research papers
A micro channel-cut crystal X-ray monochromator for a self-seeded hard X-ray free-electron laser
aRIKEN SPring-8 Center, 1-1-1 Kouto, Sayo-cho, Sayo-gun, Hyogo 679-5148, Japan, bDepartment of Precision Science and Technology, Graduate School of Engineering, Osaka University, 2-1 Yamada-oka, Suita, Osaka 565-0871, Japan, and cJASRI, 1-1-1 Kouto, Sayo-cho, Sayo-gun, Hyogo 679-5198, Japan
*Correspondence e-mail: osaka@spring8.or.jp
A channel-cut Si(111) crystal with a channel width of 90 µm was developed for achieving reflection self-seeding in hard X-ray free-electron lasers (XFELs). With the crystal a monochromatic seed pulse is produced from a broadband XFEL pulse generated in the first undulator section with an optical delay of 119 fs at 10 keV. The small optical delay allows a temporal overlap between the seed optical pulse and the electron bunch by using a small magnetic chicane for the electron beam placed between two undulator sections. Peak reflectivity reached 67%, which is reasonable compared with the theoretical value of 81%. By using this monochromator, a monochromatic seed pulse without broadband background in the spectrum was obtained at SACLA with a conversion efficiency from a broadband XFEL pulse of 2 × 10−2, which is ∼10 times higher than the theoretical efficiency of transmission self-seeding using a thin diamond (400) monochromator.
Keywords: XFELs; self-seeding; channel-cut crystals.
1. Introduction
X-ray free-electron lasers (XFELs) operating in the self-amplified ; Bonifacio et al., 1984) have generated hard X-ray beams with unique characteristics, such as ultrahigh peak power, nearly full transverse coherence and ultrashort at the femtosecond level (Huang & Kim, 2007). In the SASE scheme, spontaneous radiation emitted from an electron bunch with a random statistical modulation of the beam density is amplified while propagating through a periodic magnetic field in long undulators. However, the stochastic nature causes poor longitudinal coherence and a broad spectrum with a relative bandwidth of ∼0.3% (Saldin et al., 1999). A monochromator is widely used to monochromatize SASE-XFEL pulses, whereas the is decreased considerably by a factor of ∼30.
(SASE) scheme (Kondratenko & Saldin, 1980To generate intense and narrowband XFEL pulses in the hard X-ray regime, a self-seeding scheme has been proposed (Feldhaus et al., 1997). In this scheme, a monochromator is placed in the middle of a magnetic chicane of the electron bunch, which separates the undulators into two sections. A monochromatic seed pulse is produced from a broadband SASE-XFEL pulse generated in the first undulator section through the monochromator. At the same time, the electron bunch is detoured in the magnetic chicane and then spatiotemporally overlapped with the seed pulse downstream of the chicane. Finally, the seed pulse is amplified in the second undulator section while interacting with the electron bunch. The technical difficulty in self-seeding is to assure a temporal overlap between the electron bunch and the seed pulse. This is because a delay for multi-GeV electron beams is typically limited up to a few hundreds of femtoseconds with a chicane of ∼5 m length, whereas an optical delay is as large as several picoseconds with a conventional Si(111) double-crystal monochromator (DCM) that has a distance between the crystals of several millimetres. Amann et al. (2012) demonstrated self-seeding in the hard X-ray regime at the Linac Coherent Light Source (LCLS) (Emma et al., 2010) with a thin diamond (400) monochromator operating in the forward Bragg diffraction geometry. They used a monochromatic pulse echo as a seeding source that follows a prompt SASE-XFEL pulse with an interval of tens of femtoseconds (Geloni et al., 2010, 2011; Lindberg & Shvyd'ko, 2012) and successfully generated a narrowband XFEL beam. With the `transmission' monochromator, however, the prompt broadband SASE-XFEL pulse propagates through an optical axis common to the seed pulse, preventing accurate characterization of the seed pulse. Furthermore, the conversion efficiency – defined by the ratio of the power of a monochromatic seed pulse to that of an input XFEL pulse – of the transmission monochromator has been theoretically evaluated to be ∼2 × 10−3 (Lindberg & Shvyd'ko, 2012), being much lower than that of a usual `reflection' monochromator, which could degrade the electron bunch so as to generate an intense seeding source.
In this paper we report the development of a micro channel-cut monochromator (Bonse & Hart, 1965) as an essential optical component for achieving reflection self-seeding with a high efficiency (Inoue et al., 2019). We designed a channel-cut Si(111) crystal with a channel width of 90 µm, which gives an optical delay as small as ∼100 fs while removing the prompt SASE beam. Since an X-ray beam is reflected twice at the two opposite blades of the channel-cut crystal made of a `monolithic' single-crystal block, the optical axis of the exit beam is highly stabilized compared with a DCM composed of independent crystals (Diaz et al., 2010). After characterization of the quality of the crystal at a SPring-8 beamline, we performed a feasibility test of the reflection self-seeding at SPring-8 Angstrom Compact free-electron LAser (SACLA) (Ishikawa et al., 2012).
