2 Experimental setup

The experiment was carried out in the Short-F target chamber of the J-KAREN-P laser facility^[ Reference Kiriyama, Mori, Pirozhkov, Ogura, Sagisaka, Kon, Esirkepov, Hayashi, Kotaki, Kanasaki, Sakaki, Fukuda, Koga, Nishiuchi, Kando, Bulanov, Kondo, Bolton, Slezak, Vojna, Sawicka-Chyla, Jambunathan, Lucianetti and Mocek ^{7 ,} Reference Pirozhkov, Fukuda, Nishiuchi, Kiriyama, Sagisaka, Ogura, Mori, Kishimoto, Sakaki, Dover, Kondo, Nakanii, Huang, Kanasaki and Kando ^{8 ]} at KPSI, Japan. The p-polarized laser pulses with a central wavelength of λ ₀ ~ 820 nm, duration of 33 fs and energy up to 12 J were focused with an f/1.3 off-axis parabolic (OAP) mirror with a 45º deviation angle into a focal spot with an effective radius r _eff ~ 1.3 μm. The laser operated at 0.1 Hz, delivering typically several hundred full-power shots per experimental day.

The top right inset in Figure 1 shows the focal-spot profile recorded with the amplified pulse at approximately 10% of the full laser power attenuated by means of wedges^[ Reference Pirozhkov, Fukuda, Nishiuchi, Kiriyama, Sagisaka, Ogura, Mori, Kishimoto, Sakaki, Dover, Kondo, Nakanii, Huang, Kanasaki and Kando ^{8 ]}. We have also recorded the full-power focal-spot profile using on-shot far-field measurements through a high-reflectivity, high-optical-quality mirror. Both approaches provided fully consistent results. The on-shot pulse spectrum and near-field profiles were also measured using a portion of the beam transmitted through this mirror. The full setup used for spectral measurements (including the mirror, wedges, filters, integrating sphere, fiber and spectrometer) was absolutely calibrated using the measured spectrum and the pulse energy after the OAP mirror. We found that the pulse energy determined by integrating this absolutely calibrated spectrum is more precise than the one obtained from the near-field profile, because the calibration factor of the near-field profile depends on the spectrum of the pulse and, thus, can vary day-to-day and even shot-to-shot.

Figure 1 Experimental scheme (not to scale). The J-KAREN-P laser pulses (Ø 280 mm, 33 fs, 10 J, λ ₀ ~ 820 nm, p-polarized) were focused into an r _eff ~ 1.3 μm focal spot on a 5–20 μm stainless-steel tape target^[ Reference Kondo, Nishiuchi, Sakaki, Dover, Lowe, Miyahara, Watanabe, Ziegler, Zeil, Schramm, Ditter, Hicks, Ettlinger, Najmudin, Kiriyama, Kando and Kondo ^{26 ]} mounted at a 45º incident angle. The observation direction of the back-reflection diagnostics at 1ω is shown by the red arrow. Several reflection diagnostics (1ω and 2ω imagers, 1ω–4ω fiber spectrometer) measured the reflected beam footprint on a screen mounted perpendicular to the ‘specular reflection’ direction; a three-channel flat-field XUV spectrograph (3FF) was mounted behind a hole in the screen. The first hard X-ray spectrometer, HXRS-1, was mounted 98º off the main laser pulse direction. The second hard X-ray spectrometer, HXRS-2, and an electron spectrometer (ESM) were along the direction of the main laser pulse, while the imaging XUV spectrograph was 12º off this direction. The $\vec{B}$ symbols represent dipole magnets removing electrons from HXRS-1 and HXRS-2 and dispersing electrons in the electron spectrometer ESM. Two soft X-ray spectrometers with spatial resolution (FSSR) were mounted out-of-plane on the target front (-F) and rear (-R) sides, respectively. The insets show spatial and temporal J-KAREN-P laser pulse profiles. A tape target of 20 mm width was mounted on a double-rotating-reel setup, which could be translated linearly along the laser axis with a 0.1-μm step size (the ‘+X’ denotes direction away from the OAP mirror).

