Multispectroscopic Study of Single Xe Clusters Using XFEL Pulses

X-ray free-electron lasers (XFELs) deliver ultrashort coherent laser pulses in the X-ray spectral regime, enabling novel investigations into the structure of individual nanoscale samples. In this work, we demonstrate how single-shot small-angle X-ray scattering (SAXS) measurements combined with fluorescence and ion time-of-flight (TOF) spectroscopy can be used to obtain size- and structure-selective evaluation of the light-matter interaction processes on the nanoscale. We recorded the SAXS images of single xenon clusters using XFEL pulses provided by the SPring-8 Angstrom compact free-electron laser (SACLA). The XFEL fluences and the radii of the clusters at the reaction point were evaluated and the ion TOF spectra and fluorescence spectra were sorted accordingly. We found that the XFEL fluence and cluster size extracted from the diffraction patterns showed a clear correlation with the fluorescence and ion TOF spectra. Our results demonstrate the effectiveness of the multispectroscopic approach for exploring laser–matter interaction in the X-ray regime without the influence of the size distribution of samples and the fluence distribution of the incident XFEL pulses.

Early experimental studies started with ion spectrometry, from which, unexpected energetic ion emissions, even in the short wavelength (extreme ultraviolet to X-ray) regime, were reported [9]. This stimulated discussion regarding the dynamics in clusters based on the spectra obtained by averaging over the ensemble of shots of the incident laser pulses. Pioneering works [18,22,33,34] revealed that the properties of individual particles are concealed by the accumulation of spectra due to the laser profile and to the size distribution and structural isomers of clusters originating from the generation methods.
X-ray free-electron laser (XFEL) sources provide a new pathway for the analysis of the structure of single particles. Intense and short X-ray pulses delivered from XFELs allow for the investigation of the structure of nanoscale samples and biomolecules [35,36] in the particle-by-particle regime, based on the diffraction before destruction scheme [37]. The structural analysis of free-flying clusters has been demonstrated by single-shot diffraction experiments [18][19][20][21]23,24,32]. The combination of single-shot imaging with spectroscopy allows for the studies of the laser-matter interaction, where experimental parameters such as the size and structure of the single particle target and the intensity of the irradiated laser pulses at the interaction point can be determined as additional parameters for the data analysis. This selective multispectroscopy has recently been proven to be valid in studies using the combination of small-angle X-ray scattering (SAXS) with ion spectroscopy [18,22]. In these studies, the characteristic and systematic structural ion spectra were specified by filtering the sample size and the intensity of XFEL pulses.
In this work, we present results of enhanced multispectroscopic measurements with XFEL pulses. We recorded SAXS signals from Xe clusters in combination with ion time-of-flight (TOF) spectra and fluorescence spectra for every XFEL pulse. We observed clear diffraction patterns from Xe clusters and extracted both the XFEL fluence at the actual interaction point and the cluster size from them. We found that the XFEL fluence and the cluster size had a clear correlation with the fluorescence and ion TOF spectra. Our results on the fluence dependence of the maximum charge state and the mean charge state of Xe ions in the hard X-ray regime are in good agreement with preceding works in the soft X-ray and ultraviolet spectral regime [18,22].

