## 2 Results  
### SwissFEL Chirped Broadband Simulations  
Simulations of the SwissFEL pulse at three chirps (1%, 2%, and 4%) are presented in this paper (Figure 2). For the simulations, the results of measured beam parameters from the machine were used, when it was configured for large bandwidth operation [31]. This characterization of the electron beam was done at the injection point into the undulator, using a transverse deflector in order to obtain time-resolved beam parameters. We measured the current profile, the slice emittances, and the longitudinal phase space distribution. To the latter, we fitted a polynomial to determine the mean energy of the electron beam slices. With these parameters, we generated the input decks for the GENESIS simulation. Therefore, the results of the 2% chirp case actually reflect the existing machine settings, and the modeled pulse energy and spectral width agree well with the observed quantities. For the other two cases, the polynomial fit to the longitudinal phase space distribution was scaled by the factors 2.0 and 0.5 respectively, while keeping the other input parameters the same. This was done without demonstrating the feasibility of a different chirp at the machine. While it is straightforward to reduce the chirp, a larger chirp requires additional hardware, such as a dechirper, or a significant change in the compression configuration. Both approaches will be explored in upcoming machine studies at SwissFEL. The simulation output contains the radiation power and phase as a function of the time within the time-window of the simulation. This is the basis for the calculation of the WVD, which then is used to calculate the time-resolved central frequency and the associated width of the chirped FEL pulse. From the WVD, the flux, IF, and instantaneous FWHM (FWHM\({}_{\text{in}}\)) can be extracted for the simulated chirps (Figure 2). We evaluate two conditions. Firstly, we consider the time intervals given by BW\({}_{\text{in}}\) at different times in the pulse. Secondly, we assess the ratio between BW\({}_{\text{in}}\) and BW\({}_{\text{req}}\) to determine the expected integration time across resolutions. Among the available simulations, the largest chirp and bandwidth of 4% is expected to result in the best time resolution and was thus chosen for the following analysis. The values for IF and FWHM\({}_{\text{in}}\) vary significantly over the course of the pulse  
Figure 1: Effect of beam convergence (\(\gamma\)) and mosaicity (\(\eta\)) on the reflection bandwidth (BW\({}_{\text{req}}\)). BW\({}_{\text{req}}\) depends on the sum of \(\gamma\) and \(\eta\) and on the distance of the reciprocal lattice point from the reciprocal space origin (d\({}^{\bullet}\)). The minimum (\(\lambda_{\text{min}}\)) and maximum (\(\lambda_{\text{max}}\)) wavelengths of the spot bandwidth are shown together with the energy gradient across the reflection. (Figure 2), which means that the two points above need to be evaluated separately for different time bins. For calculations, only the central 20-fs of the WVD (between 52 and 72 fs) were included, as this is where the flux is concentrated (Figure 3). The early and late times contribute only very weakly to the total pulse intensity. This slicing reduces the available chirp from 4% to approximately 1.5%, which is the realistically usable chirp. A short-range \"single-shot\" autocorrelation of this part of the SwissFEL simulation (Figure 3d) shows that the width of a single spike at SwissFEL is expected to be on the same range as at LCLS (200 as). Figure 2: SwissFEL pulse characterization. Wigner–Ville distribution (WVD) for three available chirps: (**a**) 1% (**b**) 2%, and (**c**) 4%. (**d,e,f**) pulse characterization of the entire 120-fs 4% chirp SwissFEL pulse provided by analysis of the WVD. Instantaneous full width half maximum (FWHM\({}_{\text{in}}\)) (**d**) flux (**e**) and IF (**f**) values are plotted. The frequency chirp is observable in the IF increase over time and the FWHM\({}_{\text{in}}\) is seen to change across the pulse.