3.1 Optical path design

The schematic beamline layout of the E-line is shown in Fig. 2. Two separated beamlines, corresponding to soft and hard X-rays are sketched in red and blue, respectively, and were in close proximity to the APPES experimental end station. The soft X-ray branch passed through two series of experimental stations, REXS and inelastic RXES, while the hard X-ray branch was connected to a HAXES end station.

Fig. 2.Full-screen View

(Color online) The optical path layout of the E-line. The main optical components of the beamline were plane mirrors (SM1, SM2, SM3a/SM3b, SM7b, HM2, and HM4b), a cylindrical mirror (HM3), elliptical mirrors (SM5 and SM6), toroidal mirrors (SM4, SM7a, HM1, HM4a, and HM5), plane grating monochromators (PGM1 and PGM2), and a double crystal monochromator (DCM). All incident and deflection mirror angles for the hard X-rays were 3.5 mrad and the deflection angles for the soft X-rays are demonstrated in Fig. 2. H-slit and V-slit denote the horizontal and vertical slits, respectively. The paths, components, and distance values marked in red and blue represent the soft and hard branches, respectively. The distance shown on the ruler at the top is measured from the center of the straight section. The areas shaded in gray show the range of the front end.

With the canted angle of 2 mrad, the two undulator beams propagate until their separation is large enough to mount a separate plane mirror, SM1, which is located at distances of 15.9 m relative to the center of straight section. This keeps the Bremsstrahlung radiation within the ring tunnel and eases the radiation safety measures in the experimental hall. After the first mirror, the angular separation of the two beams increases to 1.2 degrees, allowing for the setup of two dedicated beamlines.

Although the main beam toward the HAXES station did not pass through SM1, Bremsstrahlung radiation was still generated from the scattering effect of SM1, and was considered in the design of our beamline. To block the Bremsstrahlung radiation induced by SM1, an iron tungsten nickel alloy, of size H:120 mm×V:120 mm×L:50 mm was employed as the radiation block material in the safety shutter in the front end. An optical hutch was connected to the front end in both the hard and Soft X-ray branches, while all tubes in the optical hutch were wrapped in a lead sheath to prevent the induced SM1 Bremsstrahlung radiation. In this way, the calculated radiation was below 0.5 μSv/h at the exit of the optical hutch in the soft X-ray branch.

The monochromatization of the soft X-ray in the combined beamline was based on a variable line spacing monochromator and an exit slit. Three blazed gratings with central line densities of 300, 800, and 1200 l/mm were chosen, while the variable included angle was determined using a tilting mirror SM2 in the monochromator, similar to the reported in-focus variable line spacing plane grating monochromator. [19] The grating monochromator focused the beamline to the slit at 41.8 m in the vertical direction, while the plane mirror SM3b deflected the beam to the APPES end station, as indicated by the red solid line in Fig. 2. In the front of the end station, a toroidal mirror (SM7a) was employed to refocus the soft X-ray beam in both the horizontal and vertical directions. The source of the SM7a in the horizontal direction located at 1.317 m, was the light source of the soft X-rays. The vertical source originated from the V-slit at 41.8 m. The sample point at 54.6 m was the image of SM7a in both the horizontal and vertical directions.

The hard X-rays in the combined beamline (solid blue line in Fig. 2) were pre-focused in the horizontal direction to the slit at 33 m by a toroidal mirror, HM1, while the beam was parallel aligned in the vertical direction. The source of HM1 in both the horizontal and vertical directions was located at -1.225 m and was the light source of the hard X-rays. A plane grating monochromator (PGM2) or double crystal monochromator (DCM) were used to monochromatize the incident beam. The two monochromators were placed in series and used separately by slipping the incident beam and referring to the photon energy. The fixed groove density PGM (PGM2, 800 l/mm and 1200 l/mm) covered the energy range 1500 eV–2300 eV, while the monochromatic light, with an energy range from 2300 eV–10 keV was realized by the DCM. The PGM was a Petersen-type monochromator [20] while Si(111) was mainly used as crystal in the DCM; Si(311) crystals are reserved for high energy resolution experiments. The lattice d-spacing was 0.313 nm for the Si(111) crystal and the Bragg angle was 23.3° for a beam energy of 5 keV.

