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A precise spectral characterization of every single pulse is required in many x-ray free-electron laser (XFEL) experiments due to the fluctuating spectral content of self-amplified spontaneous emission (SASE) beams. Bent single-crystal spectrometers can provide sufficient spectral resolution to resolve the SASE spikes while also covering the full SASE bandwidth. To better withstand the high heat load induced by the 4.5 MHz repetition rate of pulses at the forthcoming European XFEL facility, a spectrometer based on single-crystal diamond has been developed. We report a direct comparison of the diamond spectrometer with its Si counterpart in experiments performed at the Linac Coherent Light Source.
© 2017 Optical Society of America
1. Introduction
X-ray Free-Electron Lasers (XFEL) based on the principle of self-amplified spontaneous emission (SASE) typically have a relative energy bandwidth of ∼ 10−3 but inside this envelope a characteristic pattern of spectral spikes is present depending on the pulse duration and the fine structure (micro-bunching) that develops in the electron beam as it travels through the undulator [1]. Due to the stochastic nature of the SASE process strong fluctuations are present in the overall x-ray intensity but also the spike pattern changes from pulse to pulse. Capturing these spectral variations is essential for many experiments at XFELs, e.g. high-resolution spectroscopy and speckle techniques. To enable the desired spectral diagnostics a spectrometer must cover the entire bandwidth of the envelope with enough resolving power to characterize the spikes. Typically ΔE/E ≈ 10−5 is required implying 100 meV resolution at 10 keV x-ray energy.
Several different types of spectrometers have been implemented at XFELs which can be grouped in three main classes: i) diffraction gratings, ii) a flat analyzer crystal combined with a curved mirror and iii) a bent crystal analyzer optionally combined with a grating beam splitter to generate a dedicated branch for diagnostics. Diffraction gratings have been employed in the soft x-ray regime at FLASH [2] and at FERMI [3], but also at LCLS [4,5] and SACLA [6] in the hard x-ray regime. The gratings transmit most of the beam which remains available for experiments downstream and only the 1st diffraction order is taken for spectral analysis. The 1st order beam is generally intense enough for spectral characterization purposes and this geometry significantly lowers the heat load on the analyzer. In a different approach the spectral profile was measured using an elliptical mirror combined with a flat silicon analyzer crystal at SACLA [1, 7] at the expense of beam transmission. Earlier experiments at LCLS using an ultra-thin bent Si single crystal have shown excellent results and sufficient resolving power to visualize the spectral spikes of the SASE beam [8–10]. The disadvantage of the grating based setup in combination with an analyzer is that a long distance (typically ~ 10 m) between the grating and the analyzer is required to obtain sufficient offset of the 1st order beam and allowing an unhindered passage of the direct beam. On the other hand, bent-crystal spectrometers placed in the direct beam are much more compact than grating based devices and thus can be readily integrated into the experimental setup. At the European XFEL the unprecedented repetition rate of 4.5 MHz inside a bunch train will lead to severely increased thermal load compared to all other operating XFELs. Crystal distortions due to heating and thermal cycling are therefore likely to become a challenge [11,12].
As the heatload strongly varies with beamsize, photon energy, bunch charge and number of photons it is difficult to provide definite conclusions. However, a numerical example is given below for conditions similar to standard operation parameters of the European XFEL. At a photon energy of 10.5 keV the 20 µm thin diamond crystal absorbs approximately 1.4% of the beam energy. Under the assumption of a pulse energy of 2 mJ per pulse and 100 pulses per train with a train rate of 10 Hz, this amounts to approximately 28 mW of average absorbed power. To put this number in perspective, we have estimated the temperature increase for a single pulse and compare it to the thermal width (Darwin width) of the respective reflection. The results are summarized in Table 1 for a 10 µm Si crystal on the Si(220) and Si(440) reflection and a 20 µm diamond crystal on the C*(220) reflection at 7.6 keV as well as the C*(440) reflection at 10.5 keV. The beamsize is taken as 1 mm and the estimations reflect room temperature conditions. The calculations were performed using the program in reference [11] and the database provided by [13,14].
Table 1. Estimated temperature increase per 2 mJ incident pulse and thermal width of the reflection considering a beamsize of 1 mm and room temperature conditions.
