# Ionization of Xenon Clusters by a Hard X-ray Laser Pulse
## 3 Results and Discussions
### XFEL Pump-NIR Probe Results
Figure 5: Electron energy spectra for xenon clusters with an average size of 5000 atoms measured at the XFEL peak fluence of \(\sim\)1.8 \(\upmu\)J/\(\upmu\)m\({}^{2}\) and the NIR intensity of 5.0 \(\times\) 10\({}^{12}\) W/cm\({}^{2}\). Red and black curves depict the electron energy spectra at the time delays of +1.3 and \(-\)4.7 ps, respectively. Blue and green curves are the difference spectra obtained by subtracting the contributions of photo- and Auger electrons, shown as the black curve of Figure 1b, from the red and black ones, respectively. This finding can be ascribed to the binding being hindering by the reduction in the number of neutral atoms in the system with the increasing \(Q\) due to the NIR heating up. Another effect of the NIR heating up can be observed on the kinetic energy of Xe\({}^{+}\). The mean kinetic energy of Xe\({}^{+}\) is \(\sim\)32 eV with the irradiation from NIR probe pulses at the time delay of +1.5 ps, which is about two times higher than the mean kinetic energy without the NIR-probe pulse. In contrast, the multiply charged ions are accelerated by the violent Coulomb explosion of the charged thin spherical shell, and the singly charged ions are mostly produced via a hydrodynamic expansion of a quasi-neutral core. As discussed with regard to the electron kinetic energy spectra measured by the pump-probe method, the additional NIR laser fields initially supply energy to the quasi-free electrons within the XFEL-ignited nanoplasma. Even if part of the absorbed energy of the quasi-free electrons must be expended by the further ionization of atoms and ions as well as the emission of heated-up electrons, the electron temperature becomes higher than the conditions without the NIR probe pulse. Since the plasma sound speed, which is the characteristic speed for hydrodynamic expansion, is proportional to the square root of the product of the electron temperature and the mean charge state of the nanoplasma [38], the formation of Xe\({}^{+}\) with the high kinetic energies has also evidenced that the XFEL-ignited nanoplasma has been heated up by the NIR probe pulses. The ion TOF spectrum as a function of the time delay is illustrated in Figure 6b. One can find that the increase in the yield of multiply charged ions occurs up to \(\sim\)10 ps time  
Figure 6: Ion TOF spectra for xenon clusters with an average size of 5000 atoms measured at the XFEL peak fluence of \(\sim\)4.6 \(\mathrm{\SIUnitSymbolMicro\SIUnitSymbolMicro}\)/\(\mathrm{\SIUnitSymbolMicro}\)m\({}^{2}\) and the NIR intensity of 5.0 \(\times\) 10\({}^{12}\) W/cm\({}^{2}\). (**a**) Red and black curves depict ion TOF spectra at the time delays of +1.5 and \(-\)1.5 ps, respectively. The contributions of Xe\({}^{+}\), Xe\({}^{2+}\), Xe\({}^{3+}\), and Xe\({}^{4+}\) ions, which have been produced from the cluster ionization, are denoted with arrows. (**b**) Ion TOF spectrum as a function of time delay. Black curves of (**c**–**h**) depict ion yields of Xe\({}^{+}\), Xe\({}^{2+}\), Xe\({}^{3+}\), Xe\({}^{4+}\), Xe\({}_{2}^{+}\), and Xe\({}_{3}^{+}\), respectively, as a function of time delay. Red and blue curves in (**c**) show the yields of Xe\({}^{+}\) with low (0–15 eV) and high (15–125 eV) kinetic energies as a function of time delay, respectively. Red and blue dashed lines indicate the mean values of the red and blue solid curves at negative time delays, respectively. delay; on the other hand, the increase and decrease in the yield of singly charged ions persist until a time delay later than \(\sim\)10 ps. In order to discuss the time-delay dependence in more detail, we show the ion yields as a function of time delay in the black curves in Figure 6c-h. The yields of Xe\({}^{2+}\), Xe\({}^{3+}\), and Xe\({}^{4+}\) increased sharply from \(\sim\)0 ps, reached peaks around 2 ps, and gradually decreased until \(\sim\)15 ps. A similar time-delay dependence has been observed in the time-resolved ion spectroscopy by using the XUV pump-NIR probe method, which has been attributed to the surface plasma resonance effect [35].