# Integrated modeling of RF-induced tungsten erosion at ICRH antenna structures in the WEST tokamak

A. Kumar, W. Tierens, T. Younkin, C. Johnson, C. Klepper, A. Diaw, J.

Lore, A. Grosjean, G. Urbanczyk, J. Hillairet, et al.

► To cite this version:

A. Kumar, W. Tierens, T. Younkin, C. Johnson, C. Klepper, et al. Integrated modeling of RF-induced tungsten erosion at ICRH antenna structures in the WEST tokamak. Nuclear Fusion, 2025, 65 (7), pp.076039. 10.1088/1741-4326/ade455. hal-05266810

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# Integrated modeling of RF-induced tungsten erosion at ICRH antenna structures in the WEST tokamak*

To cite this article: A. Kumar et al 2025 Nucl. Fusion 65 076039

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

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# Integrated modeling of RF-induced tungsten erosion at ICRH antenna structures in the WEST tokamak*

A. Kumar<fnref n="1" />,** ID, W. Tierens<fnref n="1" /> ID, T. Younkin<fnref n="1" />, C. Johnson<fnref n="1" />, C. Klepper<fnref n="1" /> ID, A. Diaw<fnref n="1" />, J. Lore<fnref n="1" /> ID, A. Grosjean<fnref n="2" /> ID, G. Urbanczyk<fnref n="3" /> ID, J. Hillairet<fnref n="4" /> ID, P. Tamain<fnref n="4" />, L. Colas<fnref n="4" /> ID, C. Guillemaut<fnref n="4" />, D. Curreli<fnref n="5" /> ID, S. Shiraiwa<fnref n="6" /> ID, N. Bertelli<fnref n="6" /> ID and the WEST Teamª

E-mail: kumara@ornl.gov

Received 7 January 2025, revised 25 May 2025

Accepted for publication 13 June 2025

Published 24 June 2025

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CrossMark

## Abstract

This paper introduces STRIPE (Simulated Transport of RF Impurity Production and Emission), an advanced modeling framework developed to analyze material erosion and the global transport of eroded impurities originating from radio-frequency (RF) antenna structures in magnetic confinement fusion devices. STRIPE integrates multiple physics modules: SolEdge3x for scrape-off-layer plasma profiles, COMSOL for 3D RF rectified sheath potentials, RustBCA for erosion yields and surface interactions, and global impurity transport for 3D ion energy-angle distributions and impurity transport. The framework is applied to an ion cyclotron RF-heated L-mode discharge (#57877) in the WEST tokamak, where it predicts a thirty-fold increase in gross tungsten erosion at antenna limiters during the transition from ohmic to ICRH operation. Additionally, under ICRH conditions, a tenfold enhancement in erosion is observed when comparing RF sheath effects to purely thermal sheath conditions. High-charge-state oxygen ions (O<fnref n="6" />⁺ and above) are identified as the dominant contributors to tungsten sputtering. To validate the model, a synthetic diagnostic tool based on inverse photon efficiency (S/XB coefficients) from the ColRadPy collisional-radiative model enables direct comparison with

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<footnote n="1">¹ Oak Ridge National Laboratory, 1 Bethel Valley Road, Oak Ridge, TN 37831, United States of America</footnote>

<footnote n="2">² University of Tennessee, Knoxville, TN 37996, United States of America</footnote>

<footnote n="3">³ Institut Jean Lamour UMR 7198 CNRS—Université de Lorraine 2 allée André Guinier F-54011 Nancy, France</footnote>

<footnote n="4">⁴ CEA, IRFM, F-13108 Saint-Paul-lez-Durance, France</footnote>

<footnote n="5">⁵ University of Illinois at Urbana Champaign, Urbana, IL 61801, United States of America</footnote>

<footnote n="6">⁶ Princeton Plasma Physics Laboratory, Princeton, NJ 08536, United States of America</footnote>

<footnote>* This manuscript has been authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE). The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doi-public-access-plan).</footnote>

<footnote>ª See http://west.cea.fr/WESTteam.</footnote>

<footnote>** Author to whom any correspondence should be addressed.</footnote>
spectroscopic measurements. Model predictions using a plasma composition of 1% oxygen and 99% deuterium show good agreement with observed W − I (400.9 nm) emission for discharge #57877, supporting the accuracy of the STRIPE framework. This study focuses specifically on gross erosion calculations to demonstrate STRIPE’s capabilities. Future extensions of this work will incorporate net erosion, re-deposition, self-sputtering effects, and whole-device modeling of sputtered tungsten impurity transport. STRIPE is also being applied to other RF-heated linear and toroidal devices, offering valuable insights for antenna design, impurity control, and performance optimization in next-generation fusion reactors.

Keywords: RF heating, plasma-material interactions, integrated modeling, STRIPE

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

# 1. Introduction: context and objectives

High-power radio-frequency (RF) waves are a crucial tech-
nique for plasma heating in magnetic confinement fusion
(MCF) devices, enabling efficient energy transfer to achieve
fusion conditions. RF heating methods have proven highly
effective, as demonstrated by the 2022 deuterium–tritium cam-
paign at the Joint European Torus (JET), where ion-cyclotron
RF heating (ICRH) contributed 20% of the record-setting 59
MJ fusion energy output [1]. As fusion research progresses
toward practical energy generation, upcoming MCF-based
experimental devices like SPARC [2, 3] and Material Plasma
Exposure eXperiment (MPEX) [4–6] plan to rely heavily,
if not exclusively, on RF-based plasma heating. This trend
underscores the importance of understanding and addressing
the unique challenges posed by RF heating and current drive
in high-performance fusion environments.

One significant challenge to achieving reliable RF heating and current drive in next-generation fusion devices, including ITER, is the interaction of RF waves with plasma sheaths near material surfaces such as RF antennas structures. RF rectified potentials, or RF sheaths [7], form on these surfaces with amplitudes that can reach several hundred volts in current MCF devices [8] and are projected to reach up to kilovolts levels in future devices like ITER, where slow-wave resonances are anticipated to play a critical role [9]. These high RF potentials accelerate plasma fuel ions, such as hydrogen (H⁺), deuterium (D⁺), and light impurity ions (e.g. oxygen, boron, neon etc), towards the antenna surfaces, potentially causing substantial material erosion. An additional complication is self-sputtering, in which sputtered materials, primarily from the antenna surface, return to the surface, exacerbating ongoing erosion and altering the surface morphology.