The temporal laser pulse shape (Figure 1, bottom inset), with an effective width^[ Reference Pirozhkov, Fukuda, Nishiuchi, Kiriyama, Sagisaka, Ogura, Mori, Kishimoto, Sakaki, Dover, Kondo, Nakanii, Huang, Kanasaki and Kando ^{8 ]} of 33 fs, was measured with a commercial self-referenced spectral interferometry device (Wizzler)^[ Reference Moulet, Grabielle, Cornaggia, Forget and Oksenhendler ^{63 ]} at approximately 10% of the maximum laser power. In a separate experiment we confirmed that this method gave the same pulse duration as the full-power measurements^[ Reference Lorenz, Grittani, Kondo, Kon, Liu, Sagisaka, Ogura, Nakanii, Huang, Bierwage, Namba, Ohiro, Pikuz, Koga, Chen, Kiriyama, Kando, Esirkepov, Bulanov and Pirozhkov ^{64 ]}. The resulting peak intensity in-vacuum was up to 7 × 10²¹ W/cm². The experiments presented herein were performed in a ‘medium contrast mode’ with an approximately 10^–10 nanosecond laser contrast level, which was optimized for hard X-ray generation. The temporal shape of the pre-pulse at the nanosecond timescale was also measured on-shot by a fast photodiode. We have performed hydrodynamic simulations, showing that under our conditions, the pre-plasma scale length was a few micrometers and thus did not affect the optimum target position significantly, although it did affect the interaction physics. The small pre-plasma scale length can be proved indirectly by the fact that the pre-plasma was not visible on the 2ω interferometer, as it was completely inside the target shadow. The generation of high-order harmonics (HOHs) in the ‘specular reflection’ direction, which was detected by the three-channel flat-field (3FF) XUV spectrograph and is described in Section 7, also indicates a small pre-plasma scale length. More details on the laser contrast, pre-plasma, and physics of the hard X-ray generation will be presented elsewhere.

Figure 1 shows the experimental scheme: the main laser pulse, the 5-to-20-μm-thick stainless-steel (SUS) tape target^[ Reference Kondo, Nishiuchi, Sakaki, Dover, Lowe, Miyahara, Watanabe, Ziegler, Zeil, Schramm, Ditter, Hicks, Ettlinger, Najmudin, Kiriyama, Kando and Kondo ^{26 ]} mounted 45º off-normal and the diagnostics discussed herein:

• • (front) reflected beam footprint diagnostics (at frequencies 1ω, 2ω and 3ω);

• • (front) back-reflection diagnostics (at 1ω, the diagnostics are outside Figure 1);

• • (rear) XUV imaging spectrograph for wavelengths 17–25 nm;

• • (rear) magnetic electron spectrometer (ESM) for 20–100 MeV electrons;

• • (rear) two hard X-ray spectrometers (HXRS-1 and HXRS-2) for 0.1–10 MeV photons;

• • (front and rear) two soft X-ray focusing spectrometers with spatial resolution (FSSR-F (front) and FSSR-R (rear)) for 0.7–10 keV photons;

• • (front) 3FF XUV spectrograph, λ = 17–34 nm.

Here (front) and (rear) correspond to the observation on the front and rear sides of the target, respectively. In the latter case, the radiation was going through the target or was generated directly on its rear side.

As electromagnetic pulses (EMPs) from high-power laser–plasma interaction are known to cause problems in electronics^[ Reference Consoli, Tikhonchuk, Bardon, Bradford, Carroll, Cikhardt, Cipriani, Clarke, Cowan, Danson, Angelis, Marco, Dubois, Etchessahar, Garcia, Hillier, Honsa, Jiang, Kmetik, Krása, Li, Lubrano, McKenna, Metzkes-Ng, Poyé, Prencipe, Ra̧czka, Smith, Vrana, Woolsey, Zemaityte, Zhang, Zhang, Zielbauer and Neely ^{65 ]}, we made attempts to minimize their influence. In previous experiments we tried different motorized platforms from several companies and, finally, we found that Kohzu Precision can produce custom motorized stages and control electronics that are highly resistant to EMPs. In particular, these stages were used in our experiments for 3D target translations and rotations. EMPs did not affect our tape movement, as its control system was relatively simple and robust. At the same time, some computers and cameras related to a few diagnostics were affected by the EMPs from time to time, and had to be restarted.

Before each experiment, the initial position of the tape target was determined with an approximately 100 μm accuracy as follows. We used a focal-spot monitor consisting of an apochromatic objective lens and a high-dynamic-range charge-coupled device (CCD) camera and set a micro-needle to mark the desired focus position. The needle was positioned by illuminating it with a λ = 785 nm alignment beam (LD7 in Figure 2 of Ref. [Reference Pirozhkov, Fukuda, Nishiuchi, Kiriyama, Sagisaka, Ogura, Mori, Kishimoto, Sakaki, Dover, Kondo, Nakanii, Huang, Kanasaki and Kando8]) with an axial accuracy of a few μm, limited by the objective depth-of-focus. Then the focal-spot quality was measured as described in Ref. [Reference Pirozhkov, Fukuda, Nishiuchi, Kiriyama, Sagisaka, Ogura, Mori, Kishimoto, Sakaki, Dover, Kondo, Nakanii, Huang, Kanasaki and Kando8]. In this process, the OAP mirror was adjusted to bring the focus to the needle position, with a typical axial accuracy of better than ±5 μm, which was around a half of the Rayleigh length. Up to this point, all the positioning steps were implemented with a few-to-several-μm accuracy.

