Resonances in three-photon double ionization of Ar in intense ...

PHYSICAL REVIEW A 88, 023421 (2013)

Resonances in three-photon double ionization of Ar in intense extreme-ultraviolet free-electron laser fields studied by shot-by-shot photoelectron spectroscopy Y. Hikosaka,1,2,* M. Fushitani,2,3 A. Matsuda,3 T. Endo,3 Y. Toida,3 E. Shigemasa,2,4 M. Nagasono,2 K. Tono,5 T. Togashi,5 M. Yabashi,2,5 T. Ishikawa,2 and A. Hishikawa2,3,† 1

Department of Environmental Science, Niigata University, Niigata 950-2181, Japan 2 RIKEN, SPring-8 Center, Sayo, Hyogo 679-5148, Japan 3 Department of Chemistry, Graduate School of Science, Nagoya University, Nagoya 464-8602, Japan 4 Institute for Molecular Science, National Institutes of Natural Sciences, Okazaki 444-8585, Japan 5 Japan Synchrotron Radiation Research Institute, Sayo, Hyogo 679-5198, Japan (Received 2 July 2013; published 23 August 2013) Shot-by-shot photoelectron spectroscopy has been performed to study the three-photon double ionization of Ar in intense extreme-ultraviolet free-electron laser fields over a photon energy range of 19.6–22.0 eV. It is found that the double ionization to Ar2+ 3p −2 proceeds sequentially via the formation of singly charged Ar+ 3p −1 states and is enhanced around photon energies of 20.5 and 21.5 eV. Two types of resonance are identified in the two-photon ionization of the Ar+ 3p −1 states: (i) resonances to intermediate states at the one-photon energy level and (ii) those to autoionizing states above the Ar2+ ionization threshold. DOI: 10.1103/PhysRevA.88.023421

PACS number(s): 32.80.Fb, 32.80.Rm, 32.80.Wr

I. INTRODUCTION

The advent of extreme-ultraviolet (EUV) free-electronlaser (FEL) sources has widely opened experimental studies of nonlinear optical processes of atoms and molecules in intense EUV laser fields [1,2]. The short-wavelength laser field often leads to multiple ionization due to multiphoton absorption, the mechanism of which has been attracting particular interest [3–14]. In multiple photoionization, resonance effects play an important role in determining the photoionization pathways and the final products [5,9]; therefore, the multiple photoionization processes depend sensitively on the FEL wavelength. Current FEL operations for user experiments have been run so far in the self-amplified spontaneous-emission (SASE) regime [15], where FEL pulses fluctuate in wavelength as well as in intensity, due to their statistical origins. The wavelength fluctuation usually blurs the information on the resonance effect in multiple photoionization. To avoid the influence of the wavelength fluctuation, Martins et al. performed photoion mass spectrometry while monitoring the FEL spectrum of each single FEL shot with a monochromator, and showed that doubly charged ion yield due to two-photon double ionization in Ne is enhanced by the intermediate population to excited Ne+ states [9]. A similar approach has been demonstrated by using photoelectron spectra associated with individual FEL shots [16], because the kinetic energies of photoelectrons ejected in one-photon ionization reflect the wavelength distributions of each FEL pulse. Meanwhile, photoelectron spectroscopy in itself can provide a detailed clue to understanding the multiphoton ionization mechanism, because the kinetic energies of the electrons emitted from multiphoton ionization directly reflect the electronic states related to the ionization processes. In these respects, shot-by-shot photoelectron spectroscopy [11], in which photoelectrons emitted from multiphoton process

* †

Corresponding author: [email protected] [email protected]

1050-2947/2013/88(2)/023421(6)

are detected on a single-FEL-shot basis while monitoring each FEL spectrum with the photoelectron peak due to a one-photon process, can be a powerful experimental means for studying nonlinear optical processes of atoms and molecules in intense EUV laser fields. The power of shot-by-shot photoelectron spectroscopy has been demonstrated by disclosing resonance effects in three-photon double ionization of Ar [11] and three-photon double excitation of He [17]. Previous investigation of the three-photon double ionization of Ar, which was performed at a photon energy around hν = 21.4 eV [11], revealed that the three-photon double ionization of Ar proceeds sequentially, and the second step of the ionization, namely, Ar+ to Ar2+ 3p−2 , is enhanced by resonant intermediate excited states Ar+∗ . The resonance effect was confirmed in separate studies using conventional photoelectron spectroscopy [12–14]. In the present work, we have expanded shot-by-shot photoelectron spectroscopy on the three-photon double ionization of Ar, in order to gain a deeper understanding of the resonance effect in the double-ionization process. In an investigation over a wide photon energy range of hν = 19.6–22.0 eV, we identified two different types of resonance in two-photon ionization of Ar+ , due to intermediate Ar+∗ and autoionizing Ar+∗∗ states. II. EXPERIMENT

