High-brightness self-seeded X-ray free-electron laser covering the 3.5 keV to 14.6 keV range

50% 18 . The average peak spectral intensity was 1.7 times

T he introduction of the X-ray free-electron laser (XFEL) opened a new realm of extreme peak brightness X-ray sources with few-femtosecond pulse duration and full transverse coherence [1][2][3][4][5] . XFELs are typically based on the mechanism of self-amplified spontaneous emission (SASE), using multiple segments of an alternating magnetic field device called an undulator. However, the output radiation pulses can have noise and limited temporal coherence as the radiation starts from the electron beam shot noise. A fully coherent light source covering the X-ray region has been a long-standing issue for researchers, with longitudinal coherence remaining challenging. XFELs with good longitudinal coherence (narrow bandwidth in the frequency domain) enable a range of experiments that require high resolution (for example, resonant inelastic X-ray scattering, nuclear resonance scattering, X-ray Raman spectroscopy) or temporal coherence (for example, coherent control experiments) [6][7][8] .
A promising way to produce a longitudinally coherent X-ray is to exploit an external seeding method using an external laser with full coherency such as high-gain harmonic generation (HGHG) 9 or echo-enabled harmonic generation (EEHG) 10 . This method uses an external laser to introduce an energy modulation to the electron bunch in an undulator, followed by a density modulation in a chicane, which induces higher harmonic radiation through the nonlinear bunching process. Recently, the EEHG experiment at FERMI 11 showed a fully coherent FEL amplification at wavelengths as short as 5.9 nm, the exponentially amplified 45th harmonic of the 265-nm-wavelength seed laser. However, its radiation wavelength is limited to the soft X-ray region because the amplitude of higher harmonics decreases drastically as the harmonic number increases 11 . It is challenging to extend this external seeding to hard X-rays using the existing lasers with full coherency.
Self-seeding is a promising approach to overcome the shortcomings of SASE FELs and to realize bright, fully coherent FEL sources in the hard X-ray domain. However, existing hard X-ray self-seeded (HXRSS) FELs have limited radiation pulse energy and spectral brightness, and inadequate stability with large intensity jitter.
The idea of self-seeding 12 was proposed to overcome the limitations of SASE FELs, and later a self-seeding scheme with a four-crystal monochromator in a Bragg reflection geometry was proposed 13 . A more compact self-seeding scheme 14 that uses a single-crystal monochromator was proposed for the hard X-ray region; this design exploits the phenomenon that the forward Bragg-diffracted monochromatic beam has a small delay time, which allows a very short (<5 m) chicane. The forward Bragg diffraction (FBD) through a thin diamond crystal produces a train of monochromatic wakes that trail the main X-ray pulse by a few tens of femtoseconds 15,16 . By using a magnetic chicane to detour the electron bunch so that the electron bunch and the wake overlap in time, the monochromatic seed signal can be amplified in the downstream undulators.
The first successful demonstration of an HXRSS FEL using an FBD monochromator was performed at the Linac Coherent Light Source (LCLS), which produced 8.3-keV X-ray pulses with a bandwidth of 0.4-0.5 eV that was about 1/40-1/50 as wide as the SASE bandwidth 17 . The average pulse intensity of the HXRSS FEL pulses at the LCLS was 573 ± 290 µJ at 5.5 keV, and the intensity fluctuation was ~50% 18 . The average peak spectral intensity was 1.7 times High-brightness self-seeded X-ray free-electron laser covering the 3.5 keV to 14.6 keV range larger than in the SASE mode. In the self-seeding experiments at LCLS, including a soft X-ray self-seeding, the radiation spectrum often showed a pedestal-like distribution around the seeded frequency; this distribution limits spectral brightness 17,19,20 . The pedestals originate in longitudinal phase space modulations produced by the microbunching instability (MBI) upstream of the undulators as well as the SASE background.