Then, an SUS tape target of 20-mm width was set to the needle position. We tried several methods (see the Appendix), but we were not able to control the target position with a better than 100-μm accuracy, since the SUS target was mirror-like reflective, wrinkle-free and non-transparent. Finally, we marked the position of the needle on the camera of a 2ω interferometer^[ Reference Sagisaka, Pirozhkov, Daido, Fukumi, Li, Ogura, Yogo, Oishi, Nayuki, Fujii, Nemoto, Orimo, Nishiuchi, Hayashi, Mori, Kado, Nakamura, Noda, Choi, Sung, Ko and Lee ^{66 ]}, which observed the target along its 20-mm-long side. After removing the needle, the target orientation was adjusted by the target rotation stage to the narrowest shadow on the 2ω interferometer camera, so the tape was along the probe beam with an approximately 0.1° accuracy (therefore, the incidence angle was 45°). After that, the target was placed at the needle position with an accuracy determined by smearing of the tape image along the observation direction, caused by the defocused images of the ±10 mm tape edges, as well as the possible bending of the target edges, which was small in our case on the 100-μm scale, but may be not negligible on the required sub-10-μm scale. From this initial position, the target was shifted by 200 μm towards the OAP mirror (the negative direction in the figures). Then we irradiated the target with high-power laser pulses, performing a target position scan with 10 μm (sometimes 5 μm) steps. We note that the shot-to-shot target position variations along the laser axis were less than the depth-of-focus of the focal-spot monitor objective lens (<2 μm), and the short-term laser pointing stability was approximately 2–3 μrad, which did not affect the focusing. We stopped the scan after passing the optimum position determined consistently with several X-ray and optical diagnostics. Comparison of the final target position with the initial one determined by the interferometer revealed that the initial target position accuracy was around 50 μm.

Hereafter we describe each of the diagnostics listed above (Figure 1). For convenience, the results of all the diagnostics are given in the same section as their description. The applicability of each instrument for determination of the best in-focus target position is discussed.

3 Front-side near-infrared to visible-ultraviolet reflection diagnostics

Several NIR-to-ultraviolet (UV) diagnostics^[ Reference Pirozhkov, Choi, Sung, Lee, Yu, Jeong, Kim, Hafz, Kim, Pae, Noh, Ko, Lee, Robinson, Foster, Hawkes, Streeter, Spindloe, McKenna, Carroll, Wahlström, Zepf, Adams, Dromey, Markey, Kar, Li, Xu, Nagatomo, Mori, Yogo, Kiriyama, Ogura, Sagisaka, Orimo, Nishiuchi, Sugiyama, Esirkepov, Okada, Kondo, Kanazawa, Nakai, Akutsu, Motomura, Tanoue, Shimomura, Ikegami, Daito, Kando, Kameshima, Bolton, Bulanov, Daido and Neely ^{67 –} Reference Singh, Armstrong, Kang, Ren, Liu, Hua, Rusby, Klimo, Versaci, Zhang, Sun, Zhu, Lei, Ouyang, Lancia, Garcia, Wagner, Cowan, Zhu, Schlegel, Weber, McKenna, Neely, Tikhonchuk and Kumar ^{69 ]} were mounted in the ‘specular reflection’ direction (90º from the laser incidence direction). Two imaging cameras observed the spatial distributions of 1ω (~700–1000 nm) and 2ω (~390–410 nm) radiation scattered from a polytetrafluoroethylene (PTFE; Teflon) screen mounted in the ‘specular reflection’ direction of the laser pulses (see Figure 1). The spectrum of the reflected beam was measured using the same PTFE screen, with a NIR-vis-UV optical fiber spectrometer (1ω–4ω) having 200–1000 nm total spectral bandwidth.

The fields of view of the two cameras, partially clipped by other instruments, are shown in Figures 2(a) and 2(b). The acceptance angles were Ω₁ ≈ 80 msr and Ω₂ ≈ 100 msr for the 1ω and 2ω cameras, respectively. The absolute sensitivity of the 1ω camera together with its filters was calibrated using a small portion of the main laser beam, resulting in (7.1 ± 1.5) × 10⁻⁷ J/count. The absolute sensitivity of the spectrometer with a relatively calibrated spectral response was cross-calibrated with the 1ω camera, providing an absolute calibration reference for the whole 200–1000 nm spectral region. The 2ω camera was afterwards cross-calibrated with the spectrometer. The area observed with the spectrometer (dashed ellipses in Figures 2(a) and 2(b)) had an acceptance angle of Ω_s ≈ 8 msr. A typical spectrum is shown in Figure 2(c). The absolute energies could be determined for the first to third harmonics within the corresponding spectral ranges of (n ± 0.25)ω₀, where n is the harmonic order. The spectrometer had low sensitivity in the λ < 200 nm spectral region, and its sensitivity calibration was unreliable there, as we used two types of commercial calibrated light sources (namely, a black-body source and a deuterium-tungsten halogen lamp) with calibration data given in the spectral range of λ > 200 nm. Thus, we did not consider the fourth harmonic signal for the target positioning goals.

