0\,$nm is the (theoretical) duration of a Fourier-transform limited pulse.[]{data-label="Figure_seed_data_without_alphabeta"}](Figure_seed_data_without_alphabeta){width="50.00000%"}

For a given spectral bandwidth, the presence of chirp in the seed pulse will increase its temporal duration. At two positions separated by $4\sigma_t$ and symmetric with respect to the center of the pulse, the electron bunch experiences $13.5\%$ of the maximum intensity of a Gaussian profile seed. For our seed laser parameters, efficient seeding seems difficult below $10\%$ of the peak intensity, i.e., on the very far edges of the seed pulse. Therefore, we may consider $4\sigma_t$ as the maximum practically achievable $\Delta t$ for a given chirp. Figure \[Figure\_seed\_data\_without\_alphabeta\] displays the evolution of the spectral separation $\Delta \lambda$ between parts of the seed located at a distance $4\sigma_t$, as a function of $\sigma_t$. Two different values of the bandwidth have been considered, corresponding to the two limiting cases at FERMI@Elettra: for a seed energy per pulse below $10\,\mu$J, the spectral bandwidth is close to $\sigma_{\lambda}=0.3\,$nm whereas, for higher energies and thus intensities, nonlinear effects can broaden the spectrum up to $\sigma_{\lambda}=0.5\,$nm. For increasing values of $\sigma_t$ (i.e., for an increasing amount of chirp), $\Delta \lambda$ reaches an asymptotic value. Examining Fig. \[Figure\_seed\_data\_without\_alphabeta\], one therefore sees for the case 