Innovative Analytical Method for X-Ray Imaging and Space-Resolved Spectroscopy of ECR Plasmas

At INFN-LNS, and in collaboration with the ATOMKI laboratories, an innovative multidiagnostic system with advanced analytical methods has been designed and implemented. This is based on several detectors and techniques (Optical Emission Spectroscopy, RF systems, Interferopolarimetry, X-ray detectors) and here we focus on high resolution spatially-resolved X-ray spectroscopy, performed by means of a X-ray pin-hole camera setup operating in the 0.5− 20 keV energy domain. The diagnostic system was installed at a 14 GHz Electron Cyclotron Resonance (ECR) ion source (ATOMKI, Debrecen), enabling high precision X-ray spectrally-resolved imaging of ECR plasmas heated by hundreds of Watts. The achieved spatial and energy resolution were 0.5 mm and 300 eV at 8 keV, respectively. We here present the innovative analysis algorithm that we properly developed for obtaining Single Photon-Counted (SPhC) images providing the local plasma emitted spectrum in a High-Dynamic-Range (HDR) mode, by distinguishing fluorescence lines of the materials of the plasma chamber (Ti, Ta) from plasma (Ar). This method allows a quantitative characterization of warm electrons population in the plasma (and its 2D distribution) which are the most important for ionization, and also to estimate local plasma density and spectral temperatures. The developed post-processing analysis is also able to remove the readout noise, that is often observable at very low exposure times (msec). The setup is now under update including fast shutters and trigger systems in order to allow simultaneously space and time-resolved plasma spectroscopy during transients, stable and turbulent regimes.


Introduction
At the INFN-LNS and in collaboration with the ATOMKI Laboratories, efforts have been paid to the study, development and use of an innovative multi-diagnostic setup with advanced analytical techniques aiming at characterizing the thermodynamical properties of the ECR magnetized plasmas confined in compact traps for multidisciplinary studies. The developed multi-diagnostics setup [1,2] includes a microwave interfero-polarimeter, several RF multi-pins probes, a multi-X-ray detectors system for X-ray spectroscopy, a X-ray pin-hole camera for high-resolution 2D space resolved spectroscopy and different spectrometers for the plasma-emitted visible light characterization. In the framework of the PANDORA_Gr3 (Plasmas for Astrophysics, Nuclear Decays Observation and Radiation for Archaeometry) project [3], the multi-diagnostic system will equip an innovative compact and flexible magnetic plasma trap for measuring nuclear

