In situ wavelength calibration system for the X-ray Imaging Crystal Spectrometer (XICS) on W7-X

X-ray Imaging Crystal Spectrometers (XICSs) detect the emission of highly charged impurity ions to provide ion temperature, electron temperature, plasma flow velocity, and impurity ion density profiles. XICS systems have been used on W7-X,¹ LHD,² Alcator C-Mod,³ EAST,⁴ KSTAR, and other experiments along with an XICS system planned for ITER.⁵ The ion temperature is found from the Doppler broadening of spectral lines; the electron temperature is found from the ratio of different lines; the flow velocity is found from the Doppler shift of the lines; and the impurity ion density is found from the line intensities. In a stellarator, the radial electric field, E_r, can be inferred through measurements of the perpendicular plasma flow, u_⊥.⁶ The measured E_r profiles are important for many aspects of stellarator physics including the study of neoclassical optimization in W7-X. Existing XICS systems lack any independent wavelength calibration capability. On tokamaks, plasma flow measurements are calibrated using locked mode plasma or through reversing the plasma flow. However, on stellarators, locked mode plasmas are not available. This paper presents an independent, robust calibration design that will work for any XICS system independent of the experiment.

XICS systems use spherically bent crystals to diffract x-rays to photon counting imaging detectors. The spectral resolution of the diagnostic is produced by the crystals diffracting light of different wavelengths at different angles according to Bragg’s law. The spatial resolution comes from the spherically bent shape of the crystal. The W7-X XICS diagnostic consists of two channels utilizing two quartz crystals which measure the Ar¹⁶⁺ and Ar¹⁷⁺/Fe²⁴⁺ spectra, respectively. In particular, the Ar¹⁶⁺ channel utilizes a Quartz (11-20) crystal with a radius of curvature of 1450 mm.

Referenced above, XICS on W7-X is used to infer the radial electric field, E_r, from the perpendicular plasma flow, u_⊥. The measurement resolution of the perpendicular plasma flow, when ignoring systematic errors, is Δu_⊥ = 1 km/s (ΔE_r = 2 kV/m) with typical levels of argon puffing and a 10 ms integration time. This corresponds to a shift of the line on the detector by about 5 μm. Better resolution is available through additional time binning. The primary systematic errors in these measurements are due to the absolute wavelength calibration across the detector, which in this system, is equivalent to the absolute spatial alignment between the crystal and the detector. The absolute alignment can be considered in two parts: a constant shift across the detector and a tilt of the detector leading to a linear shift of the wavelength. Without an absolute wavelength reference, calibration is based on the ability to see a portion of the plasma on both sides of the magnetic axis and the assumption that the parallel velocity is negligible.

Changes in the absolute wavelength calibration are expected to occur at least on the time scale of thermal changes in the diagnostic or the surrounding environment. Only a few degrees of temperature change, similar to what can be expected from an air conditioning cycle, have been shown to cause thermal expansion of the crystal lattice structure and therefore lead to spectral line shifts on the order of the desired plasma flow measurements.⁷ Similarly, thermal expansion of the steel structures, that support the crystal and detector, are also on the order to potentially cause significant calibration changes. Measurements of the crystal temperature and repeated calibrations during the planned long pulse discharges can be used to compensate for any spectral line shifts due to thermal expansion.

The wavelength calibration system designed for XICS consists of a x-ray tube positioned in front of the diffracting spherical crystal in order to provide x-ray calibration lines. The specific x-ray lines produced by the chosen anode for the x-ray tube will match the system’s spectral range. This wavelength calibration design will illuminate all spatial channels on the detector simultaneously. The full spatial illumination is achieved by positioning the x-ray tube close to the spherical crystal and inside the focal points of the spherical crystal. A discussion on the modeling and experimental testing of this setup is covered later on in this paper.

The x-ray tube for this calibration system is the XRT 30 by PROTO Manufacturing, Inc. A Cadmium anode on the x-ray tube will provide the Cd Lα and Cd Lβ lines needed to calibrate the Ar¹⁶⁺ and Ar¹⁷⁺/Fe²⁴⁺ channels, respectively, for XICS. The x-ray tube will be operated up to 15 keV and 2 mA. It will be placed 100 mm from the crystals, between the crystals and the plasma. For routine operation between discharges or during long discharges, the x-ray tube is mounted on a rotating arm attached to a standard rotary feedthrough with fine motion control. This setup allows the x-ray tube to be easily rotated in and out of the line of sight of the spherical crystals.