Our calculations showed that virtually no heat is removed in the 220 ns between the pulses at room temperature, so that for few pulses the temperature increases linearly with the number of pulses. Already from a single pulse Si absorbs enough power to thermally expand beyond or on the order of the Darwin width of the reflection, although the single pulse is reflected before the heat is dissipated in the crystal and therefore does not suffer from it. This issue was also experimentally observed for 3–4 mJ pulses with a repetition rate of 120 Hz at LCLS, where Feng et al. detected significant distortions due to the thermal load when operating a 20 µm thick Si(111) crystal in vacuum [15].
Even for diamond the number of pulses that can be accepted at 4.5 MHz repetition rate before a significant shift of the Darwin curve occurs is limited. However, this energy shift is likely to be reproducible and could maybe be calibrated after careful characterization. In contrast, Si undergoes an irreversible brittle-ductile transition at about 500°C and thus poses a hard limit to the acceptable heat load. If the Darwin curve of the reflection widens it would result in a degradation of the spectral resolution. This can happen as an effect of thermal gradients that probably also will build up in the crystals under MHz illumination but this phenomenon is difficult to predict in detail.
Taking advantage of the superior thermal properties of diamond, we have developed a bent-crystal spectrometer based on ultra-thin type IIa diamond single crystals. Recent improvements in the High-Pressure High-Temperature (HPHT) synthesis process have made large high-quality single crystals available in multiple orientations, that also can be uniformly thinned down to achieve sufficient bending [16–20]. Here, we report on results obtained on a prototypical all-diamond device with a bent C*(110) analyzer crystal mechanically designed and manufactured by the Technological Institute for Superhard and Novel Carbon Materials (TISNCM, Russia).
When the almost parallel (beam divergence < 2µrad), polychromatic SASE beam impinges on the bent-crystal, as sketched in Fig. 1, the angle of incidence θ varies over the footprint of the beam. Therefore, the Bragg condition λ = 2d sin θ for reflecting lattice planes with spacing d is fulfilled for different wavelengths λ depending on the position on the crystal. Thus, the reflections are dispersed in the scattering plane and the diffracted intensities from the different wavelengths can be distinguished by position sensitive photon detection, either by a linear or by an area detector.
Fig. 1 Sketch of dispersion geometry of a bent crystal indicating the x-ray beam size z, the bending radius R, detector distance L and the scattering angle 2θ.
With an impinging beam of size z the energy range ΔE that can be covered by a bent crystal with radius R is
The energy resolution per pixel δE, here denoted pixel resolution, of the recorded spectrum depends on the pixel size Δp of the detector and the crystal to detector distance L, and is given by
When , as in the current setup, the influence of R on δE is negligible, see Eq. 2, and hence the bending radius can be tuned freely to match the desired energy range ΔE (Eq. 1). The current design of the diamond spectrometer allows for a variable R between about 0.06 m and 0.1 m, adjustable by a slider. The spectrometer has been designed to cover the entire SASE width with sufficient resolution to resolve single spikes in the spectrum and will be integrated in a diagnostic end-station at the MID instrument of the European XFEL [21].
In this paper we report on first measurements performed with this spectrometer at LCLS. The experimental setup allows for a pulse-to-pulse comparison with its Si counterpart using the beam transmitted through the diamond crystal, and the measurements prove the high resolution and stability of the C* spectrometer, also when operated in vacuum.
2. Experimental setup
The meridional bending radius of a 20 µm thick diamond analyzer crystal was adjusted by a slider-driven bending mechanism to obtain R ≈ 0.1 m. Fig. 2 shows a sketch of the slider mechanism (a), a photo of the spectrometer (b), and an interferogram of the bent crystal obtained by white-light interferometry using a Wyko NT9100 profilometer (Veeco Instruments Inc., www.veeco.com) (c) from which the sagittal and meridional bending radii can be estimated independently. All x-ray experiments were performed at the X-ray Correlation Spectroscopy (XCS) instrument at the Linac Coherent Light Source (LCLS) at SLAC National Accelerator Laboratory [22,23]. Two spectrometers operating with Si(110) and C*(110) crystals, as described above, were installed as shown in Fig. 3 (a) and (b) with the first crystal (C*) mounted inside a vacuum chamber situated about 400 m downstream from the undulator. Approximately 0.5 m further downstream the Si spectrometer was mounted in air receiving the beam transmitted through the C* crystal. The Si crystal was 10 µm thick and had a fixed bending radius of 0.05 m. The beam size was 500 × 500 µm2, as defined by a set of slits. A beam imager unit placed in the direct beam downstream of the two spectrometers allowed to align the crystals in transmission.
