1 Introduction

Laser-based ultrafast X-ray laboratory sources were vigorously developed during the last decade due to their compactness, robustness and very short (sub-picosecond) pulse duration. Progress in the technology of high-repetition-rate low-energy lasers supported this development. These lasers typically show increased both the pulse-to-pulse stability and the signal-to-noise ratio. Important breakthrough has been achieved less than one decade ago with the laser systems of a repetition rate in the kHz region delivering pulse energies of few millijoules [1–5]. Such sources have been successfully applied in many experimental techniques as diffraction [2], imaging of biological materials [6] and time-resolved absorption spectroscopy [7–10]. Synchrotron sources have the advantage of a high average flux of ~1012 ph/s but for sub-picosecond temporal resolution they need the sophisticated and expensive femtosecond slicing method [11] delivering on a sample a relatively low photon flux of ~104 ph/s in 0.1 %BW. The X-ray pulse duration of the plasma-based sources belongs inherently to the sub-ps range but this is, however, accompanied by a relatively limited photon flux. To consider the high-repetition laser plasma-based sources as excellent supplementary tools and in some aspects (pulse length) even competitive to the third generation of synchrotron sources, one needs to increase the photon flux and hence reduce acquisition time. Femtosecond laser-produced plasma sources are inherently point-like ones (diameter of ~10 μm) with a pulse duration expected to be slightly exceeding that of the pump laser. The highest achieved X-ray photon fluxes in this type of sources are in the range of 1010–1011 ph/s in 4π sr at the laser intensities covering typically a range between 1015 and 1017 W/cm2. When limited by the acceptance angle of a typical sample or diagnostic tools geometry and their throughput, the useful photon flux decreases by 6–8 orders of magnitude. This can be improved by increase in efficiency of the X-ray optics integrated with the source.

In this paper, we describe and characterize a plasma-based Kα source pumped by a commercial laser driver of 1 kHz repetition rate. While this is rather commonly spread technology, we focus on the installed source equipment and diagnostic tools. These elements including polycapillary lens and HAPG crystal facilitate measurements and the most importantly, improve significantly performance of the source as a whole. As a proof of that, we present applications that confirm the excellent spectral and temporal resolution of the setup and significant reduction in the acquisition time.

2 Experimental setup

Ti: sapphire laser of COHERENT (λ = 800 nm, 1 kHz, 50 fs, 5–8 mJ in a single pulse) was used as a driver. The measured contrast ratio of the driving pulse was 105–106. The pulse was focused by a 60° off–axis parabola (f/2) to a spot diameter of 6.8 μm (1/e 2-level) giving the maximum peak irradiation intensity up to 2 × 1017 W/cm2. A 20 μm-thick copper band with a width of 6 mm was used as a renewable target assuring each shot was meeting a fresh material surface. To get the latter, the band was transported with a speed of 2.5 cm/s between two wheels with geared DC motors. The measured maximum photon flux emitted at E ph = 8.05 keV into the full space was equal to 5.9 × 1010 ph/s. This value, if normalized to the unit solid angle, gives 4.8 × 109 ph/s/sr and compares reasonably to the value predicted in [12] for bulk Cu targets. Generally, it was considered to arrange the auxiliary equipment in the way enabling application of the photon flux in front of the target for the spectroscopy and the part emitted on the rear side of the target and enhanced by application the necessary focusing optics, for diffractometry. However, the results presented here are for rear-side emission in both cases. In fact, this does not change decisively the source performance.

The arrangement presented in Fig. 1a is dedicated to high-resolution spectroscopy and that in Fig. 1b for applications in diffractometry. Both arrangements enable pump-probe experiments with a temporal resolution limited only by the length of the pump and probe pulses. Since focused, laser is sufficiently intense to cause a significant debris level resulting in the chamber contamination and the optics deterioration, a 50-μm-thick plastic tape was moving at a speed of 2.5 mm/s in front of the focusing OAP, and the beam interaction area itself was surrounded by a housing made of Al foil. The target was placed in the geometrical focus, and the final trim was done by the band target displacement under operational conditions to maximize the output. The total conversion efficiency was estimated to be equal to ~1 × 10−5, a reasonably high value.

Fig. 1
figure 1

Experimental setup of Cu-K-alpha source with two variants dedicated to: a time-resolved X-ray spectroscopy and b time-resolved diffraction studies. The optical delay line is shown with a dashed line

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X-rays emitted from the back side of the metal tape were recorded either with an energy-dispersive X-ray PIN detector (AMPTEK, XR100CR) located at a distance of 85 cm from the source or on the chip of an X-ray CCD camera with a depletion layer. In addition, a glass polycapillary X-ray lens (IfG, GmbH, Berlin) was tested for the case when a focused photon flux is required on the sample. However, this specific arrangement is not suitable for the absorption spectroscopy experiments (see below) due to significant dimensions of the focal spot (0.6–1 mm) and the resulting loss in resolution. In fact, it is expected that the lens would be beneficial for time-resolved diffraction due to intensified photon flux.

