# From Femtoseconds to Hours--Measuring Dynamics over 18 Orders of Magnitude with Coherent X-rays
## 4 Studies
### XPCS at Free-Electron Laser Sources
#### 4.2.4 Split-And-Delay Lines  
In order to produce two FEL pulses, so-called split-and-delay lines are used. Therein, the FEL pulse is split in two pulses that proceed on different routes with tunable lengths introducing a delay between them. For dynamics studies, both pulses generate a speckle pattern whose sum is measured by the detector. The dynamics are obtained as described above, considering the intensity splitting ratio and the overlap between the two pulses. Due to spatial restrictions, delays up to few nanoseconds can be achieved by such devices. Special accelerator modi have been introduced at the FEL machines, that allow generation of double pulse, however, limited to multiples of a fundamental radio-frequency of the accelerator, e.g., 350 ps at LCLS [168; 169]. Shorter time scales, or flexible choice of longer ones, demand the application of a split-and-delay line. Here, the pulses are split either by amplitude, i.e., using thin crystals [170], or geometrically by wavefront splitting [171]. The first split-and-delay device has been installed at LCLS (see Figure 12) [172; 173; 174], others have followed or are currently under commissioning at other sources [175; 176; 177; 178]. For dynamics studies, both beams need to probe the same sample volume. This introduces several challenges, e.g., as both beams may experience different sizes or shapes, that have an impact on the measured speckle contrasts because of partially overlapping beams [179; 180]. Furthermore, the pulses are reflected by several silicon mirrors with fixed bandwidth, resulting to large pulse-to-pulse intensity fluctuations as only few of the spectral spikes generated in the SASE process are transmitted through the split-and  
Figure 11: Dynamics of liquid water measured at FEL facilities. (**a**) By changing the pulse width, the speckle contrast obtained by XSVS follows expectations from molecular dynamics simulations [30]. (**b**) Longer times are achieved using a split-and-delay device at SACLA, where the speckle contrast depends on the pulse intensity suggesting radiation-induced dynamics [31]. Figures are reprinted from [30; 31] under CC-BY 4.0.  
delay unit [157]. Nevertheless, first experiments have been successfully performed using these devices. [PERSON] et al. demonstrated the application of a hard X-ray split-and-delay line at LCLS [57]. The authors measured diffusion dynamics of gold particles of 1 nm radius. Furthermore, they demonstrated the extraction of speckle contrast for different splitting ratios as well as the importance of measuring the single pulse contrast from static samples. Instead of probing different delay points, a fixed delay of 1.3 ns was used and the \(q\)-dependence of the intermediate scattering function was analyzed. As the scattered intensity was below 0.01 photons per seconds, a dedicated maximum-likelihood approach was introduced for data analysis. [PERSON] et al. applied the split-and-delay line of SACLA for studying the dynamics of liquid water [31]. By using self-seeded X-ray pulses, the spectral width was reduced and thus the pulse energy that passed the split-and-delay-line increased. This enabled the authors to study the atomic-scale dynamics of water up to 2 ps, see Figure 11b. The speckle contrast was found to depend on the delay time as expected from theory and inelastic X-ray scattering. Furthermore, fast heating of water by the first pulse was observed at high pulse fluences, which on the one hand did not allow measurement of equilibrium dynamics from such pulses, on the other hand demonstrates the usage of split-and-delay lines for pump-probe applications. Nevertheless, these studies promise to use split-and-delay techniques in a pump-probe or laser pump - X-ray probe-probe scheme for many other questions, e.g., tracking the kinetics of melting of different materials on femto- to picosecond time scales by laser or X-ray pulses [181; 182; 183]. Figure 12: Top: Photograph of the first split-and-delay line [174] installed at the XCS instrument of LCLS.