2. Design of the micro channel-cut crystal
To achieve the reflection self-seeding with the micro channel-cut crystal, the following requirements should be satisfied: a small optical delay that is less than the maximum delay for the electron bunch and a large spatial acceptance to receive a major portion of an incident XFEL beam. The delay for the electron bunch Δte is approximately given by (Hara et al., 2013)
where θe is the deflection angle of the electron beam, c is the speed of light, L is the drift distance between the first and second dipole magnets in the magnetic chicane, and LB is the length of the magnetic field. The deflection angle can be written as
where B is the and Ee is the electron beam energy. At SACLA we tune the photon energy of XFEL beams (Eph) by adjusting the electron beam energy Ee and/or the undulator deflection parameter K according to the following relationship,
where h is Plank's constant, λu (= 18 mm) is the undulator periodic length and γ (= Ee/Ee0, where Ee0 is the rest energy of the electron) is the Lorenz factor of the electron beam. The coefficient A (= 2hc/λu) is used to simplify the equation. Setting boundary conditions Ee ≤ Ee_max (γ ≤ γmax) and K ≤ Kmax, we have a reference photon energy = Aγ2max/(1 + K2max/2). For , we usually adjust Ee to tune the photon energy Eph with a fixed K of Kmax, while we change K by fixing Ee = Ee_max for . These conditions give the delay for the electron bunch Δte as
with
Equation (4) indicates that Δte is inversely proportional to Eph for , whereas it is independent of Eph for . On the other hand, the optical delay Δtph for a single channel-cut monochromator in the symmetric case is described by
where g is the channel width of the crystal and dhkl is the lattice spacing for the (hkl) diffraction. In order to introduce the maximum delay Δte_max to the electron bunch, we apply the maximum Bmax to the dipole magnets in the chicane. The upper limit of the width gmax is defined such that the optical delay with g = gmax is equal to Δte_max, which can be written as
with C′ = CB2max/h and D′ = DB2max/h. Note that gmax is proportional to Eph for ; however, it becomes a constant value C′dhkl for . it By using a higher order diffraction with a smaller dhkl, the requirement on g becomes more severe, whereas the bandwidth of the seed and the seeded XFEL beam to be achieved could be narrower. The conversion efficiency of the monochromator using a high-order diffraction is also reduced compared with that for a low-order diffraction because of the narrower acceptance in the spectrum.
Fig. 1 shows Δte_max and the corresponding gmax as a function of Eph. Here we used the Si(111) diffraction (d111 = 3.136 Å) that is the lowest order diffraction in silicon to achieve a high conversion efficiency, and the latest parameters for the magnetic chicane at SACLA (L = 1.56 m, LB = 0.34 m and Bmax = 0.52 T) with boundary conditions Ee_max = 7.8 GeV and Kmax = 2.15. The reference photon energy is calculated to be 9.69 keV. We concluded that the requirement on the optical delay is satisfied over a wide photon energy range by using a channel-cut Si(111) crystal with g < C′d111 = 204 µm. Note that a smaller electron-beam delay is preferred for suppressing unwanted coherent synchrotron radiation and transporting an electron bunch with higher quality into the second undulator section.
For the micro channel-cut crystal the spatial acceptance is considerably limited. The acceptance in the vertical direction is practically as small as g/2 while depending on Eph and the quality of the crystal edge. In the horizontal direction the acceptance is determined by the depth of the diffracting blades, which is typically limited up to 10g because of the difficulty in fabrication of a narrow trench. The size of the XFEL beams at the middle of the magnetic chicane was evaluated to be ∼50 µm full width at half-maximum (FWHM) at 10 keV through a numerical simulation with the FEL simulation code SIMPLEX (Tanaka, 2015). Therefore, a spatial acceptance of >50 µm in both directions is needed.
