Tomographic reconstructions of the fast-ion phase space using imaging neutral particle analyser measurements

Plasma Physics and Controlled Fusion PAPER • OPEN ACCESS Tomographic reconstructions of the fast-ion phase space using imaging neutral particle analyser measurements To cite this article: J Rueda-Rueda et al 2024 Plasma Phys. Control. Fusion 66 065025 View the article online for updates and enhancements. You may also like Anti-aliasing method for ultrasonic 2D phase-sensitive motion estimator Michiya Mozumi, Ryo Nagaoka, Magnus Cinthio et al. - First fluctuation measurements using an Imaging Neutral Particle Analyzer on DIIID K.R. Gage, X.D. Du, W.W. Heidbrink et al. - Visualization of phase-space orbit topological boundary using imaging neutral particle analyzer X.D. Du, J. Gonzalez-Martin, D. Liu et al. - This content was downloaded from IP address 150.214.182.235 on 06/02/2025 at 11:23 Plasma Physics and Controlled Fusion Plasma Phys. Control. Fusion 66 (2024) 065025 (15pp) https://doi.org/10.1088/1361-6587/ad4486 Tomographic reconstructions of the fast-ion phase space using imaging neutral particle analyser measurements J Rueda-Rueda1,∗, M Garcia-Munoz1, E Viezzer1, P A Schneider2, P Oyola1, J Galdon-Quiroga1, M Salewski3, B S Schmidt3, J Garcia-Dominguez1 and ASDEX Upgrade team4 1Atomic, Molecular and Nuclear Physics, University of Seville, Seville, Spain 2Max Planck Institute for Plasma Physics, Boltzmannstr. 2, 85748 Garching, Germany 3Department of Physics, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark E-mail: [email protected] Received 9 February 2024, revised 5 April 2024 Accepted for publication 29 April 2024 Published 9 May 2024 Abstract In this paper we demonstrate how the inversion, in energy and major radius (E, R) coordinates, of imaging neutral particle analyser (INPA) measurements can be used to obtain the fast-ion distribution. The INPA is most sensitive to passing ions with energies in the range (20–150) keV and pitches near 0.5 in the core and 0.7 near the plasma edge. Inversion of synthetic signals, via 0th-order Tikhonov and Elastic Net regularization, were performed to demonstrate the capability of recovering the ground truth fast-ion 2D phase-space distribution resolved in major radius and energy, even in the presence of moderate noise levels (10%). Finally, we apply our method to measure the 2D phase-space distribution in an MHD quiescent plasma at ASDEX Upgrade and find good agreement with the slowing down fast-ion distribution predicted by TRANSP. Keywords: fast-ion diagnosis, neutral particle analyser, scintillator diagnostics, tomographic inversions 1. Introduction In future fusion reactors, suprathermal particles (fast ions, FI) will play a pivotal role in the generation of fusion power, as they serve as a crucial source of both energy (heating) and momentum (current drive) [1–3]. An inadequate confinement of fast ions can lead to a deterioration in reactor performance, and may even result in damage to the first-wall components [4, 5]. It is imperative to comprehend the mechanisms governing 4See author list of Zohm et al 2024 Nucl. Fusion https://doi.org/10.1088/ 1741-4326/ad249d. ∗Author to whom any correspondence should be addressed. Original Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. the transport and loss of suprathermal particles for the realization of a future fusion power plant. One of the primary identified causes for this particle transport and subsequent loss is their interaction with a broad spectrum of magnetic fluctuations. These fluctuations can be intrinsic to the plasma, such as neoclassical tearing modes [6,7], fishbones [8–10], or Alfvén eigenmodes [11–17], or they can result from externally applied perturbations [18–21]. Understanding and controlling these interactions are critical steps towards achieving sustainable fusion energy production. In present experiments, a direct measurement of the fastion distribution is not possible due to the limited resolution and phase space coverage of the diagnostics. This sensitivity is mathematically described by weight functions. Weight functions have been developed for neutral particle analysers (NPA) [22,23], fast-ion D-alpha spectroscopy (FIDA) [22, 24], collective Thomson scattering (CTS) [25], neutron emission spectroscopy (NES) [26,27], gamma-ray spectroscopy 1 © 2024 The Author(s). Published by IOP Publishing Ltd Plasma Phys. Control. Fusion 66 (2024) 065025 J Rueda-Rueda et al (GRS) [28,29], fast-ion loss detectors (FILD) [30], 3 MeV proton diagnostics [31] and ion cyclotron emission spectroscopy (ICE) [32,33]. Using the weight functions, the FI distribution can be inferred from measurements thanks to tomographic (regression) techniques. 