The experiment was performed using the SPring-8 Compact SASE Source (SCSS) test accelerator at RIKEN Harima [1,18,19], which provided linearly polarized FEL pulses of ∼30 μJ and ∼100 fs, at a 30 Hz repetition rate. In the course of the experiment, the single-shot spectra of FEL pulses were occasionally monitored with an optical spectrometer, and spectral widths of ∼1.7% [full width at half maximum (FWHM)] of the mean photon energies were observed, while the width of 0.6% (FWHM) can be achieved in an optimum operation of the accelerator [19]. The FEL pulses were transported by two flat mirrors into a beamline and then focused with a pair of elliptical and cylindrical mirrors to

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∼25 μm in diameter. The total throughput was estimated to be ∼35% for the fundamental FEL pulses. The intensity of each single FEL shot was monitored by a photoion-yield detector placed upstream in the beamline, where an intensity fluctuation of ∼60% (standard deviation) was observed on each FEL setting. For shot-by-shot photoelectron spectroscopy, we employed a magnetic bottle-type electron spectrometer. A strong permanent magnet located close to the FEL focus point provides an inhomogeneous magnetic field, which serves as a magnetic mirror for photoelectrons. The photoelectrons are hence guided by the weak magnetic field of a long solenoid toward a microchannel plate (MCP) detector placed at the end of a 1.5 m flight pass. An electrostatic retardation of −6.9 V was applied to the entrance of the solenoid, to improve the electron energy resolution. High collection efficiency with a 4π sr detection angle was established, which enables us to reduce the sample gas density and thus to suppress the space-charge effect. Photoelectron signals from the MCP detector were stored in a digital oscilloscope triggered by a FEL master clock and then transferred to a personal computer. The kinetic energies of the photoelectrons were calibrated by measuring Xe 4d Auger lines from single-photon ionization with the third harmonic (hν = 72.9 eV) of the FEL, where the fundamental light (hν = 24.3 eV) was highly attenuated with a gas filter placed upstream in the FEL beamline. The energy resolution of the spectrometer was estimated from the Auger peaks; it is dependent on electron energy and becomes gradually worse for increasing electron energy Ekin (for instance, a FWHM of 0.2 eV for a kinetic energy of Ekin = 10.3 eV and a FWHM of 0.45 eV for Ekin = 16.1 eV).

III. RESULTS AND DISCUSSION A. Multiphoton photoelectron spectra

Figure 1 shows photoelectron spectra of Ar measured at 12 different photon energies (∼0.2 eV intervals) over the range hν = 19.7–21.9 eV, each of which is the average of single-shot spectra recorded with 15 000 FEL pulses from an individual FEL setting. It is estimated that on each FEL setting the mean photon energies of the FEL pulses fluctuate by ∼0.25 eV (FWHM). Since a retardation voltage of −6.9 eV was applied in order to improve the resolution, the Ar+ 3p−1 photoelectrons emitted in one-photon ionization from the Ar ground state are not observed in the spectra. The doublet peaks seen around 8 eV are due to one-photon ionization of Xe mixed in the sample gas for the shot-by-shot analysis. Other structures observed in the range Ekin = 10–18 eV are ascribed to the formation of Ar2+ 3p−2 by two-photon ionization of Ar+ 3p−1 prepared by one-photon ionization of Ar [11–14]: Ar+ 3p−1 (2P3/2,1/2 ) + 2hν→Ar2+ 3p−2 (3P ,1D,1S) + e− . As shown in Fig. 1, the positions and the intensities of these multiphoton peaks vary sensitively with photon energy. In order to understand more precisely the evolution of the multiphoton structures with photon energy, a shot-by-shot analysis [11] has been performed for these photoelectron spectra. In this analysis, the single-shot photoelectron spectra composing these averaged spectra were sorted by the mean photon energies determined by the Xe+ 5p3/2 −1 peak energies,