The Experimental Setup
The X-ray pin-hole camera system is sketched in Figure 1a. The CCD X-ray camera (model Andor, iKon-M SO series) is made of 1024 x 1024 pixels, with an optimal quantum efficiency in the range 0.5 − 20 keV. It was coupled to a Pb pin-hole (thickness 2 mm, diameter Φ = 400 µm) placed along the axis, facing the chamber from the injection flange. A Titanium window with 9.5 µm of thickness was used to screen the CCD from the visible and UV light coming out from the plasma. In order to work with the ECR-plasma heated at high power, the overall pin-hole system has been redesigned, including a multi-disks lead collimator for extra shielding of scattered radiation. The multi-disks collimator consists of two lead disks with same thickness (1 mm) and different diameter Φ (2 mm, 1 mm). The lead pin-hole was placed in between the two lead disks, that were located at distances of l 1 = 40 mm far from the pin-hole at the CCD side, and l 2 = 6 mm far from the pin-hole at the plasma side. The optical magnification M was optimized to be: M = 0.244 (distance pinhole−CCD = 232 mm, distance pinhole−plasma centre = 952 mm). Other details about the setup are described in [27]. By this system the pin-hole camera was operated up to 200 W total incident power in the plasma, namely one order of magnitude higher compared to the previous measurements (where the pumping power was limited to 30 W [20,21]). This way, both stable and turbulent plasma regimes (typically triggered above certain power thresholds [28,29]) have been investigated [30,31], also studying new plasma heating methods [32,33]. (a) Sketch of the X-ray pin-hole CCD camera system, including the multi-disks collimator. On the rigth a sketch of the ATOMKI plasma chamber highlighting the different materials and relative X-ray fluorescence peaks is shown: Al for the injection endplate mesh, Ti for the extraction electrode and Ta as a liner covering the lateral chamber walls. Ar was used to generate the plasma. The sketch also shows (in white) the magnetic field lines going from the plasmoid towards the chamber walls (both endplates and lateral): electrons are shown as small bullets with different colors, red for the ones impinging on the lateral walls while yellow for the ones flowing towards the endplates. (b) Pseudo-color elaboration of X-ray flux (in logarithmic scale), putting in evidence plasma branches (radiation coming from the extraction endplate), hot spots at the magnetic pole sites on the lateral chamber walls, the extraction hole and the plasma emission. (c) Perspective front view of the plasma chamber from the same side of the X-ray pin-hole camera.
In order to allow SPhC-based quantitative space resolved spectral analysis, the 1 ATOMKI plasma chamber walls have been covered by thin layers of materials having 2 different X-ray fluorescence energies, whilst the plasma was made by Ar, having a fluores-3 cence emission around 2.96 keV. This way, even in energy integrated images, the X-rays 4 coming from the plasma are well visible, while the materials of the extraction (Titanium) 5 and injection (Aluminum) endplate and of the lateral walls (Tantalum) provide bright 6 regions of X-ray emission due to bremsstrahlung and X-ray fluorescence as well. 7 The sketch of the ATOMKI plasma chamber is illustrated in the Figure 1a (on the right). 8 This Figure reports in a pictorial way the shape of the plasma core, the so-called plasmoid, 9 that is typically contained within the iso-magnetic surface fixed by the ECR condition 10 ω RF = qB/m, where ω RF is the RF pumping frequency, B is the magnetic field, q and m the 11 electron charge and mass, respectively. From this high density core, fluxes of deconfined 12 electrons and ions escape according to the so called "loss cones". Those field lines lying 13 inside the loss cones are represented in white. Small bullets of different colors represent the 14 lost electrons, going towards the lateral chamber walls (red dots) or towards the endplate 15 (yellow dots). 16 The perspective front-view of the plasma chamber (i.e. the same view of the pin-hole cam-17 era setup) is sketched in Figure 1c. It is clearly visible the Al mesh (having a wire diameter 18 of 400 µm) that was placed on the injection endplate to keep the microwave resonator-like 19 properties of the plasma chamber, but allowing direct inspection of the chamber interior at 20 the same time, guaranteeing more than 60% of optical X-ray transmission. 21 3. X-ray Spectrally-Resolved Imaging Algorithm 22 Each photon impinging in the CCD camera releases its energy in the silicon generating 23 a characteristic number of photo electrons that is proportional to its own energy. The

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Analogue Digital Unit (ADU), corresponding to the information read by the CCD in each 25 pixel, is therefore proportional to the product of the incident photons by their energies. We 26 adopted two operative modes to acquire the images: the Spectrally Integrated (SpI) mode 27 and the SPhC mode. 28 Images obtained with long t exp (tens of sec) will be called SpI images: in this case no energy 29 discrimination is possible (but they are useful anyway, since the ADUs are related to the 30 energy content of the plasma). These acquisitions are relatively fast and it is possible to 31 monitor "on line" changes of the plasma structures or plasma losses on the chamber walls.

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A typical example of a SpI image is shown in Figure 1b. This image was collected with an • black squares, highlighting the so-called "magnetic branches", i.e. the bremsstrahlung-43 produced X-rays and X-ray fluorescence coming from extraction endplate, that are 44 due to electrons escaping axially (in yellow in the pictorial view of Figure 1a);

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• bright green squares, indicating the regions where the magnetic field lines intercept 46 the lateral walls of the plasma chamber (the ones in red in Figure 1a).

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This plasma image demonstrates the capability of this method to qualitatively separate 48 X-ray radiation coming from the plasma from that one coming from the plasma chamber 49 walls, but the more powerful investigations, able to perform local energy determination, is 50 provided by SPhC mode.

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To operate in SPhC mode the development of proper acquisition and post-processing 52 procedures was required.

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The SPhC mode is obtained by fixing a very short t exp for each of the acquired image-frame 54 (several tens of milliseconds) minimizing the probability that two (or more) photons hit the 55 same pixel or its nearest neighbours.

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SPhC t exp was empirically set-up, in such a way that only a few number of pixels were 57 illuminated on the full CCD matrix during a single-frame acquisition; a sequential acquisi-58 tion of thousands of SPhC frames then allows to reach the statistics necessary for obtaining 59 high quality X-ray fluorescence spectra and images.

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The details of each step are described, respectively, in the next five subsections. Even working in SPhC mode, some pixel-clusters are often in each of the image-frame 70 acquired: they could be associated with a single photon that interacts with more than one 71 pixel or with two (or more) photons hitting neighboring pixels. Grouping process (Gr-p) 72 aims at finding real SPhC clusters, discarding spurious events.

