# Ionization of Xenon Clusters by a Hard X-ray Laser Pulse
## 3 Results and Discussions
### Ion TOF Spectrum of Xenon Clusters Irradiated with XFEL Pulses  
In contrast to the electron spectrum, which mainly depicts the initial stage on the ionization dynamics of atomic cluster's ignition by the irradiation of hard-X-ray pulses, the ion TOF data is expected to depict the disintegration dynamics of nanoplasma in the latter stage. Figure 2a illustrates a contour map, where the horizontal and vertical axes represent the flight time and detection position of ions, respectively. In the present configuration of the X-ray beam and the detector, the ions with zero kinetic energy reached on the center of detector, \(X\sim\) 0 mm. The highly charged ions, Xe\({}^{q+}\) (\(q\) = 4\(-\)15), were detected around the center of detector, since these ions were produced only from the inner-shell photo-ionization of unbounded atoms contained in the cluster beam. The fact that the peaks of xenon isotopes are well separated (see an inset of Figure 2a) is further evidence that the kinetic energies of highly charged ions, Xe\({}^{q+}\) (\(q\) = 4\(-\)15), have been \(\sim\)0 eV. At the present peak fluence (4.6 \(\upmu\)/\(\upmu\)m\({}^{2}\)), the contribution of sequential multiple-photon absorption by an atom [16] is negligibly small. In fact, the yield of Xe\({}^{15+}\) is almost invisible is Figure 2a. We note that the highest charge state is +14 due to the single photo-absorption of xenon atoms at 5.6 keV [53]. In Figure 2a, the images of Xe\({}^{\prime+}\) (\(q\) = 1\(-\)3) and Xe\({}^{+}_{n}\) (\(n\) = 2, 3) positions widely extend along the axis of the \(X\) position. This result demonstrates that these ions have been produced via explosions of highly charged clusters, whereas the non-energetic ions, Xe\({}^{\prime+}\) (\(q\) = 4\(-\)15), have been produced from the unbounded atoms. The fact that the highly charged ions, Xe\({}^{\prime+}\) (\(q\) \(\geq\) 4), have not been produced from the ionized clusters means that the charges do not remain on the each core-ionized atoms, but promptly spread into the whole system before the ionized cluster expands. The kinetic energy spectra of Xe\({}^{+}\), Xe\({}^{2+}\), Xe\({}^{3+}\), Xe\({}^{+}_{2}\), and Xe\({}^{+}_{3}\) are shown in Figure 2b. These kinetic energies are much smaller than those of hydrodynamic decay in NIR laser experiments [58; 59; 60]. In the previous report for argon clusters [30], the kinetic energy spectra of ionic oligomer fragments confirm that the disintegration dynamics of the XFEL-ionized clusters are strongly effected by the chemical processes, distributing the increasing net charge within the center part of the system and causing bond reorganization, which induces the formation of oligomer fragments. The kinetic energy spectra show that the singly charged ions, Xe\({}^{+}_{n}\) (\(n\) = 1\(-\)3), are mainly produced from the central part of the ionized  
Figure 2: Ion TOF data obtained from Xe\({}_{5000}\) clusters at the XFEL peak fluence of 4.6 \(\upmu\)J/\(\upmu\)m\({}^{2}\). (**a**) Flight time versus position \(X\) maps. An inset depicts the magnified region of highly charged ions, Xe\({}^{\prime+}\) (\(q\) = 4\(-\)15). (**b**) Kinetic energy spectra of Xe\({}^{+}\), Xe\({}^{2+}\), Xe\({}^{3+}\), Xe\({}^{+}_{2}\), and Xe\({}^{+}_{3}\), respectively. cluster. On the other hand, for the multiply charged ions, Xe\({}^{2+}\) and Xe\({}^{3+}\), the fraction of ions with less than 20 eV of kinetic energy account for several percent or less. This finding is presumed to result from most of the multiply charged ions being strongly accelerated during dissociation from the vicinity of the cluster surface, which was reported in the EUV experiments [61]. With the present peak fluence (\(\sim\)4.6 \(\upmu\)/\(\upmu\)m\({}^{2}\)), the ionization probability of individual xenon atoms is \(\sim\)8.7%; thus, \(\sim\)430 atoms in the cluster of \(\sim\)5000 atoms are core-ionized. Therefore, \(\sim\)400 fast and \(\sim\)2900 slow electrons are emitted from the core-ionized atoms in the cluster.