3 Enhanced source performance

Figure 2b shows the enhanced emission of Cu-Kα and Cu-Kβ lines due to implementation of the polycapillary X-ray lens in the system. The data were recorded with a 600 μm pinhole in a lead disk placed in front of the PIN diode detector. Figure 2b shows a very strong pile-up and the detector dead time slightly below 50 %, what is a strong indication of a high photon flux. Hence, this is a clear evidence of the gaining effect, if compared with the system without focusing optics (Fig. 2a). The dead-time-corrected photon emission rate measured at the focal plane of the X-ray lens (focal spot 0.6–1 mm) was estimated to be at a level of ~5×107 ph/s. Enhancement by a factor of ≈550 caused by the polycapillary lens corresponds well to the expected theoretical value of 500–600 for this specific lens and arrangement. The range of expected gain was determined by the manufacturer using tracing ray method. The X-ray beam behind the focus was slightly divergent (about 2°–5°). The polycapillary lens works on the principle of the total internal reflection [13]. It consists of many glass capillaries bundled together and maintained at certain bending angle to provide the grazing angle to the incident X-rays. As the capillaries are profiled with a certain curvature radius, there is a path difference between the axial and the outermost rays. This causes some delay between the mentioned rays in the focus and that is equivalent to pulse elongation. The estimated theoretically pulse extension due to our lens was equal to 384 fs. This is the value corresponding to the increase in the path length through the outermost (the most strongly bent) capillary, if compared with the central one. Hence, the temporal resolution of the pump-probe experiments is reduced, but it is still expected to be kept well below 1 ps.

Fig. 2
figure 2

a Cu-K α and Cu-K β lines without focusing optics and b the same with the focusing glass polycapillary X-ray lens. Both signals are registered by an energy-dispersive PIN diode from Amptek (XR100CR)

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In our slitless spectrometer configuration, the source size is a crucial parameter deciding about the spectral resolution. The slit method was used to determine the source size it gave a diameter of 13 ± 2 μm. This confirms a point-like nature of the source and supports its viability for the high-resolution spectroscopy experiments. The main parameters of the described X-ray source are collected in Table 1.

Table 1 Summary of the pump laser and X-ray source parameters
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It is worth noting that at E ph = 8.05 keV, the measured Kα linewidth of 5 eV is well below the standardized in the synchrotron community relative spectral bandwidth (BW) of Δω/ω = 10−3 or 0.1 % BW.

In the first version of the photon flux measurement, the X-ray emission from rear side of the target was collected within a solid angle of 5.2 × 10−7 sr, determined by the active area of the Amptek X-ray diode. The signal registered with the X-ray diode (see Fig. 2) shows clearly both Cu-Kα and Cu-Kβ emission lines of the K shell along with a broad bremsstrahlung spectrum and the additional peaks identified as the pile-up signal. The pile-up-plagued data (Fig. 2b) was corrected using the dead-time correction formula for the actual photon counts derived in [14]. The dead-time-corrected emission rate gave a photon flux of 1.2 × 109 ph/s/sr, and this value compares well with that of 4.8 × 109 ph/s/sr, obtained in the version of the detection system using a CCD camera.

The major advantage of the applied spectrometer is its crystal. The applied coating technology enables exceptionally large surfaces (up to 150 × 300 mm2) to be covered by a thin layer of the highly annealed pyrolytic graphite (HAPG). For spectroscopic investigations, photon flux is the critical parameter deciding about the measurement dynamics and the acquisition time. Since incoherent in nature, such sources emit X-rays into the full space. Consequently, the acceptance angle of the collecting optics should be large. Typically, monocrystals (like (111)-oriented GaAs or Ge) used to be applied as monochromators or spectrometers [4]. The same role frequently fulfill toroidal Si-based Bragg mirrors [15]. However, all of them have limited acceptance angle, low integrated reflectivity and limited spectral resolution at energy above 1 keV. HAPG having a mosaic structure is a better alternative due to high collection efficiency (active area of 20 cm2 is readily available), high integrated reflectivity as well as higher resolution in the energy range between 1 and 20 keV. A very thin HAPG layer (~10–15 μm) deposited on a carefully prepared substrate has demonstrated better energy resolution than Ge-(111) single crystal [16–18]. As the crystal very large active area proved its supremacy in the spectroscopic applications, we have installed a cylindrical HAPG crystal of dimensions 36 × 50 mm2 (produced by Optigraph GmbH and BLiX, Berlin) and arranged it in the von Hamos geometry. In this arrangement, a solid angle subtended by the crystal when seen from the source was equal to 10−3 sr and the first-order integrated reflectivity was 1.35 mrad. This gave ~3.5 × 103 ph/s in Cu-Kα line on the detector, a value which is often met rather on the sample, so the improvement is evident.