2D velocity-space tomography [25,34–36] has been experimentally demonstrated based on various combinations of INPA, NPA, FIDA, CTS, GRS, NES and FILD at AUG, JET, MAST, EAST, DIII-D [24, 37–47], and is also foreseen for ITER [48]. In this article the first tomographic inversions applied to signals from the imaging neutral particle analyser (INPA) installed at the ASDEX Upgrade tokamak [49–51] as well as the analysis of the INPA instrument response and its change with plasma parameters are presented. The INPA diagnostic [52,53] obtains information of the confined FI population analyzing fast neutrals produced in charge exchange (CX) reactions between FI and neutrals injected by a neutral beam injector (NBI). These CX neutrals are ionized in-vessel by an ultra-thin (20 nm) carbon foil and deflected into a scintillator by the local magnetic field. The strike position on the scintillator, observed via a high-resolution CCD camera, allows inferring the energy and radial position of the confined FI (see [49,51] for full details on the measurement principle). Nonetheless, the analysis of INPA signals is not straightforward: the finite size of the collimator limits the resolution of the diagnostic in energy and the finite width of the distribution of NBI neutrals limits the radial resolution. Also, changes in plasma profiles will affect the reionization probability of CX neutrals towards the detector and hence the INPA signal. Even if previous work has been done in the sensitivity of the AUG INPA diagnostic [49,51], the first comprehensive description of the INPA sensitivity is presented in this article. For the weight function formalism, the INPA forward model used for synthetic diagnostic introduced in [51] is reformulated as a matrix equation, which can then be solved via regression techniques to infer the fast-ion distribution. Section 2introduces the forward problem, i.e. the calculation of the diagnostic signal given the fast-ion distribution function, section 3explores the dependence of the INPA weight function to the plasma profiles (nuisance parameters), and section 4presents the inverse problem and its application to synthetic and experimental signals. 2. Forward problem: synthetic signal calculation To calculate the INPA synthetic signal, the FILDSIM code [30] was upgraded to handle the INPA diagnostic. The code can now track the Monte Carlo (MC) markers produced by the FIDASIM code [54], which represent the input CX flux entering the INPA head. These markers are followed until they collide with the collimator or until they impinge on the carbon foil. At this foil, they are ionized and slowed down. Finally, they are deflected towards the scintillator by the tokamak magnetic field. The main changes in the FILDSIM code to accommodate for INPA simulations were the modification of the orbit-following module to handle non-homogeneous electric and magnetic fields, via a Boris leap frog algorithm [55], and the models to simulate the ionization and energy loss in the carbon foil. Furthermore, the capability of including arbitrary geometry from CAD files (via .stl files) was added, and a general speed up of the code by two orders of magnitude has been achieved. These upgrades are based on the libraries of the iHIBPsim code [56]. As already mentioned, this upgraded version of FILDSIM is coupled to the FIDASIM code [54] to produce the INPA synthetic signals and weight functions. The code workflow to calculate the synthetic signal can be seen in figure 1. There are two ways of calculating the synthetic signals: using directly the neutral flux from FIDASIM or using the weight matrix. This latter calculation is based on the fact