The problem of the large delays in Bragg-reflection monochromators 13 was overcome, and self-seeding using Bragg reflections was demonstrated at the SPring-8 Angstrom Compact Free Electron Laser (SACLA) 21 ; the design used a channel-cut Si crystal monochromator with a tiny gap of 90 µm. The seed, with a bandwidth of 1.3 eV (full-width at half-maximum (FWHM)) at 9.85 keV, was filtered from the SASE radiation by the (111) Bragg reflections from the channel-cut crystal. The average pulse energy of the self-seeded XFEL at 9.85 keV was 450 µJ, versus 780 µJ in the SASE mode. The peak spectral intensity of the self-seeded XFEL pulses was six times higher than in the SASE mode. However, the X-ray pulses had a relatively large bandwidth of 3 eV (FWHM) because of the large bandwidth of the seed signal and an energy chirp in the electron bunch. Using the Si (220) Bragg reflections from the channel-cut crystal and reducing the energy chirp, the bandwidth was reduced to 0.6 eV (FWHM) at 9.0 keV with an average pulse energy of ~250 µJ (ref. 22 ).
At the Pohang Accelerator Laboratory XFEL (PAL-XFEL), we demonstrated an HXRSS FEL using an FBD monochromator ( Fig. 1) that has favourable source features compared with the SASE mode: a high average peak spectral intensity exceeded that of SASE by a factor of 12 in the self-seeded mode; substantial improvements in the stability of self-seeding; and substantially suppressed pedestal effects. We extended the self-seeding photon energy to 3.5 keV (lowest) and 14.6 keV (highest) with high peak brightness at all photon energies. We also demonstrated that using the self-seeded XFEL can improve the data quality metrics of serial femtosecond crystallography (SFX) at high resolutions, such as multiplicity, R split (the consistency of merged intensity distributions between two half-datasets separated from the full dataset) and the signal-to-noise ratio compared with those obtained using the SASE mode.

Improving the spectral brightness of the self-seeded XFEL
To increase the spectral brightness, we used electron bunches with a higher charge (180 pC) and a longer duration (42 fs FWHM) than in previous studies 17,23 . The electron bunch energy was 8.538 GeV, the undulator parameter was 1.87 and the duration of the SASE FEL radiation pulse was 20 fs (FWHM), as measured using the cross-correlation method 23,24 . A laser heater was used to suppress the MBI (see Methods).
One prerequisite to generate X-rays with a narrow bandwidth (narrowband) and high spectral brightness for the HXRSS FELs is a narrowband seed 25 . For efficient seeding with the narrowband seed, the FEL pulse length should be increased according to the Fourier transform limit, and the duration of the monochromatic wake should be comparable to or longer than that of the lasing part of the electron beam. To generate such a seed, we used high-index Bragg reflections (that is, (33 3) or (115)) with an FBD bandwidth of ~0.1 eV, instead of the 004 reflection with an ~0.3-eV bandwidth, as typically used in short-pulse modes 17,23 , and used an FEL pulse longer than 20 fs (FWHM). Unlike the self-seeding in the reflection geometry 21,22 , the path length delay of the seed pulse does not depend on the crystal index, thus high-index Bragg reflections, such as (33 3) or (115), can be used to generate a seed bandwidth <0.1 eV. For better overlap with a long electron bunch and a higher seed intensity, we used the zeroth-order wake of the FBD signal as the monochromatic seed instead of the first-order wake that has been used in previous experiments (Fig. 1f) (details in ref. 25 and profiles of the infrared laser and the electron beam at the end of the laser heater. c,d, Initial and increased slice energy spread distribution with the laser heater turned off (c) and on (d). The colour images above the plot c and d are the energy spectrum image of the sliced electron bunch using a transverse deflector. e, Simulated longitudinal phase space of the electron beam before the undulator from the eLeGANT simulation using the parameters of PAL-XFeL for when the laser heater is off (top), and on for the SASe (middle) and the self-seeding (bottom) conditions. f, Time responses of the FBD (black dotted line), measured seeded FeL intensity (solid red line) and SASe (solid blue line) without the crystal as a function of the chicane delay, as well as of a seed pulse (green dotted line). Twenty undulators (U1-U20) were used, 8 before and 12 after the self-seeding system. Two diamond crystal plates were mounted on one holder, with the crystal surface parallel to the (100) and (110) atomic planes and a thickness of 100 μm and 30 μm, respectively. LH, laser heater; IR, infrared; UV, ultraviolet; e − , electron; E c , the reference electron energy at the LH; E, the electron energy; L0, L1, L2, L3 and L4, acceleration sections; BC1, BC2 and BC3, magnetic bunch compressor chicanes (dipoles are indicated by green rectangles); s, the longitudinal coordinate along the electron bunch; γ, the relativistic factor of the electron beam. a.u., arbitrary units. Supplementary Fig. 1). The duration of the zeroth-order wake, in this case, is sufficiently long (~65 fs) to allow for a sufficient delay of the electron bunch with respect to the SASE pulse and for full separation of the seed signal from the SASE background ( Supplementary Fig. 2).
