Calibration of a versatile multi-energy soft x-ray diagnostic for WEST long pulse plasmas

A compact multi-energy soft x-ray (ME-SXR) diagnostic is being installed on the WEST tokamak (CEA Cadarache, France) together with a multi-energy hard x-ray (ME-HXR) diagnostic¹ and a compact x-ray Imaging Crystal Spectrometer (cXICS). The main goal of this diagnostic is to provide time- and energy-resolved soft x-ray profiles with applications in impurity transport and MHD activity monitoring as well as electron temperature (T_e) profile measurements and impurity density measurements (n_z). The WEST tokamak² was designed to test the ITER-like tungsten plasma facing components³ in a long pulse (∼1000 s) scenario. In tokamaks with high-Z wall-facing components such as tungsten, the accumulation of impurities increases the radiated power, which affects the overall power balance and seriously restricts the operational domain. The ME-SXR has a sensitivity in the range 1.6–30 keV and covers the tungsten lines between 2.3 and 12 keV. It enables energy discrimination with adequate space and time resolution (≲1 cm and 2 ms), providing a high energy resolution and a unique opportunity to measure simultaneously a variety of plasma parameters. The impurity concentration n_Z will be obtained from the emission line of medium- to high-Z impurities in the energy range 2.3–12 keV. In addition to measuring plasma impurity concentrations, the ME-SXR will provide electron temperature (T_e) profiles by modeling the slope of the continuum emission in the energy range 10–21 keV, complementing the installed ECE diagnostic, which is challenged in the presence of lower-hybrid current drive due to the downshift of the electron gyro-frequency.⁴ 

In this paper, we discuss the energy calibration of the ME-SXR over three energy ranges: low (2.3–6 keV), medium (4.5–13.5 keV), and high (5.4–21 keV). Although there is a risk of saturation, the low energy range will be exclusively used to study the tungsten transport in WEST using the tungsten line emissions between 2.3 and 6 keV. The medium energy range will be used to study the tungsten emission in the range 4.5–12 keV. Finally, the high energy range will also cover the tungsten emission in the range 6–12 keV but will also be used to reconstruct electron temperature profiles and possibly study the birth of runaway electrons.⁵ A similar calibration performed in the hard x-ray range (up to 100 keV) is presented in Ref. 1.

In Sec. II, we briefly describe the ME-SXR diagnostic and its elements. In Sec. III, we detail the energy calibration procedure and describe the experimental setup for the calibration. Finally, the results of the calibration are discussed in Sec. IV.

The ME-SXR diagnostic to be installed on the WEST tokamak consists of a pinhole camera fielded with the PILATUS3 Si detector commercialized by DECTRIS Ltd. The ME-SXR will be mounted on an equatorial port in such a way that the field of view is maximized and covers most of the plasma cross section [Fig. 1(a)]. The detector has a depressurized water-cooled can-shaped casing, which is isolated from the torus vacuum using a 300 μm beryllium window. The beryllium window acts as a high-pass energy filter, and its thickness was chosen such that 50% transmission occurs at ≈3.5 keV, filtering out the high-intensity low-energy tungsten lines (from 2 keV and below) that would likely saturate the detector.

The PILATUS3 Si detector⁷ is an x-ray photon-counting detector based on reverse-biased diode array technology. The PILATUS3 is made of a single 450 μm silicon detector, which absorbs the x-ray photons and converts them into electron/hole clouds by the photoelectric effect. The charge cloud is then converted into a voltage pulse by the charge-sensitive pre-amplifiers for each of the 487 × 195 = 94 965 pixels (often referred to as 100 k) of size 172 × 172 μm². The voltage pulse is discriminated against a threshold voltage, and if the voltage of the pulse is larger than the threshold, it is recorded into a 20-bit counter, which is read out at pre-set intervals. Each one of the pixels has its own charge-sensitive pre-amplifier, a global voltage comparator, a fine 6-bit DAC trimbit setting, and a counter. By design, the trimbit setting value is an integer between 0 and 63. The pixels are organized into 16 chips containing 60 × 97 individual pixels. The threshold is set as follows: a global V_cmp threshold is set for each chip, and the voltage threshold can further be trimmed individually for each pixel using a 6-bit digital to analog converter that we will refer to as the trimbit setting $t̂$⁠.