that the signal in a pixel (i,j), Sij, of the INPA camera, can be written as the following Fredholm integral equation of the first kind: Sij ≡ˆWij (Ψ)F(Ψ)dΨ(1) where Wij is the weight (sensitivity) of the diagnostic, Fthe fast ion distribution function and Ψstands for the set of variables sampled in the phase space. Assuming toroidal symmetry and averaging over the gyrophase, just four coordinates suffice to span the phase space of fast particles. For example, as TRANSP (NUBEAM) code [57,58]: (R,z,E,λ)5; being major radius, height over the mid-plane, energy and pitch angle, respectively. However, the dependency of the weight function on λand zis solely coming from geometric origin. Neglecting the dependency on this geometric factor with energy (which comes from the small de-focus of the optics), it is possible to decouple this dependency in an isolate term of the weight matrix: Wij (R,z,E,λ)≡˜ Wij (R,E)G(z,λ|R)(2) where Grepresents the diagnostic sensitivity in the (z,λ)space for a given R, and ˜ Wij(R,E)the radial and energy dependencies. Gsatisfies the normalization condition: ˆG(z,λ|R)dzdλ=1.(3) Despite of the exact analytic form of G, owing the fact that it satisfies this normalization condition, it is direct to write equation (1) as: Sij =ˆ(˜ Wij (R,E)ˆG(z,λ|R)F(R,z,E,λ)dλdz)dEdR (4) but the latter is just the fast-ion distribution weighted averaged on (z,λ)over the field of view of the INPA at a point R,⟨F⟩INPA. Hence: Sij =ˆ˜ Wij (R,E)⟨F⟩INPA (E,R)dEdR.(5) 5The pitch is defined as: λ=−v∥/v, where v∥is the projection of the FI velocity on the magnetic field. 2 Plasma Phys. Control. Fusion 66 (2024) 065025 J Rueda-Rueda et al Figure 1. Flow diagram for the calculation of synthetic signal with the upgraded FILDSIM code. The numerically calculated G(z,λ|R)and the width of the marginal distributions as a function of Rcan be seen in figures 2(a)–(c) respectively. Taking a discrete and uniform grid to represent the phase space, equation (5) can be written as a matrix problem: Sij =∑ α,β ˜ Wαβ ij ⟨Fαβ⟩INPA ∆E∆R(6) where Greek letters span the phase space while Latin indexes the camera pixel space. The same equation can be written in the case that the camera signal is remapped using the strike map, as explained in [51]. As the grid is finite, the 2 indexes can be collapsed into one: k=i+j#i(7) γ=β+α#β(8) where #iare the total number of rows of the signal matrix and #βthe total number of rows in the fast-ion distribution matrix. Hence, equation (6) reads as: Sk=∑ γ ˜ Wγ k⟨Fγ⟩INPA ∆E∆R≡∑ γ ˜ Wγ′ k⟨Fγ⟩INPA (9) where in the last step, the constant grid spacing was included in the weight. The synthetic signals calculated with both methods (direct track of FIDASIM MC markers and matrix product with the INPA weight function) are shown in figure 3, for the plasma profiles shown in figure 4and the fast-ion distribution of figure 8(e). Except for a minor deviation of the signal level near the magnetic axis (R∼1.75 m), coming from the finite grid size, the agreement of both methods in terms of signal output is excellent. Both are also equivalent in computation time, as the calculation of the weight matrix also requires a full FIDASIM 3 Plasma Phys. Control. Fusion 66 (2024) 065025 J Rueda-Rueda et al Figure 2. INPA sensitivity in pitch and z space. (a) Example at R=1.75 m. (b) Width of the marginal distribution in z, as function of R. (c) Equivalent for the case of the pitch angle. Calculated for shot #40 284 t=1.17 s. simulation. However, once the weight matrix is computed, synthetic signals for many distribution functions can be computed rapidly, just requiring a matrix multiplication [59]. 3. INPA phase-space sensitivity function 3.1. Zero order dependency Assuming a mono-energetic NBI, the flux of photons reaching the CCD camera, Φγcan be written as: Φγ=ˆΩ0 dΩˆσCX (vrel)vrel ·F(E,λ0, r+ rp) nn( r)A 4πe− |  r| d0(  r,E)P2(E)drdE(10) where Ω0is the solid angle observed by the INPA, rthe distance taken from the INPA pinhole, Ethe energy of the FI, σCX(vrel)the cross section, at the relative velocity between the neutral and the FI, Fthe fast-ion distribution, λ0the pitch angle explored at the point r, rpthe pinhole position, nnthe neutral density, Athe pinhole area, d0the mean free path of CX neutrals in the plasma and P2a polynomial which takes into account optical transmission, ionization efficiency in the carbon foil and scintillator yield [51]. The weight matrix, in r,E-coordinates would be: W∝ˆΩ0 σCX (vrel)vrelnn( r)A 4πe− |  r| d0(  r)P2(E)dΩ.