FIG. 1. (Color online) Photoelectron spectra of Ar measured at 12 different photon energies (∼0.2 eV intervals) in the range hν = 19.7–21.9 eV. Each spectrum is the average of single-shot spectra recorded with 15 000 FEL pulses. A retardation voltage of −6.9 eV was applied to improve the resolution.

and then the single-shot spectra within every 50 meV photon energy range were averaged. The two-dimensional map in Fig. 2(a) compacts the photoelectron spectra thus derived. Here, spectra recorded at FEL intensities larger than 3 × 1012 W/cm2 were used in the analysis, in order to reduce the intensity variation of the FEL pulses among the different segments. The mean and the standard deviation of the FEL intensity distribution in each segment are indicated in Fig. 2(b). On the two-dimensional map in Fig. 2(a), the electron yields for the formation of Ar2+ are remarkably enhanced around hν = 20.5 and 21.5 eV, implying that resonances occur around these particular photon energies. The kinetic energy of a photoelectron emitted by a two-photon ionization process may be written as Ekin = 2hν − [E(Ar2+ ) − E(Ar+ )], where E(Ar2+ ) and E(Ar+ ) are the energies of the final Ar2+ state and a spin-orbit level of the Ar+ 3p−1 states, respectively. The kinetic energies expected for the formations of the different Ar2+ 3p−2 states are represented on the two-dimensional map in Fig. 2(a) with diagonal lines. Since the two resonance structures seen around hν = 20.5 eV (Ekin = 11.5 and 13.5 eV) lie near the diagonal lines for the formation of the 1D and 3P states of Ar2+ 3p−2 , they are attributed to the two-photon ionization to these Ar2+ states. Similarly, the three resonance structures around hν = 21.5 eV (Ekin = 11.2, 13.8, and 15 eV) correspond to the formation of the Ar2+ 3p−2 (1S,1D,3P ) states. The FEL intensity dependences of the yields of these enhancement structures are plotted in Fig. 3, using logarithmic scales for both the horizontal and vertical axes. All the data show nonlinear response to the FEL intensity, confirming that

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FIG. 2. (Color online) (a) Two-dimensional map showing Ar2+ 3p −2 photoelectron spectra as a function of mean photon energy. The diagonal red lines describe the kinetic energies expected from energy conservation for the formation of the Ar2+ 3p −2 (3P ,1D,1S) states by two-photon absorption from either 2P3/2 (solid) or 2P1/2 (broken) of Ar+ 3p −1 . The map was derived by a single-shot-basis analysis, where only the single-shot spectra from FEL pulses with intensities more than 3 × 1012 W/cm2 were admitted. (b) Mean intensities and standard deviations of the intensity distributions of the FEL pulses admitted in the analysis. (c) Calculated oscillator strengths [23] for the transition from either Ar+ 3p −1 (2P3/2 ) (solid) or Ar+ 3p −1 (2P1/2 ) (broken) to Ar+ excited states. The two curves are obtained by integrating the electron yields in (a) over the ranges of Ekin = 10–17 eV (blue solid) and Ekin = 12.9–13.8 eV (red broken), respectively, where the latter range covers the most pronounced autoionization structure.

they are associated with multiphoton absorption. While the double ionization to Ar2+ requires the absorption of three photons, the observed slopes of the yield curves are about 2 at ∼1011 W/cm2 . This suggests that the processes are partly saturated even in this FEL intensity range. B. Resonances around hν = 20.5 eV

One finds on the map in Fig. 2(a) that the ridges of the two resonance structures seen around hν = 20.5 eV extend vertically at Ekin = 11.5 and 13.5 eV and do not follow the diagonal lines expected for the nonresonant two-photon absorption to the 3P and 1D states of Ar2+ 3p−2 . The observed vertical structures suggest that some excited states Ar+∗∗ located above the Ar2+ 3p−2 threshold are populated by a two-photon transition from Ar+ 3p−1 , which subsequently decay into the Ar2+ states by autoionization: Ar+ 3p−1 + 2hν → Ar+∗∗ , Ar+∗∗ → Ar2+ 3p−2 + e− . FIG. 3. (Color online) Intensities of Ar2+ structures as a function of the FEL intensity: the enhancements around hν = 21.5 eV for the formation of 3P (green squares), 1D (blue circles), and 1S (red triangles) and the enhancement around hν = 20.5 eV for the formation of 1D (open circle).

