# Characterization of W production during ICRF operations: experiments and modeling

Guillaume Urbanczyk, R. Ochoukov, V. Bobkov, S. Shiraiwa, R. Bilato, N.

Bertelli, W. Tierens, L. Colas, R. Dux, M. Dreval, et al.

► To cite this version:

Guillaume Urbanczyk, R. Ochoukov, V. Bobkov, S. Shiraiwa, R. Bilato, et al. Characterization of W production during ICRF operations: experiments and modeling. Nuclear Fusion, 2025, 65 (4), pp.046018. 10.1088/1741-4326/adbd52. hal-05018598

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Submitted on 3 Apr 2025

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# Characterization of W production during ICRF operations: experiments and modeling

To cite this article: G. Urbanczyk et al 2025 *Nucl. Fusion* 65 046018

View the [article online](#) for updates and enhancements.

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# Characterization of W production during ICRF operations: experiments and modeling

G. Urbanczyk<sup>1,2,*</sup>, R. Ochoukov<sup>1</sup>, V. Bobkov<sup>1</sup>, S. Shiraiwa<sup>3 ID</sup>, R. Bilato<sup>1 ID</sup>, N. Bertelli<sup>3 ID</sup>, W. Tierens<sup>4 ID</sup>, L. Colas<sup>5 ID</sup>, R. Dux<sup>1</sup>, M. Dreval<sup>6</sup>, L.F. Lu<sup>7</sup>, W. Helou<sup>8</sup>, the ASDEX Upgrade Team<sup>a</sup> and the EUROfusion Tokamak Exploitation Team<sup>b</sup>

E-mail: guillaume.urbanczyk@ipp.mpg.de and roberto.bilato@ipp.mpg.de

Received 7 December 2024, revised 12 February 2025

Accepted for publication 6 March 2025

Published 20 March 2025

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CrossMark

## Abstract

For successfully heating plasma with waves in the ion cyclotron range of frequencies (ICRFs), mitigating impurity production is just as crucial as maximizing power coupling, especially in high-Z environments (Urbanczyk et al 2021 *Nucl. Mater. Energy* 26 100925). ICRF can effectively deposit energy on ions, modify turbulence-driven transport, and enhance fusion reaction efficiency, but only when its power coupling has minimal impact on impurity production. To do so, one must rely on a toroidal array of at least three active elements excited with appropriate phasing and power ratio to reduce the currents induced on the antenna frame below levels critical for physical sputtering. In contrast to classic two-strap antennas, which are optimized for dipole phasing with equal power on both straps, three-strap antennas in ASDEX Upgrade (AUG)—but also four-strap antennas in JET, Alcator C-Mod, SPARC and ITER—offer the possibility to act also on the power ratio between the central and outer straps. With optimal settings, impurity production can be reduced substantially, making the ICRF compatible with the high-Z wall (Bobkov et al 2017 *Plasma Phys. Control. Fusion* 59 014022). This paper explores the characteristics of the AUG three-strap antennas in terms of impurity production, as well as the key role of plasma composition in this process. Numerical simulations were performed using SSWICH and Petra-M (finite element codes) to quantify impurity

<figure><img src="image_7.png" /></figure>

<footnote n="1"><sup>1</sup> Max-Planck-Institut für Plasmaphysik, Boltzmannstrasse 2, D-85748 Garching, Germany</footnote>

<footnote n="2"><sup>2</sup> Institut Jean Lamour UMR 7198 CNRS—Université de Lorraine, 2 allée André Guinier, F-54011 Nancy, France</footnote>

<footnote n="3"><sup>3</sup> Princeton Plasma Physics Laboratory, Princeton, NJ 08540, United States of America</footnote>

<footnote n="4"><sup>4</sup> Oak Ridge National Laboratory, Oak Ridge, TN, United States of America</footnote>

<footnote n="5"><sup>5</sup> CEA, IRFM, F-13108 Saint Paul-Lez-Durance, France</footnote>

<footnote n="6"><sup>6</sup> Institute of Plasma Physics, National Science Center, Kharkov Institute of Physics and Technology, Kharkov, Ukraine</footnote>

<footnote n="7"><sup>7</sup> Southwestern Institute of Physics, PO Box 432, Chengdu 610041, China</footnote>

<footnote n="8"><sup>8</sup> ITER Organization, Route de Vinon-sur-Verdon, CS 90 046, 13067 St. Paul, Lez Durance Cedex, France</footnote>

<footnote><sup>a</sup> See Zohm et al 2024 (https://doi.org/10.1088/1741-4326/ad249d) for the ASDEX Upgrade Team.</footnote>

<footnote><sup>b</sup> See Joffrin et al 2024 (https://doi.org/10.1088/1741-4326/ad2be4) for the EUROfusion Tokamak Exploitation Team.</footnote>

<footnote>* Author to whom any correspondence should be addressed.</footnote>
production and compare with experimental results. Energies of ions falling on antenna limiters (measured with probes) are well predicted by both codes. These tools are then used to further describe the source of the impurity, namely the gross erosion of tungsten from an ICRF antenna, for different plasma mixtures. Results are also compared to spectroscopy data. Ultimately, we show that deleterious effects of the ICRF on plasma surface interactions will be weaker in plasmas containing larger fractions of highly ionized heavier low-Z impurity, which is typically relevant for experiments relying on impurity seeding.

Keywords: ICRF heating, tungsten erosion, RF simulation, plasma-surface interactions, impurity mitigation

(Some figures may appear in colour only in the online journal)

# 1. Introduction

Radiofrequency-induced impurity release and the associated sputtering of plasma-facing components have been recognized as critical issues since the early days of fusion research. Fundamental studies, such as those presented in Stix's classic work [1], laid the groundwork for understanding the formation of RF sheaths. In the late 1980s, experimental and theoretical investigations began to unravel the complex interplay between RF sheath rectification and impurity production. Grigor'eva et al [2] provided early insights into the mechanisms of metal impurity release in torsatron. Concurrently, pioneering experiments on the W7-A Stellarator with a proposal for toroidally broad antennas for the ion cyclotron resonance heating (ICRH) underscored the challenges posed by RF-induced potentials [3]. Together, these foundational works have not only highlighted the persistent challenges of impurity control in ion cyclotron range of frequency (ICRF)-heated discharges, but have also guided modern strategies in antenna design and plasma-facing component protection.