The trimbit setting was initially used to enable homogeneous white plate calibration to account for small inhomogeneities in electronics. In this paper, we take advantage of a custom calibration of the trimbit setting to set different energy thresholds across the detector. This calibration is explained in detail in Sec. III.

The goal of the PILATUS3 calibration is to find the mapping between the trimbit setting $t̂$ and the energy threshold E_th for each pixel of the detector, which will hereafter be referred to as the $t̂−Eth$ curve. The calibration procedure is similar to the one in Ref. 8. When exposed to a monochromatic source, the response curve of the detector to a scan in the trimbit setting is an error function that is often called an S-curve,^6,9

where $N(t̂)$ is the number of photon counts. An example of an S-curve measured by a single pixel after being exposed to the 4.51 keV Ti Kα emission is shown in Fig. 2. The parameters of interest in this calibration are the inflection point a₀ of the S-curve, which corresponds to the trimbit threshold of a pixel for a given incident x-ray energy threshold E_th, and a₁, which is related to the width of the S-curve and, consequently, to the achievable energy resolution of the pixel. a₁ is due to electronic noise, charge sharing, and the energy spectrum of the incident x ray. The amplitude a₂ of the error function depends on the flux of the x-ray source and exposure time. The slope a₃ in the linear term models the charge sharing. Finally, a₄ and a₅ describe the linear offset due to the background signal.

The measurements are performed with several monochromatic x-ray sources (Sec. III B) with emissions at different energies. The mapping between the trimbit setting and the energy threshold $t̂=f(Eth)$ is obtained for each pixel, and f(E_th) is well-approximated by the quadratic function

For each pixel, the experimentally measured f(E_th) is fitted to the quadratic function defined in Eq. (2) to ensure the continuity of the mapping. The results of the calibration are discussed in Sec. IV.

The measurements for the calibration were performed at DECTRIS Ltd. in Switzerland. X-ray emission from a high-voltage (50–150 kV, 25–45 mA) tungsten tube is emitted toward a rotating wheel on which several metal samples are made available (Fig. 3). In each case, either the Lα or Kα lines from the metal samples (Table I) are re-emitted toward the PILATUS3 detector in such a way that the emission is homogeneous across the detector. The distinct emission from the Lα and the Kα lines is achieved by a careful use of voltages in the tungsten tube. 11 metallic targets are used for a total of 15 emission energies ranging between 2.04 keV for zirconium and 24.2 keV for indium. For each emission energy, the trimbit setting $t̂$ is scanned from 0 to 63, and for each $t̂$⁠, the exposure time is set to several minutes, leading to an average exposition time of about 8 h for each energy calibration range. In the particular cases of Br, Zr, and Mo, the Kβ lines (13.30, 17.7, and 19.6 keV, respectively)—although less bright—are also excited.

In the following, the calibration is performed in three energy ranges: low (2.3–6 keV), medium (4.5–13.5 keV), and high (5.4–21 keV), the accessibility of which is determined by using the gain of the pre-amplifier. For each energy range, the trimbit setting scan was performed on each of the ∼100 k pixel. An example of the measured S-curves by a single pixel after being exposed to different metallic line emissions is shown in Fig. 4. For better visualization, the curves are normalized so that the response is equal to one when the threshold is half of the threshold corresponding to the incident photon energy. The linear background is also subtracted.

The a₀ parameter is identified for each curve in Fig. 4 and the $t̂−Eth$ curve is shown in Fig. 5. The error bars and uncertainty of the fits shown in Fig. 5 are representative of all pixels across the detector. In particular, the error bar in the determination of a₀ in the Mo (2.29 keV) measurements is larger than the other ones because the inflection point of the S-curve occurs close to the limit value of $t̂=0$⁠. We also found that the energy thresholds corresponding to the Zr Lα, Ag, and In Kα lines at 2.04, 22.16, and 24.2 keV, respectively, are outside the accessible energy threshold range with the gains used for the pre-amplifier, which is the reason why the corresponding results are not displayed here. The bump in the Br, Zr, and Mo curves indicated in Figs. 4(b) and 4(c) is due to the Kβ emission. For those cases, the fluorescence from the L-shell lines falls outside of the measurement range and is not measured. In the future, to improve the accuracy of the determination of the a₀ parameter, a “double S-curve” fit will be used for those elements.