(1a) (1b)

Since the resultant photoelectron energy is determined only by the energy difference between the autoionizing states and the final Ar2+ states, the Ekin values are independent of the mean photon energy, as observed in autoionization from doubly excited He states [17,20]. On the map in Fig. 2(a), the

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TABLE I. Autoionizing Ar+∗∗ states relevant to the enhancements of the two-photon ionization from Ar+ 3p −1 , observed in a photon energy range of 19.6–22.0 eV. Label A1 A2 A3 A4, A4 A5 A6

Ionization energy (eV)a

Possible assignment

Ionization energy, calculated (eV)

55.6 56.4 56.7 56.9 57.9 58.7–59

[3p −3 (2D)]3d 2 2D [3s −1 3p −1 (1P )]4d 2D [3s −1 3p −1 (1P )]4d 2P [3p −3 (2D)]3d 2 2D

55.57b 56.5b 56.75b 56.94b

[3p −3 (D)]3d 2 (1G) 2 G7/2 , [3p −3 (2D)3d (1D)]4s 2D5/2

58.56c , 58.75c

a

Determined from the observed kinetic energies. [22]. c [14]. b

two vertical structures around Ekin = 11.5 and 13.5 eV are observed in identical photon energy ranges. This observation implies that autoionization from common, or closely lying, Ar+∗∗ states produces both the 1D and 3P states of Ar2+ 3p−2 . A closer look at the autoionization resonance around Ekin = 11.5 eV reveals that it consists of at least two peaks at Ekin = 11.3 and 11.6 eV [indicated in Fig. 2(a) as A2 and A3]; at least two autoionizing Ar+∗∗ states contribute to the process. From the energies of the two peaks and the double-ionization threshold (45.126 eV [21]) of Ar for the formation of Ar2+ 3p−2 (1D), the energies of the observed Ar+∗∗ states are determined to be 56.4 and 56.7 eV with respect to the Ar ground state. The autoionizing states responsible for the observed process should have odd parity, as they need to be populated by two-photon absorption from Ar+ 3p−1 . Here we assign the observed Ar+∗∗ states to the 2D and 2P states of Ar+ [3s −1 3p−1 (1P )]4d, the ionization energies of which are calculated to be 56.5 and 56.75 eV [22], respectively. The ionization energies and the assignments of the Ar+∗∗ states are summarized in Table I. Fine structures are also visible for the autoionization structure at Ekin = 13.5 eV in Fig. 2(a) (see also Fig. 1), which are not clearly resolved due probably to the different J levels of the final Ar2+ 3p−2 (3P ) state. Assuming that the peak at Ekin = 13.5 eV [indicated in Fig. 2(a) as A4] is due to autoionization into J = 2 of Ar2+ 3p−2 (3P ), the corresponding Ar+∗∗ state should lie at 56.9 eV. The Ar+∗∗ state is possibly assigned to a doubly excited state of Ar+ [3p−3 (1D)]3d 2 with a calculated ionization energy of 56.94 eV [22]. The shoulder on the low-kinetic-energy side of the autoionization structure [Ekin = ∼13.3 eV, A4 in Fig. 2(a)] can be reasonably explained by the autoionization from this Ar+∗∗ state into J = 0 and/or J = 1 of Ar2+ 3p−2 (3P ). In Fig. 2(c), the yields of the autoionization structure around Ekin = 13.5 eV are plotted against the mean photon energy (red broken curve). The autoionization yields show a broad peak with a maximum around hν = 20.45 eV. The peak energy is almost one-half of the energy difference between the Ar+ 3p−1 (2P3/2,1/2 ) states and the autoionizing Ar+∗∗ states, as expected for nonresonant two-photon absorption [process (1a)]. Also, the peak photon energy is only slightly smaller (∼0.1 eV) than the transition energy from Ar+ 3p−1 (2P1/2 ) to the excited state Ar+ [3p−2 (1S)]4s (2S) at hν = 20.567 eV [21] [I 1 in Fig. 2(c)]. The intermediate resonance to the Ar+ [3p−2 (1S)]4s

(2S) state may in principle contribute to the enhancement of the two-photon transition to the autoionizing Ar+ states; however, the effect of the double-resonance process must be unimportant in this case, because the second transition from Ar+ [3p−2 (1S)]4s (2S) to Ar+ [3s −1 3p−1 (1P )]4d requires the simultaneous excitation of two electrons. C. Resonances around hν = 21.5 eV

The resonance structures around hν = 21.5 eV in Fig. 2(a) exhibit broader widths along the Ekin direction, compared to the sharp features due to autoionization resonances seen around hν = 20.5 eV. The previous shot-by-shot photoelectron spectroscopic study [11] showed that double ionization in this energy region can be explained by resonances to intermediate excited states: Ar+ 3p−1 + hν → Ar+∗ , Ar+∗ + hν → Ar2+ 3p−2 + e− .