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On this purpose, we introduced the S parameter representing the maximum cluster size 74 (defined as the number of neighbours pixels in a cluster) that can be considered as due to a 75 single-photon event. Clusters larger than S are filtered out. Noise contribution is removed 76 by setting a threshold L.

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In more detail, the algorithm works in the following way: maximum: for them, in the STEP-3 described below we will see that the code 89 will associate the integrated total charge to a single photon energy, whose  Figure 2c).

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(a) (b) (c) Figure 2. ROI of 20X30 pixels analyzed implementing the three different steps (described in the text) of the Gr-p: a) after the STEP-1; b) after the STEP-2; c) after the STEP-3.
In Figure 2 a ROI of 20x30 pixels has been processed by Gr-p with S=5 and L=10 as 99 input parameters.

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In order to perform the energy calibration, four characteristic peaks corresponding 113 to the Ti K α , Ti K β , Ta L α and Ta L γ fluorescence peaks have been considered. The energy 114 and channel values of each peak are summarized in the Table 1  The calibrated spectrum, expressed in logarithmic scale, is shown in Figure 5a, whilst 117 a zoom in the energy range 1-15 keV, where all characteristics peaks are highlighted by 118 labels, is shown in Figure 5b. Fluorescence peaks (the K α and K β of Titanium, the L α , L β , 119 L γ and M α of Tantalum) and of the plasma (K α and K β of Argon) have been highlighted by 120 appropriate labels.

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The estimated energy resolution is 0.326 keV at 8.1 keV (corresponding to the Ta L α line).

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(a) (b) Figure 5. (a) Typical X-ray spectrum expressed in logarithmic scale after energy calibration, the red line is the exponential fit performed in the 30 − 100 keV range. (b) Typical calibrated X-ray spectrum with the labels of each characteristic peak.
Dimer and escape peaks of the silicon-made CCD are also visible. This latter peak is 123 an artifact, due to the probable Si Kα X-ray photons generation inside the detector: these 124 photons can escape from the detector volume, thus reducing the effective detected energy 125 of some incident rays by ∼ 1.74 keV ( Si Kα X-ray energy). The escape peak coming from 126 Ti fluorescence overlaps with the Ar Kα fluorescence. Consequently, methods to minimize 127 these contributes have been also implemented. Several papers [34][35][36] demonstrated that 128 the escape peak generation efficiency is typically of the order of 3% of the main Kα peak.

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So, the algorithm considers an escape peak efficiency Z of the 3% of the main Ti Kα peak, 130 and removes this contribution pixel-by-pixel both in the whole matrix and in the spectrum.    It comes out that at the lowest S the spectrum shows the higher resolutions but the 150 lowest intensities. In addition, since at the lowest S we have an overfiltering of larger 151 clusters, the maximum energy (consequently, the electron temperature that is inversely 152 proportional to the spectrum slope [15]) decreases as a function of S, as shown in the Figure   153 7b.

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To account for these effects, and also to reduce the impact of dimer and escape peaks, the 155 implemented algorithm optimizes the input S and L parameters (we set three L=5, 10, 15 156 values: for L = 5 and L = 15 the code run for five values of S=1 − 5, for the case L = 10 157 we have S from 1 to 10) for improving as much as possible the I MP I EP and I MP I DP ratios (where 158 I MP , I EP and I DP are, respectively, the main peak intensity, the escape peak intensity and 159 the dimer peak intensity). By adding the same relative weight of the three optimization procedures (low escape, low 172 dimer, high intensity), the optimal values were: L=10 and S=2. In case of low statistic, L=10 173 and S=5 resulted to be the best compromise.

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In summary, the whole process described in the previous sections (i.e. from raw data to 175 calibrated and optimized spectra) is summarized in the sketch shown in Figure 8.

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Let us now consider, for sake of example, the image shown in Figure 9a. The image 178 is the result of the analysis of a number of image-frames N f r = 4200 acquired with 179 t exp = 500 ms, at 1 MHz of readout rate and full-frame (1024x1024 pixels) acquisition mode.

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The spectrum of the full size image is the one shown in the Figure 7a (for S=5 and L=10).