The accessible energy ranges are determined by the trimbit value $t̂$ needed to set the energy threshold E_th. As mentioned earlier, the trimbit setting value is an integer between 0 and 63. If the required $t̂$ to set a given E_th is outside of this range, the detector cannot be configured properly. The highest achievable energy threshold is therefore given by the energy threshold corresponding to $t̂=63$⁠. Figure 6 shows the entire set of values taken by the $t̂−Eth$ curves by the pixels of the detector for the three calibrations, and we notice that this value varies substantially and can differ by several keV from one pixel to the other. Taking into account all the pixels of the detector, we obtain a higher limit for the achievable range of 6, 13.5, and 21 keV for the low, medium, and high energy ranges, respectively. The lowest accessible energy threshold is, on the other hand, given by the energy of lines that did not provide satisfactory results for the energy calibration since the inflection points of the S-curve were often found to be at negative $t̂$ values. We find 2.3, 4.5, and 5.4 keV for the low, medium, and high energy ranges, respectively.

The quality of the $t̂−Eth$ curve fit is investigated by defining χ² as $χ2=∑s(a0,s−t̂(Es))/t̂(Es)$⁠, where E_s is the energy of the x-ray source, a_0,s is the a₀ parameter obtained by fitting the S-curve corresponding to the energy source s, and $t̂(Es)$ is the trimbit setting corresponding to E_s and is given by the $t̂−Eth$ curve. The distribution of χ² across the detector for each calibration is shown in Fig. 7. The white pixels are either dead pixels or pixels for which either the S-curve or the $t̂−Eth$ curve did not provide satisfactory results. The overall quality of the fit is found to be good (χ² < 1). In the case of the low-energy calibration, some pixels are found to have χ² > 1. For this calibration, χ² > 1 is caused by the difficulty in determining a₀ in the case of the 2.29 keV L_α emission of Mo. This difficulty in determining a₀ is due to the fact that the $t̂−Eth$ curve is pushed to lower $t̂$ values.

There are two main limiting factors for the energy resolution of the detector. The first one is due to the fact that the trimbit setting of the detector is by default an integer. For a desired energy threshold E_th, the equivalent trimbit setting $t̂$ can be retrieved from the $t̂−Eth$ curve. Often, $t̂$ is a decimal number and must be rounded to the nearest integer value $T̂$ since the trimbit setting applied to the detector is an integer. We define δE as the standard deviation of $|Eth(t̂)−Eth(T̂)|$⁠, the difference between the requested energy threshold $Eth(t̂)$ and the effective energy threshold $Eth(T̂)$⁠. δE as a function of E_th is shown in Fig. 8(a) for the three energy ranges. The first observation is that for each energy calibration, δE is a decreasing function of E_th; this is due to the quadratic shape of the energy function. We also see that for all three energy ranges, δE remains small compared to E_th. In fact, for the low, medium, and high energy ranges, we have δE < 50, 100, and 270 eV, respectively, which are <0.06 E_th. We will see in the following that this δE is not the limiting factor for the energy resolution.

The second limit for the energy resolution is related to the width of the S-curve and the a₁ parameter. For an ideal high-pass filter, a₁ would be equal to zero. We have seen, however, that a₁ has a final width due to electronic noise, charge sharing, the energy spectrum of the incident x-ray, and the Fano factor. The impact of the finite value of a₁ on the energy resolution can be estimated by computing $ΔE=|Eth(a0+a12)−Eth(a0−a12)|$⁠. The results are shown in Fig. 8(b). Here, we find that the achievable energy resolutions for the low, medium, and energy ranges are 330, 640, and 950 eV, respectively.

In summary, we have presented the calibration of the PILATUS3 detector of the novel ME-SXR diagnostic over three energy ranges of interest for impurity transport studies and electron temperature profile measurements: low (2.3–6 keV), medium (4.5–13.5 keV), and high (5.4–21 keV). The achievable energy resolutions are found to be mainly limited by the width of the response curve of the detector when exposed to a monochromatic source. This finite width of the S-curve is due to electronic noise, charge sharing, and the energy spectrum of the incident x ray. For the low, medium, and high energy ranges, we find an energy resolution of 330, 640, and 950 eV, respectively.

This work was supported by the U.S. DOE-OFES under Contract No. DE-AC02-09CH11466.

The data that support the findings of this study are available from the corresponding author upon reasonable request.