The assembled calibration design is pictured in Fig. 1. For simplicity, the flanges, nipples, feedthroughs, cooling lines, and cabling have been hidden from rendering in Fig. 1. The vertical shaft pictured connects the rotary feedthrough to the rotating arm holding the x-ray tube in addition to a counterweight balancing the x-ray tube. The two arms extending from the upper middle portion of the vertical shaft are physical safety stopping arms that prevent the x-ray tube from being positioned such that x-rays would enter the W7-X experiment. A post fastened to the top flange is the non-rendered component that will limit the motion of the arms.

Figure 2 shows how the calibration system will replace the top flange on the chamber that houses the crystal. On the left, the crystal chamber is shown with new addition placed on top. Progressing to the right in Fig. 2, the location of the calibration design can be seen with respect to the spherical crystal. Shown here, the x-ray tube is in the active position required for illumination of one of the detector channels. The system can be rotated to place the x-ray tube in position for the second crystal. In the stored position, the x-ray tube will be rotated behind the crystal and will not limit any current capabilities of the XICS system. Extra ports have been put on the top flange to allow the installation of a camera to ensure that the rotary system is functioning properly.

Figure 3 shows the placement of the X-ray tube in relation to the crystal and the plasma. This top-mounted arrangement of the x-ray tube in the chamber holding the crystal allows convenient access for installation and maintenance of the wavelength calibration system.

In order to validate the calibration design, X-ray Imaging Crystal Spectrometer Ray Tracing (XICS-RT) was developed as a tool to analyze and test the proposed design. XICS-RT is an object-oriented, ray tracing code written in Python that simulates the x-ray source, the spherical crystal, and the detector. The rays of a desired wavelength are generated with a random direction inside a cone defined by the spread of the source. The rays are propagated to the crystal location, and only those satisfying the Bragg condition are diffracted toward the detector. The detector counts all incident rays and outputs a Tagged Image Format (TIF) image file.

Using XICS-RT with the actual geometry of the XICS system on W7-X coupled with the physical characteristics of the x-ray source, the available configuration space for positioning the x-ray tube such that the detectors are illuminated over the full vertical extent was determined. Figures 4 and 5, respectively, show the horizontal and vertical projections of the configuration space. If the x-ray source is positioned anywhere inside this configuration envelope and directed at the spherical crystal, then the full vertical extent of the detector will be illuminated. The optimal position is along the center of the configuration envelopes.

XICS-RT was verified using an analytic formulation that was developed to understand the geometry of a spherical crystal x-ray spectrometer. Figure 6 shows this geometry. The two circles represent spheres having radii of R and R cos θ_B with R being the radius of curvature of the spherical crystal and θ_B the Bragg angle. The crystal’s width extends from C₋ to C₊ with C₀ being the center of the crystal. M is the center of curvature of the crystal, and P is the location of the planar detector. The rays, which are incident on the center of the crystal and diffracted according to the Bragg angle θ_B, must be tangential to the sphere with radius R cos θ_B. In order to satisfy the Bragg condition at the center of the spherical crystal, the source must lie on the $C0Q0¯$ line. For practical considerations, the source is inside the Q₀ position at some arbitrary Q₋ location.

With the source located inside the focal lengths of the crystal, the resulting image on the detector is produced from a virtual image. The location of the virtual image (not shown in Fig. 6) is at the intersection of the lines $Q−M¯$ and $PC0¯$⁠. With this virtual image, a characterization of the detector image can be made by rotating all rays which satisfy the Bragg angle about the $Q−M¯$ axis.

Using the actual geometry of XICS, Fig. 7 shows the comparison of XICS-RT to the analytical formulation. In Fig. 7, the vertical extent of the detector refers to the height of the planar detector that is illuminated by an x-ray source positioned at the corresponding location. Any vertical extent above the solid horizontal line (the physical height of the detector) corresponds to the full illumination of all spatial channels on the detector. The plateau region in Fig. 7 resulted from the finite width of the detector plane; the decaying region resulted from the fixed spread of the x-ray source (chosen to match the actual x-ray tube). Good agreement was found between XICS-RT and the analytical formulation.

Testing of the calibration design has been completed at the Plasma Science and Fusion Center (Cambridge, MA) using the High Resolution X-ray Crystal Imaging Spectrometer with Spatial Resolution (HIREXSR, an almost identical system to XICS).³ An x-ray tube (the same model as the one in the calibration design) with a Cadmium anode at 9.5 kV, 0.5 mA was positioned in front of the diffracting crystal at a distance of 4 cm with the angles satisfying the Bragg condition. With an exposure of 500 s (acceptable for wavelength calibrations), full illumination of the two working modules of the detector was found.

Figure 8(a) shows the resulting image from the central module of the detector produced by the Cadmium Lα₁ and Cadmium Lα₂ lines. Figure 8(b) is the XICS-RT produced image with the simulated x-ray source having the same spread, size, and distance from the spherical crystal as the actual experiment but only including the Cd Lα₁ line in the simulation. Figure 8(c) illustrates the agreement between the two by plotting the vertically centered, binned rows from each image.