This cycle of erosion and re-deposition introduces impurities into the scrape-off-layer (SOL) neutral gas and plasma environment, posing a risk of impurities migrating into the plasma core. This issue is particularly problematic during high-confinement mode (H-mode) operations, as longer plasma confinement times increase impurity retention in the core, potentially degrading plasma performance [10, 11]. Recent studies have observed substantial material erosion at RF antenna structures and subsequent transport of these

impurities towards the bulk plasma during helicon and ICRH
in both linear [12, 13] and toroidal MCF devices [14]. In
past, several efforts to mitigate impurity generation have been
explored, including (1) wall boronization at TEXTOR [15],
(2) toroidal phasing of antenna straps at JET [16] and ASDEX
Upgrade (AUG) [17, 18], and (3) the use of field-aligned ICRH
antenna arrays at Alcator C-Mod [19]. However, the fusion
community recognizes the need for more advanced strategies
and a deeper understanding of RF-enhanced impurity produc-
tion to minimize the impact on plasma performance in future
reactor-grade fusion environments.

To address these challenges, this study introduces STRIPE (Simulated Transport of RF Impurity Production and Emission), a comprehensive modeling framework for studying RF-induced plasma-material interaction (PMI) at ICRH antenna structures in fusion devices. STRIPE integrates advanced computational tools across various physics fidelity levels (see section 2), enabling detailed simulations of impurity sources originating from ICRH antenna structures in MCF experiments. STRIPE simulation results are directly compared to observed tungsten (W) erosion at the ICRH antenna limiters in the WEST Tokamak during a targeted L-mode ICRH discharge (#57877), with a particular focus on identifying impurity sources originating from the antenna under both RF and thermal sheath conditions.

WEST, with its all-W plasma-facing components (PFCs), provides an optimal environment for systematically studying impurity sources from both the divertor and main-chamber components, including ICRH antenna limiters. The device’s long-pulse operational capability-recently demonstrated by sustaining plasma for up to 1337 s (22 min) [20]-makes it uniquely suited for extended studies of PMI under long-duration tokamak conditions. Recent research in WEST [14] highlighted significant tungsten impurity generation from main-chamber ICRH antenna structures. However, computational tools were not available at the time to model RF sheath effects associated with active ICRH heating. That study instead focused mostly on lower hybrid (LH)-enhanced W erosion at a non-active ICRH antenna and did not account for self-sputtering or net erosion/ (re) depsotion at the antenna limiters. The STRIPE framework addresses these limitations by providing a high-fidelity simulation platform capable of
modeling RF sheath interactions, ion energy-angle distributions (IEADs), and surface response in realistic 3D geometries. While STRIPE is capable of simulating net erosion, re-deposition, and self-sputtering, this study focuses specifically on gross erosion analysis at the WEST ICRH antenna limiters and its validation using W-I spectroscopic data from discharge #57877. This work is especially relevant to ITER, which has adopted an all-tungsten PFC design, highlighting the importance of predictive modeling tools for impurity control in high-power, reactor-grade fusion environments.

This paper is organized as follows: section 2 introduces the STRIPE modeling framework, detailing the computational tools and methodologies used to simulate W erosion and impurity transport in RF antenna structures. Section 3 describes the modeling of the WEST background plasma, providing the plasma conditions and profiles necessary for STRIPE inputs. Section 4 discusses additional inputs required for STRIPE, including RF sheath boundary conditions and material erosion yield calculations. Section 5 presents the synthetic diagnostic method developed to convert simulated W erosion flux into photon emission, allowing comparison with experimental data. Section 6 presents the main results on W erosion at the WEST ICRH antenna limiters, comparing thermal and RF sheath cases and validating model predictions with experimental observations. The discussion in section 7 explores the implications of these findings for PMI in fusion devices, potential improvements in the STRIPE framework, and future directions. Finally, summary of this work is presented in section 8.

## 2. STRIPE—an integrated modeling framework for RF-PMI

To accurately estimate material erosion and the transport of sputtered impurities at ICRH antenna structures in fusion devices, it is essential to model physical processes across multiple temporal and spatial scales. This complexity necessitates an integrated framework, which the STRIPE model addresses by combining several specialized computational tools, each capturing different aspects of the physics involved. The key components of this modeling framework are outlined below:

* **Background Plasma Profiles:** A primary input to the STRIPE framework is the plasma background, including electron density, temperature, and ion fluxes. These parameters are obtained using fluid-based SOL plasma transport codes, such as SOLPS [21, 22] and SolEdge3x [23, 24]. For this study, the WEST SOL plasma background is modeled with SolEdge3x, which provides profiles of both plasma and light impurities (e.g. oxygen) across the SOL and far-SOL regions on an extended computational grid which extends radially to the main-chamber and antenna PFCs. Using extended-grid SOL transport codes like SolEdge3x is crucial, particularly when experimental diagnostics are unavailable to characterize plasma and impurity profiles near the antenna structures, where PMI are most intense. Details of these simulations are provided in section 3.

* **RF Sheath Boundary Conditions and RF Wave Propagation:** The influence of RF sheath effects on wave propagation and sheath rectifications is modeled using the sheath-equivalent dielectric layer technique [8, 12, 13]. In this approach, thin dielectric layers adjacent to PFCs mimic the behavior of RF sheaths by incorporating spatially varying complex permittivity $\epsilon$ and conductivity $\sigma$. These properties are derived from a sheath impedance model [25] that depends on local plasma parameters, including electron density, temperature, magnetic field orientation, and RF voltage amplitude. The resulting dielectric medium is implemented in COMSOL Multiphysics via a custom material definition.

An iterative procedure is used to achieve self-consistency: the initial estimate is $\sigma = 0, \epsilon = 1$ in the sheaths, then the RF field is solved, and the resulting sheath potential is used to update these dielectric properties. This cycle is repeated until convergence. This approach enables full-wave simulations that self-consistently resolve rectified sheath potentials and their influence on the RF field, within the cold plasma approximation.