Materials and Methods
The experiment was carried out at the experimental hutch 3 of beamline 3 at the SACLA XFEL [38]. The details of the experimental setup have been described in detail elsewhere [39]; thus, we only summarize the experimental conditions briefly. A schematic of the experimental setup is shown in Figure 1. The wavelength of the XFEL was 2.2 Å (corresponding to a photon energy of 5.5 keV). The XFEL pulses were focused with a Kirkpatrick-Baez (KB) mirror system to a focal spot size of 1.5 × 1.3 µm 2 (full width at half maximum). The average peak fluence of the XFEL pulses during the measurements, J 0 , was determined to be approximately 16 µJ/µm 2 . The stray light from the KB mirror system was reduced using a 0.3 × 0.3 mm square aperture in a 0.5 mm tungsten plate, installed 200 mm upstream of the interaction point. Xe clusters were prepared by expanding Xe gas adiabatically through a pulsed valve equipped with a convergent-divergent nozzle with a diameter of 200 µm and a half angle of 4 • . The stagnation pressure P 0 and temperature T 0 were 21 bar and 300 K, respectively. For the experiments, we used extremely large clusters by timing the valve closure to the after-pulses as described in detail by Rupp et al. [23]. The shot-by-shot scattering signals were recorded using an octal multiport charge-coupled device (MPCCD) sensor [40]. The detector covered a scattering angle range of 0.10-2.8 • , which corresponds to a momentum transfer of q = 0.049-1.4 nm −1 . In coincidence with each scattering signal, the fluorescence photons from the clusters were detected with two MPCCD single sensors set in the plane determined by the directions of XFEL and cluster pulses. Be windows separated the sensors from the main chamber. The ions were extracted with a TOF spectrometer equipped with microchannel plates and a delay-line anode (Roentdek HEX 80) [3].  Figure 2 shows examples of SAXS images, fluorescence spectra, and ion TOF spectra from Xe clusters recorded in coincidence for each FEL pulse. Under our experimental conditions, the hit rate determined by the ratio of observed SAXS signals in the octal MPCCD sensor to the total number of FEL shots was less than 0.1%. Therefore, the recorded data of each FEL shot were considered to originate from a single cluster in the focus of the FEL pulse. In the SAXS images, we observed clear concentric diffraction rings which suggest a spherical shape of the Xe clusters. We analyzed the SAXS images with respect to the size of the Xe clusters as well as the fluence of XFEL pulses at the actual interaction point, described in detail in the following section. The obtained values of cluster size and XFEL fluence are summarized below in the panels (a), (d), and (g) in Figure 2. Further, Figure 2a-c shows the SAXS, fluorescence, and TOF spectra recorded at the highest fluence. Here, the diffraction pattern had a high intensity. The fluorescence spectrum shows an evident peak at around 5 keV, at the high energy side of the dark signal peak of the MPCCD sensor around 0 keV. Highly-charged ions were observed in the TOF spectrum. As the XFEL fluence decreased, as shown in Figure 2d-i, the SAXS signals got weaker, the yield of fluorescence photons decreased, and less highly charged ions were observed, while ions in the lower charge state appeared more prominently. These results indicate that XFEL-cluster interaction can be studied more accurately using size-and fluence-selective measurements, i.e., by eliminating the washout of characteristics of single targets due to their size distribution and laser profile [18,22,33,34].

Figure 2.
Characteristic results of the multispectroscopic measurements. Each diffraction image, fluorescence spectrum, and ion TOF spectrum shown in (a-c), (d-f), and (g-i) are observed from Xe clusters with the radii of cluster and the fluence (r 0 , J 0 ) of (130 nm, 9.2 µJ/µm 2 ), (68 nm, 6.7 µJ/µm 2 ), and (72 nm, 2.1 µJ/µm 2 ), respectively. Scattered intensity was observed in the upper region of the diffraction images (a,d,g), which came from the parasitic scattering of the XFEL pulses due to the configuration of the upstream optical system.

Analysis of Small-Angle X-ray Scattering Data
The majority of the observed SAXS images exhibited concentric rings suggesting spherically shaped clusters. Additionally, we observed a few images indicating nonspherical clusters under the present conditions [41], as reported in the preceding works [20,21,23]. For the concentric ring SAXS images, we deduced both the radii of clusters and XFEL fluences by assuming a single uniformly dense sphere. It is noted that the absorption efficiency of 5.5 keV photons by a Xe atom is very low and the scattering from electrons bound to Xe atoms can be expressed by Thomson scattering [42]. In the regime of infrared to soft X-ray, the scattering is well described by Mie scattering [43], where the absorption efficiency of a Xe atom is much higher [20]. Figure 3a shows the typical radial profiles derived from diffraction images and the corresponding fitting curves. The fits, assuming a single uniformly dense sphere and Thomson scattering, reproduced the experimental results well. Figure 3b shows the histogram of radii of the observed Xe clusters and a curve (black dotted line) describing a log-normal distribution of the cluster size. The cluster radii peaked around 70 nm, but also much larger clusters were observed. The large cluster's radii go well beyond the well-known scaling law [44,45] (25-44 nm) as a result of our specific experimental conditions, i.e., timing the jet to an after pulse to generate extremely large clusters [23].

