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Abstract
We present a method to accurately control the photon energies for hard X-ray Self-seeding schemes with a single crystal monochromator in transmissive geometry. The energy calibration is performed by measuring which pairs of the machine pitch and yaw angles for different crystallographic planes reflect the X-ray at the same wavelength. The free parameters of an analytical formula for the self-seeding energies are determined by fitting the observed intersections and the normalized derivative with respect to the pitch and yaw angles in the observed intersections. The method requires a hard X-ray spectrometer, but it does not rely on its absolute energy calibration. Instead, identifying the self-seeded energies above the SASE background or the monochromatic notches within the SASE bandwidth is sufficient for the calibration.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
X-ray Free Electron Lasers (XFEL) are the brightest sources of X-rays for scientific applications [1–5]. XFELs are used in several fields of scientific investigation, including biology, chemistry, matter in extreme conditions, condensed matter physics and atomic, molecular, and optical physics [6,7]. Existing XFELs operating in the hard X-rays are based on the Self-Amplified Spontaneous Emission (SASE) [8,9]. Machines based on external seeding schemes like HGHG [10] or EEHG [11] present better temporal coherence and wavelength stability but have so far only produced softer X-rays down to about $4$ nm wavelength. Self-seeding schemes have been designed to increase the temporal coherence of a SASE FEL. In self-seeded schemes, the SASE X-ray pulse produced in the first section of the undulator line is first monochromatized and then amplified in a downstream undulator section. Different monochromator schemes have been proposed or used including single crystal transmissive geometry [12–16], four bounce monochromator [17], two bounce micro-channel cut monochromator [18] and grating-based [19].
In the basic self-seeding scheme, the same electrons produce the SASE pulse in the first undulator section and amplify the monochromatized X-ray in the second section. However, this prevents attaining the highest seed power because if the energy spread increases too much due to the SASE process in the first section, lasing in the downstream section may be spoiled. This issue has been overcome by using the fresh-slice technique [20–22], albeit producing shorter pulses. To also retain the full-length pulse duration and increase the flux, the double-bunch self-seeding has been proposed [23].
An analytical and accurate formula for the Hard X-ray Self-Seeding (HXRSS) in transmissive geometry is beneficial for a fast tune-up of the beam, avoiding lengthy scans to find frequency overlap between the supported amplification bandwidth and the monochromatized energy, and even more, it is needed for the operation of two-color self-seeding schemes [15], and to remove other unwanted self-seeding lines far from the desired one by using both degrees of freedom of the system.
In this paper we will describe the calibration of the self-seeding diamond crystal orientation performed at LCLS. The technique was first applied at LCLS-I (2014), and has been recently re-applied (in 2021) to recommission the newly installed, now vertically polarized LCLS-II undulator system. The advantage of the vertical polarization consists in a higher throughput of X-rays to the hard X-ray instruments by combining horizontal X-ray diffraction geometries with flexibility and stability [24–26].
A formula with several free parameters such as angular offsets and initial orientation of the diamond is derived analytically, and the free parameters are calculated for the installed system by fitting the observed intersections between the notch energies of different crystallographic planes for pairs of machine angles, and their normalized derivatives. This analysis is critical to the operation of modern, self-seeded light sources combining an understanding of FEL physics and x-ray crystallography to achieve a control of the absolute photon energy on the order of 1 eV and relative photon energy control in the meV level.
2. Methods
The hard X-ray self-seeding system is installed on the new hard X-ray undulator line after the $14$-th undulator segment, with $18$ more segments installed downstream to amplify the monochromatized X-ray pulse. The monochromator system is composed of a pair of diamond crystal monochromators used in transmissive geometry that can be alternatively inserted in the beam path and a magnetic chicane. The magnetic chicane allows delaying the electron beam up to $50$ fs, limited by the geometry of the vacuum chamber and bellows. The chicane is used to overlap the electron bunch with the monochromatic wake of the x-ray transmitted pulse and to avoid collision of the electron bunch with the diamond. Both diamonds installed have the face cut along $\left (0,0,4\right )$ plane. The diamonds are placed in holders attached to two rotation stages, pitch, and yaw, enabling two degrees of freedom. The top part of Fig. 1 schematically represents the undulator and the monochromator section layout.