(11) From this expression, it is clear that the overall response of the INPA diagnostic sensitivity to ion or electron temperature (Ti and Terespectively) is small. As changes in temperatures only affect the signal via changes in the mean free path of the CX neutrals (d0) and given that the energy of the fast CX neutrals is well above the electron and ion temperatures, large changes in Teor Tiimply only moderate changes in d0. Nonetheless, notice that the experimental INPA signal itself will strongly depend on temperature, as it is proportional to the total number of fast-ions, which roughly scales with the slowing down time (as ∼T3/2 e). On the contrary, changes in density strongly affect the diagnostic weight function. There is a double exponential dependency on density: the penetration of the beam neutrals into the plasma, nn( r), and the re-ionization of CX neutrals towards the diagnostic, e− |  r| d0(  r)with d0depending on density. The plasma Zeff (Zeff is defined as: Zeff ≡∑iniZ2 i newhere niand Zidenote the density and charge of the different ion species, respectively, and nethe electron density.) will also affect significantly to the weight function, as for a fixed electron density, different Zeff implies different ion densities and different beam penetration and re-ionization probability. 3.2. Numerical calculation of the INPA weight function Equation (6) can be rewritten as: Sαβ =∑ ων ˜ Wων αβ ⟨Fων⟩∆E∆R =∑ ij Tij αβ ∑ ab Oab ij ∑ ων Ξων ab ⟨Fων⟩∆E∆R(12) where the signal is assumed to be remapped in energy and radius at the scintillator, and the weight matrix presented in the introduction was decomposed in three different matrices: •Tij αβ the translation matrix, presented in [51], which relates camera pixel position with points of the phase space. It only depends on the diagnostic characteristics (foil energy loss and ionization rate, scintillator yield and detector geometry) and the magnetic field orientation at the head •Oab ij the optical model, which relates strike points in the scintillator with their position in the camera sensor, this matrix includes the finite focus and distortion of the optics and the overall transmission factor •Ξων ab , which is the probability of a cell of the phase space given by ων, to contribute at the emission in a point ab of the scintillator. It is heavily affected by plasma parameters and scales as presented in the section 3.1. 4 Plasma Phys. Control. Fusion 66 (2024) 065025 J Rueda-Rueda et al Figure 3. Comparison of the synthetic signals calculated with a full Monte Carlo simulation and using the weight function. (a) 2D synthetic signal. In colour, the Monte Carlo simulation, in grey contours, the signal calculated with the weight function. Dashed green lines indicate the performed cuts along the synthetic signal (shown in subplots b and (c). (b) Energy profiles of the simulations. (c) Radial profile of the simulations. Figure 4. Inputs profiles for the reference simulation in FIDASIM. # 40 284, t=1.17 s. Obtained from integrated data analysis (IDA). The matrix, Tij αβ, can be fully determined by launching Monte Carlo markers as detailed in section 5 of [51]. Model of the distortion included in the matrix Oab ij is adjusted to calibration frames, as also described in [51], and the absolute transmission factor is applied following the relation obtained in the first AUG INPA measurements during MHD quiescent phases. The last matrix is obtained from the synthetic signal where a delta fast-ion distribution function is used as input. This latter calculation is equivalent to the calculations done for other FI diagnostics [30,35]. The gross weight function [48,60] of the diagnostic (the sum of all ˜ Wαβ shown in equation (12)), calculated for the plasma profiles shown in figure 4, can be seen at figure 5(a). Notice how the weight is heavily biased towards the larger radii, due to the NBI neutral