Another prerequisite to increase the spectral brightness is to suppress the pedestal-like distribution around the central seed frequency. This effect originates in the MBI induced by bunch compression, which creates detrimental sideband modulation of the electron bunch. Once the sidebands are generated, the electron oscillations are driven by the multiple-frequency ponderomotive potential. As a result, the efficiency of FEL generation at the carrier frequency is reduced, and the spectral quality is degraded by the diversion of radiation power into sideband frequencies 26,27 . A laser heater can efficiently suppress the MBI in both the SASE 28-31 and SXRSS 20 modes; however, for HXRSS, improvement of the spectral brightness using a laser heater has not been reported in the literature.
A laser heater can suppress the MBI and increase the peak spectral intensity in the self-seeded mode (Fig. 2). The pedestal around the centre peak is notably reduced as the slice energy spread (σ e ) increases, and as a result the peak intensity increases (Fig. 2a). These results show that the sideband amplification due to the MBI is effectively suppressed, so that only the main peak is amplified. The fraction of the FEL intensity enclosed within the bandwidth shows that the spectral purity is remarkably increased when the laser heater is used (Fig. 2b). As the slice energy spread increases, the peak intensity (solid red line in Fig. 2c) also increases; it reaches its maximum when the slice energy spread is ~27 keV. The optimal slice energy spread for the self-seeded mode is about 5 keV higher than for the SASE mode. To substantially suppress the pedestal effects due to the MBI, a longitudinal phase space with energy modulation further suppressed is required even though the slice energy spread is increased (Fig. 1e). However, the total sum of the spectrum (blue dotted line in Fig. 2c) remains almost constant until the slice energy spread by laser heater is 27 keV; this result supports the hypothesis that the unsuppressed MBI channels the radiation power into the sidebands.
Single-shot spectra maps (Fig. 3a) were obtained using a 0.26-eV-resolution Si (333) curved-crystal single-shot spectrometer 32 (Supplementary Fig. 3) for 9.7-keV X-rays in the SASE and self-seeded modes. The measured bandwidths of X-rays were 13.0 ± 0.1 eV in the SASE mode and 0.35 ± 0.01 eV in the self-seeded mode (Fig. 3b); the latter dropped to 0.24 eV after deconvolution from the spectrometer resolution. More accurate measurements were obtained by using a 0.09-eV-resolution Si (333) flat-crystal scanning spectrometer; they reveal a time-averaged bandwidth of 0.21 ± 0.01 eV in the self-seeded mode, which drops to 0.19 eV after deconvolution (Fig. 3c). The FBD seed bandwidth in the (33 3) Bragg reflection from the diamond crystal is 0.06 eV (Table 1), and its Fourier-transform-limited pulse duration is 30 fs (FWHM). But the resultant bandwidth of the self-seeded XFEL increased to 0.19 eV because of the energy chirp of the electron bunch and the shorter FEL pulse duration of 20 fs. Assuming the same pulse duration in the self-seeded mode as the SASE FEL radiation pulse (20 fs) and Gaussian pulse shape, the Fourier-transform-limited HXRSS FEL radiation bandwidth should be ~0.1 eV. The single-shot pulse bandwidth is definitely smaller than the 0.19-eV averaged bandwidth, thus the PAL-XFEL HXRSS pulses are less than a factor of two larger than the Fourier transform limit.