The resulting sheath-aware boundary conditions are integrated into the STRIPE framework to model sheath-enhanced sputtering, localized power deposition, and impurity transport as described in section 4.1. Further details on the sheath model and numerical implementation in COMSOL are provided in appendix A.

* **CAD Defeaturing of the ICRH Antenna Structures:** Realistic geometry representation is crucial for STRIPE modeling, particularly in finite-element simulations requiring precise computational geometry of RF antenna structures. However, engineering CAD models must undergo 'defeaturing' -removing non-essential details and refining the mesh in critical areas-to balance computational efficiency and accuracy.

* **Material Erosion Yield and Surface Interaction Physics:** The RustBCA code [26, 27] is utilized to simulate ion-surface interactions at the atomic scale, delivering data on sputtering and reflection yields over a wide spectrum of incident ion energies (ranging from a few eV to 10000 eV) and angles (0–90°). This tool focuses on ion-surface interactions, particularly sputtering, reflection, and implantation, which are difficult to model analytically due to the limitations of empirical or semi-empirical formulas in addressing complex geometries, multi-component surfaces, or dynamic plasma-material coupling. Using the Binary Collision Approximation (BCA) as a computationally efficient alternative to n-body molecular dynamics methods, RustBCA enables accurate and scalable simulations. While molecular dynamics provides more detailed insights, it is computationally infeasible for intricate RF antenna geometries, making RustBCA a practical and efficient solution for high-fidelity surface interaction modeling within STRIPE.
* **Ion Energy-Angle Distributions (IEADs):** To accurately simulate material sputtering from complex 3D RF antenna geometries, the STRIPE framework computes IEADs at PFCs through localized sheath-scale simulations. Tracer ions (e.g. O<sup>x+</sup>) are launched from the sheath entrance with half-Maxwellian velocity distributions and tracked through local electric and magnetic fields. Their motion includes full gyromotion, E × B drift, Coulomb collisions, and sheath acceleration, and continues until surface impact. Local plasma conditions-including electron and ion temperatures, density, and sheath potential, sheath electric field-are specified at each surface mesh element. The numerical framework used in global impurity transport (GITR) is based on a Monte Carlo particle-tracking approach and is described in appendix B.

In GITR, ion acceleration near material surfaces is modeled using sheath potentials combined with a spatial electric field distribution. The total sheath potential, $V_{sheath}$, is specified differently for thermal and RF sheath conditions, but the electric field profile is computed using a common analytic form based on the Brook's model [28].

For thermal sheath conditions, the sheath potential $V_{sheath}^{thermal}$ is calculated from classical sheath theory [29, 30], typically using:

$$V_{sheath}^{thermal} = k_{sheath} T_{e,surf}, \quad (1)$$

$$k_{sheath} = \left| \frac{1}{2} \log \left( 2\pi \frac{m_e}{m_i} \right) \right| \left( 1 + \frac{T_{i,surf}}{T_{e,surf}} \right)$$

where $T_{e,surf}$ and $T_{i,surf}$ are the local electron and ion temperatures respectively, and $m_e$, $m_i$ are the electron and ion masses respectively.

For RF sheath conditions, the rectified DC sheath potential $V_{sheath}^{RF}$ is provided by full-wave COMSOL simulations using the sheath-equivalent dielectric layer method [8].

In both cases, the spatial distribution of the sheath electric field is defined using the Brook's model, which assumes an exponential decay across the Debye and magnetic presheath layers:

$$E_n = V_{sheath}^{RF} \left[ \frac{f_D}{2\lambda_D} \exp \left( -\frac{r}{2\lambda_D} \right) + \frac{1-f_D}{\rho_i} \exp \left( -\frac{r}{\rho_i} \right) \right] \quad (2)$$

where r is the distance from the surface, $\lambda_D$ is the Debye length at the start of the sheath, $\rho_i$ is the ion Larmor radius, and $f_D$ is the fractional voltage drop across the Debye sheath. This expression enables consistent modeling of the electric field profile for ion tracing in both thermal and RF sheath conditions.

For each surface element i, the effective sputtering yield is calculated as:

$$Y_{\text{eff}}(i) = \int_{\theta=0}^{90^{\circ}} \int_{\mathcal{E}_{\text{min}}}^{\mathcal{E}_{\text{max}}} Y_i(\mathcal{E}, \theta) f_i(\mathcal{E}, \theta) d\theta d\mathcal{E}, \quad (3)$$

<figure><img src="image_4.png" /><figcaption>**Figure 1.** STRIPE framework workflow for modeling material erosion and global impurity transport originating from RF antenna structures. Components include SolEdge3x for SOL plasma profiles, COMSOL for RF sheath potentials, RustBCA for sputtering/reflection yield calculations, GITR for particle tracking, and ColRadPy for synthetic diagnostic conversion to brightness, $I_\phi$ (i.e. photon flux) for experimental comparison.</figcaption></figure>

where $Y_i(\mathcal{E}, \theta)$ is the angle- and energy-resolved sputtering yield from RustBCA, and $f_i(\mathcal{E}, \theta)$ is the local IEADs.

The gross tungsten erosion flux is then computed by summing over all surface elements:

$$\Gamma_{\text{gross},W} = \sum_{i=1}^{N} Y_{\text{eff}}(i) \cdot \Gamma_{\text{ions}}(i), \quad (4)$$

where $\Gamma_{\text{ions}}(i)$ is the ion flux to element i. This $\Gamma_{\text{gross},W}$ provides the initial condition for subsequent impurity transport modeling in STRIPE. In the present study, the STRIPE framework uses IEADs and gross erosion computed via GITR to characterize impurity sourcing. Modeling of net erosion and re-deposition will be addressed in future work.