In spectroscopy, one of the most stringent requirements alongside with the collection efficiency of the X-ray optics is energy resolution. The graphite thin layer (15 μm) was prepared on half-cylindrical glass substrate. A diffraction angle of 13.2° (1st order) resulted in an acceptance angle of 0.05 rad measured along the dispersion direction [18]. Strong energy (wavelength) dispersion of the wave reflected from the crystal enabled separation of the closely spaced (~20 eV) two components of the Cu-Kα lines (Kα1 and Kα2) within an exposure time of only 5 s. Figure 3a shows an image of both Kα line components recorded with a deep depletion CCD camera (ANDOR, ikon-M), and Fig. 3b presents the lineout of this image. De-convolution process of the composite structure presented in Fig. 3b and the following correction accounting for the natural width of the emitted line determined the widths of the individual components and the resolution of the spectrometer. Corrected widths of both lines were equal to 4.5 eV, and it gave a resolution (E/ΔE) value of ≈1,800 (precisely 1,780) for both Kα1 (8.0463 keV) and Kα2 (8.0267 keV). This is a very high resolution for the applied geometry, and it confirms the high quality of the HAPG elements reported. Using this high resolution or equivalently high angular and linear dispersions, we are able to extract noticeably narrow part of the spectrum in the vicinity of the required wavelength, including that within the bremsstrahlung background. To be efficient, the last option requires some corrections in the pump power to increase the background level. It was found that reduction in the average power of the pump laser system from 4.8 to 3 W and following small correction (maximizing the output) in the position of the target relative to the optimum focus for Cu-Kα emission resulted in the increase in the bremsstrahlung radiation level around the nickel absorption edge by factor ~5. Nevertheless, the increase in the photon flux on the sample and detector used to be obtained dominantly by the increased collection power of the spectrometer. Owing to this property, the total photon flux of Kα radiation available on the sample within the acceptance angle of the diagnostic was in our specific arrangement (16 cm from the source) equal to 4.7 × 106 ph/s.

Fig. 3
figure 3

a Cu-Kα1 and Cu-Kα2 lines recorded with a CCD camera; b lineout of the image on the camera chip

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Physics of the generation process is reasonably well understood (e.g., see ref. [2]), and the peculiarity of the plasma-based X-ray sources is their inherent sub-picosecond pulse duration. This timescale (but not the real pulse width) has been confirmed by indirect measurements using cross-correlation technique based on phase transitions in crystalline materials, mostly semiconductors [19–21]. Upper bound of the pulse duration has been established at a level of 300–600 fs [22]. In contrast to these measurements, we applied the cross-correlation technique based on the transmission signal through a 4 μm-thick polycrystalline sample of metallic nickel. The sample was heated by a small split of the main driving laser pulse delivering an average power of 60–600 mW loosely focused on the sample to a spot of 2.9 mm in diameter. Heating causes, especially in the transient metal like nickel, nonequilibrium ultrafast relaxing electron distribution [23] and femtosecond modification of electron localization connected with transfer of the angular momentum [24]. We assume that these mechanisms, rather that ultrafast diffraction, are involved in the observed fast changes in the X-ray absorption. Using a variable delay (scan step of 250 fs) between the IR heating pulse and the X-ray pulse, we have found (see Fig. 4) an upper limit of the X-ray pulse duration to be of 323 ± 47 fs. This value was extracted by de-convolution of the record in the experiment edge in the transmission dependence on pump-probe delay. Fig. 4a, b demonstrates the result of application of the first derivative to the edge visible in Fig. 4a, and an interpolation of the resulting curve by a Gaussian profile (smooth fit). Interestingly, the theoretical value of the emission duration for the optimum-driving intensity in a bulk material obtained using the formula τ x ≈ τ L + τ a = τ L +100Z −0.4 l 0.8 given in [12] was equal to 336 fs, and this compares favorably with the value derived from the experiment. In the above expression, Z is the atomic number of the target, l [μm] is the target thickness, τ L = 50 fs is the laser pulse length, and τ a the length of the afterglow emission. The onset of the changes in the transmission signal was also used to synchronize arrival of the pump and probe (X-ray) beam with the heating pulse (pump) on the sample.

Fig. 4
figure 4

a The transmitted X-ray intensity as a function of the delay time between the optical pump (600 mW of average power) and the X-ray probe pulse (zero is the beginning of the scan and the negative delay corresponds to the pump pulse following the X-ray probe). The transmission falls down on the timescale comparable with the length of delay step (300 fs); here, synchronization was biased by a constant interval b after de-convolution (derivative) of the transition edge, it gave an upper limit of the pulse width of the X-ray being transmitted as equal to 323±47 fs (FWHM-full width at half maximum)

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Seemingly, the method applied in the measurement took advantage of the probe high average photon flux owing to the applied very efficient crystal spectrometer.