(2a) (2b)

Here, the energy distribution of the photoelectrons ejected in process (2b) reflects the mean spectral width (∼0.4 eV) of the FEL pulses, and the corresponding resonance structures thus appear in Fig. 2(a) with broader widths along the Ekin direction than the structures due to autoionization [process (1b)]. The photoelectron kinetic energy in process (2b) can be described as Ekin = hν − [E(Ar2+ ) − E(Ar+∗ )], where E(Ar+∗ ) is the energy of the intermediate resonance state Ar+∗ [11]. This equation implies that the corresponding structures should extend diagonally with slopes of unity (i.e., hν − Ekin = const) on the two-dimensional map. Indeed, the slope of the main ridge of the island structure for the formation of Ar2+ 3p−2 (1S) is close to unity. Although the slope of the Ar2+ 3p−2 (3P ) island ridge is apparently steeper than unity, it is possibly due to the overlap of the contributions from the different combinations of the initial Ar+ 3p−1 (2P1/2,3/2 ) and final Ar2+ 3p−2 (3P0,1,2 ) spin-orbit sublevels. On the other hand, the Ar2+ 3p−2 (1D) resonance structure shows an intense part that runs vertically on the lower-energy side. This internal structure indicates that processes other than process (2) contribute to the resonance structure, and the process is probably the two-photon ionization from Ar+ 3p−1 proceeding via additional resonance to autoionizing Ar+∗∗

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states from the intermediate resonance Ar+∗ state: Ar+ 3p−1 + hν → Ar+∗ , Ar+∗ + hν → Ar+∗∗ , Ar+∗∗ → Ar2+ 3p−2 + e− .

(3a) (3b) (3c)

A recent study [14] suggested that such a double-resonance process is important for the three-photon double ionization to Ar2+ 3p−2 in this photon energy range. In particular, it was suggested that the resonances to the autoionizing states (3c) are crucial in determining the rate of the double ionization and that without the autoionizing resonances, the double ionization is ∼102 times less for all the Ar2+ 3p−2 states (3P , 1D, and 1S) [14]. Note that, however, no clear signature of such resonances (which would reveal themselves as vertical structures) is identified in the present study for the Ar2+ 3P and 1S states [see Fig. 2(a)], suggesting that the enhancement by the second resonance (3c) is not very significant. From the observed kinetic energy of the vertical feature in the Ar2+ 3p−2 (1D) resonance structure, the Ar+∗∗ states contributing to the process can be estimated to lie in the range 58.7–59 eV. The previous study showed theoretically that several doubly excited Ar+∗∗ states with the configurations of 3p−2 nl n l are located in (and just below) this ionization energy range [14]: two high-lying Ar+∗∗ states at 58.56 and 58.75 eV have strong autoionization preference into the Ar2+ 3p−2 (1D) continuum and the other lower states lying in the range 58.18–58.48 eV do not. Therefore, the two high-lying Ar+∗∗ states are possibly populated from the transition from the intermediate Ar+ [3p−2 (1D)]3d (2P1/2,3/2 ) states and the autoionization of these Ar+∗∗ states contributes to the enhancement of the Ar2+ 3p−2 (1D) formation (Table I). Here, the transition energies from the intermediate Ar+∗ [3p−2 (1D)]3d (2P1/2,3/2 ) states to these two Ar+∗∗ states are 21.1–21.4 eV, which agrees with the first transition energy (∼21.5 eV), within the FEL spectral width (FWHM of ∼0.3 eV). In Fig. 2(a), while the resonance structures for the formations of the 1D and 1S states of Ar2+ 3p−2 are seen in almost the same photon energy range, the resonance structure for the Ar2+ 3p−2 (3P ) formation lies lower by ∼0.15 eV. This observation clearly implies that different intermediate Ar+∗ states contribute to the formation of Ar2+ 3p−2 (3P ) and Ar2+ 3p−2 (1D and 1S). The resonance structure for formation of the Ar2+ 3p−2 (3P ) state, seen at hν = ∼21.3 eV, is attributed [11] to resonant transitions to an intermediate state, Ar+ 3p−1 (2P1/2 )→Ar+ [3p−2 (1D)]3d (2 D3/2 ) [21.251 eV [14], I 3 in Fig. 2(c)] and Ar+ 3p−1 (2P3/2 )→Ar+ [3p−2 (1D)]3d (2D5/2 ) [21.367 eV [21], I2 in Fig. 2(c)]. In the previous study performed in a limited photon energy range of hν = 21.0–21.4 eV [11], the intermediate Ar+∗ states participating in the resonance structures for the double ionization to 1D and 1S states of Ar2+ 3p−2 were tentatively assigned to the Ar+ [3p−2 (1D)]3d (2P3/2 ) and Ar+ [3p−2 (1D)]3d (2P1/2 ) states. The present investigation in the wider energy range now discloses that the 1D and 1S resonances show centers around hν = 21.5 eV, which is close to the transition energies from Ar+ 3p−1 (2P1/2 ) to Ar+ [3p−2 (1D)]3d (2P3/2 ) [21.447 eV [21], I 4 in Fig. 2(c)] and Ar+ [3p−2 (1D)]3d