Using these inputs, GITR predicts material erosion on the RF antenna surfaces. To facilitate direct comparison with experimental data, synthetic diagnostics are employed, incorporating inverse photon efficiency (S/XB) and photon emissivity coefficients (PEC) from the ColRadPy collisional radiative model [31]. This diagnostic process translates impurity flux data into brightness or photon flux $I_\phi$, producing line emission results that can be directly compared with experimental spectroscopic measurements for validation. The complete STRIPE framework workflow is illustrated in figure 1. Currently, in STRIPE framework, coupling between SolEdge3x, COMSOL, RustBCA, and GITR is performed manually, with each code providing input to the next stage of the workflow in a sequential, modular manner.
The predictive accuracy of material erosion and impurity transport within STRIPE, as also discussed later in section 7.4, heavily relies on the precision of the input parameters and models outlined here. In this study, we apply STRIPE to simulate RF-induced W erosion at the ICRH antenna structures within the toroidal geometry of the WEST tokamak, as outlined in section 3.

### 3. Modeling of the WEST background plasma

The WEST tokamak features a fully metallic environment designed for steady-state operation, with key components optimized for PMI studies relevant to ITER. A critical aspect of these studies is the configuration of RF heating systems and diagnostics deployed within the vessel.

Figure 2 provides a detailed view of the WEST inner vessel, showcasing a magnetic field line (blue dashed line) that connects the upper Pecker probe on the Antenna Protection Limiter to the upper left corner of the Q2 ICRF antenna. The visible spectroscopy diagnostics (red dashed lines) are embedded in the high-field side wall, specifically targeting the Q2 ICRH antenna limiters. The image also highlights the baffle structure and the divertor region. The divertor primarily consists of W-coated graphite tiles, with 12 tiles equipped with ITER-like W monoblocks to simulate realistic plasma-facing conditions. This configuration supports detailed diagnostics of PMI and impurity generation under high-power RF heating scenarios relevant to ITER.

To simulate W erosion at the ICRH antenna structures, this study utilizes experimental conditions from WEST L-mode discharge #57877 (figure 3). This discharge serves as a representative WEST plasma scenario, beginning with an ohmic heating phase from $t=0$ s to $t=5$ s, followed by ICRH from $t=5$ s to $t=10$ s.

Figure 3 shows (a) the plasma current profile $I_p$, and (b) the power input profiles: $P_{ohm}$ (black curve) for ohmic heating; $P_{Q1}$ (red curve) and $P_{Q2}$ (blue curve) for ICRH power applied through the Q1 and Q2 RF antennas, respectively; along with the total radiated power ($P_{rad,bulk}$). Additionally, (c) depicts the area integrated total brightness ($I_{\phi, total}$ [photons/s]) of the W-I 400.9 nm line measured at the Q2 antenna. These profiles provide a detailed overview of the heating stages, power distribution, and associated tungsten emission.

In this discharge, the plasma current ramps up to $I_p = 0.5$ MA by $t=1$ s and maintains this flattop until $t=10$ s. During the ohmic phase, the applied power is approximately $P_{ohm} = 0.6$ MW, resulting in $I_{\phi, total}$ (ohmic) $= 1.323 \times 10^{15}$ photons/s at Q2 antenna. At $t=5$ s, the activation of ICRH through the Q2 antenna increases the total input power to approximately $P_{in} = 2.3$ MW, with $P_{Q2} = 1.7$ MW. This transition from the ohmic to the ICRH phase also leads to an increase in $I_{\phi, total}$ (ICRH) $= 3.38 \times 10^{16}$ photons/s, representing a factor of 25 enhancement. This observation is compared with the simulation data later in section 6.4.

<figure><img src="image_5.png" /><figcaption>**Figure 2.** View of the WEST inner vessel showing a magnetic field line (blue dashed) connecting the upper Pecker probe on the Antenna Protection Limiter (APL) to the upper left corner of the Q2 ICRF antenna. The image highlights the visible spectrometer's lines of sight (red dashed) embedded in the high-field side wall, focusing on the Q2 ICRF antenna limiters. Also visible are the baffle and the divertor, which consists primarily of W-coated graphite tiles, with 12 tiles featuring ITER-like W monoblocks.</figcaption></figure>

For the simulations, two specific time points are analyzed: $t=3$ s for the ohmic phase and $t=8$ s for the ICRH phase as also shown in figure 3. These will henceforth be referred to as the *ohmic phase* and the *ICRH phase*, respectively, in this paper.

The plasma simulations for both phases are conducted using the SolEdge-EIRENE package, which combines the SolEdge multi-fluid plasma code [23] with the EIRENE Monte Carlo neutral particle solver [32]. This study uses the latest version, SolEdge3x [33, 34], configured for 2D simulations with an axisymmetric wall assumption.

In present, the plasma composition is set to 99% D⁺ and 1% oxygen, where oxygen serves as a proxy for all light impurities present during the WEST discharge. The oxygen density in the SolEdge3x simulations is fixed at 1% and spatially homogeneous, initialized from the core boundary. This concentration effectively models impurity behavior and radiative losses, though in WEST experiments it typically ranges between 0.1% and 10% [14, 24]. Subsequent sections will demonstrate that W erosion estimates based on this 1% oxygen concentration agree well with experimental data.

To account for radiative losses in the SOL, the net power crossing the separatrix ($P_{sep}$) was adjusted from the experimentally measured input power, with values of $P_{sep} = 0.4$ MW for the ohmic phase and $P_{sep} = 1.0$ MW for the ICRH phase.
<figure><img src="image_6.png" /><figcaption>**Figure 3.** Time evolution of (a) the plasma current profile ($I_p$) for WEST L-mode discharge #57877, showing a ramp-up phase until $t = 1$ s, followed by a flattop at $I_p = 0.5$ MA maintained until $t = 10$ s. (b) Power input profiles: $P_{ohm}$ (black curve) for ohmic heating, $P_{Q1}$ (red curve) and $P_{Q2}$ (blue curve) for ICRH power applied through the Q1 and Q2 RF antennas, respectively, and the total radiated power ($P_{rad,bulk}$). (c) Total brightness of the W-I 400.9 nm line measured at the Q2 antenna. The transition from the ohmic phase ($t = 0-5$ s) to the ICRH phase ($t = 5-10$ s) is characterized by an increase in power from $P_{ohm} = 0.6$ MW to a total input power of approximately 2.3 MW, with $P_{Q2} = 1.7$ MW during the ICRH phase. This transition also shows a factor of 25 enhancement in the total brightness measurement.</figcaption></figure>