Today, most mainstream designs of future fusion-reactor-relevant tokamaks consider it mandatory for any plasma-facing material to be made of high-Z materials, with tungsten (W) being the most likely candidate. When using ICRF in high-Z environments, focusing solely on maximizing wave coupling is not sufficient to achieve better performance in long discharges [4, 5]. It is crucial to also minimize parallel RF electric fields to keep impurity production below critical levels.

Currently, the most efficient technique to minimize parallel RF electric fields is exposed under [6]; it consists in setting the phases and amplitudes of RF currents on the antenna straps in such a way that each strap induces currents of similar amplitude but opposite directions on the limiters, achieving net cancellation. This technique has been successfully applied to the ASDEX Upgrade (AUG) using the three-strap AUG antenna, extended to the four-strap Alcator C-Mod field-aligned antenna [7], and is envisaged for ITER (see [8] and references therein) and SPARC.

It is important to note that two-strap antennas with passive limiters cannot employ this cancellation technique. As detailed in [9], proximity effects lead to a situation where reducing the potential on one limiter inherently increases it on the other, ultimately worsening the overall conditions. In other words,

beyond operating with symmetric power in dipole phasing (180°), two-strap antennas have no additional means to mitigate the fields induced on their plasma-exposed structures, making their operation in high-Z environments particularly challenging. In contrast, effective cancellation of RF currents requires an array of at least three active elements—whether these are straps or, potentially, active limiters.

Moreover, while mitigating the RF electric field is critical, it is not the only factor contributing to material erosion. The second key ingredient is the flux of particles impinging on the limiter, whose composition and density have a tremendous influence on the sputtering yield. Thus, controlling impurity production also involves managing the composition and intensity of these particle fluxes.

In this study, we focus on two AUG discharges featuring different excitations of the three-strap ICRF antennas. Both discharges operate in dipole phasing (180°) but differ in the balance of power between the central and outer straps (well-balanced versus poorly balanced).

Section 2 presents experimental results that illustrate the importance of optimizing the antenna excitation to mitigate ion energies and impurity production.

In section 3, we employ the finite element codes—SSWICH [10, 11] and Petra-M [12]—to reproduce key RF-related observations. Rather than focusing solely on the parallel electric field, our simulations capture the nonlinear physics of the RF sheath, which converts the oscillating RF potentials into a steady rectified potential ($V_{DC}$) on the limiters. This rectified potential serves as the best proxy for successful ICRF operation because it directly correlates with the ion energy measured in section 2. By accurately deriving $V_{DC}$ from the RF electric fields and potentials, the simulations enable a direct quantitative comparison with experimental ion energy profiles, confirming the efficacy of optimized antenna excitation in mitigating sheath potentials.

Section 4 extends our simulation efforts to include the second critical aspect of the sputtering. Here, we incorporate a model that accounts for various plasma compositions and local densities to assess their impact on the sputtering yield of the particle flux impinging on the limiters. An increase factor, $\Lambda$ (defined in equation (4)), is introduced to quantify how much more tungsten is eroded when powering an ICRF antenna under different plasma conditions. This analysis highlights the
interplay between RF field effects and the plasma environment, offering key insights into impurity production control. Ultimately, we show that in addition to the beneficial efforts made to optimize the RF settings of the system, ICRF-induced impurity production will also be weaker in plasmas seeded with heavier low-Z impurity, which is foreseen as routine operation for future devices like ITER.

## 2. Experiments in AUG

### 2.1. Experimental setup

AUG is a medium-sized tokamak with a full-W wall (except for the boron-coated limiters of the two-strap ICRF antennas which are not considered in this work). In each discharge of the present study (L-mode), plasma was confined by a toroidal magnetic field of $B_T = -2.5$ T and heated by a pair of three-strap ICRF antennas powered by 350 kW at 36.5 MHz via the 3 dB splitters (cf figure 4 in [13]). Antenna outer straps (cf down arrow in figure 1) are powered by one generator, and the central strap by another generator (cf up arrow in figure 1), allowing a change to the power ratio between inner and outer straps ($P_{cent}/P_{out}$). The plasma current $I_p$ was scanned in seven steps between 0.4 and 1 MA (cf figure 2); our goal was here to change the tilt-angle of the magnetic field lines. As in the studies reported in [14, 15], on each $I_p$ step, the reciprocating retarding field analyzer (RFA) (mounted on the AUG midplane manipulator) plunged radially. For each plasma current step, the probe magnetically connects to different poloidal heights of the neighboring antenna limiter (figure 3), and we can reconstruct a 2D map (radial-poloidal) of the mean parallel ion energy $<W_{II,i}>$ in the bottom left corner of the three-strap antenna (cf bluish region in figure 1). Since this quantity is assessed from an integral of the current-voltage characteristics, it is fairly robust and insensitive to changes in density within a given range for which the sensitivity of the measurements was optimized [16]. In the next section, the plasma potential rectified by the presence of RF-sheath ($V_{DC}$) will be calculated both with Petra-M and SSWICH codes, respectively explained in sections 3.1 and 3.2. $V_{DC}$ representing the potential drop across the sheath, namely the acceleration that ions undergo when crossing the sheath, will be directly compared to the RFA measurement of $<W_{II,i}>$.

In addition, five visible spectroscopy lines of sight are monitoring the top left corner of the three-strap antenna (cf reddish region in figure 1), measuring the intensities of WI (407.4 nm) and DI (410 nm) spectral lines. These intensities are converted into W outflux and the effective W sputtering yield using the procedure described in section 2.1. Similarly, in section 4, we will compare these measured quantities with the calculated ones.

We will compare two discharges, during which each ICRF antenna coupled 350 kW, powered in dipole phasing (180°), with different power balances as illustrated in figure 1:

$$ (a) P_{cent}/P_{out} = 3/2 \quad (#37147) $$

$$ (b) P_{cent}/P_{out} = 1/8 \quad (#37150). $$

### 2.2. Experimental results

Parallel ion energy measured by RFA shows features consistent with the antenna excitations (figure 4), based on previous studies [13]. When the excitation is presumably optimized to minimize the field rectification ((a)—#37147), the ion energy is indeed well-mitigated ($<W_{II,i}> <60$ V). Energies up to 110 V are, however, observed when the power balance is not optimized ((b)—#37150). While these energies characterize the ion acceleration through the RF sheaths—which is a good criterion to assess rather if the ICRF antenna design and excitation are optimal (the smaller the better)—they cannot serve as figure of merit to give a final verdict on the impurity production issue. Hereafter, we will therefore go one step forward and analyze visible spectroscopy data, to also take into account the composition of the plasma and the influx of ions on the erosion of tungsten on the antenna frame.