density and towards higher energies, due to the scintillator emission (which scales linearly with energy), transmission through the plasma (the factor d0from equation (10), which grows with energy) and efficiency of the carbon foil (which also grows with energy as the foil blocks the pass of low energy particles). At large energies (above 85 keV), it starts to decrease due to the decreasing CX cross sections. The sensitivity of the scintillator pixel centered at R=1.85 m and E=60 keV (and with a width in radius of 1.5 cm and 2 keV in energy) can be seen at figure 5(b). As expected, only a small portion of the phase space (10 keV and 6 cm of FWHM in energy 5 Plasma Phys. Control. Fusion 66 (2024) 065025 J Rueda-Rueda et al Figure 5. Example of weight function of the INPA diagnostic. (a) Gross weight of the INPA diagnostic. (b) Weight for a pixel centered at R=1.85 m and E=60 keV. Calculated for #40 824 and t=1.17 s. and radius, respectively) contributes to the pixel. The size of this weight in energy and radius space reflects the diagnostic resolution. 3.3. Dependence on plasma profiles In order to asses the effect of the plasma profiles in the INPA sensitivity a set of simulations where these profiles were varied was carried out. In each simulation, electron density, temperature and Zeff profiles were varied independently while changes in main ion density, ∆ni, were extracted from quasineutrality. For the ion temperature the following was imposed: ∆Te/Te= ∆Ti/Ti. The results from the scan can be seen in figure 6. Subplots (a–e) show the overall trend in the instrument response for different values of Zeff while subplots (f– k) show the projection of gross weight function when just one of the variables is varied. As explained in section 3.1, changes in plasma temperature have a small effect on the diagnostic response (less than a 5% even for large 25% changes in temperature). On the contrary, changes in the plasma density strongly affect the INPA response. Changes in Zeff have a moderate impact on the overall response of the INPA. This is because the changes in main ion density are related to the changes in Zeff via: ∆ni ni =−∆Zeff Zimp −Zeff (13) where Zimp represent the charge of the main impurity, assumed to be carbon, Zimp =6. This implies that for moderate values of the effective charge, Zeff ∼2, the relative changes in the main ion density would be: ∆ni ni ∼∆Zeff 4. Hence, in the case of ∆Zeff ∼2, a large relative variation in Zeff of 25% implies a moderate change in the main ion density of about 10%. 3.4. Dependence on fast-ion density Four different populations of neutral particles can be distinguished in a tokamak: NBI injected neutrals, thermal neutrals, thermal halo neutrals and fast halo neutrals. The NBI neutrals are those directly injected by the NBI. Thermal neutrals are those naturally present in the plasma, for example those released by the reactor wall. The thermal halo neutrals are a cloud of neutrals originated from CX reactions between the NBI neutrals and the thermal ions [61]. This cloud of neutrals is shifted towards the direction of plasma rotation. The fast halo neutral are a cloud of neutrals originated from the interaction of the FI with the NBI and thermal halo neutrals. Therefore, the signal can be divided into four contributions: the one coming from the interaction of FI with the NBI neutrals, the one coming from the interaction of FI with the thermal halo neutrals, the one coming from the interaction with the fast halo neutrals and the one coming from the interaction with the thermal neutrals. The thermal halo contribution dominates the AUG INPA signal [51]. The density of halo neutrals is related with the plasma main ion density: the larger the 6 Plasma Phys. Control. Fusion 66 (2024) 065025 J Rueda-Rueda et al Figure 6. Changes in the weight function due to plasma profile changes. (a)–(e) Relative changes in the total INPA sensitivity as a function of the changes in temperature and density for each change in Zeff. (f)–(k) Projection of the instrument response of the INPA. (f)–(g) are calculated for ∆ne= ∆Zeff =0, (h)–(i) for ∆Te= ∆ne=0, and (h)–(i) for ∆Te= ∆Zeff =0. 