We designed a prototype micro channel-cut crystal, as shown in Fig. 2(a), which satisfies all of the above requirements near 10 keV. The channel width g was set to 90 µm, which gives an optical delay of 119 fs at 10 keV, as shown in Fig. 1. The overlap length of the two diffracting blades was designed to be 0.2 mm so as to obtain a spatial acceptance in the vertical direction of at least 50 µm while avoiding the use of an area near the crystal edge. The depth of the channel is ∼0.6 mm, being sufficiently larger than the horizontal beam size. The dimensions of the crystal are 10 mm × 10 mm × 10 mm to facilitate handling of the crystal while the right upper part is removed to place a beam stopper just downstream of the first blade, which is required to block the unwanted transmission beam propagating through the crystal. We note that a single channel-cut monochromator imposes a transverse shift of the beam axis Δh described by
where θB is the The shift is less than 180 µm with a micro channel-cut crystal of g = 90 µm, which is acceptable for all the optical components at SACLA. Although the shift can be compensated by using a double channel-cut monochromator operating in the (+, −, −, +) geometry, the optical delay becomes twice as large as that in the single channel-cut monochromator.
The micro channel-cut crystal was made of a floating-zone Si single-crystal block. An ultra-narrow trench with 60–70 µm width and ∼0.6 mm depth was formed with a dicing blade. Then the , as described in Section 3.2.
of 10–15 µm depth was removed through solution etching. Finally, the working area was moderately polished with fine slurry. Since the channel width of the crystal is one of the most important parameters and difficult to measure with an optical microscope, we accurately characterized the channel width with an X-ray beam using equation (8)The crystal was mounted on a dedicated holder [Fig. 2(b)] with a beam stopper made of tungsten of 250 µm thickness. The position of the crystal was finely adjusted by positioning screws so as to fit the incident surface to the bottom surface of the beam stopper, as shown in Fig. 2(c).
3. Characterization of the micro channel-cut crystal
3.1. Experimental setup
We characterized the micro channel-cut crystal using X-ray reflection topography and rocking curve measurements at the 1 km-long beamline BL29XU of SPring-8 (Tamasaku et al., 2001). A 10 keV X-ray beam emitted from an undulator was monochromated by a SPring-8 standard Si(111) DCM (Yabashi et al., 1999). The size of the X-ray beam was reduced to 500 µm [horizontal (H)] × 50 µm [vertical (V)], with a four-jaw slit located 987 m downstream of the source. The rocking curve was measured with two ion chambers, while the reflection topographs were taken with a high-resolution X-ray camera with a pixel size of 325 nm (Kameshima et al., 2019) placed at ∼1 m downstream of the crystal.
3.2. Results
Fig. 3(a) shows a reflection profile under the Bragg condition. Both the incident and reflected beams were observed in the field of view of the camera (∼665 µm × 665 µm) simultaneously. A slightly curved reflection profile was observed due to the variation of the channel width along the horizontal direction. The variation of Δh, however, was less than a few micrometres except near the crystal edge, which could provide a negligible variation of the optical delay. From equations (6) and (8) with the shift Δh = 176 µm at 300 µm far from the edge, the channel width g and the corresponding optical delay Δtph at 10 keV were evaluated to be 90.0 µm and 119 fs, respectively, which agrees well with the design value. The spatial acceptance, defined by the maximum size of the reflected beam, was evaluated to be ∼600 µm (H) × 100 µm (V) by using a larger X-ray beam.
Fig. 3(b) shows a rocking curve to be measured. The peak reflectivity reached 67% while the ideal reflectivity was calculated to be 81%. The reduction in reflectivity was associated with residual surface roughness and damage in the illumination area of the crystal. The imperfection of the crystal also produced speckles on the reflected beam, as shown in Fig. 3(a). We assumed that the speckles originated from the modulation of phase due to the surface undulation. The phase shift Δφ caused by the variation in surface height hS is then given by
where δ is the deviation from unity of the real part of the n (= 1 – δ + iβ). Fig. 4(a) shows the distribution of phase shift calculated from the surface morphology on the crystal measured with an optical microscope. A large phase shift of ∼π/2 with high spatial frequencies of ∼65 mm−1 could occur within the footprint of the X-ray beam. We consider that this assumption is reasonable because the spatial frequency of the distribution of phase modulation is consistent with that of the speckles. To evaluate the influence of the distorted wavefront on the self-seeding process, we performed an FEL simulation with Ee = 7.8 GeV and K = 2.1015 (Eph = 10 keV) under the following simple conditions: (i) a monochromatic seed pulse is produced from a broadband SASE pulse with a located at the exit of the magnetic chicane (without optical delays), (ii) the phase modulation is introduced to the seed pulse after the (iii) the seed pulse and electron bunch start to interact with each other after propagating through 6 m free space and (iv) the electron bunch is perfectly overlapped with the seed pulse in both time and space when the phase modulation is not introduced. Other parameters were not optimized to focus on the influence of the phase modulation. Fig. 4(b) shows a comparison between simulated gain curves with and without the phase modulation. This simulation implies that the distorted wavefront of the seed pulse does not provide serious degradation in the amplification process, possibly because the phase modulation with high spatial frequencies is smeared while propagating through the second undulator section, and the TEM00 spatial mode in the seed pulse is preferentially amplified. Note that this simulation did not take into account the reduction in peak reflectivity, which could decrease the spectral of the seed and the resultant seeded XFEL beam while providing a similar trend of the gain curve to this simulation.