(2P1/2 ) [21.498 eV [21], I 5 in Fig. 2(c)]; thus the assignment in the previous study [11] is confirmed. From the standpoint of photoionization from the intermediate Ar+∗ states, one finds that each state shows a strong preference in the final Ar2+ 3p−2 continua: while the [3p−2 (1D)]3d (2P3/2,1/2 ) states preferably ionize into the Ar2+ 3p−2 (1D,1S) continua, the ionization from the Ar+ [3p−2 (1D)]3d (2D3/2 ) states proceeds favorably into the Ar2+ 3p−2 (3P ) continuum. D. Other resonances

Apart from the remarkable resonance structures discussed above, one can find other resonance structures in Fig. 2(a). Weak vertical structures are discernible around (Ekin ,hν) = (10.5 eV,19.8 eV) and (Ekin ,hν) = (12.7 eV,21.0 eV), indicated in Fig 2(a) as A1 and A5, respectively. These structures are attributable to two-photon transitions to autoionizing Ar+∗∗ states and their decay to the Ar2+ 3p−2 (1D) state [process (1)]. The ionization energies of the autoionizing Ar+∗∗ states relevant to the resonances around hν = 19.8 and 21.0 eV are determined from the kinetic energies to be 55.6 and 57.9 eV, respectively. While the Ar+∗∗ state at 55.6 eV can be assigned to the [3p−3 (2D)]3d 2 2D state with a calculated ionization energy of 55.57 eV [22] (see Table I), no theoretical information is available for the Ar+∗∗ state lying at 57.9 eV. Around the top of the two-dimensional map, resonance structures are partially seen for all three final states of Ar2+ 3p−2 , where the 1D formation is most significantly enhanced. The resonances can be attributed to the transition to an intermediate state [process (2)], Ar+ 3p−1 (2P3/2 )→Ar+∗ [3p−2 (1D)]3d (2 D5/2 ) (22.267 eV [21]). IV. SUMMARY

Three-photon double ionization of Ar in intense FEL fields (∼1012 W/cm2 ) has been studied over a wide photon energy range of hν = 19.6–22.0 eV with the SCSS Test Accelerator at RIKEN Harima. It was found by shot-by-shot photoelectron spectroscopy that the double-ionization process is enhanced by resonances in the two-photon ionization of Ar+ in two different manners; the enhancement around hν = 20.5 eV is due to resonance to autoionizing Ar+∗∗ states around the two-photon level from the Ar+ 3p−1 states, and the enhancement around hν = 21.5 eV is essentially due to the intermediate excited Ar+∗ states lying at the one-photon level. The present study demonstrates that different types of resonances contribute to the determination of the main pathways of multiphoton multiple ionization in intense EUV FEL fields. ACKNOWLEDGMENTS

The authors are grateful to the SCSS Test Accelerator Operation Group at RIKEN for continuous support in the course of the study. We thank James Harries (JAEA) for a careful reading of the manuscript. Y.H. and A.H. thank Yamada Science Foundation for financial support. Y.H. acknowledges support from JSPS KAKENHI (Grant No. 24540425). This work was performed with the approval of the SCSS Test Accelerator Operation and Utilization Committee.

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