7 Plasma Phys. Control. Fusion 66 (2024) 065025 J Rueda-Rueda et al Figure 7. (a) Changes in the halo density due to the increase of the fast-ion concentration. (b) Changes in the INPA weight function due to the changes in the FI concentration. thermal ion density, the larger the halo neutral density. Hence, for a fixed electron density and Zeff, if the concentration of fast-ions grows, the thermal ion density decreases and hence the halo density decreases; thus, reducing the INPA sensitivity. This reduction is not compensated by the increase of the fast halo neutral, as CX reaction cross sections are smaller at higher energies, thus, the fast halo contribution, per neutral, to the sensitivity is smaller than the thermal halo contribution. A scan in fast-ion density was performed, reaching up to 30% of the core electron density. For all cases, a flat fastion profile was assumed. As can be observed in figure 7, the INPA sensitivity decreases up to 40% due to the thermal halo dilution. However, the INPA signal would still be larger with the larger fast-ion concentration, as the increase due to having more fast particles is larger than the decrease due to the smaller sensitivity. If the concentration of FI in the plasma is large, the INPA inversions should be done as an iterative process: a first inversion should be performed using an estimated concentration of fast-ion to calculate the WF; secondly, the INPA weight function should be recalculated considering the observed amount of FI. The process needs to be repeated until a convergence is reached. Typically, two inversions are enough to obtain changes below 10% on the reconstructed distribution. 4. Inverse problem: inferring the FI distribution The inverse problem is the inference of the fast-ion distribution from the measurements using the forward model described in the previous section. The goal is to determine the unknown distribution in equation (9) from the measurements. A naive inversion, i.e. using the linear regression, is ill-conditioned. Various regularization techniques can be used to allow inversion as done for CTS [35] or FIDA [38] for example. In this work, two inversion techniques were considered to perform the regularization: 0th-order Tikhonov and Elastic Net. For 0th-order Tikhonov, the cost function to minimize can be written as: C(F) = ||WF −S||2 2+α||F||2 2(14) where || ||2, indicates the L2norm of the array and αis the regression hyper-parameter. For the case of Elastic Net, it can be written as: C(F) = ||WF −S||2 2+αl1||F||2 1+1 2α(1−l1)||F||2 2(15) where || ||1indicates the L1norm of the array, and l1is a second hyper-parameter which balances the relative strength of the 1-norm and 2-norm of the distribution in the regularization. The 0th-order Tikhonov regularization promotes smooth solutions, whereas the Elastic Net promotes sparse solutions. In both inversions, the fast-ion distribution is obtained by minimizing the cost function: Fα=argminF(C(F)) (16) constrained to positive values of F, to avoid non-physical solutions. Having just one INPA installed at AUG, it is not possible to infer the 4D distribution function as there is no possibility of unravelling the line integration on λand z, presented in section 2, with enough accuracy. Hence, our aim is to reconstruct the average distribution ⟨F⟩INPA (E,R). 8 Plasma Phys. Control. Fusion 66 (2024) 065025 J Rueda-Rueda et al functions from ion cyclotron emission data using deep neural networks Rev. Sci. Instrum. 92 053528 [33] Schmidt B S, Salewski M, Reman B C G, Dendy R O, Dong Y, Järleblad H, Moseev D, Ochoukov R, Rud M and Valentini A 2023 Velocity-space sensitivity and inversions of synthetic ion cyclotron emission Phys. Plasmas 30 092109 [34] Egedal J and Bindslev H 2004 Reconstruction of gyrotropic phase-space distributions from one-dimensional projections Phys. Plasmas 11 2191 [35] Salewski M et al 2012 Tomography of fast-ion velocity-space distributions from synthetic CTS and FIDA measurements Nucl. Fusion 52 103008 [36] Salewski M et al 2013 Combination of fast-ion diagnostics in velocity-space tomographies Nucl. Fusion 53 063019 [37] Salewski M et al 2016 High-definition velocity-space tomography of fast-ion dynamics Nucl. Fusion 56 106024 [38] Jacobsen