Fluorescence Spectroscopy
We evaluated the energy and the number of fluorescence photons coming from Xe clusters for the spectra shown in Figure 2b,e,h. Under conditions where the intensity of the incident beam is not extremely high, the number of fluorescence photons from a cluster, N f lu , can be assumed to be proportional to the product of J 0 and the cluster volume, i.e., the number of atoms in the cluster N (∝ r 3 0 ). On the other hand, the number of scattered photons, N scat , is proportional to the product of J 0 and N 4/3 (∝ r 4 0 ) considering spherical shaped clusters. Therefore, one can expect a relation between N f lu and N scat as N f lu × r 0 ∝ N scat . We extracted the number of fluorescence photons from xenon clusters by subtracting the background signals in the fluorescence spectra. We also estimated N scat from SAXS data, and checked the correlation between N f lu × r 0 and N scat , as shown in Figure 4a. In Figure 4a, there is evidence of a linear correlation between N scat and N f lu × r 0 , indicating that the observed fluorescence and scattering photons came from the same targets for each XFEL shot. We also plotted the position of the fluorescence photon peak in Figure 4b. A broad peak was found to be located at 4 keV; the position of this peak was not changed by the FEL fluence. The observed peak position corresponds to the fluorescence energies of the Xe atomic L α and L β lines. Therefore, these photons are a result of the radiative decay of inner-core excited Xe atoms in the cluster. These results show that fluorescence spectroscopy monitoring of the fluence of the incident pulses offers the possibility of studying the degree of inner ionization of samples under an intense laser field [5,6,28,46].  Figure 5 shows ion TOF spectra of Xe clusters taken under different conditions for high FEL fluences (∼8 µJ µm −2 ) in panels (a)-(c) and low FEL fluences (∼3 µJ µm −2 ) in panels (d)-(f), respectively. The charge distributions of the detected ion yields extracted from each TOF spectrum are shown in the insets of each ion TOF spectrum. Substantial TOF intensity of singly charged Xe ions was observed at a lower XFEL fluence irrespective of cluster size. On the other hand, singly charged ions were suppressed and more highly charged ions were generated at higher XFEL fluence. To investigate the dependence of the charge state on other observables, the maximum charge state and the average charge state were extracted from each TOF spectrum. (c,f) 80 nm. TOF spectra observed for high FEL fluences (∼8 µJ µm −2 ) are shown in (a-c) , and those observed for low FEL fluences (∼3 µJ µm −2 ) are shown in (d-f). Ion charge states of each peak were determined by a simulation using SIMION [47]. The charge distributions of the detected Xe ions extracted from each TOF spectrum are shown in the insets. The yields of doubly charged ions and singly charged ions are less reliable due to the lowering of detection efficiency and the saturation of the signal, which were caused by the detection of a large number of highly charged Xe ions. The baseline of spectra is corrected because it was modulated due to the lowering of detection efficiency and the detection of a large number of ions. Figure 6a,b show the XFEL fluence dependence of the maximum charge state (Z max ) and the apparent averaged charge state (Z ave ) of Xe ions. Z max increased steeply and saturated at around 12 as the XFEL fluence increased. Z ave also increased with the XFEL fluence. In the current data set, both Z max and Z ave seemed to show a slight dependence on the cluster size, but further discussion regarding the size dependence is difficult because there are limited data. Elucidation of the size dependence is an important theme for furthering our understanding of the laser-matter interaction. The strong dependence of the charge state of Xe ions on the fluence of the XFEL pulses is in agreement with the preceding studies using soft XFELs with 91 eV [18] and 800 eV [22]. Moreover, the suppression of singly charged ions and the steep increase in charge state with higher fluence also agrees well with the results using 800 eV XFEL pulses [22], suggesting the efficient suppression of electron-ion recombination. Notably, the saturated charge state observed in this study was also lower compared to the preceding studies. This difference may be due to the different excitation energy, deposition energy, and ionization efficiency of the incident photons.

Conclusions
We carried out multispectroscopic measurements of single Xe clusters at SACLA. The SAXS signals, fluorescence spectra, and ion TOF spectra of giant xenon clusters were recorded simultaneously on a shot-by-shot basis. The radii of the clusters and the XFEL fluences at the reaction point were evaluated from SAXS data, and the ion TOF spectra and fluorescence spectra were sorted according to the obtained parameters. After sorting, we found a clear size and FEL fluence dependence in both the ion TOF and fluorescence spectra. The present results demonstrate the importance of removing the averaging effects of the size distribution of the clusters as well as the laser fluence profile to obtain deep insights into the laser-matter interaction. The information extracted from our single-shot single-particle data sets, the first in the hard X-ray regime and the first containing inner-shell fluorescence information, is in good agreement with the findings of previous studies using similar styles of single-shot approaches in the soft X-ray and ultraviolet spectral regime. Our work underlines the potential of size-and fluence-selective spectroscopy for advancing the research in laser-matter interaction. Bridging Human, Environment and Materials". C.B. and K.R.F. acknowledge support from the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences through SLAC and Argonne National Laboratories.

Conflicts of Interest:
The authors declare no conflict of interest.