Impurity outflux (in our case tungsten outflux from the limiter) is the result of each ion species influx on the target material $\Gamma_{ion}^{in}$ multiplied by their respective sputtering yields $Y_{ion(i) \to W}$ (probability to sputter an atom see [17]):

$$ \Gamma_{W}^{\text{out}} = \sum_{i} \Gamma_{\text{ion}(i)}^{\text{in}} \cdot Y_{\text{ion}(i) \to \text{W}}. \quad (1) $$

As far as experiments with deuterium plasma are concerned (see AUG [18], Alcator C-Mod [19], Tore Supra [15]), regardless of the plasma composition, it is usually assumed that the deuterium flux is representative of all particle fluxes, so that a proxy of the average efficiency of an ion to sputter a W atom (the so-called effective sputtering yield $Y_{eff}$) can be estimated as follows:

$$ Y_{\text{Eff}} = \frac{\Gamma_{W}^{\text{out}}}{\Gamma_{\text{ions}}}. \quad (2) $$

Note this assumption is not always reasonable; typically, in devices relying on wall-conditioning, or simply where the pumping capacity is not optimal, low-Z materials heavier than deuterium, despite smaller fractions, dominate the erosion mechanism (e.g. oxygen in WEST [20]). In AUG deuterium-hydrogen plasmas, boronizations (boron coating) are performed once to twice per month. Boron is therefore expected to be the main contributor to sputtering. Its abundance roughly decreases from a few percent right after a boronization down to around 0.01% after several hundreds of discharges. Since the experiment of the present study was performed about 100 discharges after the last boronization, we expect less than 1% B in the mixture. Knowing precisely this concentration to accurately derive the effective sputtering yield proves challenging. Checking the sensitivity of the conclusion to the fraction of the different elements in the plasma mixture is therefore important, as addressed in section 4.

In addition, determining a given ion flux is not straightforward. The light received from the plasma is collected by endoscopes and carried through optical fibers to the spectrometer. From calibrated line of the spectra, the photon flux emitted by the concerned specie $\phi_{ion}$ [Ph m$^{-2}$ s$^{-1}$ sr$^{-1}$] is extracted and converted in particle flux rates $\Gamma_{ion}$ [atm m$^{-2}$ s$^{-1}$]
<figure><img src="image_8.png" /><figcaption>**Figure 1.** Three-strap ICRF antenna in ASDEX Upgrade. Arrows indicate the currents direction at a given time on the straps, here in the case of a dipole phasing (180°) with a power ratio (a) $P_{cent}/P_{out} = 3/2$ corresponding to the optimal excitation of our study, and (b) $P_{cent}/P_{out} = 1/8$ corresponding to an unbalanced excitation. On the left limiter, the top reddish corner is monitored by five visible spectroscopy lines of sight measuring WI line, and the bottom bluish corner is monitored by the RFA probe.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Figure 2.** On the left, AUG top cross-sectional view, with reciprocating RFA with reference discharge (#37147) on the right. ICRF powers of a three-strap antenna were modulated during a stepped scan of the plasma current with an RFA plunge on each step. Core (black) and edge (blue) line averaged densities also change as the plasma current is scanned.</figcaption></figure>

using S/XB coefficients. S/XB are functions of the local electron temperature and density and can be assessed from ADAS database [21, 22]. For W ions in the scrape-off-layer (SOL) plasma with $T_e \approx 20$ eV and $n_e \approx 10^{18} m^{-3}$, we typically use $S/XB_W = 20$, leading to the tungsten outfluxes in figure 5, expressed in atoms $m^{-2} s^{-1}$.

To further ease data interpretation and provide an intuition on how local tungsten sources increase when the ICRF antenna is powered, we further integrate these rates on the surface of the limiter wetted by the plasma. This leads to a tungsten total

outflux for each limiter, expressed in [atm s$^{-1}$ limiter$^{-1}$],

$$ \Gamma_{Wtot} = \iint_{\text{Limiter}} \Gamma_{W}. \qquad (3) $$

This quantity can be assessed when the ICRF antenna is inactive (cf black case in figure 6(a)) and powered (colored cases in figure 6(a)). Finally, taking the ratio of both tells us how much more tungsten is emitted per limiter when an ICRF antenna is powered,
<figure><img src="image_10.png" /><figcaption>**Figure 3.** On the left, outer wall view of AUG with the RFA mounted on the midplane manipulator, which plunges radially at different plasma currents (cf figure 2), and magnetically connects to different poloidal heights of the three-strap ICRF antenna left limiter. The colormap represents RFA measurements of the mean parallel ion energy <W<sub>II,i</sub>> on field lines connected to the active antenna—quantity in principle comparable to V<sub>DC sheath</sub>.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>**Figure 4.** Mean parallel ion energies <W<sub>II,i</sub>> nearby bottom left corner of three-strap ICRF antenna measured by RFA probe during I<sub>p</sub> scan. Both cases stand for dipole phasing with different power ratio between center and outer straps, respectively (a) P<sub>cent</sub>/P<sub>out</sub> = 3/2 and (b) P<sub>cent</sub>/P<sub>out</sub> = 1/8.</figcaption></figure>

$$ \Lambda = \Gamma_{W_{tot}}^{\text{ICRH}\to\text{ON}} / \Gamma_{W_{tot}}^{\text{ICRH}\to\text{OFF}}. \quad (4) $$

Λ quantifies how much more tungsten is sputtered from the limiter when the ICRF antenna is powered (cf legends of figure 6(a)). One must yet remain careful when jumping to conclusions on plasma contamination because this factor is only representative of the source term, regardless of W transport effects. In particular, one cannot expect strict consistency between this factor and tungsten concentrations in the core (figures 5 and 6), without accounting in the analysis, for the different penetration efficiency of all the sources [23]. Nonetheless, the different radial location of all plasma facing components in the vessel adds another layer of complexity, specific to each device, preventing from strictly generalizing the analysis.