Figure 2 The fields of view of the 1ω (a) and 2ω (b) cameras imaging a PTFE screen mounted perpendicular to the ‘specular reflection’ direction. The geometric center of the reflected beam is marked with white circles. The dashed ellipses denote the spectrometer observation area. (c) Typical absolutely calibrated reflected spectrum. The energy values calculated within the (n ± 0.25)ω₀ spectral bandwidths (colored) are given for harmonic orders n = 1, 2, 3.

Along with the ‘specular reflection’ diagnostics, we also used 1ω back-reflection beam diagnostics. The main purpose of the back-reflection diagnostics is laser safety, as a significant portion of the laser energy can be back-reflected and consequently damage the compressor gratings and/or laser amplifiers. However, this instrument could potentially be useful for determining the best focus position in certain cases.

Figure 3 shows the normalized energy (with respect to the total pulse energy on-target) detected with all the NIR-vis-UV reflection diagnostics, including the 1ω (Figure 3(a)) and 2ω (Figure 3(b)) imagers, 1ω–4ω spectrometer (Figures 3(a)–3(c)) and the 1ω back-reflection (Figure 3(d)), recorded for the scanned target position. Here X ₀ represents the best focus position, which was consistently determined by multiple diagnostics for each SUS thickness, as described in detail in Section 9. Thus, X – X ₀ denotes the SUS target displacement from the best focus position.

Figure 3 Normalized energy from the four reflection beam diagnostics versus the target position X (‘–’ denotes the direction towards the OAP mirror, and X ₀ corresponds to the best focus position). All values are normalized by the on-target pulse energy E ₀. The plots in (a) and (b) are for the 1ω and 2ω diagnostics, respectively, where the upper data (black) are from the imagers, while the lower data (red) are integrated from the 1ω–4ω spectrometer within (1 ± 0.25)ω₀ and (2 ± 0.25)ω₀, correspondingly. (c) The 3ω data integrated within the (3 ± 0.25)ω₀ band from the 1ω–4ω spectrometer. (d) The normalized back-reflected energy.

Figure 3(a) shows normalized energy determined from the 1ω ‘specular reflection’ diagnostics, both the 1ω imager and spectrometer signal within the (1 ± 0.25)ω₀ band. The data from both instruments were in good correlation. There was a double-peak structure in the vicinity of the best focus and a gradual signal increase from both diagnostics towards X – X ₀ ~ –150 μm, as the interaction probably entered the highly reflective plasma mirror regime. These multi-peak features made the 1ω diagnostics not useful for determination of the best target position.

Figure 3(b) shows the dependence of the 2ω normalized energy on X – X ₀, determined from the 2ω imager (upper points) and spectrometer signal within the (2 ± 0.25)ω₀ band (lower points). Both cases reveal single-peak structures that can be approximated with Lorentzian fits, giving the best focus position with approximately 4 μm discrepancy and 24 μm full width at half maximum (FWHM), indicating that 2ω ‘specular reflection’ diagnostics determine the best focus position with an approximately 12 μm accuracy.

Figure 3(c) depicts the energy of the 3ω radiation determined from the 1ω–4ω spectrometer via integration within the (3 ± 0.25)ω₀ spectral band. In the 3ω case, the peak was even more prominent, with small data point fluctuations, indicating an approximately 5 μm target position accuracy.

Figure 3(d) shows the dependence of the normalized back-reflected energy on the relative target position, revealing a broad dip, instead of a peak at the X ₀ position, and a broad peak at X – X ₀ ≈ –100 μm. Thus, the 1ω back-reflection, along with other 1ω reflection diagnostics, was not suitable for determination of the best focus position.

4 Rear-side extreme ultraviolet spectrograph and electron spectrometer

Behind the target, three diagnostics were placed: an XUV imaging spectrograph, an ESM and HXRS-2. In this section we describe the first two instruments, while HXRS-2 will be discussed in the next section, along with the HXRS-1 diagnostics of the same type.