4. Feasibility test at SACLA
We tested the micro channel-cut monochromator at BL3 of SACLA (Tono et al., 2017) in which 21 undulator modules (U1–U21) are implemented. The magnetic chicane with a length of 5.1 m is placed between U8 and U9. A SASE XFEL beam needed for producing a monochromatic seed was generated with five undulator modules (U4–U8) in the first undulator section. The averaged power of the SASE XFEL beam was estimated to be 4.8 GW (48 µJ within a 10 fs pulse width) at 10 keV with a bandwidth of ∼30 eV in FWHM. The micro channel-cut monochromator was placed at the middle of the magnetic chicane. The size of the SASE beam in the monochromator was evaluated to be ∼65 µm (H) × 45 µm (V) in FWHM through knife-edge scans with the beam stopper, which was consistent with the results of the FEL simulation. Fig. 5 displays the averaged spectrum of the seed without amplification in the second undulator section measured by scanning a speckle-free Si(220) channel-cut crystal (Hirano et al., 2016), placed in experimental hutch 2, 167 m downstream of the monochromator. The spectrum shows a nearly ideal bandwidth of ∼1 eV in FWHM without broadband background, indicating that the crystal successfully produced a seed beam while removing the transmitted SASE beam. With the power of the seed of ∼88 MW (0.88 µJ, 10 fs), the conversion efficiency was experimentally estimated to be 2 × 10−2, which is ∼10 times higher than the theoretical efficiency of the transmission monochromator with a diamond (400) crystal. Note that the relative bandwidth of the seed produced with the Si(111) micro channel-cut monochromator, 1.3 × 10−4, was approximately three times wider than that with the diamond (400) monochromator, which primarily contributes to the increase of the conversion efficiency. However, this result suggests that the efficiency for reflection-based monochromators used in this study could be higher than that for transmission-based monochromators even if the seed bandwidths are identical.
5. Conclusions and future perspectives
In conclusion, we have developed a micro channel-cut Si(111) crystal monochromator for self-seeding in hard X-ray FELs. The channel width was evaluated to be 90.0 µm, which gives an optical delay of 119 fs to a 10 keV seed pulse. A clean seed beam without broadband background in the spectrum was obtained through the micro channel-cut monochromator at BL3 of SACLA. An unprecedented high conversion efficiency from a broadband SASE beam to a seed of 2 × 10−2 was experimentally confirmed, allowing one to use an original SASE beam at moderate intensities and, therefore, a high-quality electron bunch can be used for amplification of the seed.
Although the clean and intense seed pulse to be available with the micro channel-cut monochromator and the resultant high-quality electron bunch should increase the spectral et al., 2013; Hirano et al., 2016), called plasma chemical vaporization machining (PCVM) (Mori et al., 2000), is a promising approach for this purpose. Furthermore, a seeded XFEL beam generated with the micro channel-cut monochromator using the Si(111) diffraction will not be fully coherent in time because the bandwidth of the seed (∼1 eV) is wider than the typical spike width of the SASE beam (∼0.4 eV) (Inubushi et al., 2012, 2017; Osaka et al., 2017). Generation of fully coherent XFEL pulses could be realized by using a high-order diffraction of which the bandwidth is narrower than the spike width. Achieving fabrication of the speckle-free micro channel-cut crystal through the PCVM technique allows one to use a high-order diffraction with nearly ideal conversion efficiency and spectral of the seed, which should pave the way to realization of fully coherent XFELs with high intensities.
of seeded XFELs, further enhancement of spectral will be achieved if the surface quality of the crystal is improved. Chemical etching with atmospheric pressure plasma employed for fabrication of speckle-free crystal optics (OsakaAcknowledgements
The authors would like to thank the staff of SPring-8 and SACLA facilities for their continuous support. We would also like to thank Dr Y. Kohmura for his support in the characterization of the micro channel-cut crystal at BL29XU of SPring-8, and Drs T. Hara, T. Inagaki, H. Ohashi and Y. Inubushi for their help in installing the monochromator to BL3 of SACLA. We are grateful for the valuable advice from Drs H. Tanaka, S. Goto, K. Tamasaku, T. Tanaka, K. Togawa, K. Tono and T. Ishikawa.
Funding information
The following funding is acknowledged: Special Postdoctral Researcher Program of RIKEN; JSPS KAKENHI (grant No. 18K18307). The characterization of the crystal was carried out with the approval of RIKEN (Proposal Nos. 20170003 and 20180061.
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