# From Femtoseconds to Hours--Measuring Dynamics over 18 Orders of Magnitude with Coherent X-rays
## 4 Studies
### XPCS at Free-Electron Laser Sources  
Revealing ultrafast dynamics on molecular length scale is a key science question motivating the design and construction of free-electron lasers in the hard X-ray regime in the last two decades. The LCLS [143; 144], SACLA [145], PAL-XFEL [146], and SwissFEL [147] provide single pulses with repetition rates around 100 Hz, whereas the European XFEL [148] is based on superconducting accelerator technology and allows for experiments using MHz rates. Due to the exceptional coherence obtained at these facilities, they are supposed to be perfectly suited for XPCS and XSVS experiments. Especially in the soft X-ray regime, their high degree of coherence was proven by double-slit experiments [60; 149; 150; 151]. For hard X-rays, coherence properties have been obtained from speckle patterns from amorphous samples as discussed above [59; 152; 153; 154; 155].  
Due to the short pulse length in the femtosecond range, XFEL facilities are particularly suited for XSVS experiments, using both double pulses from a split-and-delay line or single pulses with varying lengths. Examples for both are presented below. Apart from that, even with repetition rates in the 100 Hz range, XFEL sources provide still an average coherent flux per second that exceeds storage-ring source by two to three orders of magnitude. This enables studies of slow dynamics in weakly scattering materials in the range of milliseconds. Furthermore, MHz repetition rates have become available at the European XFEL and will be provided at LCLS-II, which can currently only be achieved for special cases at storage-ring sources as shown in the previous section. However, the application of such sequential-mode XPCS at FEL sources is challenging for several reasons [156]:  
1. Because of the exceptional high peak intensity the sample may be damaged after the first pulse.  
Figure 9: MHz XPCS from diffusion of silica nanoparticles in water at (**a**) beamline 8-ID of APS using a prototype of the XSPA detector [81] and (**b**) beamline P10 of PETRA III using AGIPD [35]. The inset in panel a shows the relaxation time as function of \(q\), the solid line is a fit with the slope of \(-2\). Figure from [81] reproduced with permission of the International Union of Crystallography, figure from [35] reproduced under CC-BY 4.0.  
2. SASE fluctuations of energy, intensity and coherence, but even more pointing, wavelength and beam size may lead to decorrelation as every pulse probes a different sample spot under different beam conditions [157; 158].
3. Typically, the full SASE beam without monochromator (pink beam) is used at FEL sources, making large \(q\) experiment impossible because the large bandwidth leads to very low speckle contrasts (see Figure 6).  
Attempts how to circumvent these challenges are discussed in the following two sections, presenting the first sequential-mode XPCS experiments at LCLS, SACLA and European XFEL. This studies particularly demonstrate the performance of sequential-mode XPCS, double-pulse XSVS using split-and-delay devices as well as single pulse XSVS as proposed more than a decade ago as a science case for such FEL [156; 159].