## 3 Discussion  
The analysis presented here concludes that, given the polychromatic chirped XFEL pulse currently available at SwissFEL, the instantaneous bandwidths throughout the pulse correspond to time intervals between \(\approx\) 50-150 as. In principle, this matches the shortest possible time that high-resolution reflections can spend in stimulated conditions (Figure 5). In order to analyze diffraction to the maximum possible time resolution determined by the instantaneous bandwidth, the precise position in the chirped pulse needs to be determined by fully resolving the X-ray energy for each reflection, with additional deconvolution of rare multiples. This would rely on stationary analysis with full knowledge of the chirped pulse spectral parameters. The intensity profile would need to be known as wavelength normalization from polychromatic data requires multiple symmetry-related reflections to be measured which are stimulated by different energies to derive a \(\lambda\)-curve. For spontaneous X-ray sources, they are typically fitted to Chebyshev polynomials [59; 60; 61; 62; 63]. Time-resolving structure factor amplitudes within the chirped pulse therefore prevents \(\lambda\)-curve fitting. The chirp magnitude may additionally contribute to the experimental time resolution, as between 2 fs and 8 fs elapse for the \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Input Parameter** & \multicolumn{3}{c}{**Value**} \\ \hline UNIT\_CELL\_A-AXIS & \(-41.745625\) & \(-19.906780\) & \(47.598270\) \\ UNIT\_CELL\_B-AXIS & \(24.133776\) & \(-43.948139\) & \(-43.482101\) \\ UNIT\_CELL\_C-AXIS & \(31.530138\) & \(-7.105332\) & \(24.681583\) \\ EXPOSURE FACTOR & 1 & & \\ GAIN & 1 & & \\ BACKGROUND & 20 & & \\ BIG\_CRYSTAL & TRUE & & \\ BEAM\_STDDEV & 0.1 & 0.1 & \\ CELL\_STDDEV & 0.04 & 0.04 & 0.04 \\ ORIENTATION\_STDDEV & 0.04 & 0.04 & 0.04 \\ OSCILLATION\_RANGE & 0.01 & & \\ DETECTOR\_DISTANCE & 59.1 mm & & \\ INCIDENT\_BEAM\_DIRECTION & 0.0 & 0.008727 & 0.99999619 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Input parameters for SIM-MX simulations. Figure 8: Comparison of the time/energy streaking in space in the same reflections at two different chirps (top panels against bottom panels). Reflections are labeled with their Miller indices. instantaneous frequency to be modified by the magnitude of the instantaneous bandwidth (Figure 3). The practical limit to the time resolution, purely from the point of X-ray diffraction observation, will therefore be affected by the ability to determine the X-ray energy for each reflection, which reports on the progression of time within the chirped XFEL pulse. Practically, a stationary analysis would find a wavelength assignment with high accuracy. While the chirp magnitude from the simulation remains relatively constant at approximately \(\approx 5\) eV/fs in the central part of the pulse that contains most intensity (Figure 3c), the instantaneous bandwidth varies between values of 40 eV and 10 eV (Figure 3a). Therefore, a resolution of 200 as would require experimental determination of a change of \(\approx 1\) eV in the instantaneous frequency from the integrated intensities. Considering the spectral structure of XFEL pulses, there may be limits arising from signal-to-noise to fully exploit the time-resolved analysis of chirped-pulse crystallography. From the simulations performed, gradients across individual low-resolution reflections are observable as well as different high-resolution reflections integrated by different energies over the course of the single pulse. It is clear that an increase in chirp magnitude allows a better distinction of specific energies: maximizing this parameter will become crucial when addressing the signal-to-noise ratio in an experimental setting. While this result is based solely on the properties of the XFEL pulse and reciprocal space, there are still several limitations that currently lower the experimentally achievable time resolution from its theoretical limit.