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The Energy-filtered Imaging consists in selecting only those pixels which were loaded by 182 only those photons having an energy in a given energy interval ∆E. 183 We plotted images using ∆E corresponding to the fluorescence peaks of Ar, Ti and Ta,  195 In our case, SpI images at t exp = 50s (see Figure 1b) display Ar intensities orders of 196 magnitude lower than magnetic branches or poles. The same happens in SPhC mode.

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In this latter case, we optimized t exp and N f r acquiring different datasets, taking into 198 account the hugely different local emissivities. In particular (see Table 2), we used t exp = 199 0, 5 s that was suitable to have good photon counting changes in the low intensity ROIs,   Since the degree of the missing information is spatial-dependent, the implemented 225 algorithm operates by exploring any pixel in each image-frame, as done for the Gr-p, but 226 in this case the goal is to define two "masks" that are necessary to obtain the HDR image:     Figure 14.

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Finally, a similar HDR procedure has been applied to the basic spectra too. Middle: the I Plasma acquired images for the same cases of the row above. Bottom: the same of the rows above, but after HDR post-processing.   In the case shown in Figure 16, it has been considered an impacting RON flux equal to 262 half of the initial flux during the readout time of one row (t r RO ). This fraction (0.5, in this 263 example) has been called β. 264 In more details, in Figure 16 (Figure 15), demonstrating the effectiveness of the described procedure.

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Moreover, considering the difference from the Start HDR Image and the Forward Image, 297 it is possible to obtain the so called "Displaced RON Image" consisting of all RON photons 298 collected during the RO time and placed in wrong positions (see Figure 18).

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These RON photons from one hand represent a spurious contribution because they are 300 placed in wrong pixel position but, on the other hand, they are "good" events because are 301 true photons coming from the plasma setup that impact on the CCD. It has been possible 302 to relocate them in the correct pixel position, increasing the statistics. 303 Figure 18. From left to right: Start HDR Image; Forward Image; Displaced Readout Noise Image.
In the previous example, a β parameter of 0.5 has been considered, but the real experimental β parameter (which depends of the t RO ) has been estimated. The measurements have been performed setting a readout frequency of 1 MHz (10 6 pixels/sec), so the readout time of one single pixel t p RO is 10 −6 s; subsequently, the readout time of one row RO r t results 1024 · 10 −6 = 0.0010124 s. Therefore, the β parameter is: β represents, in other words, the fraction of flux impacting in a single row during its own (see also the Table 3 for comparing ADU of the experimental acquired images).  processed image is called "Normalized Backward Image" and is shown in the Figure   347 23f.

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The images shown in Figure 23 are Argon-energy filtered.

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It is worth to point put how the post-processed images quality dramatically improves if 350 compared to the original one. The proper handling of RON after the elaboration of the 351 "Normalized Backward Image" is evident, and also spatial resolution increases.

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In Table 3 it is possible to observe that the total counts of the Start HDR Image  performed by applying the whole set of aforedescribed algorithms is reported in [38].

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Once post-processed the X-ray images by means of the advanced algorithm, two 386 important complementary analyses of the SPhC images can be simultaneously performed: 387 a) the HDR Energy-filtered Imaging and b) the HDR Space-filtered Spectroscopy.

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By means of the HDR energy-filtered imaging it is possible to obtain the imaging of the 389 elemental distribution, distinguishing the emission, and the correspondent image, coming 390 from each material. Pixels highlighting photons due to fluorescence peaks are shown in the 391 last column of Figure 27: 27b, 27c, 27d respectively for the Ar-, Ti-and Ta-energy-filtered.

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In this way, it is possible to study the plasma structure and morphology changes and to 393 investigate in details the plasma confinement and losses dynamics. the deconfined plasma flowing along the magnetic branches until the more external region 408 ROI 6 . More details about the experimental results are described in [30,38]. 409 Finally, it is important to mention that both the whole spectrum and the spectra in each 410 ROI can be analysed in order to locally estimate the plasma parameters, in term of electron 411 temperature and electron and ion densities, by comparing experimental spectrum vs.

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In this paper an innovative analytical method developed for performing space-421 resolved high resolution X-ray spectroscopy, has been presented. The algorithm has 422 been finalized to analyze the raw data acquired using the X-ray pin-hole camera tool and 423 represents a powerful method for plasma structure evaluation, plasma confinement and 424 losses dynamics investigations and for locally determining plasma density and temperature.

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In particular, the developed tools now enable Single Photon-Counting operations mini-426 mizing read-out effects and with high signal-to-noise rations, allowing energy-resolved 427 investigation pixel-by-pixel, also providing the local plasma emitted spectrum in a High-