Tungsten erosion and contamination of the core vary very consistently with ICRF powering. By comparing blue (optimized) and red (not optimized) curves in figure 6, impurity production can indeed be mitigated with the right power balance, to compensate the image currents in the limiters induced by each strap. However, by comparing the blue (optimized ICRF) with the black (P<sub>ICRF</sub> = 0) curves in figure 6(a), we see that even with an optimized excitation, powering the ICRF still leads to an order of magnitude increase in the local source (Λ<sub>37147</sub> = 12.2). We believe it is the case partially because of the composition of the plasma, for which the level of sputtering without ICRF remains particularly low, and suddenly jumps by several orders of magnitude when the antenna is powered. This argument is explained in further detail in the third section of the paper.
<figure><img src="image_12.png" /><figcaption>**Figure 5.** Colormaps of tungsten outfluxes [atoms m⁻² s⁻¹] assessed from neutral tungsten (WI line) measurements by visible spectroscopy along the three-strap ICRF antenna top left corner (cf red area in figure 1) for the cases corresponding to figure 4. On top of it are superposed the ICRF power modulations (white dotted lines) and the core tungsten density around Tₑ = 1 keV, assessed from treatments combining core tungsten spectroscopy, temperature and density measurements [24].</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>**Figure 6.** Comparison of each excitation case, respectively in (a) the edge; with poloidal profiles along ICRF antenna limiter (cf red region on the top left corner in figure 1) of the tungsten outflux assessed by averaging visible spectroscopy data in the dotted intervals of figure 5 (4.3–4.4 s) and (b) the core; with time evolutions of the tungsten concentration around Tₑ = 1 keV, assessed from treatments combining core tungsten spectroscopy, temperature and density measurements [24].</figcaption></figure>

Figure 6(b) also shows that, the smaller the plasma current, the faster the tungsten content increases in the core. We first thought that this may result from modification of the transport, but after investigating, the transport was rather constant along the discharge. Instead, we believe this is an effect of the W source itself. This can be seen on figure 5, but only partially because only one corner of one antenna was monitored. The influence of the plasma current, or more precisely the magnetic field tilt-angle, is believed to be negligible, but it may actually play a role. This aspect is currently under investigation and will be discussed in a dedicated study.

Note that some discrepancies are inevitable, since AUG is a full tungsten tokamak, neither limiters of active ICRF antennas nor magnetically connected objects are the only contributors to the core contamination by tungsten. Trends observed in visible spectroscopy (edge) are therefore correlated to some extent with those observed on SXR spectroscopy (core), but

other sources like the divertor and other limiters also contribute. Disentangling contributions from various sources to plasma contamination is very important to shed light on the various possibilities to optimize ICRF antennas and their operation, but doing so requires dedicated experiment [4, 5, 18, 23, 25–28] which fall out of the scope of the present paper.

### 3. RF simulations

The goals of this section are (i) to validate RF simulations against experiments and (ii) to compare modeling results from two different RF codes, Petra-M and SSWICH. For each code, basic information on the physics they contain are provided first; the key inputs (excitation and density profiles figure 7) and their numerical requirements. Results are then shown and compared. Finally, for different assumptions on the plasma
<figure><img src="image_14.png" /><figcaption>**Figure 7.** Density profiles constructed from reflectometry and lithium beam diagnostics data, measured within an interval of 200 ms. In the simulations, to avoid numerical issues associated to the lower hybrid resonance ($n_e = 3.2 \cdot 10^{16} \text{m}^{-3}$ at 30 MHz, cf black dots), minimal density was fixed at $10^{17} \text{m}^{-3}$ (cf green dots).</figcaption></figure>

composition, the production of impurities is assessed and compared to experiments in section 4.

### 3.1. Petra-M code

Petra-M is an open-source finite element code under the RF SciDAC framework [29], using MFEM library for the finite element discretization (mesh) [30], and $\pi$Scope for data visualization [31]. In studies relying on the old version of the code, RF sheath boundary conditions (RF-SBC) were not taken into consideration [32]. Actually, until [12], non-linear RF-SBCs were never implemented in any antenna 3D code. Petra-M so far distinguishes itself from other tools as it allows the application RF SBCs directly on limiters (2D surfaces), thanks to a reformulation of the RF sheath physics using a magnetic scalar potential together with a Helmholtz decomposition. On the surfaces where RF SBCs are applied (limiters in our case), the RF potential ($VRF$) is calculated. Since the RF contribution to potentials is in most cases much larger than the thermal one (e. $VRF \gg T_e = 10$ eV), the recertified potential ($V_{DC}$) is assumed to change linearly with $V_{RF}$ ($V_{DC} \approx 3 \cdot k \cdot T_e + 0.6 \times V_{RF}$) as explained in section 2.2 of [33]. Models were solved on the Perlmutter supercomputer [34] typically requiring about 5 min and 1Tb of RAM to solve the 13 million degrees of freedom problem.

Concerning the key inputs in Petra-M, we try to keep them as close as possible to the experimental ones, they yet differ in the following aspects:

- The antenna 3D geometry was flat instead of curved (cf figure 8(d) & [11]). This choice was made, essentially, to allow the comparison of Petra-M results with those from SSWICH, where a simplified geometry must be used (cf 2D slice in column ② of figure 8). Petra-M is, however, sophisticated enough to perform the same simulation with a more realistic curved geometry of the antenna, which will be addressed in a separate study.

- Density is measured from the core to the edge by combining reflectometry and Lithium beam diagnostic data. For high densities in the core, measurements are precise, typically down to a level a bit below the fast wave cutoff density. Their precision drops drastically in the far SOL, where error bars rise in the order of $10^{18} \text{m}^{-3}$. Since densities below $10^{18} \text{m}^{-3}$ become uncertain, we took the average values of several profiles and used them as a proxy for all simulations (cf green profile in figure 7), only changing the antenna excitation. This method ensures that the green profile is representative of the average situation, neglecting uncertain variations at the very edge and guaranteeing a smooth transition to the minimum density ($10^{17} \text{m}^{-3}$). While the fast wave cutoff density is not the only one to play a role on waves coupling, it is, usually, the one with the largest influence; note that its location does not move (cf blue circle in figure 7), so that all profiles can, in first approximation, be considered equivalent from the perspective of the coupling. To guarantee the good behavior of finite element simulations, densities must remain above the lower hybrid resonance and sharp transitions must be avoided. Sharp transitions are, typically, a problem for red profiles which reach the minimum density too abruptly (cf red triangles in figure 7). When using such profiles in the simulations, surface waves were parasitically excited and power was reflected at the abrupt transition, leading to numerical aberrations. Instead of working with instantaneous profiles, we therefore average them over some time interval to get rid of low-density variations, whose measurements are often uncertain in most tokamaks. To tackle the problem of the lower hybrid resonance singularity, one option would be to implement the hot plasma dielectric tensor, which is beyond the scope of our numerical tools, and one can also add collisions, but their frequency remains speculative. Finally, dealing with sharp variations of the density could be handled with enough numerical resources to refine the mesh enough to smoothly capture inhomogeneities.