The simulation setup includes a gas puff at the outer midplane (OMP) at $z = 0$ m, calibrated to match electron density measurements from the OMP reflectometer. A 'transport mode' was applied to approximate turbulence, using fixed diffusive transport coefficients to represent perpendicular transport. The particle and momentum transport coefficients were set to $D = \nu = 0.4 \text{ m}^2 \text{ s}^{-1}$, typical for WEST L-mode discharges, with ion and electron energy transport coefficients of $\chi_i = \chi_e = 1.0 \text{ m}^2 \text{ s}^{-1}$ [24]. In the current simulations, fixed perpendicular transport coefficients were applied for both the ohmic and ICRH phases. This choice is made to ensure consistency between simulations and to isolate the effects of sheath physics and impurity sources without introducing additional uncertainty from varying transport assumptions. A recycling coefficient of $R = 0.99$ was applied at the wall, and a pump albedo coefficient of $R_{pump} = 0.95$ was used, consistent with the WEST pumping system. Drifts are deactivat-ated in these simulations and consequence of this assumption is later discussed in section 7.2.

Figure 4 displays the simulated background plasma profiles for multiple species, offering insight into the plasma conditions surrounding the ICRH antenna limiters. These profiles include key parameters such as electron density ($n_e$), temperature ($T_e$), and flux ($\Gamma_e$); D$^+$ ion density ($n_{D^+}$), temperature ($T_{D^+}$), and flux ($\Gamma_{D^+}$); and high-charge-state oxygen O$^{8+}$) ion density ($n_{O^{8+}}$), temperature ($T_{O^{8+}}$), and flux ($\Gamma_{O^{8+}}$). The green lines in the top-left subplot illustrate the LOS used

for measuring line emissions at the ICRH antenna limiters in WEST experiments.

Each subplot provides 2D-spatial distributions of these quantities, essential for understanding how plasma conditions vary near the antenna. The purple dashed lines on all the subplots in figure 4 show critical magnetic boundaries including inner core boundary, separatrix and LCFS. The outer wall of WEST is indicated by the thick black line. These profiles serve as the background plasma conditions for STRIPE simulations, particularly informing the modeling of PMI at the antenna limiters.

Fractional abundance analysis for oxygen ions under similar WEST plasma conditions, as presented in [14], indicate that high-charge-state oxygen ions, specifically O$^{6+}$ and above, dominate the light impurity population in the SOL near the ICRH antenna limiters. These highly ionized species play a significant role in W sputtering due to their enhanced energy transfer capabilities during ion-surface interactions, driven by their elevated charge states.

To validate the SolEdge3x simulation results against experimental data for WEST discharge #57877, figure 5 presents radial profiles at the OMP. Figure 5(a) compares the electron density $n_e$- from SolEdge3x simulations (with $P_{sep} = 1.0$ MW, ICRH phase) to reflectometry measurements, showing good qualitative agreement. The blue curve represents the simulated $n_e$- profile, while the purple squares correspond to experimental data. For reference, SolEdge3x-predicted densities for deuterium ions ($n_{D^+}$) and fully stripped oxygen ions ($n_{O^{8+}}$) are also shown.

Figure 5(b) displays the corresponding temperature profiles from SolEdge3x. These include the electron temperature $T_e$, as well as the temperatures of D$^+$ and O$^{8+}$. Direct experimental measurement of $T_e$- is limited in this regime due to sheath rectification effects, which reduce the reliability of reflectometry-based temperature diagnostics. Moreover, no reliable $T_e$- data are available during the ohmic phase ($t < 5$ s) for this discharge. Nonetheless, the consistency between simulated and measured $n_e$- profiles supports the use of SolEdge3x outputs as background inputs for STRIPE modeling.

The fluid simulations provide a steady-state background for STRIPE modeling; thus, the SolEdge3x results will be referred to as 'background plasma' in subsequent sections.

# 4. Additional inputs to the STRIPE framework

This section details the additional inputs and configurations required for the STRIPE framework to model W erosion at the WEST ICRH antenna limiters accurately.

## 4.1. Application of sheath-aware boundary conditions in COMSOL for WEST

In the context of STRIPE modeling on WEST, rectified RF sheath potentials are computed using COMSOL Multiphysics with the sheath-equivalent dielectric approach described
<figure><img src="image_7.png" /><figcaption>**Figure 4.** Plasma profiles obtained from SolEdge3x simulation with $P_{\text{sep}}$ = 1.0 MW are presented for various species: (a) electron density ($n_e$-), (b) electron temperature ($T_e$-), (c) electron particle flux ($\Gamma_e$-), (d) D⁺ ion density ($n_{D+}$), (e) D⁺ ion temperature ($T_{D+}$), (f) D⁺ ion flux ($\Gamma_{D+}$), (g) oxygen-8⁺ ion density ($n_{O8+}$), (h) oxygen-8⁺ ion temperature ($T_{O8+}$), and (i) oxygen-8⁺ ion flux ($\Gamma_{O8+}$). The purple dashed traces represent the inner core boundary, separatrix, and LCFS, while the thick black line indicates the outer wall of the WEST Tokamak. $n_{O8+}$ is approximately 1% of $n_e$. The green lines in the top-left subplot illustrate the line of sight (LOS) used for measuring line emissions at the ICRH antenna limiters in WEST experiments.</figcaption></figure>

earlier. This technique mimics the behavior of RF sheaths via thin dielectric layers placed adjacent to PFCs, where spatially varying permittivity and conductivity are derived from local plasma parameters and RF fields [8]. The model solves Maxwell's equations in a cold plasma background to capture full-wave behavior and its impact on sheath rectification.

The COMSOL geometry includes the full WEST ICRH antenna structure, including Faraday Screen (FS) bars and RF limiters, as shown in figure 6. The rectified DC sheath

potentials exhibit strong asymmetries across these structures, arising from spatial variations in magnetic field orientation, antenna geometry, and plasma parameters. These computed voltages, $V_{\text{sheath}}^{\text{RF}}$ are then used as boundary conditions in STRIPE to drive erosion and impurity source terms.

