## 3 Hard X-Rays  
Figure 3 shows single-pulse spectra of Xenon 2p\({}_{3/2}\) measured with the hxPES [16] at the SASE1 beamline. The undulator gap was tuned for 9450 eV radiation. Binding energy is E\({}_{B}=4786.47\) eV [13] and natural line broadening is \(\Gamma=2.60\) eV [36]. At this photon energy, the anisotropy parameter is \(\beta\approx 1.47\)[14] and the photoionization cross-section is \(\sigma\approx 0.04\) Mb [11]. Although the spectrometer has 12 flight tubes, it was equipped with only four detectors during these measurements. Now, two additional detectors have been assembled and installed on the device to improve the signal statistics. Figure 3a presents electron TOF spectra from one single photon pulse recorded with the four available detectors. The signal from scattered light defines a prompt that represents the instant of ionization subtracted by 0.83 ns due to the time it takes photons to reach the detectors. The peaks in region 5 ns-15 ns are related to valence photoelectrons and Auger-Meitner electrons where the high kinetic energy leads to short TOF. Around 30 ns, we see the Xe 2p\({}_{3/2}\) photoelectrons that have been decelerated from very high kinetic energies, around 4660 eV, to only a few 10 eV. The retardation voltage was set to \(-4630\) V. Figure 3b shows the Xe 2p\({}_{3/2}\) spectra converted from TOF to spectral distribution according to our calibration function. The gray area plot shows the spectral distribution for an average of 100 pulses. As is expected from the polarization function, Equation (8), for linear horizontal polarization and a positive anisotropy parameter, the intensity reaches a maximum at 0\({}^{\circ}\) and 180\({}^{\circ}\), and is decreased at 150\({}^{\circ}\). The detector located at 90\({}^{\circ}\) provides only a minor contribution to the total intensity. The challenge in the hard X-ray regime, for single-pulse photon diagnostics, is the poor photoionization cross-section with the consequence that one detector alone does not provide sufficient statistics to represent the actual spectral distribution, and thus it is needed to combine the signals from several detectors. Figure 3c  
Figure 2: (**a**) Krypton LMM and LMN Auger–Meitner lines measured with hxPES at \(\hbar\omega=12\) keV. Retardation voltage was tuned in the range 1300 to 1610 V. The detector at 90\({}^{\circ}\) was used, and the digitizer was configured to 4 GSs\({}^{-1}\). The conversion to kinetic energy is made for each retardation voltage and is based on numerical inversion of the analytical calibration using Equations (1)–(7). Panels (**b–f**) show expanded views of each band A–H. Dashed lines indicate final states.  
shows the sum of the four detectors (red line). As a means to validate the reliability of the photoelectron spectrum and of the calibration, we compare with a spectrum measured for the same photon pulse by the downstream located HIREX (HIgh REsolution hard X-ray) spectrometer [7]. This is a single-shot spectrometer, based on a bent crystal as a dispersive element, and a MHz-repetition rate strip detector. Optionally, an upstream diamond diffraction grating can be used in transmission to split off a small fraction (0.1%) of the photon beam for this analysis instead of using the zero-order direct beam which is propagated to and used at the experiment endstation. The HIREX and the hxPES are two complementary and independently calibrated devices for spectral diagnostics. At 9 keV, the HIREX offers a high spectral resolution of about 0.3 eV, but in contrast to the PES, it is partially invasive and has a measurement rate of 0.5 MHz limited by the currently used Gotthard-I detector, whereas the PES can provide diagnostics up to the maximum repetition rate of 4.5 MHz available at European XFEL. Figure 3d shows five subsequent single-shot photon pulses measured with both the PES and the HIREX.