Fig. 1. Top: Hard X-ray Self-Seeding (HXRSS) installation schematics (not to scale). A magnetic chicane and diamond monochromator are located between two undulator sections. The monochromator assembly has two diamonds crystals, one below and one above the nominal the X-ray path. They can be alternatively set into the X-ray path by vertical motion, or fully retracted by horizontal motion. Bottom: Self-seeding diamond crystal rotations in the HXRSS chicane, and the corresponding lattice planes.
The accelerator coordinate system has $z$-axis coincident with the beam propagation direction, pointed in the direction of the experimental stations, $y$ is the vertical direction, pointing to the ceiling, and $x$ completes a clockwise $(x,y,z)$ orthogonal system of coordinates. Within our derivation, the origin of the system of coordinates will be the middle point of the intersection between the beam propagation direction and the faces of the diamond monochromator.
By design, the pitch stage rotates the diamond around the $y$ direction. The yaw stage is mounted on the pitch stage and therefore rotates with it. The rotation axis of the yaw stage when the pitch angle is $\theta =90^\circ$ degrees is parallel to the $x$-axis. For $\theta =0^\circ$ degrees of pitch angle, the yaw stage rotation axis is parallel to the $z$-axis, and effectively becomes roll. The rotation axis, the beam propagation direction and the normal to the lattice planes $\left (0,0,4\right )$ and $\left (2,2,0\right )$, are represented in the bottom part of Fig. 1.
When both rotation angles equal $0^\circ$ degrees, the normal to the $\left (0,0,4\right )$ crystallographic plane is parallel to $x$, and the normal to the $\left (2,2,0\right )$ crystallographic plane is parallel to $z$. Therefore, by design the machine pitch angle corresponds to the grazing angle to the main cut plane. The direction of reciprocal lattice vector $\left (h,k,l\right )$, is parallel to:
whereFig. 2. Photon energies attainable in the first installation of self-seeding, for different diamond reflections as function of the pitch angle, with fixed yaw angle. (a) design condition with 0$^\circ$ degrees yaw angle. (b) design condition with non-zero yaw angle. In this case split lines do not merge for any pitch angle. (c) machine photon energies from the 2014 calibration.
A rotation matrix $M_h$ has been introduced to model the initial position of the diamond in the holder, modifying Eq. (1) into
The design pitch rotation axis $\mathbf {\hat {p}}$ are changed into the modified one $\mathbf {\hat {p}}_m = M_{ap} \mathbf {\hat {p}}$, and the design yaw rotation axis $\mathbf {\hat {y}}$ becomes $\mathbf {\hat {y}}_m = M_{ay} \mathbf {\hat {y}}$. Each of the three matrices $M_h$, $M_{ap}$, and $M_{ay}$ is modeled as the product of subsequent rotations $Rot_x(\mathbf {\hat {x}},\alpha )$, $Rot_y(\mathbf {\hat {y}},\beta )$ and $Rot_z(\mathbf {\hat {z}},\gamma )$, taking care to avoid the application of a rotation parallel to the unit vector to be rotated first. With the modified model, the normal $\mathbf {h}_{hkl}$ to a crystallographic plane $(h,k,l)^T$ after the rotations isThe photon energy is calculated using Eq. (7) and Eq. (8), obtaining a modified version of Eq. (9).