For input plasma conditions, the electron density profile $n_e$- is obtained from reflectometry measurements in WEST discharge #57877 (figure 5). Since electron temperature data near the antenna is limited, a uniform value of $T_e$- = 10 eV
<figure><img src="image_8.png" /><figcaption>**Figure 5.** Radial profiles at the OMP for WEST discharge #57877. (a) Comparison of electron density $n_e$- from SolEdge3x simulations (blue) with reflectometry measurements (purple squares). Also shown are SolEdge3x predictions for deuterium ion density $n_{D+}$ (red) and oxygen ion density $n_{O^{8+}}$ (green circles). (b) Corresponding temperature profiles from SolEdge3x for electrons $T_e$- (blue), deuterium ions $T_{D+}$ (red), and oxygen ions $T_{O^{8+}}$ (green circles). Profiles are computed for a power crossing the separatrix of $P_{sep}$ = 1.0 MW (ICRH case).</figcaption></figure>

is assumed to enable consistent sheath impedance estimates. While simplified, this temperature provides a reasonable basis for sheath modeling in the absence of strong gradients or resonance effects.

A critical modeling detail is the treatment of the plasma density in front of the FS bars. Reflectometry measurements do not extend past the RF limiters into this region. To address this gap, a parameterized extrapolation of the density profile is employed, following the methodology described in [8]. This extrapolated profile ensures that sheath potentials can be evaluated across the entire antenna-facing surface, including areas behind the RF limiters where direct diagnostics are unavailable.

It is important to note that while the present discharge (#57877) does not encounter a LH resonance (LHR) within the antenna-facing region, this is not always the case. In

<figure><img src="image_9.png" /><figcaption>**Figure 6.** COMSOL-calculated rectified DC sheath voltage (VDC) on the WEST ICRH antenna structures, including Faraday Screen (FS) bars. The voltage distribution exhibits clear asymmetry, attributed to variations in electron density, magnetic field orientation, and antenna geometry [8].</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>**Figure 7.** WEST ICRH antenna geometry used in STRIPE modeling: (a) original CAD model of the antenna, and (b) simplified computational domain highlighting antenna limiters where spectroscopic measurements are available.</figcaption></figure>

discharges with lower densities—below LHR—slow wave propagation near the antenna can become more prominent, leading to enhanced wave-plasma interactions. These interactions may significantly increase rectified sheath potentials and modify RF field penetration. Accurately modeling such scenarios in COMSOL is challenging due to the short wavelengths and complex field structures associated with the LHR. Addressing these effects will be an important aspect of future modeling efforts and discussed later in section 7.4.
## 4.2. CAD defeaturing and mesh refinement for ICRH antenna structures

A realistic computational geometry is essential for STRIPE's finite-element analysis. However, the original CAD model of the WEST ICRH antenna, shown in figure 7(a), is defeatured to eliminate small or intricate features that are computationally costly and unnecessary for modeling. This reduction focuses computational resources on regions of interest, such as the antenna limiters, shown in figure 7(b). For this study, the analysis is confined to the antenna limiters where spectroscopic measurements are available, excluding the FS region. The full antenna geometry will be modeled in future simulations.

## 4.3. Tungsten erosion yield calculation

The STRIPE framework integrates RustBCA, a BCA code [26, 27] optimized for simulating ion-material interactions, to calculate the sputtering yield for W under ion impacts from D⁺, oxygen, and W ions across a range of $\mathcal{E} = 10-10000$ eV and $\theta = 0-90^{\circ}$. The sputtering yield results, presented in figure 8, reveal significant dependencies on ion energy and angle. For example, figure 8(a) shows deuterium's low sputtering yield across most impact angles with a very high sputtering threshold of ~250 eV, while figures 8(b) and (c) highlight higher yields for oxygen and W ions at specific angles and energies.

Figure 8 illustrates general trends in sputtering yield as a function of ion energy and incident angle for various ion species, derived under simplified conditions. These trends do not consider factors such as geometry curvature, magnetic field orientations, sheath effects, or plasma-specific variations.

## 4.4. IEADs and gross W erosion flux

The methodology for coupling GITR with RustBCA to compute IEADs and $Y_{eff}$ is described in section 2. This section focuses on the calculation of $\Gamma_{gross,W}$ on the WEST ICRH antenna limiters, with emphasis on the plasma and sheath conditions that define the boundary conditions for the GITR simulations.

Figures 9 and 10 present vertical profiles of charge-resolved oxygen ion parameters and sheath potentials at the Q2 antenna left limiter for the ICRH and ohmic cases, respectively. The profiles are spatially resolved along discrete LOS and averaged over the fiber's focal width (90 mm) [35]. These inputs serve as boundary conditions for the GITR simulations.

For the ICRH case, the profiles (figure 9) show that $O^{6+}$ and $O^{8+}$ dominate $n_O$, peaking near $z \sim 0.1$ m. $T_O$, averaged over the LOS focal width, ranges from 4-5.5 eV and is relatively uniform. $\Gamma_O$ exhibits a midplane dip near $z \sim 0.1$ m, consistent with a flow stagnation point, while the upper region shows higher fluxes dominated by high charge states. The RF-enhanced $V_{sheath}$ reaches >150 V near the top of the limiter, expected to increase ion impact energy and $Y_{eff}$.

In the ohmic case (figure 10), $n_O$ and $\Gamma_O$ are overall lower, and the sheath potential remains below 20 V. Similar vertical trends in ion profiles persist, with a midplane minimum in

$\Gamma_O$ and elevated values toward the top. However, the lower $V_{sheath}$ is expected to significantly reduce ion acceleration and sputtering.

These profiles are used to initialize GITR by launching $10^4$ tracer ions per surface element from the sheath entrance, with energy sampled from local $T_O$ and $V_{sheath}$, and angular distributions based on local surface normals. Each of the ~20 000 surface elements received a unique charge- and location-specific IEAD, combined with RustBCA data to compute $Y_{eff}$ using equation (3). The resulting $\Gamma_{gross,W}$ was computed as the product of $Y_{eff}$ and $\Gamma_O$ for each surface element as shown in equation (4).