A cylindrical mirror HM3 deflected the beam to the combined beamline station, focusing the beam in the vertical direction to the slit at 44.6 m, and the source was located at -1.225 m. In the following, a bended toroidal mirror (HM4a) was employed to refocus the hard X-ray beam. The source of the HM4a in the horizontal direction was located at 33 m and was the H-slit of the combined hard X-rays. The vertical source originated from the V-slit at 44.6 m. The sample point at 54.6 m was the image of HM4a in both the horizontal and vertical directions.

Except for the soft/hard X-ray combined beamline, the individual soft and hard X-ray branches were designed so that the platform with multiple methods could be carried out. In the soft X-ray branch, the photon energy ranged from 130–1500 eV, which covered the K-edge of nonmetal elements (e.g., B, C, and N) and L-edge of most transition metals (e.g., Fe, Co, Ni, and Mn). A linear translation of the plane mirror from SM3b to SM3a, deflected the beam to the soft X-ray branch, as expressed by the red dashed line (Fig. 2). A toroidal mirror, SM4, was designed to capably move in the soft X-ray branch, so that the optical beam could be refocused and deflected out of the storage ring to the REXS station. The source of SM4 in the horizontal direction was located at 1.317 m, and was the light source of soft X-ray, and the vertical source originated from the V-slit at 41.8 m. The sample point at 45 m was the image of SM4 in both the horizontal and vertical directions. When the toroidal mirror SM4 was offline, the soft X-ray passed through the REXS chamber directly and was refocused by an elliptical Kirkpatrick-Baez mirror SM5 in the horizontal direction and SM6 in the vertical direction to the inelastic RXES end station at 51.2 m. The sources of SM5 and SM6 in the horizontal direction were 1.317 and 41.8 m (V-slit), respectively.

Meanwhile, by shifting the cylinder mirror HM3 away from the combined hard X-ray beamline, the incident beam reached the hard X-ray branch directly and the refocusing optical mirror, HM5, transported the beam into the HAXES end station at 45.6 m. The source of HM5 in the horizontal direction was located at 33 m and was the H-slit of the hard X-ray branch. The vertical source originated from the hard X-ray source at -1.225 m. Herein, the hard X-ray branch covered an energy range from 3–18 keV modulated by the DCM, so the K-edges of the most frequently used elements were considered.

3.2 Plane mirror in the front end

Due to the complicated experimental platform and compact optical components in the constructed beamline, the plane mirror, SM1 was designed to be located in the front end so that the soft and hard X-rays were separated efficiently. In this way, the components in the beamlines were well arranged in a limited space, and the deflection angle of the optical mirrors (SM3b) could be reduced because of increments in the horizontal space relative to the storage ring, improving the photo flux in the soft X-ray branch end stations. Moreover, the location of SM1 in the front end ensured that the Bremsstrahlung radiation was within the ring tunnel and eased radiation safety measures in the experimental hall.

Due to the large radiation dose at SM1, a side-cooling solution was chosen instead of internal water cooling because the latter has more potential risk of water leakage caused by degraded glue that binds to the upper plate and bottom block with embedded channels. The key issue of the feasibility was to evaluate the surface error in the side cooling condition. By applying side water with a speed of 5 L/min, the calculated maximum temperature was 38.7ºC via finite-element analysis, which is low enough to maintain the safety of such a plane mirror. The root mean square (RMS) value of the thermal deformation was estimated to be 8.95 and 3.97 μrad along the tangential (along the X-ray propagation) and sagittal (perpendicular to the X-ray propagation) directions, respectively, within the spot size range.

Assuming that the thermal deformation of SM1 was 10 and 5 μrad along the tangential and sagittal directions, respectively, the resolving power at the exit slit of the soft X-ray in the combined beamline was kept at 22182 (E/ΔE) at 244 eV (Figs. 3a and 3b), indicating a minimal difference (~9%) with an ideal plane mirror, far beyond the required value (15000 for 244 eV). Moreover, the full width at half maximum (FWHM) of the simulated spot size at the end station of the combined soft X-ray beamline was H:78 μm×V:32 μm with the assumed surface error, while the simulated spot size was H:63 μm×V:32 μm in the ideal case. The spot difference in the horizontal direction did not lead to an obvious difference in the APPES analysis for isotropy materials, such as chemical catalysis. The simulated spot sizes are shown in Fig. 3c and Fig. 3d. This suggests that the design of SM1 in the front end with side water cooling does not obviously affect the beam resolution and spot size at the end station, which is a good choice for balancing the limited space, flux performance, and risks.