- The power excitation on each coaxial port does not take the influence of the matching circuit into account, but corresponds to the net power coupled in the experiment ($P_{\text{injected}} - P_{\text{reflected}}$).

### 3.2. SSWICH code

The Self-Consistent Sheaths and Waves for Ion Cyclotron Heating (SSWICH) is a finite element open-source code based on COMSOL and Livelink with Matlab. Details on the slow-wave version used in the present study can be found in [10]. Details on the full-wave version can be found in the latter [35]; note this ‘full-wave’ version showed discrepancies likely coming from the fast wave, whose $k$ vector changes in the poloidal direction, making the poloidal multi 2D approach somewhat unreasonable. A 3D version would therefore be required to capture the influence of each wave mode on the sheath physics, which is ongoing [36]. Hence, our choice in the present study is to use the slow-wave version described in figure 8.
<figure><img src="image_15.png" /><figcaption>Figure 8. Key steps of a typical SSWICH simulation: (1) extract a 2D (poloidal, toroidal) E-field map at the antenna aperture from RAPLICASOL (a COMSOL-based 3D antenna code without sheath boundary conditions (2) along the poloidal direction and aligned with B field lines, slice this 2D map into 1D E field distributions and feed them to SSWICH multi 2D simulations with sheath boundary conditions (3) combine results from each slice into 3D distributions. Like in figure 1, the area probed with RFA during the experiment is materialized by the blue dotted square on the bottom right map.</figcaption></figure>

1) Part ① consists in running a 3D antenna code (ex: RAPLICASOL [37], TOPICA [38–40], HFSS [41], Petra-M [12]) with metallic boundary conditions, and the antenna in vacuum, some distance away from the plasma or dielectric; this is because so far, non-linear RF-SBCs on a 2D surface were never successfully implemented in COMSOL (on which SSWICH relies). This allows us to retain key details of the 3D geometry (e.g., Faraday screen) and extract a 2D (poloidal, toroidal) electrical (E) field map at the antenna aperture (between the Faraday screen and the leading edge of the limiter).

2) Part ② consists in slicing this E field map into 1D distributions aligned with the B field lines. At each poloidal height, a 2D simulation is performed, using a simplified geometry, fed with a 1D E-field distribution and facing a plasma surrounded by perfectly matched layers[42] to emulate radiations to infinity (no reflection). This simplification of the geometry surfaces which are either parallel or perpendicular to magnetic (B) field lines removes the possibility of direct resonance cone excitation from the limiters [43]. Each 2D simulation consists of three steps:

a. solving the wave propagation equation reduced to a slow wave on the whole domain with linear boundary conditions:

$$ \varepsilon_{//} \Delta_{//} E_{//} + \varepsilon_{\perp} \Delta_{\perp} E_{//} + k_{0}^{2} \varepsilon_{//} \varepsilon_{\perp} E_{//} = 0 \quad \rightarrow \mathbf{E}_{//} = \mathbf{E}_{\text{RF}}. $$

b. Determine RF-sheath voltage by integrating $E_{RF}$ on surfaces where SBCs are applied:

$$ -\nabla_t V_{\text{RF}} = \vec{E}_t, \quad V_{\text{RF}} = -i \frac{E_t}{k_z} \quad \rightarrow \mathbf{V}_{\text{RF}}. $$

With $\vec{B} = B_0 \cdot \vec{e}_z$

c. compute plasma DC potential rectification caused by non-linear SBCs applied on the limiters:

$$ \nabla \cdot \mathbf{J} = 0, \mathbf{J} = \sigma \nabla V_{\text{DC}} \quad \rightarrow \mathbf{V}_{\text{DC}}. $$

With boundary conditions on each surface:

$$ \left\{ \begin{array}{l} \text{Metallic surfaces} \triangleright \mathbf{J} \cdot \mathbf{n} = 0 \\ \text{Sheath} \qquad \triangleright J_n = J_{is}^{\perp B} |nx| \left( 1 - \min \left( \frac{J_{is}^{\perp B}}{J_{is}^{\perp B}}, \exp \left( \frac{e(V_f + V_b - V_{\text{DC}})}{K_B T_e} \right) \right) \right) . \\ \text{Inner plasma} \qquad \triangleright V_{\text{DC}} = V_f \end{array} \right. $$
<figure><img src="image_16.png" /><figcaption>**Figure 9.** DC sheath potentials along AUG-three-strap antenna lateral limiters, calculated with Petra-M for dipole phasing and different power ratios corresponding to the two experimental cases detailed in section 2.1 (see figure 4). Like in figure 1, the area probed with RFA during the experiment is materialized by the blue dotted square.</figcaption></figure>

And the conductivity $\sigma$ tuned as in [10].

3) In part ③ each slice results are extracted from COMSOL and stored in text files. The final treatment consists in recombining them to generate a 3D set of results and plot them along 2D (radial-poloidal) maps, in the vicinity of the limiter surface.

### 3.3. DC rectified potential calculations

Rectified sheath potentials calculated with Petra-M (figure 9) and SSWICH (figure 10) are in good agreement with each other, and with the RFA probe measurements (figure 4), not only qualitatively but also quantitatively for both cases:

a) The ‘optimized’ excitation (#37147) succeeds in reducing the fields intensity by bringing maxima under 50 V, resulting in a drop of the sputtering efficiency and tungsten erosion as will be shown in section 4.

b) The non-optimal tapered case (#37 150) excites potentials up to 110 V. We will see in the next section (cf figure 12) that such values typically push ion energies above sputtering thresholds, through the range where the yields increase sharply and non-linearly, having deleterious consequences on the erosion.