Pump-probe method is the standard method for the time-resolved studies. To demonstrate the improved performance of the experimental arrangement, an X-ray absorption near-edge spectroscopy (XANES) experiment was conducted with the use of a 4 μm-thick Ni foil (commercially available from Goodfellow). As the intensity of 2 × 1017 W/cm2 on the copper target was selected to maximize generation of Kα radiation, we started to look for increase the photon flux of the background in the way described earlier. Reduction in the intensity by ≈40 % to a value of 1017 W/cm2 accompanied by the target position modification maximized the bremsstrahlung signal in the XANES-related measurements. The bremsstrahlung background obtained in this way was experimentally determined to have, close to the nickel absorption edge (8,330 eV), a brightness of 4.7 × 107 ph/s/srd/0.1 %BW. This is an exceptionally high value (less than two orders below the Kα emission level) giving a good basis for further reduction in the acquisition time due to the high-performance optics. The bremsstrahlung photon flux on the sample, determined by the acceptance angle of the spectrometer crystal, was equal to 2.7 × 105 ph/s/0.1 % BW. Figure 5 shows the Ni XANES spectrum after accumulation of the X-ray signal during only 15 min. The graph in Fig. 5a shows an expanded K-absorption edge at 8,331 eV along with the oscillations caused by interference of 4p electrons wave functions with the neighbor scattering elements (peaks B, C, D). The spectral resolution of the arrangement was sufficient to reveal a fine pre-edge structure (Fig. 5b). This is usually caused by quadrupole (weak) 1 s-3d transitions, and it can be sometimes accompanied by the dipole 1 s-4p transition. Both are considered as a structure geometry test [25]. Low-to-negligible level of these components suggests strong center-symmetric environment in the used sample. A small inflection on the edge [26], typical for the transition metals (situated in the periodic table around cobalt), was also observed in our measurement on nickel.

Fig. 5
figure 5

Ni foil irradiated by laser plasma X-ray source for X-ray absorption near-edge spectroscopy: a cold sample with the inset showing pre-edge (A) and near-edge fine structure of Ni (B, C, D); b expanded A area showing two weakly pronounced shoulders (1,2) in the pre-edge spectrum

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It was claimed in Ref. [26] that the weakly pronounced shoulder (B in the inset of Fig. 4) on the absorption edge is, together with the first two main peaks, a feature of the fine local structure of the density of p states in the 4p band in nickel. The characteristic features (lobs) B, C and D positioned here at 8,347, 8,359.3 and 8,410.4 eV, respectively, show a reasonable agreement with the spectroscopic data bank values. The D-peak is usually ascribed to the free electron states in the 4f sub-shell. The possibility to distinguish all these features in the XANES spectrum confirms high performance level of the diagnostic tools integrated with the Kα source in the presented arrangement. This assessment is supported by a very short acquisition time of 15 min. Typical reported values in this type of the experiment are about 30 min.

4 Conclusions

To summarize, we have developed a compact, laboratory-scale, bright kHz Cu-Kα X-ray source operating at 8.05 keV and equipped with the advanced diagnostic tools. The diagnostic tools including HAPG spectrometer and the multi-capillary X-ray optics improved significantly performance of the source increasing markedly the photon flux available on the sample and the detector in both considered in the text arrangements. The used elements increased primarily collecting power (acceptance angle) of the detection system and offered its larger throughput. As a consequence, this resulted also in much more efficient use of the background radiation (bremsstrahlung) being the base for application of XANES and EXAFS techniques. Efficient and of high-throughput HAPG spectrometer with a resolving power of 1,800 has been constructed and used to demonstrate the source feasibility for the planned applications in time-resolved high-resolution spectroscopy. The test conducted as a XANES experiment on a commercial Ni foil revealed clearly the fine structure of the 4p-electrons directly at the absorption edge. The low acquisition time of only 15 min supports the source viability for the high-resolution X-ray spectroscopy.

As far as the spectral brightness is concerned, the source with its diagnostic tools shows comparable performance to that of the XANES-dedicated soft X-ray (below 500 eV) beamline of the advanced laser light source (ALLS) reported in [27]. The reported brightness at 500 eV is only slightly above that estimated for our source at 8 keV. Following the analysis given in [27], we believe that the performance of the presented source with the integrated HAPG spectrometer is in the terms of brightness and the photon flux available for the detection system comparable or even slightly better than that of a conventional synchrotron-based source when using slicing technique and undulator. Additionally, the sub-picosecond X-ray pulse duration has been estimated by a cross-correlation technique applied to an Ni foil when this was heated by a short laser pulse at variable delay.