The self-seeded mode had a 12 times higher average peak spectral intensity than the SASE mode (Fig. 3b), but this number is limited by the spectral resolution of the single-shot spectrometer. The average pulse energy of the PAL-XFEL HXRSS is 0.85 ± 0.14 mJ, or 57% of the average pulse energy in the SASE mode (1.5 ± 0.12 mJ), as measured by the electron energy loss scan 33 . We carried out undulator tapering for 20 undulators, and adding more undulators downstream of the monochromator would further increase the intensity of the self-seeded FEL pulse ( Supplementary Figs. 4 and 5). The ratio of the integrated spectral area of the single-shot spectrometer for the SASE mode to the self-seeded mode is 1.64; this ratio is consistent with the XFEL intensity ratio of 1.76 (1.5 mJ to 0.85 mJ) that was measured  by the electron energy loss scan. Overall, the peak brightness of the PAL-XFEL HXRSS is calculated to be 3.2 × 10 35 photons s -1 mm -2 mrad -2 0.1%BW -1 , which is 40 times higher than that of SASE. The radiation pulse energy of the PAL-XFEL HXRSS is both high and very stable. The self-seeded mode has a consistently higher intensity than the SASE mode (Fig. 3d). In the self-seeded mode, >94% of the shots have an intensity higher than the average SASE intensity (that is, >1 arbitrary unit (a.u.)). Such seeding stability is mainly due to the stability of the PAL-XFEL, which has a very small shot-to-shot electron energy jitter of 0.012% (r.m.s.) 23,31 . The resultant shot-to-shot fluctuation of the central radiation wavelength of the SASE FEL was measured to be 0.025% (r.m.s.), which is half the Pierce parameter ρ = 5 × 10 −4 (relative SASE bandwidth, ~5.6 × 10 −4 ), thus self-seeded pulses are almost always amplified.

Widely tunable self-seeded XFEL
The FBD monochromator of the PAL-XFEL HXRSS was designed to cover the photon energy range from 3.5 keV to 14.6 keV (ref. 23 ); its crystal holder accommodates two thin diamond crystals, one with a thickness of 100 μm (crystal cut C[100]) to cover photon energies of 5 keV and above and one with a thickness of 30 μm (crystal cut C[110]) 34,35 to cover photon energies below 5 keV. The Bragg reflection crystal index below 5 keV is (111), and a thinner crystal is preferred for a higher rate of transmission of SASE pulses at a lower photon energy. The mechanical design of the monochromator is based on one developed by the Advanced Photon Source at Argonne National Laboratory for the LCLS HXRSS project 17,36 .
Using the same method for the 9.7 keV self-seeding, we could achieve a similar self-seeding performance at 14.6 keV. For a high photon energy, high-index Bragg reflections (53 3) can be used to generate a narrowband seed ( Table 1). The seeded 14.6-keV FEL's average pulse energy is 0.26 ± 0.07 mJ (28% jitter in r.m.s.). The self-seeded mode had a 6.2 times higher average peak spectral intensity than the SASE mode (Fig. 4c), which is relatively lower than the 9.7-keV seeded FEL. This is because eight undulators before the monochromator is not enough to generate SASE at seeding for 14.6 keV; one more undulator is necessary to generate enough SASE signals. The bandwidth of the 14.6 keV seeded FEL is SASe and self-seeded FeL spectra measured by a single-shot spectrometer. b, SASe and self-seeded FeL spectra averaged over 1,000 shots, with the peak value of the SASe spectrum set to 1, and E c = 9.7 keV. c, Crystal angle-scanning spectrum measurement with a Si 333 flat-crystal scanning spectrometer. each data point is an average of 150 shots. The y axis represents the photodiode current normalized by a quadratic beam position monitor (QBPM) for the FeL intensity measurement. The step of the crystal angle scan was 0.0001°, which corresponds to 0.022 eV. d, Histogram of radiation intensity (for 1-eV bandwidth around peak) expressed relative to the average SASe intensity (1 a.u.) for the SASe and self-seeded (SS) modes. Histogram data represent the 1,000 single-shot spectra measurements in a. The 33 3 Bragg reflection was used in the diamond FBD monochromator. The electron bunch delay in the magnetic chicane was 30 fs. a.u., arbitrary units.