Fig. 3.Full-screen View

(Color online) Resolution at the exit slit for the soft X-ray-based combined beamline; (a) for the ideal case of SM1 without surface error and (b) assuming the surface error of SM1 was 10 and 5 μrad along the tangential and sagittal directions, respectively. (c) The simulated beam spot at the soft X-ray-based combined beamline end station with ideal SM1 and (d) the beam spot when assuming the surface error of SM1 was 10 and 5 μrad along the tangential and sagittal directions, respectively. Herein, the ray tracing employed the Gaussian beam as the light source and its divergence angle was confined by a 4 sigma acceptance angle.

3.3 Grating monochromator in the combined hard X-ray beamline

The thermal loading carried by the high harmonic was relatively large because the light source was located in the vacuum undulator. The localized power density reached 1.7–1.9 W/mm² in the hard X-ray combined beamline, and the calculated surface error of the monochromator was 23 μrad with a water flow of 7 L/min, greatly lowering the energy resolution of the beamline.

As the thermal deformation of silicon crystals induced by heat loads depend on the thermal conductivity and thermal expansion coefficient, liquid-nitrogen-cooled silicon crystals have been successfully used at high heat loads[21,22]. Heat and surface errors can be effectively reduced by liquid nitrogen cooling[23]. A simulation of the plane mirror in PGM2 was conducted at 2000 eV under the temperature of liquid nitrogen (~77 K) with a thermal convection coefficient of 3000 W/m²K[24]. The footprint on the reflection mirror was H:70 mm×W:5 mm and the model of the reflection mirror in PGM2 is shown in Fig. 4a. By applying an incident total power of 152.4 W in finite-element analysis, the distribution of the temperature with a maximum value of 84 K was obtained (Fig. 4b), low enough to maintain the stability of the plane mirror in PGM2. The stress and deformation of such a plane mirror under cooling by liquid nitrogen is shown in Figs. 4c and 4d. The calculated maximum surface error was 0.88 μrad, with an RMS value of 0.47 μrad within the spot size range, small enough to meet the requirement of the desired surface error (<2 μrad). Therefore, liquid nitrogen was selected to cool the plane mirror of the grating monochromator in the combined hard X-ray beamline.

Fig. 4.Full-screen View

(Color online) (a) Model of the reflection plane mirror with an Si substrate in PGM2 in the hard X-ray of the combined beamline. (b) The distribution of temperature in the reflection plane mirror. (c) The stress analysis based on the reflection plane mirror. (d) The deformation of the reflection plane mirror under liquid nitrogen cooling.

3.4 Beam spot overlap in the combined beamline

To maintain the overlap ratio between the soft and hard X-rays, special considerations are involved in this platform. First, all focusing mirrors in the combined beamline, such as the toroidal mirror SM7a in the soft X-ray and the cylindrical mirror HM3/toroidal mirror HM4a in the hard X-ray, were placed vertically with respect to the ground so that the beam spot at the APPES end station would not be far from the center in the vertical direction. Second, two vertically switching toroidal and plane mirrors, were placed in the same chamber before the APPES end station; SM7a/SM7b and HM4a/HM4b for the combined soft and hard X-rays, respectively. Herein, the plane mirrors of SM7b and HM4b deflected the large beam spots for both the soft and hard X-rays, respectively, to the end station, producing a general overlap. Finally, a high-resolution mono beam position monitor BPM (e.g., ZnSe) was employed to locate the soft and hard X-ray beam spots accurately by the fluorescence effect with the aid of CCD.

4.1 Beam spots at the end stations

In the simulation, the spot sizes at the APPES end station in the combined beamline for both the soft (H:69.1 μm×V:36.7 μm for 244 eV) and hard (H:63.0 μm×V:27.1 μm for 2000 eV) X-rays were comparable with a high overlap ratio (Figs. 5a and 5b), indicating the rationality of the optical path design.

Fig. 5.Full-screen View

Simulated beam spot at the APPES end station produced by (a) soft X-rays of the combined beamline at 244 eV with an FWHM spot size of H:69.1 μm × V:36.7 μm and (b) hard X-rays of the combined beamline at 2000 eV with an FWHM spot size of H:63.0 μm × V:27.1 μm. Surface errors, including thermal deformation of SM1 and slope error of other mirrors were considered in the simulations. The ray tracing employed an undulator source with 0.01%BW for the soft X-rays with an exit slit of 30 μm.