Fig. 2 Diamond spectrometer developed by TISNCM with the conceptual design in (a) and a photograph of the prototype device in (b). (c) shows an interferogram from which the bending radii can be estimated.
Fig. 3 (a) Sketch of the beamline and XCS hutch with important components in the near- and far experimental halls (NEH and FEH) indicated. (b) Photograph of the experimental setup with two spectrometers in series.
The vertically diffracted x-rays were converted to visible light via a Ce:YAG scintillator screen and the images recorded by a 120 Hz microscope camera, providing an effective detector pixel size of approximately 5 µm. Figure 4 shows examples of 2D single pulse images of the dispersed intensity for the C*(220) spectrometer (a) and for the Si(440) spectrometer (b). To obtain the desired spectra I vs E these images are integrated perpendicular to the dispersion direction, assuming negligible spectral variations over the horizontal beam direction. The data were taken using the pink SASE beam (no seeding, no monochromator) with 180 pC bunch charge and 33 fs pulse duration at 120 Hz. The nominal photon energy was 7.6 keV for the C* (220), Si (220), and Si (440) reflections while it was 10.5 keV for the C* (440) reflection. To access the Bragg angle for the C*(440) reflection the spectrometer had to be mounted in air on the goniometer otherwise hosting the Si spectrometer.
Fig. 4 Randomly selected single pulse raw images for (a) C*(220) and (b) Si(440). (c) Integrated single pulse C*(220) spectrum with zoom (d) showing two spikes that are barely resolvable.
Fig. 5 (a) Single pulse spectra for C*(220) and Si(220) and (b) for C*(220) and Si(440) spectrometers.
Energy calibrations of the spectrometers were achieved using the semi-transparent C*(111) beam-splitter monochromator of the upstream X-ray Pump Probe (XPP) instrument as a reference [24,25]. When inserted into the beam this calibrated monochromator takes out a specific energy that can be identified as a notch in the spectrum. In particular, this notch becomes visible in spectra averaged over many pulses, see Fig. 6. The theoretical width of the notch is given by the Darwin width of the C*(111) reflection and hence the measured notch width also gives a hint of the spectrometer resolution [25], see section 3.2.
Fig. 6 Average 2D image from C*(220) (a) and Si (440) (b) spectrometers. Two spectral notches are clearly visible in the Si (440) image. c) shows the integrated average energy profile of the C*(111) notch for all spectrometers shifted to the central energy.
3. Results and discussion
3.1. Energy resolution
A particular strength of our experimental setup is the direct comparison between the performance of the diamond and the Si spectrometers for every pulse. Figure 4 shows the raw 2D image of the dispersed intensity for the C*(220) spectrometer (a) and for the Si(440) spectrometer (b). The scattered intensity from the C*(220) spectrometer is much narrower perpendicular to the dispersion direction than for Si(440). This is due to an anticlastic sagittal bending of the diamond crystal, which was measured to be about 0.39 m by white light interferometry, see Fig. 2. The sagittal bending focuses the scattered radiation in a direction perpendicular to the dispersion direction and this can be an advantage in order to increase the intensity per pixel. Likewise, in the present setup the detector was mounted close to the sagittal focus distance. The different size and shape of the Si crystal [8] as well as its fully enclosed mounting inhibit strong anticlastic bending for the Si spectrometer.
Figure 5 compares integrated single pulse spectra measured by different reflections: C*(220), Si(220), and Si(440). The lower resolving power of the Si(220) spectrometer, compared with C*(220), is clearly visible, as illustrated in Fig. 5 (a). On the other hand, the resolutions are comparable for the C*(220) and Si(440) setups, as is visible in Fig. 5 (b).
