# Ionization of Xenon Clusters by a Hard X-ray Laser Pulse
## 2 Experiment  
The experiments were performed at experimental hutch EH3 of beamline BL3 [41] of SACLA [3]. The apparatus used has been reported in detail elsewhere [37]. The photon energy and the photon bandwidth of X-ray pulses were 5.5 keV and \(\sim\)33 eV (full width at half maximum; FWHM), respectively. The XFEL pulse frequency was 30 Hz. The X-ray pulse has been characterized by its temporal duration that is shorter than ten femtoseconds [42]. A Kirkpatrick-Baez (KB) mirror arrangement focused the X-ray laser on the interaction point [43]. The focused beam size of the X-ray beam was measured to be \(\sim\)1 \(\upmu\)m (FWHM). A beam-position monitor [44], which was located upstream of the KB mirror arrangement and calibrated by a calorimeter [45], recorded pulse energies of XFELs shot-to-shot, and the recorded fluctuation was \(\pm\)11% (22% FWHM). At the interaction point, the XFEL peak fluence was estimated to be \(\sim\)4.6 \(\upmu\)/\(\upmu\)m\({}^{2}\) on average using a calibration procedure employing yields of oligomer fragments from ionized argon clusters [30]. The intensity of the X-ray pulses was attenuated by aluminum foils located upstream on the KB mirror arrangement. The transmittances of the aluminum foils with thicknesses of 25 and 50 \(\upmu\)m were 38% and 15%, respectively. The clusters were produced by an adiabatic expansion of xenon gas through a 250 \(\upmu\)m nozzle at room temperature. The stagnation pressures were 0.24, 0.32, and 0.65 MPa. The averaged cluster sizes, \(<\)N\(>\), were estimated to be 500, 1000, and 5000 atoms, respectively, according to the scaling law [46]. The radii of clusters were 21, 26, and 44 A, respectively. The uncertainty of the averaged cluster size was estimated to be \(\pm\)20% by the fluctuation of the stagnation pressure. Two skimmers, whose inner diameters were 0.5 and 2 mm, respectively, skimmed the cluster beam at 20 and 400 mm from the nozzle. The second skimmer was located 250 mm from the interaction point. The cluster beam perpendicularly intersects with the XFEL beam. At the interaction point, the transverse length of the cluster beam was estimated to be \(\sim\)2 mm (FWHM), i.e., shorter than the Rayleigh lengths of XFELs (\(\sim\)8 mm). Thus, electrons and ions were yielded from a cylindrical space with a diameter of \(\sim\)1 \(\upmu\)m and a height of \(\sim\)2 mm along the propagation direction of the X-ray beam. To probe the XFEL-ionized clusters, we employed NIR laser pulses with 800 nm wavelength. The focal size and pulse duration of the NIR laser were 200 \(\upmu\)m (FWHM) and 82 fs (FWHM), respectively. The X-ray and NIR lasers overlapped at the interaction point with a small angle (\(<\)1\({}^{\circ}\)). The intensity of the NIR laser was adjusted using a neutral density filter up to 5.0 \(\times\) 10\({}^{12}\) W/cm\({}^{2}\), which was too weak to ionize the ground state of xenon atoms. Our experimental results supported this conclusion (not shown). A temporal jitter between the XFEL and NIR pulses significantly restricts the intrinsic temporal resolution of the pump-probe method, determined by the temporal durations of the two pulses [47]. We did not record the arrival times of the XFEL and NIR laser pulses and thus assumed that the temporal resolution was equivalent to the typical temporal jitter between the pump-probe pulses (\(\sim\)800 fs (FWHM)) [36]. The scheme of pump-probe experiment is described in detail elsewhere [37]. Kinetic energy spectra of electrons and ionic fragments as a function of the pump-probe time-delay were measured by employing electron velocity map imaging (VMI) and ion time-of-flight (TOF) spectrometers [48], respectively. From the flight time and detected position (\(X\), \(Y\)), the kinetic energies of ions were obtained. Here, we defined the \(X\) and \(Y\) axes as being parallel to the polarization direction and the propagation of the XFEL beam, respectively.