Except for the APPES end station at the combined beamline, the beam spots at inelastic RXES and REXS end stations in the soft X-ray branch are demonstrated in Figs. 6a and 6b. The observed spot size at the sample point of the inelastic RXES station was H:17.6 μm×V:3.5 μm with an exit slit of 30 μm and was small enough to obtain good spectral resolution. On the other hand, the simulated spot size at the REXS was H:62.2 μm×V:53.6 μm with an exit slit of 30 μm. The calculated divergence angle was 1.92 mrad and was small enough to produce negligible spectrum broadening in the REXS measurement. Moreover, the designed spot size for the HAXES station was H:68.6 μm×V:11.0 μm, as shown in Fig. 6c.

Fig. 6.Full-screen View

Simulated beam spot at the (a) inelastic RXES end station for the soft X-rays of the combined branch at 244 eV with a FWHM spot size of H:17.6 μm×V:3.5 μm, (b) REXS end station at 244 eV with a spot size of H:62.2 μm×V:53.6 μm, and (c) hard X-ray HAXES end station of the combined beamline at 5 keV with a spot size of H:68.6 μm×V:11.0 μm. Surface errors including thermal deformations of SM1 and slope errors of other mirrors were considered in simulation. The ray tracing employed an undulator source with 0.01%BW and 0.1%BW for the soft and hard X-rays, respectively, with a 30 μm exit slit.

4.2 Resolving power

The resolving power is calculated by E/ΔE, where E is the incident photon energy, ΔE is the beamline resolution contributed by the spot-size-limited resolution ΔE_spot, ΔE_diff is the diffraction-limited resolution, and ΔE_slit is the exit slit limited resolution, as expressed by the Eq.(1):

$\Delta E={(\Delta E_{\text{spot}}^{\text{2}}+\Delta E_{\text{diff}}^2+\Delta E_{\text{slit}}^{\text{2}})}^{1/2}.(\text{formula }1)\left[26\right]$

Herein, the exit slit limited resolution ΔE_slit is determined by the following formula,

$\Delta E_{\text{slit}}=d\times E^2\times \cos \beta /(1.24\times k\times N\times f)，$

where d is the fixed width of exit slit, β is the exit angle at the grating, k is the diffraction order, and f is the exit arm [27].

The resolving power results of the combined soft X-rays are shown in Fig. 7a with an exit slit of 30 μm. The maximum resolving power surpassed 15000 below 400 eV using a grating line density of 800 l/mm. In detail, the calculation confirmed that a resolving power of 9356 at hν=244 eV was achieved with a 300 l/mm grating line density. Meanwhile, a resolving power of 9809 and 10167 were achieved with grating line densities of 800 l/mm and 1200 l/mm, respectively.

Fig. 7.Full-screen View

(Color online) (a) Resolving power (E/ΔE) as a function of photon energy with a 30 μm exit slit. The three lines correspond to the result of three grating line densities (300, 800, and 1200 l/mm). The cosine ratio C_ff (cosβ/cosα, where α and β are the incident and reflection grazing angle of gratings, respectively) was assumed to be 2, 2.6, and 3.65 for gratings with line densities of 300, 800, and 1200 l/mm, respectively. The ray tracing (with slope error) using a Gaussian beam source showed two distinguished spots for the combined soft X-ray beamlines at (a) hν=244 eV, (b) hν=900 eV, and (c) hν=1500 eV, with grating groove densities of 300 l/mm, 800 and 1200 l/mm, respectively. Surface errors, including thermal deformation of SM1 and slope errors of the other mirrors were considered in the simulations.

A Gaussian beam source was further employed to confirm the distinguished beam spots for the corresponding resolving power. Ray tracing (Figs. 7b-7d) at 244, 900, and 1500 eV (grating line densities of 300, 800, and 1200 l/mm, respectively) demonstrated that beam spots with resolving powers of 9356, 9809 and 10167, respectively, could be obviously separated at the exit slit.