0.32 eV limited by the energy chirp of the electron bunch, and the peak brightness is 1.3 × 10 35 photons s -1 mm -2 mrad -2 0.1%BW -1 , 26 times higher than SASE. For low photon energy below 5 keV, only low-index Bragg reflections (111) are possible, so the FBD bandwidth is relatively large (0.79 eV). The bandwidth of the 3.5 keV seeded FEL is 0.95 eV, limited by the FBD bandwidth. As a result, the peak brightness is 6.1 × 10 33 photons s -1 mm -2 mrad -2 0.1%BW -1 , only 11 times higher than SASE. The average pulse energy of the 3.5 keV seeded FEL is 0.93 ± 0.14 mJ (14.6% jitter in r.m.s.). For 3.5 keV, the self-seeded mode had a 3.2 times higher average peak spectral intensity than the SASE mode (Fig. 4a). The pedestal from the SASE background is substantial at 3.5 keV because the SASE growth rate is high enough to compete with the amplified seed signal (Fig. 4b). For the 3.5 keV self-seeding, only six undulators before the monochromator are used for SASE.

SFX with a self-seeded XFEL
Using the 9.7 keV self-seeded XFEL, we performed a demonstration experiment of SFX [37][38][39][40] to map out the three-dimensional structure of the lysozyme from chicken egg white, and performed a comparative analysis of the results obtained using the narrowband HXRSS FEL and the broadband SASE FEL. It was expected that the use of seeded FEL pulses with their higher reproducibility and cleaner spectrum might result in SFX data of superior multiplicity to that collected using SASE mode and accelerate the convergence of the merged reflection intensities 40 , meaning that a reduced number of indexed images would be required for analysis. However, in a previous study 41 , compared with SASE, the self-seeded XFEL did not show any improvement in the data quality metrics of SFX.
We collected and processed two datasets for the self-seeded (111,467 images) and SASE (107,397 images) modes (Supplementary Table 2). SFX data quality metrics such as multiplicity, signal-to-noise ratio, R split and correlation coefficient strongly depend on the number of images ( Fig. 5a and Supplementary Fig. 6). The self-seeding data show superior metrics compared with the SASE data at high resolutions, contrary to a previous report 41 ; the multiplicity of the self-seeded datasets is almost 1.4 times larger than in the SASE datasets ( Fig. 5a and Supplementary Table 2). And Fig. 5b clearly shows that the number of found peaks against resolution shells is shifted to higher resolutions for the self-seeded mode (SS1) than the SASE mode (SASE1) (Supplementary Fig. 7). At high resolutions over 2.3 Å, the SS1 peaks dominate the SASE1 peaks by 4.4 fold. After refinement, we compared the models with their structure maps (SS1 and SASE1) and found a slight improvement in the mFo-DFc maps (unbiased electron density map) of the self-seeded mode compared with those of the SASE mode ( Supplementary Fig. 8).

