## 5 SASE Performance in the Sub-Angstrom Regime  
Based on the obtained electron bunches through start-to-end simulations in Section 4, dedicated SASE simulations are carried out with a main goal of exploring the lasing performance of the facility in the sub-angstrom working regime. This study is organized by utilizing electron bunches energized to different energy levels that are practically available at the facility, that is, 7.3 GeV, 14 GeV and 17.5 GeV. An electron beam energy of 14 GeV is typically applied for routine user operation at the European XFEL. A full design energy of 17.5 GeV has been demonstrated in test runs. A reduced beam energy to 7.3 GeV is mainly relevant to a future CW operation mode as aforestated. At 14 GeV and 17.5 GeV, achievable photon energies above 20 keV are considered, while a case at a frequently requested photon energy of 9.3 keV by the users is given for reference at 14 GeV. At 7.3 GeV, the accessible shortest photon wavelength is limited by the period of the existing undulators. Thus, the lasing results at 7.3 GeV are given at lower photon energies of 5.3 keV and 7.8 keV, only for demonstrating the obtained qualities of the electron bunches. For simulation of the SASE process, the well-established GENESIS code [58] is used. Note that only the existing undulators with a undulator period of 4 cm are considered in these simulations. An average beta function is set according to [12] with a technical limit regarding the smallest beta function of 15 m at our facility. Linear and quadratic tapers are applied to improve the lasing intensities at different resonant photon wavelengths. Figure 8 shows the SASE performance of the optimized electron bunch generated with a 56 MV/m cathode accelerating gradient at a final beam energy of 14 GeV. The pulse energy evolution along the undulator beamline is simulated for three photon energies, as shown in (a) 9.3 keV, (b) 20 keV and (c) 25 keV. The inset plots illustrate the SASE power distributions by the end of the undulator beamline. The dashed lines represent exponential fits to the gain curves for estimating the gain length in each case. As shown, at a frequently requested photon energy by the users of 9.3 keV, the SASE intensity can reach about 4.4 mJ with a gain length of less than 4 m. Pushing the photon energy to 20 keV, the bunch still lases with an intensity of 2.3 mJ using a gain length of about 6 m. At 25 keV, that is less than half angstrom, millijoule-level SASE intensity can be achieved with about 7 m gain length. It can be seen that, using the low-emittance electron bunch, the facility is capable to provide high-power photon beams above 25 keV using about 80% of the total energy gain available from the accelerator. Note, in addition, that the choice of the accessible photon  
Figure 7: Current profiles (**left**) and slice emittance (**right**) along the bunches at the entrance of SA1 undulators using multiple peak accelerating gradients at the cathode. wavelength is set according to the undulator parameter K via practical gap adjustment for the existing undulators. As a reference, at a frequently requested photon energy of 9.3 keV by the users at an electron beam energy of 14 GeV, the measured gain length is typically about 5 m. Given the room for further improving the bunch quality in the machine, the agreement between the simulated and measured gain lengths can be further improved at this photon energy. However, at other photon energies, especially those above 12 keV, the measurement data are not yet systematically available.