In the combined hard X-ray beamline, the resolving power as a function of photon energy was calculated (Fig. 8a) for a 30 μm exit slit. Resolving powers of 3710 and 4545 were achieved with 800 and 1200 l/mm grating line densities, respectively, for hν=2000 eV. The distinguished beams obtained by the ray tracing simulation using a Gaussian beam source (Fig. 8b) further confirmed that a resolving power of 4545 (hν=2000 eV) could be achieved with a 1200 l/mm grating line density. The resolving power at a high energy of 5000 eV in the combined hard X-ray beamline was calculated to be ~7200 (ΔE=0.7 eV) using a Si(111) crystal in DCM.

Fig. 8.Full-screen View

(Color online) (a) Resolving power as a function of photon energy with an exit slit of 30 μm. The two lines correspond to the gratings with line densities of 800 and 1200 l/mm. The C_ff was 3.0 for both gratings. (b) The ray tracing (with slope error) using a Gaussian beam source shows two distinguished spots for the combined hard X-ray beamline (2000 eV) with a grating groove density of 1200 l/mm. (c) Photon counts as a function of photon energy using a 0.1%BW undulator source at hν=5000 eV, and the DCM with a Si(111) crystal was used to produce white beam monochromatization.

4.3 Photon flux

The photon flux calculation was confined by its resolving power (e.g., the exit slit was 30 µm for the soft X-rays). The derived transmission efficiency at the sample position for the soft X-ray in the combined beamline includes the reflectivity of the mirror, the grating optimized efficiency, and the surface roughness of the optics, as shown in Table S1a (Supporting information). The flux at the end station was estimated by multiplying the flux of the undulator (Fig. 1a) with the transmission efficiency of each mirror and efficiency of monochromators (Fig. S1a - S1c). The flux of the undulator was calculated from the SPECTRA code [18] and the transmission efficiencies of the mirrors were obtained from the XOP software [28]. The theoretical flux at the APPES end station reached 10¹² phs/sec with an exit slit of 30 μm in the energy range 130–1500 eV (Fig. 9a) and 2.6×10¹² phs/sec with a resolving power of 9356 (exit slit 30 μm) at 244 eV in the combined soft X-ray beamline with a grating line density of 300 l/mm.

Fig. 9.Full-screen View

(Color online) (a) Photo flux at the combined soft X-ray APPES end station in the energy range 130–1500 eV, with three frequently used grating line densities of 300, 800, and 1200 l/mm. (b) Photo flux at the combined hard X-ray APPES end station in the energy range 1500–2300 eV, with a frequently used grating line density of 800 l/mm (both 800 and 1200 l/mm covered the whole energy range; thus, 1200 l/mm is not shown). (c) Photo flux at the combined hard X-ray APPES end station in the energy range 2300–10 keV with monochromatization by DCM. 0.1%BW was selected for both the soft and hard X-ray flux calculations.

Compared with the soft X-ray combined beamline, the soft X-ray branch was designed with one more mirror (Table S1b), so the flux at the final inelastic RXES station was approximately 22% lower than that at the combined soft X-ray beamline. The theoretical flux in the soft X-ray branch end station (inelastic RXES) was estimated to be 2.0×10¹²phs/sec with a resolving power of 9356 (exit slit 30 μm) at 244 eV with a grating line density of 300 l/mm.

Similarly, the derived transmission efficiency at the sample position for the PGM2 based hard X-ray (1500–2300 eV) in the combined beamline is shown in Table S2a. All mirrors were coated by a parallel Rh/Cr layer with a desired surface roughness smaller than 0.3 nm. The flux at the APPES end station was greater than 5×10¹¹phs/sec with an exit slit of 30 μm in the energy range 1500–2300 eV (Fig. 9b), while it was 2.2×10¹²phs/sec with a resolving power of 3710 (exit slit 30 μm) at 2 keV in the hard X-ray-based combined beamline for a grating line density of 800 l/mm.

The transmission efficiency at the sample position for the DCM based hard X-ray (2300 eV–10 keV) in the combined beamline is shown in Table S2b. The flux at the APPES end station was 5×10¹²phs/sec in the energy range 2300 eV–10 keV (Fig. 9c), while it was 1.8×10¹³phs/sec with a resolving power of 7200 at 5 keV in the hard X-ray-based combined beamline for monochromatization by DCM.

The hard X-ray branch was designed with one less mirror (Table S2c), and the flux at the HAXES station was ~10% higher than that at the combined hard X-ray beamline by DCM. The theoretical flux at the hard X-ray branch end station was estimated to be 1.98×10¹³phs/sec with a resolving power of 7200 at 5 keV.