The spectra from the silicon and diamond spectrometer mounted in air and vacuum, respectively, are mutually consistent on a single pulse basis, indicating a high stability of the diamond device even under vacuum conditions. In comparison, thermomechanical vibrations induced by the FEL beam were observed for a silicon spectrometer when mounted in vacuum [15].
A coarse estimate of the energy resolution can be obtained by measuring the separation between two barely resolvable features in a spectrum [8], as illustrated in Fig. 4 (d). The energy resolutions estimated in this way are summarized in Table 2 together with the expected effective resolutions δEeff obtained as convolutions between the Darwin width of the spectrometer reflection and the pixel resolution δE (Eq. 2). The energy width of single spikes in the SASE spectrum is inversely proportional to the duration Δt of the x-ray pulse as Δt = Ch/dE where h is Planck’s constant and C is a factor that depends on the pulse shape and number of modes. These measurements indicate C in a range from 2 to 4.
Table 2. Estimated energy resolution from spike features.
Figure 6 shows spectrometer images averaged over ∼3000 single pulses for a) C*(220) and b) for Si(440). The averaged spectra indicate a typical SASE bandwidth of 24 eV at 7.6 keV and thus a relative bandwidth of ∼ 3 × 10−3, as anticipated (including the LCLS electron beam energy jitter). As described in the experimental section, the XPP beam-splitter monochromator was inserted to intercept the beam upstream and the resulting spectral notch is clearly visible in both images. In the Si(440) image an additional tilted notch produced by the upstream C*(220) spectrometer can also be seen (see Section 3.2 for further discussion about the tilted notch).
Zooms of the integrated average spectra are shown in Fig. 6 (c) to illustrate the notch produced by the beam-splitter monochromator as seen by the C*(220), C*(440), Si(220) and Si(440) spectrometers. The notch can be used for energy calibration and a verification of the spectrometer’s calculated effective resolution δEeff. The experimental width of the notch was determined from the FWHM of a Gaussian fit to the inverse peak. The expected width of the spectral notch is given by a convolution of the C*(111) Darwin width and δEeff. When imaged by the C*(220) spectrometer, there is an excellent agreement with calculations (2.1% deviation, Table 3). For the C*(440) spectrometer it is more difficult to determine the notch width due to the high resolution revealing a pronounced non-Gaussian line profile. The comparison between experimental results and calculations are summarized in Table 3.
Table 3. Quantitative comparison of expected and measured widths of the spectral notch.
For the C*(440) spectrometer one can expect a resolution significantly lower than defined by the ideal Darwin width alone, especially in comparison with the C*(220) variant. This is caused by a strain gradient influence that becomes stronger for high order reflections. One can roughly estimate the effect of the strain: the variation of the Bragg condition on the depth t due to deformation is given as δθd = νLex/R tan θB (with the Poisson ratio ν = 0.2, bending radius R). For C*(440), the value of δθd = 67µrad over an extinction length Lex = 13.5µm strongly exceeds the intrinsic Darwin width of 8 µrad. This can be compared with δθd = 7µrad over Lex = 4µm and a Darwin width of 16.5 µrad for C*(220). To take such strong deformations properly into account, one must use a full scale formalism based on Takagi-Taupin differential equations [26]. As it was shown in [27] for thin strongly bent crystals of quartz and silicon, the intrinsic reflection curves in this case can exceed the reflection curve of a flat crystal by more than 10 times.
Nonetheless, spectrometers operating with C* crystals broaden the notch considerably less than Si spectrometers. Previously published results [15] indicate that this comparison would become even more favorable for C* if the Si crystals were operated in vacuum, like the C* spectrometer. Unfortunately, experimental limitations prevented us from making such a direct comparison with both devices operating in vacuum.
3.2. The tilted notch
Similar to the spectral notch originating from the XPP beam-splitter monochromator, the bent-diamond crystal of the spectrometer also produces a notch in the spectrum measured by the Si crystal downstream, see Fig. 6 (b). The dispersion curves (reflected energy vs position on crystal) for C*(220), Si(220) and Si(440) intercept in one point which, with optimal alignment, appears at the central energy of the SASE spectrum, see Fig. 7 where the dispersion relations are shown. This interception point will create a spectral notch in the downstream crystal. The energy width of the tilted notch in this experiment is approximately 13 eV, therefore the dashed lines mark ± 6.5 eV as a visual aid. No dispersion is expected normal to the scattering plane so the notch is expected to appear as a straight line perpendicular to the scattering plane in the spectra recorded with the Si crystals.