A S et al 2016 Inversion methods for fast-ion velocity-space tomography in fusion plasmas Plasma Phys. Control. Fusion 58 045016 [39] Jacobsen A S, Salewski M, Geiger B, Korsholm S B, Leipold F, Nielsen S K, Rasmussen J, Stejner M and Weiland M (ASDEX Upgrade Team) 2016 Benchmark and combined velocity-space tomography of fast-ion D-alpha spectroscopy and collective thomson scattering measurements Plasma Phys. Control. Fusion 58 042002 [40] Weiland M, Geiger B, Jacobsen A S, Reich M, Salewski M and Odstrcˇil T (ASDEX Upgrade Team) 2016 Enhancement of the FIDA diagnostic at ASDEX Upgrade for velocity space tomography Plasma Phys. Control. Fusion 58 025012 [41] Weiland M et al 2017 Phase-space resolved measurement of 2nd harmonic ion cyclotron heating using FIDA tomography at the ASDEX Upgrade tokamak Nucl. Fusion 57 116058 [42] Salewski M et al 2017 MeV-range velocity-space tomography from gamma-ray and neutron emission spectrometry measurements at JET Nucl. Fusion 57 056001 [43] Madsen B, Salewski M, Huang J, Jacobsen A S, Jones O and McClements K G (M Team) 2018 Velocity-space tomography using prior information at MAST Rev. Sci. Instrum. 89 10D125 [44] Madsen B, Salewski M, Heidbrink W, Stagner L, Podest` a M, Lin D, Garcia A, Hansen P and Huang J (DIII-D Team) 2020 Tomography of the positive-pitch fast-ion velocity distribution in DIII-D plasmas with Alfvén eigenmodes and neoclassical tearing modes Nucl. Fusion 60 066024 [45] Madsen B et al 2020 Fast-ion velocity-space tomography using slowing-down regularization in EAST plasmas with coand counter-current neutral beam injection Plasma Phys. Control. Fusion 62 115019 [46] Su J et al 2021 Reconstructions of velocity distributions from fast-ion D-alpha (FIDA) measurements on EAST Plasma Sci. Technol. 23 095103 [47] Du X D, Van Zeeland M A, Heidbrink W W, Stagner L, Wingen A, Lin D J and Collins C S 2020 Resolving the fast ion distribution from imaging neutral particle analyzer measurements Nucl. Fusion 60 112001 [48] Salewski M et al 2018 Alpha-particle velocity-space diagnostic in ITER Nucl. Fusion 58 096019 [49] Rueda-Rueda J, Garcia-Dominguez J, Viezzer E and Schneider P A 2021 Design and simulation of an imaging neutral particle analyzer for the ASDEX Upgrade tokamak Rev. Sci. Instrum. 92 043554 [50] Garcia-Dominguez J, Rueda-Rueda J, Viezzer E, Schneider P A, Ayllon-Guerola J, Garcia-Munoz M, Hidalgo-Salaverri J, Mancini A, Videla M and Herrmann A 2022 Imaging neutral particle analyzer engineering design and installation for the ASDEX upgrade tokamak IEEE Trans. Plasma Sci. 50 4138 [51] Rueda-Rueda J et al 2024 Commissioning of the imaging neutral particle analyser for the ASDEX Upgrade tokamak Plasma Phys. Control. Fusion 66 035008 [52] Du X, Van Zeeland M, Heidbrink W and Su D 2018 Development and verification of a novel scintillator-based, imaging neutral particle analyzer in DIII-D tokamak Nucl. Fusion 58 082006 [53] Lin D, Du X, Heidbrink W and Zeeland M V 2020 Validation of the imaging neutral particle analyzer in nearly MHD quiescent plasmas using injected beam ions on DIII-D Nucl. Fusion 60 112008 [54] Geiger B et al 2020 Progress in modelling fast-ion D-alpha spectra and neutral particle analyzer fluxes using FIDASIM Plasma Phys. Control. Fusion 62 105008 [55] N R Laboratory (ed) 1970 Proc. 4th Conf. on Numerical Simulation of Plasmas (Naval Research Laboratory) pp 3–67 [56] Garcia-Dominguez J, Rueda-Rueda J, Viezzer E, Schneider P A, Ayllon-Guerola J, Garcia-Munoz M, Hidalgo-Salaverri J, Mancini A, Videla M and Herrmann A 2023 Commisioning Submitted [57] Hawryluk R J 1981 An empirical approach to tokamak trans-port Phys. Plasmas Close Therm. Cond. 119 [58] TRANSP Code 2018 (https://doi.org/10.11578/dc.201 80627.4) [59] Salewski M et al 2018 Deuterium temperature, drift velocity, and density mea-surements in non-Maxwellian plasmas at ASDEX Upgrade Nucl. Fusion 58 036017 [60] Schmidt B S et al 2024 A new FILDSIM model for improved velocity-space sensitivity modelling and reconstructions Plasma Phys. Control. Fusion 66 045004 [61] Geiger B 2012 Fast-ion transport studies using FIDA spectroscopy at the ASDEX Upgrade tokamak PhD Thesis Ludwig-Maximilians-Universität München 15