The final erosion maps (sections 6.1 and 6.2) reflect these inputs-showing enhanced erosion where both ion flux and $V_{sheath}$ are elevated, particularly in the upper limiter region for the ICRH case.

# 5. Synthetic diagnostic method for converting $W-I$ erosion flux to photon emission

A synthetic diagnostic is developed within STRIPE to convert modeled neutral W (commonly referred as $W-I$ in spectroscopy) erosion flux into brightness (photon emission), $I_{\phi,W-I}$ for direct comparison with experimental spectroscopic data, utilizing the collisional radiative code 'ColRadPy' [31]. This diagnostic leverages S/XB coefficients for $W-I$ impurities, which represents the impurity flux to photon emission ratio.

Figure 11(a) presents the S/XB factor for the $W-I$ 400.9 nm line emission, calculated using ColRadPy, as a function of $T_e^-$ and $n_e^-$. This factor serves as a basis for linking $\Gamma_{gross,W}$ to the observable $I_{\phi,W-I}$. To accurately reflect the plasma conditions in WEST, the S/XB values are interpolated using the density and temperature profiles from SolEdge3x, depicted in figure 4. The resulting S/XB($T_e^-$, $n_e^-$) values, derived from SolEdge3x's $T_e^-$ and $n_e^-$ for the WEST case, are shown in figure 11(b).

The interpolated S/XB factor is then applied to convert the modeled $\Gamma_{gross,W}$, into $I_{\phi,W-I}$, using:

$$I_{\phi,W-I} = \frac{1}{A} \int \frac{\Gamma_{gross,W}}{4\pi S/XB} dA \quad (5)$$

where A represents the optical viewing area with radius set to 90 mm as per previous diagnostic measurements [35].

This synthetic diagnostic validates STRIPE's model predictions by comparing calculated $I_{\phi,W-I}$ with spectroscopic measurements from WEST discharge #57877, benchmarking the framework's performance in capturing RF-induced sheath effects and ion impacts on W erosion.

# 6. Results: W erosion at the WEST ICRH antenna limiters

This section presents the predicted $\Gamma_{gross,W}$ at the WEST ICRH antenna limiters using the STRIPE framework, as described in section 4.4. Both thermal and RF sheath scenarios are analyzed for the ICRH phase and thermal sheath only in ohmic phase
<figure><img src="image_11.png" /><figcaption>**Figure 8.** RustBCA-simulated sputtering yield for W due to impacts from (a) deuterium (D), (b) oxygen (O), and (c) W ions. The yield is shown as a function of incident ion energy and angle, highlighting differences in sputtering behavior across ion types.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>**Figure 9.** Vertical profiles of oxygen ion parameters and sheath potential at the antenna left limiter in WEST during the ICRH case ($P_{\text{sep}}$ = 1 MW). Data at each LOS are shown, averaged over the fiber's focal spot. Subfigures show: (a) ion density $n_O$, (b) ion temperature $T_O$, (c) ion flux $\Gamma_O$, and (d) RF and thermal sheath potentials $V_{\text{sheath}}$, all as functions of vertical position $z$.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>**Figure 10.** Vertical profiles of oxygen ion parameters and thermal sheath potential at the antenna left limiter in WEST during the ohmic case ($P_{\text{sep}}$ = 0.4 MW). Data at each LOS are shown, averaged over the fiber's focal spot. Subfigures show: (a) $n_O$, (b) $T_O$, (c) $\Gamma_O$, and (d) thermal $V_{\text{sheath}}$, all as functions of $z$.</figcaption></figure>

to evaluate how rectified sheath potentials modify impurity-driven erosion patterns. Emphasis is placed on the dependence of sputtering on magnetic geometry, ion charge state, and sheath potential.

## 6.1. Magnetic field incidence and its role in erosion localization

A key geometric factor influencing local erosion is the angle between the magnetic field vector and the surface normal.

This angle determines the directionality of ion impact and the component of kinetic energy delivered normal to the surface, which directly affects sputtering yield. Figure 12 shows the spatial distribution of the magnetic field angle on the WEST ICRH antenna limiter surfaces, expressed as $\cos\theta_B$, where $\theta_B$ is the angle between the magnetic field and the surface normal.

Regions with $\cos\theta_B \approx 1$ (shown in red) correspond to nearly normal magnetic field incidence, promoting strong sheath-aligned ion acceleration and higher normal energy
<figure><img src="image_14.png" /><figcaption>**Figure 11.** ColRadPy-calculated S/XB factor for W-I 400.9 nm line emission: (a) S/XB as a function of $T_e^-$ (blue curve) and $n_e^-$ (red curve); (b) interpolated S/XB matching SolEdge3x profiles from figure 4.</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>**Figure 12.** Magnetic field angle relative to the surface normal at the WEST ICRH antenna limiters. The color scale represents $\cos\theta_B$, where 1 indicates perpendicular incidence and 0 indicates tangential incidence. Regions with high $\cos\theta_B$ promote stronger ion impact normal to the surface, leading to enhanced sputtering.</figcaption></figure>

deposition-conditions favorable for sputtering. In contrast, regions with $\cos\theta_B \sim 0$ (green) indicate field lines nearly tangential to the surface, where ions strike at shallow angles and sputtering efficiency is greatly reduced.

This angular dependence plays a critical role in shaping the erosion patterns under both thermal and RF sheath conditions. As demonstrated in the following subsections, regions of enhanced tungsten erosion predicted by STRIPE align closely with zones of higher $\cos\theta_B$, confirming that magnetic field orientation is one of the primary driver of erosion localization on the antenna limiters.

## 6.2. Erosion results: ICRH phase with thermal sheath

In the thermal sheath regime, $V_{\text{sheath}}^{\text{thermal}}$ is governed by classical Bohm conditions and is relatively low, typically on the order of 25 V as shown in figures 9 and 10. Even so, high-charge-state impurity ions can gain significant energy through sheath acceleration. Figure 13 presents the STRIPE-predicted (a) $Y_{\text{eff}}$ and $\Gamma_{\text{gross},W}$ in ICRH phase under thermal sheath conditions for oxygen ions with charge states $x \ge 6$.