Fig. 7 Calculations on the dispersion for bent C*(220), Si(220) and Si(440) orientation, based on Eq. 1.
However, in the experiments a tilted spectral notch from the diamond is observed in the spectra of the Si crystal, see Fig. 6. The most probable origin of the observed tilt is a slight tilt misalignment of the crystal with respect to the beam. Together with the anticlastic bending this could lead to dispersion in the horizontal direction which would appear as a tilted notch in the spectra. Unfortunately, during the experiment it was not possible to rock the diamond crystal to attempt aligning the notch and thereby unambiguously determine the origin of the tilt. If two identical spectrometers are placed in series the spectrum recorded by the downstream device will vanish as the dispersion curves overlap perfectly. However, a slight tilt of one spectrometer could possibly prevent this perfect alignment and hence facilitate parallel operation, e.g. to measure the spectrum before and after interaction with a sample. Alternatively, the second spectrometer could be flipped (rotated 180° around the incident beam) and hence scatter x-rays downwards but such an arrangement might be difficult due to space constraints. Further investigations of the “tilted notch” effect and the anticlastic bending are foreseen to clarify these issues.
3.3. Bent-diamond spectrometer at the European XFEL
Due to the European XFEL’s high pulse repetition rate of 4.5 MHz, implementation of a bent-diamond spectrometer bears mainly two challenges: i) The crystal is exposed to a much higher heat load than in the tests outlined above, and ii) a spatially resolving detector capable of recording images at this repetition rate is required. To address i) we are planning to integrate a cooling mechanism into the design of the setup even if the heat transfer efficiency of the diamond crystal itself will not be very high due to its small thickness and the bender geometry. The heat transfer from the spectrometer is further limited by the poor thermal contact at the base of the bent crystal and studies are underway to improve the thermal contact i.e. by a thin, soft metal foil. Active cooling will be achieved by connecting the copper support of the diamond holder to a cooling circuit via a flexible copper braid. The extent to which cooling will be crucial for the operation of the diamond spectrometers at the European XFEL remains to be studied when the facility starts operating. Concerning ii), since standard 2D optical camera systems and scintillator screens are not suitable for such high image rates, the signal will be collected by a linear detector, such as the Gotthard detector with 25 µm pixel size currently under development at the Paul Scherrer Institute in Switzerland [28]. To counteract the larger pixel size in comparison to the present experiment, the detector will be positioned at a distance of about 1 m, providing an energy resolution of ca. 0.11 eV for the C*(220) reflection at 7.6 keV. This detector will be capable of operating at the full repetition rate of the European XFEL. However, a linear detector cannot provide information about spectral dependencies in the direction perpendicular to the scattering plane so only integrated spectra are obtained. This may hamper the observation of e.g. spatial chirp of the electron beam or other unwanted behavior. Also, a tilted notch, like in the LCLS experiment, will be difficult to observe with only 1D information. Possibly, a 2D detector operating at lower repetition rates could provide this information.
4. Conclusion
We have successfully demonstrated the use of an ultra-thin diamond single crystal bent to 0.1 m radius as hard x-ray FEL spectrometer. Measurements were performed at the XCS instrument of LCLS at 120 Hz repetition rate and the diamond spectrometer was directly compared with its Si counterpart for every single pulse. For the C*(220) reflection an energy resolution slightly better than for Si(440) was measured. Both devices fully cover and resolve the spectral fine-structure (spikes) of the entire SASE spectrum. However, the C*(220) spectrometer achieved these results being installed in vacuum, which is an additional advantage. C*(440) was tested at higher photon energy providing an ultra-high resolution option (∼ 100 meV, or less). Implementation of the diamond spectrometer is planned at the MID instrument of European XFEL [21].
Funding
Use of the Linac Coherent Light Source (LCLS), SLAC National Accelerator Laboratory, is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Contract No. DE-AC02-76SF00515.
Acknowledgments
The authors would like to thank Idoia Freijo Martín, European XFEL, for assisting in the characterization of the crystals with the white-light interferometer.
References and links
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