In figure 9, potential patterns on both limiters can have different amplitudes because Petra-M applies SBCs directly on the 3D geometry, which is not homogeneous along the poloidal direction when approaching the corners. In figure 10 however, since SSWICH assumes that the limiter geometry does not change along the poloidal direction, and that the parallel conductivity is over 100 times larger than the perpendicular one, the potentials are homogeneous along field lines, so that the potential patterns have exactly the same amplitudes on both limiters, which is why figure 10 only represents patterns on one limiter. In medium size tokamaks like AUG and WEST, the rather low level of turbulence and collisionality at

<figure><img src="image_17.png" /><figcaption>**Figure 10.** DC potentials along AUG-three-strap antenna limiter calculated with SSWICH for dipole phasing and different power ratios corresponding to the two experimental cases detailed in section 2.1. Like in figure 1, the area probed with RFA during the experiment is materialized by the blue dotted square.</figcaption></figure>

the edge lead to much larger conductivities in parallel than perpendicular directions. This is also why the RFA measurements performed several meters away from the antenna are still representative of what happens near the limiter to which it magnetically connects. Note also that the RFA measurements (figure 4) suggest that the rectification extends radially away from the limiter way beyond the typical dimensions of RF sheath expansion predicted by theory and simulations [44]. This could then likely be an effect of diffusion in the perpendicular direction. In large future devices like ITER, the collisionality in the edge is expected to be much larger than in current devices, enhancing perpendicular transport. The perpendicular conductivity will likely increase compared to typical values in current devices, which we explored and further discussed in [45].

Therefore, while the agreement between codes and measurements is certainly a crucial requirement to gain confidence
in these modeling tools before using them to further predict what may happen in future devices like ITER [45–48], some currently valid assumptions may require a careful revisit.

## 4. Impurity source estimation

To fully assess if a given excitation is suitable to develop a scenario with it, these calculated potentials must be converted into local impurity outfluxes. We can then integrate these fluxes to be on areas wetted by the plasma to provide a global estimation of the impurity source, expressed in atoms sputtered per second per limiter (written in white at the bottom of each colormap in figures 12 and 14). Finally, the situations with and without ICRF are compared; their ratio (written in red on each colormap) is the new figure of merit that we propose, to assess how much more tungsten is locally eroded when an ICRF antenna is powered.

To do so, one must first establish the composition of the plasma as ‘realistically’ as they can. In the case of our experiment, we know quite accurately that it was performed in deuterium plasmas with about a 4% minority fraction of hydrogen and more than a hundred discharges after the last boronization (i.e. less than 0.5% boron). We can then combine the corresponding signals from charge exchange spectroscopy to see if we can reproduce the $Z_{eff}$ measured. Doing so, we figured that a small fraction of another low-Z impurity misses bridging the gap. Since most of the AUG outer wall components are built using W coated graphite tiles and that the graphite head of the RFA probe was also plunged seven times into the plasma, it is reasonable to assume another 0.5% of carbon in the mixture. A small fraction of W (<0.001%) is finally added, consistent with the global level of interactions. Finally, the fractions of low-Z impurities above-mentioned are further subdivided to account for the different abundances of key ion states. In our case, $B^{3+}$ and $C^{4+}$ typically account for the largest fractions as they are the most stable (He-like) and hence abundant states (cf figure 5.7 in [49] for boron). Note that the higher the charge, the stronger the acceleration through the sheath, and the lower the incident energy required to sputter atoms. In figure 11, the sputtering yield of each species are plotted in different colors and the effective sputtering yield of the mixture is plotted in black. Using figure 11, potentials in figure 10 are then converted into an effective sputtering yield.

To finally deduce the outflux of tungsten atoms, resulting from limiter bombardment by plasma, we must assess the area effectively wetted by the plasma, to assess the effective flux [18]. In the case of the AUG 3-strap antenna limiter, a toroidal band of 4 cm is considered wetted by the plasma. Finally, since the B field lines reach limiter tiles with an average angle of incidence of $\alpha = 13^{\circ}$, the parallel incident flux is spread,

$$ \Gamma_W = Y_{Eff}(V_{DC}) \cdot \Gamma_{Isat} \cdot \sin(\alpha). \quad (5) $$

In this simplified model, only the dependence of the sputtering on the incident energy of the ions (including temperature effects) is retained, both the dependence of the

<figure><img src="image_18.png" /><figcaption>Figure 11. Effective sputtering yield of a deuterium plasma with a 4% H minority, 0.4% B due to boronization, 0.2% C due to probe reciprocations, 0.001% W, and the mixture containing all ions:</figcaption></figure>

$$ Y_{Eff}^{MIX} = [4Y_{Eff}^{H+} + 95Y_{Eff}^{D+} + 0.12(Y_{Eff}^{B+} + Y_{Eff}^{B2+}) + 0.16Y_{Eff}^{B3+} + 0.06(Y_{Eff}^{C2+} + Y_{Eff}^{C3+}) + 0.08Y_{Eff}^{C4+} + 0.001Y_{Eff}^{W2+}] / 100. \text{ Details of the so-called 'optimistic' and 'ITER-like' mixtures are further given in figure 14.} $$

sputtering yield with the angle of incidence and ions Larmor radius effects are neglected. Our choice to neglect these is conservative, because, regardless of the incidence angle, we assume the ions always fall on the limiter with the angle that maximizes the sputtering yield, which will lead to source overestimations and rather safe conclusions. However, by taking the sputtering dependence with the incident angle into account without including Larmor radius effects in the model, we would be implicitly working under the optical approximation which is known to be invalid for ions in edge plasma [50], and by doing so, would risk miscalculating the sources.

Tungsten outflux rates expressed in $[\text{atm m}^{-2} \text{s}^{-1}]$ (number of tungsten atoms being sputtered each second per square meter) are shown in figure 12 for the same cases as in figure 10. Consistently with potential maps in figure 10, ‘optimal’ excitation succeeds in cutting by half the number of atoms emitted per limiter with respect to the unoptimized excitation. However, some moderate level of sputtering is taking place along the full height of the limiter, because even at the lowest energies, the presence of highly ionized states in the ‘realistic’ mixture makes sputtering already significant at low energies.

While accurately determining the composition of the plasma is important, it is in practice very challenging, and the complexity rises with the number of species in the mixture, insofar as $Z_{eff}$ signals can be reproduced by more combinations of species. One must then have a greater knowledge of their device's current state and history, as diagnostics rarely monitor all the species that eventually play a role. For our experiment in AUG, in addition to the ‘realistic’ mixture exposed in figure 11, also provided in figure 13, so-called ‘optimistic’ and ‘ITER-like’ mixtures, respectively standing for rather cold plasma long after the last boronization and Neon seeded DT plasma mixtures:
<figure><img src="image_19.png" /><figcaption>**Figure 12.** Tungsten outflux rates [W atoms s⁻¹ m⁻²] along a limiter of an AUG three-strap antenna, calculated with SSWICH code for the 'realistic' gas mixture detailed in figure 10. At the bottom of each map, written in white, is the total tungsten outflux integrated on the wetted surface along the height of the limiter $\Gamma_{Wtot}^{ICRH \to ON}$ [W atoms s⁻¹ limiter⁻¹]. Just above in red, is the factor</figcaption></figure>

$\Lambda = \Gamma_{Wtot}^{ICRH \to ON} / \Gamma_{Wtot}^{ICRH \to OFF}$ by which each ICRF limiter source increases when the antenna is powered. Further assessment of these sources for 'optimistic' and 'ITER-like' assumptions on the plasma composition are given in figure 14. Like in figure 1, the area monitored by visible spectroscopy lines of sights is materialized by the red dotted square.