4.1 XUV imaging spectrograph

An XUV imaging spectrograph based on a Mo/Si aperiodic multilayer mirror (MM)^[ Reference Kolachevsky, Pirozhkov and Ragozin ^{70 –} Reference Pirozhkov and Ragozin ^{72 ]} and a transmission diffraction grating was mounted 12º off the laser direction. The XUV acceptance angle was 3.6 msr, corresponding to an approximately 2º cone half-angle. The operating range, 17–25 nm, was defined by the multilayer structure optimized for maximum uniform reflectance in the 12.5–25 nm range^[ Reference Vishnyakov, Mednikov, Pertsov, Ragozin, Reva, Ul’yanov and Shestov ^{73 ,} Reference Ragozin, Mednikov, Pertsov, Pirozhkov, Reva, Shestov, Ul’yanov and Vishnyakov ^{74 ]} and absorption cutoff at the aluminum L_2,3 edge at λ ≈ 17 nm in the optical blocking filters. Imaging spectrographs of this type are used in different forms, for example in the combination of an MM with a transmission grating^[ Reference Barysheva, Garakhin, Kolesnikov, Pirozhkov, Polkovnikov, Ragozin, Shatokhin, Smertin, Svechnikov and Vishnyakov ^{75 ]} or a varied line space (VLS) reflection grating^[ Reference Vishnyakov, Kolesnikov, Kuzin, Negrov, Ragozin, Sasorov and Shatokhin ^{76 ,} Reference Shatokhin, Kolesnikov, Sasorov, Vishnyakov and Ragozin ^{77 ]}. Such XUV spectrographs have been employed in experiments on coherent soft X-ray generation via frequency upshift of the laser pulse reflected from a relativistic ‘flying mirror’^[ Reference Kando, Pirozhkov, Kawase, Esirkepov, Fukuda, Kiriyama, Okada, Daito, Kameshima, Hayashi, Kotaki, Mori, Koga, Daido, Faenov, Pikuz, Ma, Chen, Ragozin, Kawachi, Kato, Tajima and Bulanov ^{78 ]} and via the BISER mechanism^[ Reference Pirozhkov, Esirkepov, Pikuz, Faenov, Ogura, Hayashi, Kotaki, Ragozin, Neely, Kiriyama, Koga, Fukuda, Sagisaka, Nishikino, Imazono, Hasegawa, Kawachi, Bolton, Daido, Kato, Kondo, Bulanov and Kando ^{41 ]}.

A spherical aperiodic Mo/Si MM with a radius of curvature of R = 1000 mm was mounted in a geometry providing M ≈ 2.1 spatial magnification. We used two Al-based free-standing absorption filters to block the NIR-vis-UV radiation: the first filter (0.65 μm thick Al) was mounted in front of the mirror and operated in the double-pass regime, while the second filter (Al/Zr multilayer^[ Reference Volodin, Gusev, Drozdov, Zuev, Klyuenkov, Lopatin, Luchin, Pestov, Salashchenko, Tsybin and Chkhalo ^{79 ]}, 0.2 μm) was in front of the CCD. A free-standing transmission diffraction grating with a groove density of 5000 lines/mm was situated 139 mm from the CCD chip.

Figure 4(a) shows a typical XUV spectrum for a 5-μm-thick SUS target close to the best focus position (X ₀). The XUV spectrum contained the zeroth diffraction order and a spectrally resolved continuous first diffraction order in the 17–22 nm spectral region. The zeroth diffraction order was triple-shaped due to diffraction on the grating support structure, which was perpendicular to the dispersion direction. Each spot in the zeroth diffraction order image was elongated due to the astigmatism introduced by the spherical focusing MM operating at a small, but non-zero, incidence angle. The spectrum decay at λ > 20 nm was due to absorption of the Al/Zr multilayer filter^[ Reference Volodin, Gusev, Drozdov, Zuev, Klyuenkov, Lopatin, Luchin, Pestov, Salashchenko, Tsybin and Chkhalo ^{79 ]}. Taking the typical CCD spectral sensitivity^[ Reference Vishnyakov, Kirichenko, Reva, Rizvanov, Plastinin and Kuzin ^{80 ,} Reference Vishnyakov, Shcherbakov, Pertsov, Polkovnikov, Pestov, Pariev and Chkhalo ^{81 ]} and the spectral filter transmission into account, the total XUV radiation yield on the target rear side was estimated to be approximately (26 ± 3) × 10⁻¹⁰ J/sr for the 5-μm-thick SUS target and (3.8 ± 0.8)×10⁻¹⁰ J/sr for the 15-μm-thick SUS target.

Figure 4 (a) Typical spatially resolved XUV spectrum; λ = 0 denotes the zeroth diffraction order. (b) Dependence of the integrated zeroth order on the target position (‘–’ is towards the OAP mirror) for 5-μm- and 15-μm-thick targets, and their Lorentzian fits. (c) Dependence of the integrated ESM yield on the target position for a 15-μm-thick target. The dashed line shows the ESM noise level.

