashed line represents the results obtained using an ideal, constant current, chirpless electron beam. The solid line shows simulation results for an electron beam with a current profile corresponding to Fig. \[Figure\_ebeam\_measurement\] and energy chirps of $1\,$MeV/ps (linear) and $7\,$MeV/ps$^2$ (quadratic).[]{data-label="Figure_output_Perseo"}](Figure_output_Perseo){width="50.00000%"}

For this set of data, the spectral peaks have similar bandwidths $\sigma_{\lambda} \approx 0.028~nm$, and the temporal pulses have similar durations, i.e., $\sigma_t \approx 30~fs$. According to these numbers, the duration of each sub-pulse is $\approx 1.6$ times greater than the Fourier-transform limit for a Gaussian spectrum. The distance from the Fourier-transform limit can be further 