<figure><img src="image_20.png" /><figcaption>**Figure 13.** Three mixtures effective sputtering yields.</figcaption></figure>

1) **optimistic**: 0.2% B⁺ and 0.001% W⁺

2) **AUG-Realistic**: -0.5% B with the following ions abundances: 10% B⁺, 10% B²⁺ and 80% B³⁺

- 0.5% C with the following ions abundances: 10% C²⁺, 10% C³⁺ and 80% C⁴⁺

- 0.001% W²⁺

3) **ITER-like**: 49% D⁺, 49% T⁺, 2% (0.16 Ne⁷⁺, 0.34 Ne⁸⁺, 0.22 Ne⁹⁺, 0.28Ne¹⁰⁺) and 0.01% W²⁺.

Note the maxima of simulated rates in figure 12 (4 · 10¹⁸ atm m⁻² s⁻¹) are close to these assessed from visible spectroscopy in figures 5 and 6 (5 · 10¹⁸ atm m⁻² s⁻¹). This

probably means that our assumptions on the 'realistic' mixture were somewhat reasonable; discrepancies are either due to the fractions of low-Z impurity or/and to the abundance of their ionized states. One can easily tweak the mixture until achieving a perfect match with the experimental data. This exercise, however, presents limited practical interest as experimental data treatments can also carry errors of comparable magnitude. Our goal is instead to provide an intuition on how tungsten sources in the ICRF limiters increase when the antenna is powered.

To do so, we integrate these rates on the surface of the limiter wetted by the plasma (cf equation (3)). This leads
<figure><img src="image_21.png" /><figcaption>**Figure 14.** Tungsten outflux rates [W atoms s⁻¹ m⁻²] along a limiter of an AUG-three-strap antenna, calculated with SSWICH code for respectively ‘optimistic’ and ‘ITER-like’ gas mixtures. At the bottom of each map, written in white, is the total tungsten outflux integrated on the wetted surface along the height of the limiter $Γ_{Wtot}^{ICRH→ON}$ [W atoms s⁻¹ limiter⁻¹]. Just above in red, is the factor $Λ = Γ_{Wtot}^{ICRH→ON} / Γ_{Wtot}^{ICRH→OFF}$ by which each ICRF limiter source increases when the antenna is powered.</figcaption></figure>

to a tungsten total outflux for each limiter, expressed in [atm s⁻¹ limiter⁻¹], and written in white at the bottom of each map. These ‘white numbers’ can then be compared when the ICRF antenna is inactive—assuming no RF-induced potentials along the limiters—vs when the antenna is powered, with rec- tified potentials along the limiter. Taking their ratio leads to the factor Λ introduced in equation (4), written in red in all the maps of figures 12 and 14.

Comparing the three excitations of our experiment for a given plasma composition, the increase in tungsten produc- tion when powering an antenna with optimal settings (left maps) is indeed always much better (lower) than when not optimized. More importantly, when comparing Λ factors in the ‘optimistic’ vs the ‘ITER-like’ cases respectively exposed at the top and bottom of figure 14, we see that they are always at least over two orders of magnitude higher in the ‘optim- istic’ than the ‘ITER-like’ mixtures. This result is somewhat counter-intuitive; this is because a mixture is deemed ‘optim- istic’ regarding the background level of interactions without ICRF. However, when ICRF is powered, the relative energy increase is therefore more dramatic when starting from an ‘optimistic’ situation than from a ‘ITER-like’ one. To put it differently, the relative increase caused by the ICRF is much larger for an ‘optimistic’ mixture with a small frac- tion of singly ionized species than in ‘ITER-like’ mixtures with a large fraction of highly ionized species. This is basic- ally because the ‘optimistic’ mixtures are unlikely to sputter impurities at low energies (without ICRF) but start playing a role as the ICRF is powered. The ‘ITER-like’ mixtures, on

the contrary, shift sputtering thresholds toward lower ener- gies, so that their deleterious influence can already be observed without ICRF. The ultimate result is not straightforward, as it results from complex synergies between two non-linear phe- nomena: namely the RF→DC potential rectification and the sputtering.

Note also that while incident energies (or sheath poten- tials), can be well measured by the RFA probe (figure 4) and simulated with the Petra-M (figure 9) and SSWICH codes (figure 10), estimating the production of impurities very much depends on the mixture of plasmas considered, which in gen- eral is more difficult to diagnose. When comparing the val- ues of these increase factors, we see that the experimental assessment ones (cf Λ values in figure 6(a) legend) have a similar order as the simulated one (Λ ≈ 15 in case (b)). However, note the Λ tends to infinity (over 4 orders of mag- nitude) when assessed with an ‘optimistic’ mixture (cf top row in figure 14). While it is reasonable to consider that the physical sputtering is the dominant mechanism of tung- sten production in medium size tokamaks, other mechanisms that are not addressed in the present study could also play important roles, such as charge exchange of low-Z impurit- ies, recycling, and chemical sputtering. One can therefore use these tools to assess the level of impurity production for a plasma composition as realistic as possible, but also keep in mind that erosion cannot be reduced to the physical sput- tering only, because in experimental conditions, a complex variety of mechanisms together contribute to plasma-surface interactions.
The main conclusion is therefore that while deleterious effects of ICRF on plasma surface interactions can be mitigated with appropriate excitation, they will always exist to some extent. However, considering the amplification of thermal sheath erosion caused by the presence of highly ionized heavier low-Z impurities, we believe powering the ICRF in strongly seeded plasmas will have a more marginal influence on impurity production, which should typically be the case of ITER [45, 48].