The integrated yields in the zeroth and the first diffraction orders were proportional, with a higher signal-to-noise ratio in the zeroth order. Figure 4(b) gives the dependence of the normalized integrated zeroth order signal on X – X ₀ for 5 and 15 μm target thicknesses. The Lorentzian-fit curves show that the target thickness affected the precision of the target positioning: 60 μm FWHM for the 15-μm-thick target and a narrower 40 μm FWHM for the 5-μm-thick target. Deviations of the fitted peaks from the optimal target position were within approximately 5 μm for both thicknesses, meaning that the XUV imaging spectrograph provided target positioning with an approximately 20–30 μm accuracy for 5-to-15-μm targets. For 20-μm targets, the XUV signal-to-noise ratio was lower than unity, so precise target positioning was not achievable. The vertical error bars in Figure 4(b) represent solely statistical errors due to shot-to-shot signal variations.

5 Rear-side hard X-ray spectrometers (HXRS-1 and HXRS-2)

Two HXRSs^[ Reference Armstrong ^{82 ,} Reference Rusby, Armstrong, Brenner, Clarke, McKenna and Neely ^{83 ]} were mounted behind the target (Figure 1): HXRS-1 was 98º from the laser axis, approximately along the laser electric field direction, 1.7 m from the target, and HXRS-2 was on the laser axis, behind the ESM, 4.2 m from the target.

Each of the two HXRS instruments consisted of a linear X-ray absorption array built of 10 LYSO (Lu_1.8Y_0.2SiO₅) scintillator crystal plates of 2 mm thickness and 10 mm × 30 mm area, with 2-mm-thick tungsten filters between each pair of plates from #4 to #9 (the numeration of the plates starts from #0). The fluorescence emitted from the LYSO array was monitored with a complementary metal oxide semiconductor (CMOS) camera. Dipole magnets (Figure 1) in front of the HXRSs prevented electrons from reaching the instruments. The scintillator sensitivity allowed for registering hard X-ray radiation with the photon energies from approximately 20 keV to 10 MeV, the best sensitivity being 0.1–2 MeV. The harder X-ray radiation was detected by deeper scintillators with higher numbers in the array. A full description of the HXRS design and data processing is given in Ref. [Reference Armstrong, Neely, Kumar, McKenna, Gray and Pirozhkov84]. In our setup the plate #9 signal was unreliable as, in addition to the X-rays coming through the other scintillators and tungsten filters in the array, its response included X-rays reflected from the walls of the experimental area. This did not affect other scintillators due to the surrounding lead shielding.

Figure 5 presents data from HXRS-1 (top) and HXRS-2 (bottom). The scintillator plate number in the array is shown next to the instrument name. The thicker the target, the stronger the recorded HXRS signal was. Figures 5(a) and 5(d) show typical scintillator plate #0 dependences for both instruments, exemplified by dependences for 10-μm-thick targets. The plots contain multi-peak structures, making this channel unsuitable for precise target positioning, although the central peak might be attributed to the best target position.

Figure 5 HXRS scintillator plate signals versus target position X (‘–’ is towards the OAP mirror, X ₀ is the best focus). (a)–(c) HXRS-1 (off-axis), (d)–(f) HXRS-2 (on-axis). (a) HXRS-1 plate #0, 10-μm-thick SUS. (b) HXRS-1 plate #5, 10-μm-thick SUS. (c) HXRS-1 plate #5, 5-μm-thick SUS. (d) HXRS-2 plate #0, 10-μm-thick SUS. (e) HXRS-2 plate #3, 10-μm-thick SUS. (f) HXRS-2 plate #2, 5-μm-thick SUS. Lorentzian fits are shown, where applicable. Scintillator plate #0 was the closest to the interaction point. The error bars in all the frames are due to the CMOS camera noise.

Figures 5(b) and 5(e) show middle scintillator plate signals for 10-μm-thick targets for HXRS-1 and HXRS-2, respectively. The middle plates were most reliable for thick target positioning due to high signal-to-noise ratios and single peaks in the dependences. There was a narrow peak for the on-axis HXRS-2 (Figure 5(e), 16 μm FWHM fit), and a broad peak for the off-axis HXRS-1 (Figure 5(b), >300 μm FWHM). This shows that the target positioning precision was approximately 5 μm for the on-axis HXRS-2, while it was more than 100 μm for the off-axis HXRS-1.

Even with the thinnest 5-μm SUS target, the on-axis HXRS-2 middle scintillators were still capable of positioning the target with an approximately 5 μm accuracy (Figure 5(f)), although with a lower signal-to-noise ratio than for thicker targets. The off-axis HXRS-1 middle scintillators were not applicable for determining the best in-focus position of 5-μm SUS targets (Figure 5(c)).

