## 3 Recent Progress in Accelerator  
Since the user service started, we have tried to continuously improve the FEL performance, and providing the best FEL pulse energy has been pursued as a first priority. For that purpose, FEL tuning has been conducted every week before user service. Figure 2 shows the measurement results of the FEL pulse energy in 2020. The horizontal axis is dated from January to December and the vertical axis is the FEL pulse energy. Different colors show the provided photon energies for each user service. Note that most of the user services in the hard X-ray beamline were provided with more than 1.2 mJ of pulse energy. Increasing the photon energy range has been a second priority of FEL performance improvement. The design value of the maximum photon energy of the PAL-XFEL is 12.4 keV with 9.65 GeV electron beam energy for an undulator parameter K of 1.87. At PAL-XFEL, the maximum available energy of the electron beam is 11 GeV, and 14.5 keV FEL was achieved at the same undulator parameter K, with an electron beam energy of 10.44 GeV. The measured FEL pulse energy was 650 uJ [30]. This indicates that a higher photon energy can be obtained with a lower undulator parameter K, and a FEL saturation of 20 keV was achieved for the first time at the PAL-XFEL in 2020. The electron beam energy was 10.4 GeV and the undulator parameter K was 1.4. The measured FEL energy using the e-loss scan was 408 uJ, which corresponds to 1.26 \(\times\) 10\({}^{11}\) photons/pulse. The measured FEL spectrum bandwidth was 25.3 eV rms (0.13% of the center photon energy), and the FEL pulse width (FWHM) was 11 fs. The undulator gap scan was conducted for 20 undulators to check the FEL saturation as shown in Figure 3. Here, quadratic undulator tapering was applied for the last six undulators, and the calculated gain length was 3.43 m.  
Since the noisy spectrum and limited temporal coherence of SASE FELs, two self-seeding methods were proposed to overcome the drawback of the SASE FELs. The first method uses a single-crystal monochromator to generate a hard X-ray self-seeding FEL. When a seed X-ray pulse from the upstream undulators passes through a thin diamond crystal, a train of monochromatic wakes can be obtained after the seed X-ray pulse with a few tens of femtoseconds delay from the forward Bragg diffraction (FBD). A magnetic chicane adds a time delay in the electron beam to make an overlap with the monochromatic  
Figure 2: Provided FEL pulse energy for user services in 2020.  
wake for the amplification in the downstream undulators [31; 32; 33]. The first experimental results of the hard X-ray self-seeding FEL were achieved in LCLS. 8.3 keV and X-ray pulses were obtained with a bandwidth of 0.4\(\sim\)0.5 eV and the average peak spectral intensity was increased by 1.7 times more than the SASE FEL case [8]. The second method of self-seeding FEL generation involves using a four-crystal monochromator in a Bragg reflection geometry [34] and an experimental result was achieved in the SACLA [35]. They succeeded in making a channel-cut Si (111) crystal monochromator with a small gap of 90 \(\upmu\)m. A self-seeding FEL with a 3 eV bandwidth was obtained at 9.85 keV and the peak intensity was six times larger than the SASE FEL case. A relatively large bandwidth came from the large bandwidth of the seed beam and an energy chirp in the electron bunch. In the case of a Si (220) Bragg reflection and reduced energy chirp, the bandwidth of the self-seeding FEL was reduced down to 0.6 eV at 9.0 keV [36]. In the PAL-XFEL, two diamond crystals in the (100) and (110) orientations were installed in the middle of hard X-ray undulators to a generate self-seeding FEL with FBD [37]. The spectral purity and peak of the self-seeded FEL were consistently improved using a laser heater and optimized crystal conditions over a hard X-ray range from 3.5 keV to 14.6 keV. Figure 4 shows an intensity comparison between the SASE and self-seeding FELs of 9.7 keV photon energy.