## 5. Conclusions

During experiments at AUG, different phasing and power ratios between central and outer straps were explored with the three-strap ICRF antennas. For the two cases studied, the plasma current and therefore magnetic field lines tilt-angle were scanned. For each value of the current, the RFA reciprocating probe plunged in the plasma, magnetically connecting to different poloidal heights of the ICRF antenna limiter, allowing us to reconstruct 2D maps along the antenna limiter of the mean parallel ion energy $<W_{II,i}>$ (figure 4), which can be interpreted as the ions incident energy on the limiters. This physical quantity changed consistently with the antenna excitation, showing the differences between situations with optimized balance vs. non-optimized imbalanced power on inner and outer straps. This quantity is further benchmarked by rectified sheath potentials computed with both Petra-M (figure 9) and SSWICH (figure 10) codes. All agree well with one another, not only qualitatively but also quantitatively within 10% margin. While these measurements and calculations account for the non-linear way of the sheath potential to get rectified in presence of ICRF heating, this only constitutes one of the two aspects of the global picture.

The second aspect is the sputtering, leading to materials erosion and plasma contamination by impurities. The sputtering yield increases non-linearly with the energy of incident particles. The success of ICRF plasma heating therefore depends strongly on the regime of sputtering.

For each excitation scenario, sputtering-induced tungsten production at the plasma edge and core contamination were monitored using visible and UV spectroscopic measurements (figure 6). While core contamination results are presented and briefly discussed, a comprehensive analysis would require accounting for all impurity sources in the vessel and modeling their transport into the core—a task that lies beyond the scope of this study and is addressed further in the following section on limitations and future perspectives. Moreover, the similar behavior of $Z_{eff}$ in both discharges prevented a clear distinction between optimal and non-optimal excitations, likely because the carbon contribution from the RFA probe overshadowed the tungsten signal from the limiters.

By focusing on the plasma edge, our results demonstrate that the optimized excitation (dipole phasing with $P_{cent}/P_{out}$ = 3/2) effectively mitigates tungsten production compared to the non-optimal excitation. However, in comparison with a situation where the antenna is inactive, powering the antenna enhances tungsten gross erosion by an

order of magnitude (cf $\Lambda > 10$ in figure 6(a)). Simulations further show that the plasma composition plays a key role in this increase. As shown in the sputtering curves of the optimistic mixture (top left graph in figure 14), when plasmas are mostly composed of singly ionized light species ($H^+$, $D^+$), none of them is usually energetic enough ($E_{in} \approx 3 \cdot T_e$) to cause sputtering without the ICRF being powered ($Y_{eff} \ll 10^{-7}$). When RF is applied, potentials are rectified by the excitation of the RF sheath, and incident energies suddenly jump ($E_{in} \approx V_{DC}$) in the deleterious regime of sputtering ($Y_{eff} > 10^{-5}$). The ratio between a situation with and without ICRF power can then reach several orders of magnitude (up to 4, considered infinite by Matlab, as shown in figures 14(a) and (b)). On the contrary, when plasmas are also composed of highly ionized low-Z impurities ($Ne^{7+}$ to $Ne^{10+}$) as will likely be the case for ITER plasmas, not only does their larger mass give them larger yields but also the acceleration that they undergo through the sheath being as strong as their degree of ionization, even without ICRF power, these already cause substantial sputtering ($Y_{eff} > 10^{-4}$). While adding ICRF power worsens the sputtering situation, $Y_{eff}$ increases much slower above $10^{-4}$ (figures 14(c) and (d)), so that the ICRF-specific jump in impurity production becomes less and less dramatic (less than an order of magnitude) as larger fractions of low-Z impurity are injected into the plasma, e.g. to reduce divertor heat loads.

## 6. Limits and perspectives

First, the sputtering model used in this study does not self-consistently compute the self-sputtering, but globally applies the same realistic dose of tungsten in the mixture, corresponding to what is iteratively obtained for a potential of 100 V. The model can be refined to locally adjust the mixture by adding more or less W, depending on the level of sputtering expected. By modulating the weight of the self-sputtering, this could change the local picture. This effect could be particularly relevant to assess the risk of triggering a self-sputtering avalanche. As far as tungsten is concerned, fortunately, this risk has been cleared in [51], where 'it is shown that the possibility of a W self-sputtering avalanche by ions circulating in the magnetic pre-sheath can be ruled out due to the smallness of the sputtered W neutral energies, which means that they do not penetrate very far into the pre-sheath before ionizing; thus the W ions do not gain a large kinetic energy as they are accelerated back to the surface by the pre-sheath/Debye sheath electric field; leading to modest self-sputtering yields'.

Second, in our study, we placed ourselves under the perspective of the ICRF antenna frame, bombarded by an influx of ions from the plasma, leading to a gross erosion of tungsten atoms. Since neither redeposition nor transport effects were taken into account, our estimations only shed light on the gross source. To now assess the net flux of impurity penetrating in the confined plasma, transport ingredients should be added. Even though, unlike for divertor sources, the screening of metallic impurities sputtered from the main chamber walls is known to be rather weak in small to medium size tokamaks
such as Alcator C-Mod [19] and AUG [18], it may or may not be the case in future devices like ITER [52] or SPARC.

Efforts are being made to understand the redeposition [53, 54]. Most of them rely on PIC simulations involving assumptions (1D) that prevent them from extrapolating their conclusions straightforwardly to macroscopic objects as complex as ICRF antennas. Together with the enhancement of numerical capabilities, the highly integrated modeling promises better treatments in the near future (ex: GITR [55], hPIC2 [56]). However, taking all relevant effects self-consistently into account in a realistic 3D geometry at the antenna scale still implies relying on a few questionable physical assumptions, and bounds most sophisticated tools for restricted HPC environments.

## Acknowledgment

The whole AUG ICRF team, are all warmly acknowledged.

This work has been carried out within the framework of the EUROfusion Consortium, funded by the European Union via the Euratom Research and Training Programme (Grant Agreement No. 101052200—EUROfusion). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Commission. Neither the European Union nor the European Commission can be held responsible for them.

The views and opinions expressed herein do not necessarily reflect those of the ITER Organization.

This research used resources of the National Energy Research Scientific Computing Center (NERSC), a U.S. Department of Energy Office of Science User Facility located at Lawrence Berkeley National Laboratory, operated under Contract No. DE-AC02-05CH11231.

The PPPL work was supported by the US Department of Energy under Contract Number DE-AC02-09CH1146.

## ORCID iDs

G. Urbanczyk https://orcid.org/0000-0002-4026-6802

S. Shiraiwa https://orcid.org/0000-0001-5249-0441

R. Bilato https://orcid.org/0000-0002-0578-9333

N. Bertelli https://orcid.org/0000-0002-9326-7585

W. Tierens https://orcid.org/0000-0002-6979-8140

L. Colas https://orcid.org/0000-0002-4573-3326

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