6 Front-side and rear-side soft X-ray focusing spectrometers with spatial resolution

Two soft X-ray FSSRs have been assembled on both the front (FSSR-F) and rear (FSSR-R) target sides. The FSSRs were based on spherically bent mica and quartz crystals, respectively (2d = 2.36 Å in the latter case) with a curvature radius of R = 150 mm to ensure radiation focusing and high spectral resolution, up to an approximately 10⁴ value^[ Reference Faenov, Pikuz, Erko, Bryunetkin, Dyakin, Ivanenkov, Mingaleev, Pikuz, Romanova and Shelkovenko ^{85 –} Reference Hölzer, Wehrhan, Heinisch, Förster, Pikuz, Faenov, Pikuz, Romanova and Shelkovenko ^{87 ]}.

The FSSR instruments were mounted out-of-plane, 786 and 819 mm above the horizontal plane containing the laser axis for the FSSR-F and FSSR-R instruments, respectively. FSSR-F was mounted at an in-plane angle of 8.5° ± 0.1° from the target normal and an out-of-plane angle of 17.6° ± 0.1°, with a distance from the FSSR-F crystal to the interaction point of 2600 mm. The mica crystal employed in FSSR-F gave a resolving power of λ/Δλ ~ 2500 at the central wavelength of λ ₀ = 0.1875 nm in the m = 8 diffraction order corresponding to a wavelength of 1.5 nm in the first diffraction order.

FSSR-R was mounted at an in-plane angle of 10.1° ± 0.1° from the target normal and an out-of-plane angle of 23.1° ± 0.1°. The quartz crystal provided λ/Δλ ~ 3000 resolving power at a wavelength of λ ₀ = 0.1812 nm in the m = 8 diffraction order, corresponding to λ = 1.45 nm in the first diffraction order. The distance from the FSSR-R crystal to the interaction point was 2045 mm.

An example of the spectrum registered with FSSR-F is shown in Figure 6(a). The spectrum covered a 1.31–1.63 nm range of wavelengths in the first diffraction order. In this spectrum, the spectral components of the other diffraction orders overlapped, thus making it possible to observe Fe K_α (λ = 0.194 nm) in the m = 8 diffraction order and Cr K_α (λ = 0.229 nm) in the m = 7 diffraction order. Most of the signals registered with the FSSR-F and FSSR-R detectors in the vicinity of the best in-focus target position were bremsstrahlung emitted from the laser–solid interaction. Spectral filters composed of 2-μm-thick C₃H₆ and 0.4-μm-thick Al were placed in front of the CCD camera for the FSSR instruments. An additional narrow strip of a 25-μm-thick C₃H₆ as a spectral filter allowed for suppressing m = 1 and m = 2 diffraction orders and thus catching the bremsstrahlung radiation in the m = 3 diffraction order.

Figure 6 (a) A typical FSSR-F spectrum recorded in the vicinity of the best in-focus target position. The spectrum covers wavelengths from 0.165 to 1.63 nm in different diffraction orders from m = 1 to m = 8. Strong characteristic lines Fe K_α (λ = 0.194 nm) and Cr K_α (λ = 0.229 nm) were observed in m = 8 and m = 7 diffraction orders, respectively. The continuous signal corresponds to bremsstrahlung. A narrow strip of a 25-μm C₃H₆ filter allows for observing a narrow portion of the spectrum, suppressing emission from lower diffraction orders (m = 1, m = 2). (b), (c) FSSR-F data for 15-μm SUS targets, integrated within an area without (b) and with (c) the 25-μm-thick C₃H₆ filter. (d), (e) FSSR-R integrated bremsstrahlung signal for 15-μm (d) and 5-μm (e) SUS targets. (f) FSSR-R Fe K_α integrated signals for 15- and 5-μm SUS targets. The black error bars correspond to statistical shot-to-shot signal variations, while the smaller colored error bars are due to CCD camera noise. Lorentzian fits are shown, where applicable.

Figures 6(b)–6(f) give the FSSR-F and FSSR-R data. Figures 6(b) and 6(c) show the FSSR-F spectrally integrated signals without a spectral filter (which was a sum of the two regions with blue shading in Figure 6(a)) and with the 25-μm C₃H₆ spectral filter (with violet shading in Figure 6(a)), respectively, for the 15-μm SUS target. A clear approximately 40-μm FWHM single peak occurs in both cases, assuring the best in-focus target positioning with a better than 20 μm accuracy.

Figures 6(d) and 6(e) show spectrally integrated bremsstrahlung signals (in the 1.35–1.54 nm spectral region in the first order of diffraction) from FSSR-R for 15- and 5-μm-thick targets, respectively. Multi-peak behavior was observed for the 15-μm target (Figure 6(d)), with one of the peaks (~20 μm FWHM) corresponding to the best in-focus target position. The second peak can be explained by the fact that soft X-rays can be effectively generated from large-area spots at a relatively low intensity. Since the distance between the peaks was approximately 100 μm, this can give a 10 μm accuracy if the target is put within a 50 μm range from the best focus position using other diagnostics.