Conclusion
The PAL-XFEL HXRSS successfully demonstrated a FBD selfseeded XFEL with high peak brightness (3. mrad -2 0.1%BW -1 at 9.7 keV) and stability. We used high-index Bragg reflections [(33 3) or (115)] to exploit a narrow seed bandwidth <0.1 eV and a long wake duration of ~65 fs. A longitudinal phase space with energy modulation further suppressed is required to substantially suppress the pedestal effects due to the MBI and amplify the central seed signal solely. A very small shot-to-shot electron energy jitter of 0.012% allowed >94% of the shots to have an intensity higher than the average SASE intensity. We could achieve a similar self-seeding performance at a photon energy of 14.6 keV using high-index Bragg reflections (53 3). The bandwidth of the 14.6 keV seeded FEL was 0.32 eV limited by the energy chirp of the electron bunch, and the peak brightness was 1.3 × 10 35 photons s -1 mm -2 mrad -2 0.1%BW -1 . The peak brightness of the 3.5 keV seeded FEL was 6.1 × 10 33 photons s -1 mm -2 mrad -2 0.1%BW -1 . The pedestal from the SASE background is substantial at 3.5 keV because the SASE growth rate is high enough to compete with the amplified seed signal. We revealed that the self-seeding data show superior metrics compared with the SASE data at high resolutions through a demonstration experiment of SFX; the multiplicity of the self-seeded datasets was almost 1.4 times larger than that of the SASE datasets. Extremely intense and ultrashort XFEL pulses are required to achieve high-resolution single-particle imaging without the need of crystallization 42 . The XFEL pulse intensity has to be increased by two to three orders of magnitude to improve the spatial resolution 42 . The combination of self-seeding and undulator tapering was considered a feasible way to realize the required intensity in the simulation 43 . This study experimentally shows that adding more undulators with a proper undulator tapering would further increase the self-seeded FEL's intensity, demonstrating the feasibility of self-seeding for a narrowband terawatt (TW) FEL.

Online content
Any methods, additional references, Nature Research reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at https://doi.org/10.1038/ s41566-021-00777-z.
where J 1 is the Bessel function of the first kind. The appropriate delay of the electron bunch with respect to the SASE signal allows full separation of the seed signal from the SASE signal. A single-shot spectrometer measurement clearly shows ( Supplementary Fig. 2) that the seed pulse and electron bunch are both well separated from the background SASE. A 30-fs delay of the electron bunch allows it and the seed pulse to be separated temporally from the background SASE; with a 15-fs delay, they overlap with the background SASE. The optimum delay of the electron bunch was found to be ~35 fs. The duration of the SASE FEL pulse generated upstream of the FBD monochromator was measured to be 20 fs (FWHM) for a 180-pC charge bunch with a length of 42 fs (FWHM). With the crystal planes of (115) and (33 3), the electron bunch delay of ~30 fs is long enough to separate the seed pulse from the SASE while still generating enough seed power, because the zeroth wake trail, which extends to 50 fs, can be chosen rather than the first wake trail. However, for the (004) plane at 9.7 keV, the peak of the first wake trail is located around the delay of 15 fs, where the seed pulse partially overlaps the SASE background ( Supplementary Fig. 1). As long as the seed signal dominates the sidebands, the small difference in the wake amplitude ( Supplementary Fig. 1) does not make a big difference, because, eventually, the seed signal will grow to dominate the other frequency sources.
Spectrum measurement. Spectra for SASE and self-seeding were measured using a single-shot spectrometer that uses a curved Si crystal. The spectrometer was calibrated by collecting single-shot images of the seed pulse from a (115) diamond crystal plane; this pulse had a seed bandwidth of 0.05 eV (Supplementary Fig. 3). In this measurement, the 8 undulators upstream of the diamond crystal were used, with the 12 undulators downstream remaining open. The dip in the curve corresponds to the seed pulse and E c = 9.7 keV. The measured bandwidth of the single-shot spectrometer was 0.26 ± 0.04 eV. A flat-crystal scanning spectrometer was used to improve the resolution of the single-shot spectrum measurements, rather than using the curved spectrometer. A flat Si 333 crystal was used, with an angle-scanning device. The angle of the crystal was finely changed to measure the spectrum. The minimum step of the crystal angle was 0.0001°, which corresponds to 0.022 eV. The measured bandwidth of the self-seeded mode was 0.21 ± 0.01 eV (FWHM) (Fig. 3c), and the deconvoluted width was 0.19 eV, taking into account the Si 333 bandwidth of 0.086 eV.

Data availability
The raw data CXI files and geometry files have been deposited in the Coherent X-ray Imaging Data Bank (CXIDB; https://www.cxidb.org/). The coordinates and structural factors have been deposited in the Research Collaboratory for Structural Bioinformatics (RCSB) under the accession codes 7BYO/7D01/7D04 (for lysozyme from the self-seeded mode) and 7BYP/7D02/7D05 (for lysozyme from the SASE mode). The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.