_Applied_  
_sciences_  
_The Magnitude and Waveform of Shock Waves_  
_Induced by X-ray Lasers in Water_  
**[PERSON] 1,2,*(r)**, [PERSON] 3, [PERSON] 4(r), [PERSON] 3(r), [PERSON] 3,**  
**[PERSON] 3(r), [PERSON] 3, [PERSON] 1, [PERSON] 5, [PERSON] 5,**  
**[PERSON] 5, [PERSON] 6(r), [PERSON] 5 and [PERSON] 3,6,* 1 Department of Physics, Rutgers University-Newark, Newark, NJ 07102, USA; [EMAIL_ADDRESS]**  
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The development of X-ray free-electron laser facilities (XFEL) operating in the keV photon energy regime [18; 19] opened new possibilities for depositing large energy densities in materials. Very high intensities (10\({}^{20}\) W/cm\({}^{2}\)) can be achieved with XFEL pulses because X-rays can be focused more tightly than visible light [20], and the femtosecond duration of the pulses allows the creation of high energy densities, of nonequilibrium states, and the observation of nonlinear X-ray interactions with matter [21; 22; 23].  
Given the high intensity and the femtosecond duration of XFEL pulses, they are expected to launch shock waves. In samples with thicknesses much smaller than the X-ray absorption length, the shock waves will have a cylindrical symmetry. Such shocks were observed using time-resolved optical imaging, initially in water microjets [24] and afterwards in liquid microdroplets [17]. The shocks launched by XFEL pulses may damage soft samples, such as protein crystals carried in liquid jets for serial femtosecond crystallography [25], in experiments performed at XFELs that generate MHz pulse repetition rates. While the initial experiments carried with 1.1 MHz pulse trains at the European XFEL [26] did not observe shock damage in protein crystals [27; 28; 29], it remains possible that shock damage will occur if such experiments are conducted at the maximum possible pulse rate of 4.4 MHz [30].  
The reflection of XFEL shocks at the surface of liquid jets and drops was observed to lead to spallation in droplets [17] and to the generation of shock trains in jets [24; 30]. In both cases these phenomena had features not observed in similar experiments with pulsed optical lasers, including the generation of very large negative pressures in drops [17], and the generation of very large sound intensities in jets [30]. The quantitative characterization of these phenomena had large uncertainties or significant noise, which was caused in part by incomplete knowledge of the properties of the initial shock launched by the XFEL pulse, such as the shock waveform.  
Here, we report a more precise characterization of shock waves induced by hard XFEL pulses in water, based on measurements of the surface velocity of water microdrops during the reflection of the shock. Improvements in the experimental design allowed us to resolve and measure the decay of the shock pressure after the shock discontinuity, while covering a range of one and a half orders of magnitude in the XFEL pulse energy.