In an attempt to identify possible calibration schemes, several indirect illumination calibration methods were investigated. These methods were motivated in order to provide a calibration source that would use the full crystal surface, mimicking the plasma. For the first test, a Cu x-ray tube was used to illuminate a thick Cadmium sheet in an attempt to excite reflection x-ray fluorescence. With a 2 mm thick Cadmium sheet placed approximately 30 cm in front of the crystal, the x-ray tube was positioned to the side of the crystal and aimed at the Cadmium sheet such that the illuminated area was in the line of sight of the full crystal. Next, transmission x-ray fluorescence was attempted with a thin 2 μm Cadmium foil, placed 2 cm from the crystal between the crystal and the Cu x-ray source. Finally, direct x-ray reflection of a Cd x-ray tube was tested using Cadmium, steel, and carbon sheets as the reflecting surfaces. All attempted methods failed to produce any detectable Cadmium lines on the detector, even after integration times of many hours. The lack of detectable x-ray emission is likely attributable to very small fluorescence yields. The indirect calibration methods were abandoned in favor of direct illumination of the spherical crystal by the x-ray tube as described in this paper.

The wavelength calibration accuracy of this design is limited by the random and systematic errors present in the system. The first random error in the wavelength calibration is the positioning of the x-ray tube at the optimal Bragg angle location which is dependent upon the rotary feedthrough. Figure 9, the results of a positioning test using XICS-RT, shows the change in position of the spectral lines (both the peak pixel location and a Gaussian fit pixel location) with a change in the angular rotation of the rotary feedthrough. Using the slope of the line fit to the Gaussian fit pixel location, the half-step of the rotary feedthrough (0.0019°) corresponds to a spectral shift of 2 × 10⁻⁷ Å (0.0005 pixels). Another random error is the ability to fit the spectral lines of the data. From the experimental testing with a 500 s exposure, the fitting error in the location of the calibration line is 1.5 × 10⁻⁷ Å (0.0004 pixels). The third possible random error is thermal expansion of the crystal or support system during the calibration exposure time. This limits the maximum integration time that can be used during the calibration and can be potentially mitigated through characterization of the thermal effects on spectral line shifts coupled with precise temperature measurements.

The first systematic error to be quantified is the precision of the wavelength of the Cadmium lines (Lα and Lβ) to be used for calibration. A literature study produces the most precise measurements to be 3.956 35 ± 0.000 04 Å and 3.738 23 ± 0.000 04 Å, respectively.⁸ Two additional systematic errors arise because the x-ray tube is much smaller than the plasma and much closer, meaning only a fraction of the crystal will be used to diffract the calibration x-rays (compared to the plasma light using the full crystal). First, this difference will produce a change in the shape of the spectral lines. Second, depending on the location of the x-ray tube, a spectral line shift will also occur. Both of these systematic errors will be modeled using XICS-RT. A high quality correction is expected; however, the final accuracy of this procedure will depend on our ability to accurately characterize the extent and angular spread of the x-ray source, as well as the rocking curve of the crystal. Figure 10 demonstrates XICS-RT’s ability to produce plasma spectra (the image has been rotated for this paper). This image was generated using a slab Ar¹⁶⁺ plasma (only the W-line simulated) at 5 keV placed at the distance of 3.5 m from the crystal. Given an absolute position accuracy of 1.5 mm (the estimated value based on available remote measuring methods for the x-ray tube location relative to the crystal center), an absolute wavelength accuracy of 1 × 10⁻⁵ Å (1 km/s) is achievable. The future addition of a collimating slit may allow an in situ calibration of the position of the x-ray tube with respect to the crystal edges, allowing a significant improvement in the absolute calibration.

A wavelength calibration system using direct illumination of the spherical diffracting crystal has been developed, tested, and designed for XICS on W7-X. This system will provide a wavelength calibration across the whole detector with very high accuracy (limited mainly by integration time) but with a single remaining systematic offset. The random error in the measurement is estimated to be 3 × 10⁻⁷ Å (50 m/s) with a systematic error of 1 × 10⁻⁵ Å (1 km/s). This greatly improves the ability to measure perpendicular flow profiles to high accuracy and will allow, for the first time on W7-X, parallel flow velocities to be simultaneously measured up to the larger systematic accuracy. Future improvements of the systematic accuracy are expected from future planned improvements in the determination of the absolute location of the x-ray source and cross calibration with other diagnostics.

Research was supported by the U.S. DOE under Contract No. DE-AC02-09CH11466 with Princeton University. This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 under Grant Agreement No. 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission. We thank MIT PSFC for the use of their facilities in testing the calibration schemes.