Figure 6(f) shows dependences of the Fe K_α signals integrated in the 0.1925–0.1942 nm spectral region in the eighth diffraction order on X – X ₀ for the 15- and 5-μm-thick SUS targets. Contrary to the previous cases, the Fe K_α signals increased when the target moved away from the best focus. Thus, the Fe K_α line was not suitable for the target positioning.

7 Three-channel flat-field spectrograph

The 3FF grazing incidence spectrograph^[ Reference Neely, Chambers, Danson, Norreys, Preston, Quinn, Roper, Wark and Zepf ^{88 ]} was mounted in the ‘specular reflection’ direction behind a hole in the screen used for the NIR-vis-UV diagnostics. The 3FF is a slit-less version of a flat-field spectrograph employing a VLS grating operating at a grazing incidence angle of 4.2º (i.e., 85.8º off-normal), designed for recording a broad spectral region of 5–90 nm^[ Reference Neely, Chambers, Danson, Norreys, Preston, Quinn, Roper, Wark and Zepf ^{88 –} Reference Ragozin, Vishnyakov, Kolesnikov, Pirozhkov and Shatokhin ^{90 ]}. For a spatial resolution and a better signal-to-noise ratio, three gold-coated grazing incidence mirrors having shapes of elliptical cylinders were employed. The horizontal acceptance angles were slightly different for the three channels: 0.15º for the shallow-angle mirror, 0.20º for the central mirror and 0.26º for the high-deviation-angle mirror.

The VLS grating manufactured by Hitachi on a spherical substrate with R = 5649 mm had an average central groove density of 1200 lines/mm. The vertical acceptance angle of 0.087º was defined by the r = 2425 mm distance from the source to the center of the VLS grating, and by the 50 mm × 30 mm grating aperture. Thus, the acceptance angles for the three channels were 3.9×10^–6, 5.2×10^–6 and 7.0×10^–6 sr, respectively. A single-pass 0.65-μm-thick Al filter was mounted in front of the 3FF spectrometer, defining the 17–34 nm operating spectral range.

It is well known that relativistic laser–solid interaction is an intense source of HOH generated mostly in the ‘specular reflection’ direction^[ Reference Teubner and Gibbon ^{91 ,} Reference Thaury and Quéré ^{92 ]}. However, since the harmonics’ divergence can be narrow, we did not observe them in many shots, partly due to the small acceptance angles. Also, HOH generation depends on the pre-plasma scale length^[ Reference Kim, Pae, Kim, Kim, Yun, Yun, Sung, Lee, Yoon, Yu, Jeong, Nam and Lee ^{93 ,} Reference Kahaly, Monchocé, Vincenti, Dzelzainis, Dromey, Zepf, Martin and Quéré ^{94 ]} and intensity, defined in our case by the laser contrast and X – X ₀ shift.

Figure 7(a) shows a typical 3FF spectrum with HOH. Figures 7(b) and 7(c) show the dependences of the 3FF signal on X – X ₀ for 10- and 15-μm-thick SUS targets, respectively. The 3FF data had an approximately 50 μm broad peak in the vicinity of the best focus, with a clear dip of the signal near the middle. There was a lower peak at X – X ₀ ~ 120–140 μm. Within the main 3FF peak, the estimated dimensionless amplitude a ₀ was greater than 10, reaching approximately 60 at focus. Therefore, the main HOH generation mechanism was the relativistic oscillating mirror^[ Reference Bulanov, Naumova and Pegoraro ^{95 ,} Reference Lichters, Meyer-ter-Vehn and Pukhov ^{96 ]}.

Figure 7 (a) 3FF spectrum with harmonics. The upper and lower parts correspond to the shallow- and high-deviation-angle mirrors, respectively. Dashed lines show the Al filter cutoff (λ = 17 nm) in the first and second diffraction orders. (b), (c) Integrated 3FF signal versus target position for 10- and 15-μm SUS targets, respectively. The error bars correspond to shot-to-shot signal variations.

We did not observe harmonics in many shots, probably due to the small acceptance angles. Along with this, the optimum combination of the laser intensity and the pre-plasma scale length might not be satisfied in every shot. The presence of the HOH had been recorded within the ±25 μm distance from the best in-focus target position only, while the relative difference in the integrated signals from the shots with and without harmonics was around 20%.

Thus, the 3FF spectrometer can determine the best in-focus target position with an approximately 25 μm accuracy, using both the integrated 3FF signal and visual observation of harmonics. The dip in the 3FF signal close to the best focus position X ₀ can be used to place the targets with an approximately 5 μm accuracy, although this result may be laser-contrast-dependent.