3. Results and discussion
To collect the data needed to characterize the monochromator and the system orientation, several scans were taken where many crossings between different reflections can be observed. In the presented measurement, the downstream amplification stage was also set up, and therefore we observed the position of the self-seeding peaks on the spectrometer. It is also possible to do the characterization, observing the notches in the SASE spectrum given by the monochromator reflections. The advantage of using the amplified self-seeded signal is of being easily detectable, also at the far end of the SASE bandwidth, while measuring the notches avoids the risk of frequency shift happening in the downstream section because of the electron bunch energy profile; since energy chirped beam may cause a frequency shift, due to micro-bunching compression or decompression. Each of the scans has been performed close to a pair of angles where crossings between reflections are visible, withing the spectrometer range. As an example, Fig. 3(a) shows the raw data measured at an energy of about $10.850$ keV. The pitch angle was kept fixed at 106.92$^\circ$ degrees, while the yaw angle was scanned between 1.3$^\circ$ and 1.8$^\circ$ degrees. Six self-seeded lines can be observed in this particular case. Subsequently an algorithm finds the self-seeded peak locations. However, only peaks aligned on lines, and that are not too close to the intersections are used for fitting, as shown 3(b). Finally, each of the lines is fitted, and intersections are found, as in Fig. 3(c). The information used to fit the model to characterize the diamond orientation are the pair of pitch and yaw angles at which an intersection between the lines is observed, and the relative derivative of the lines at the intersection location. All the derivatives on a single scan are normalized to the derivative of a chosen line at one of the intersections. Care is taken that the normalizing derivative is one of a steep line. Data were collected for different pitch angles as around $90^\circ$, $107^\circ$ and $120^\circ$ degrees covering most of the machine pitch operating range. The machine yaw angle was kept close to $1.5^\circ$, the angle close to the one that brings split lines to the same photon energy. A better characterization of the yaw rotation stage could be achieved by observing self-seeding in the entire operating range; however, it was not done during the performed measurement.
Fig. 3. (a) Raw data collected in a single scan. (b) Identified self-seeded peaks. (c) Fitted Diamond $(h,k,l)$ reflections and crossings. Color scale is arbitrary.
Figure 4 shows the superposition of the fitted monochromator system model with the raw data after the fit. All the data in Fig. 4 have been included in the fitting algorithm. Figure 4, unlike Fig. 3 has the photon energy axis calibrated by using the fitted model itself.
Fig. 4. Superposition between the fitted model of Diamond reflections $(h,k,l)$ and the raw data. All of the data included in this figure have been used to fit the model. Color scale is arbitrary.
To show that the fitted model accurately works also on data that has not been used for the fit, Fig. 5 shows the crossing of $11$ reflections around 12.4 keV, for machine pitch angle close to 102$^\circ$ degrees and machine yaw angle of 1.6$^\circ$ degrees.
Fig. 5. Superposition between the previously fitted model of Diamond reflections $(h,k,l)$ and the raw data not included in the fitting. Color scale is arbitrary.
The energies according to the fitted model have been calculated for the pair of angles where each of the 33 intersections visible in the experimental data of Fig. 5 have been observed. The maximum half distance between the calculated energies at the intersection locations is 0.40 eV, while the average one is 0.17 eV, showing an excellent agreement also for the dataset not included in the fit. The main free parameters of the presented fit are a yaw offset of $\approx -2.21^\circ$ degrees, a pitch offset of $\approx -0.47^\circ$ degrees, a roll rotation of $\approx -0.29^\circ$ degrees of the crystal in the holder, a rotation of the yaw axis of $\approx 1.38^\circ$ degrees, and a rotation of the pitch axis of $\approx -0.72^\circ$ degrees. To obtain an excellent agreement between the model and the experimental data it is sufficient to fit on the yaw and pitch offsets and the roll rotation of the diamond in the holder, instead using only yaw and pitch offsets produces poor results.
4. Conclusion
We described a technique to characterize the hard X-ray Self-seeding system in transmissive geometry in a Free-Electron Laser. The method requires a SASE beam at different energies produced upstream of the monochromator system and a spectrometer. Self-seeded amplification was established in the downstream section to collect the presented data. The method does not rely on the photon energy calibration of the spectrometer since only the angles at which crossings between different reflections are observed and the normalized derivatives are used to characterize the system; however, absolute photon energy is obtained at the end of the characterization process. The method was successfully used at LCLS in 2014 after the initial commissioning of the Hard X-ray self-seeding system, and during the recent recommissioning at LCLS in 2021.
Funding
U.S. Department of Energy, Office of Science (DE-AC02-76SF00515).
Acknowledgments
A.A.L. and F.-J.D. derived the formulas. A.A.L. conceived the characterization method and analyzed the experimental data. All authors participated in the experiments and co-wrote the manuscript.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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