## 4 Soft X-Rays: Polarization  
The regular planar undulators at the European XFEL contain permanent neodymium magnets arranged to generate linearly polarized radiation with the polarization axis in the  
Figure 3: Single pulse at 9450 eV. (**a**) TOF spectra for the same pulse recorded on detectors in four different orientations. Retardation is \(-4630\) V. (**b**) Single-shot Xe 2p\({}_{3/2}\) peak transformed from TOF to photon energy (black line). Average of 100 pulses (gray area). (**c**) Sum of spectra from all four detectors (red line). Same pulse detected on HIREX (orange area). (**d**) Five typical single-shot photon pulses measured with both the hxPES and the HIREX. horizontal plane. To obtain variable polarization in the soft X-ray regime, an afterburner consisting of four APPLE-X helical undulators was implemented behind the SASE3 planar undulator system [23]. The sxPES supported the commissioning of the afterburner with online polarization photon diagnostics. Figure 4a-c shows the TOF spectra for Neon 1s a few dozen eV above the resonance on eight detectors in different orientations with respect to the polarization vector of light for three different polarization configurations. The binding energy (E\({}_{B}\)) is 870.2 eV and the natural line width is \(\Gamma=0.24\) eV. The Ne 1s photoionization cross-section at this photon energy range is \(\sigma>0.2\) Mb, and the anistropy parameter is \(\beta=2\)[10,12]. The pulse energy is about 100 uJ. We have averaged 20 pulses for each spectrum to improve the signal-to-noise ratio. The retardation voltage is fixed at 6 V. The angle-resolved measurement with the undulator tuned to 900 eV at horizontal linear polarization is presented in Figure 4a. The distribution is anisotropic with the Ne 1s peak intensity close to zero at 90\({}^{\circ}\). The intensity increases as a function of the angle and reaches its maximum at 0\({}^{\circ}\). Figure 4b shows the angle-resolved spectra for 885 eV at vertical linear polarization, where the intensity is maximum at 90\({}^{\circ}\) and vanishes at 0\({}^{\circ}\). The wider TOF distribution for vertical polarization compared to horizontal polarization is related to the lower photon energy and subsequent lower electron kinetic energy, which corresponds to a longer TOF and a broader distribution. Figure 4c presents the spectra for circular polarization at 890 eV where angular dependence is isotropic. Figure 4: The intensity of electron TOF spectra with sxPES displays angular dependence for different settings of the helical undulator: horizontal (**a**), vertical (**b**) and circular polarization (**c**). (**d**) N\({}_{2}\) KVV lines are used for detector signal normalization. (**e–g**) Angular intensity distribution is presented in polar plots with 14 detectors active. Fitting with Equation (8) gives us the degree of linear polarization and the tilt angle. (**h**) Angular distribution with helical undulator set to \(+45^{\circ}\) at 1000 eV taken at a different occasion with all 16 detectors active. The detector and flight-tube performance is not identical; thus, the peak intensity must be normalized, which is accomplished with Auger-Meitner lines whose polar and azimuth intensity distribution is nearly isotropic. In particular, the N\({}_{2}\) KVV transition energies in the range 357 eV to 367 eV are useful for this purpose [37]. Figure 4d presents electron TOF data for eight of the detectors from an N\({}_{2}\) target at \(\hbar\omega=700\) eV with \(-261\) V retardation voltage. The data are averaged over 20 pulses for reliable statistics. The intensity of the KVV peak at about 17 ns (shaded green area) is used to normalize the detector performance by calculating a calibration factor for each detector. In addition to the Auger-Meitner band, the N\({}_{2}\) 1s peak (\(\beta=2\)) is seen at about 27 ns. These data were collected with the helical undulator tuned to elliptical polarization, thus explaining the almost isotropic distribution of N\({}_{2}\) 1s photoelectrons.