Erosion is concentrated on the front-facing limiter surfaces, where magnetic field lines intersect more normally and the sheath electric field aligns with ion trajectories. High-charge-state oxygen ions especially $O^{6+}$ to $O^{8+}$-dominate the erosion due to their larger energy gain across the sheath. For instance, $O^{8+}$ ions gain up to 200 eV ($8e \times 25$ V), significantly more than $O^{5+}$ ions, which reach only 125 eV. This leads to a sharp increase in sputtering yield for higher charge states, as confirmed by RustBCA surface response simulations. In contrast, $D^+$ ions gain only 25 eV, well below the sputtering threshold for W (250 eV), and thus contribute negligibly to erosion in this regime.

The vertical erosion profile shows a pronounced asymmetry, with a local minimum near the OMP ($z=0$). This dip is attributed to a combination of magnetic geometry and parallel plasma flow stagnation. At the midplane, field lines become tangential to the limiter surface, reducing normal ion flux. Simultaneously, plasma flow stagnates along field lines in this region, further limiting the number of ions reaching the surface. These combined effects result in suppressed sputtering at the midplane and define the spatial baseline for erosion in the absence of RF sheath effects.

## 6.3. RF sheath case: ICRH phase erosion results

In the presence of ICRH-driven RF sheaths, the local sheath potential is no longer governed by classical Bohm sheath physics alone. Instead, RF rectification processes produce strong localized DC potentials that can reach several hundred volts. In this study, the spatial distribution of $V_{\text{sheath}}^{\text{RF}}$ is computed using COMSOL full-wave simulations of the WEST ICRH antenna [8], with peak values approaching 300 V (see figure 6).

As shown in figure 14, the elevated sheath potentials significantly increase ion impact energy and, consequently, the sputtering yield. $O^{8+}$ ions can now gain up to 2400 eV ($8e \times 300$ V), leading to $Y_{\text{eff}}$ much higher than in the thermal sheath case. $\Gamma_{\text{gross},W}(O^{x+} \rightarrow W)$ with RF sheath increase by approximately an order of magnitude, with erosion becoming highly localized and asymmetric.

The strongest erosion is observed on the upper limiter surfaces, consistent with the COMSOL-calculated distribution of $V_{\text{sheath}}^{\text{RF}}$. These regions also correspond to high magnetic incidence (see figure 12) and favorable plasma flow, enabling efficient sheath-aligned ion acceleration. Near the midplane, however, erosion remains suppressed due to weaker RF fields
<figure><img src="image_16.png" /><figcaption>**Figure 13.** 3D maps of (a) effective sputtering yield, $Y_{\text{eff}}(O^{x+} \rightarrow W)$, and (b) gross erosion flux, $\Gamma_{\text{gross,W}}(O^{x+} \rightarrow W)$, for oxygen ions with $x \ge 6$ under thermal sheath conditions. Erosion is localized to front-facing surfaces where magnetic field lines are more normal to the surface, enhancing normal ion impact and sputtering.</figcaption></figure>

and the continued presence of flow stagnation and tangential magnetic geometry.

Despite the increase in sheath potential, $D^+$ ions still do not exceed the W sputtering threshold for most surface locations and thus remain insignificant contributors to $\Gamma_{\text{gross,W}}$ under RF sheath conditions.

Overall, the comparison between figures 13 and 14 demonstrates that RF sheath rectification substantially amplifies W erosion. This enhancement arises not only from increased ion impact energy but also from spatial asymmetries introduced by localized RF field structure, antenna geometry, and magnetic topology.
<figure><img src="image_17.png" /><figcaption>**Figure 14.** 3D maps of (a) effective sputtering yield, $Y_{\text{eff}}(O^{x+} \rightarrow W)$, and (b) gross erosion flux, $\Gamma_{\text{gross},W}(O^{x+} \rightarrow W)$, for oxygen ions with $x \ge 5$ under RF sheath conditions. Rectified sheath potentials up to 300 V significantly enhance impact energies, particularly for $O^{8+}$, resulting in localized erosion hotspots on upper limiter surfaces.</figcaption></figure>

## 6.4. Integrated tungsten erosion flux at the ICRH antenna limiters

This section evaluates the area-integrated gross W-erosion flux, $G_{\text{gross},W}(O^{x+} \rightarrow W)$, at the WEST ICRH antenna limiters. Erosion estimates were generated using the STRIPE framework across three operating scenarios: (i) RF sheath conditions during ICRH phase, (ii) thermal sheath conditions during

ICRH phase, and (iii) thermal sheath conditions during ohmic phase. The integrated flux is calculated by summing local sputtering fluxes over all limiter surface elements, using charge-resolved oxygen ion fluxes and energy-angle distributions informed by GITR and COMSOL-based sheath potentials.

Table 1 summarizes the contributions from high-charge-state oxygen ions ($O^{5+}-O^{8+}$) and $D^{+}$, along with the total integrated erosion flux for each case. As expected, $O^{8+}$ ions
<table><caption>**Table 1.** Area-integrated gross W erosion flux, *G* [particles/s], computed using STRIPE for the WEST ICRH antenna limiters.</caption><thead><tr><th>Sheath Condition</th><th>O<sup>8+</sup></th><th>O<sup>7+</sup></th><th>O<sup>6+</sup></th><th>O<sup>5+</sup></th><th>D<sup>+</sup></th><th>Total Flux</th></tr></thead><tbody><tr><td>RF (ICRH)</td><td>2.263 × 10<sup>17</sup></td><td>1.681 × 10<sup>17</sup></td><td>4.02 × 10<sup>16</sup></td><td>1.109 × 10<sup>15</sup></td><td>9.673 × 10<sup>11</sup></td><td>4.348 × 10<sup>17</sup></td></tr><tr><td>Thermal (ICRH)</td><td>1.928 × 10<sup>16</sup></td><td>1.101 × 10<sup>16</sup></td><td>2.579 × 10<sup>15</sup></td><td>8.950 × 10<sup>14</sup></td><td>0</td><td>3.285 × 10<sup>16</sup></td></tr><tr><td>Thermal (Ohmic)</td><td>8.050 × 10<sup>15</sup></td><td>4.860 × 10<sup>15</sup></td><td>6.450 × 10<sup>14</sup></td><td>2.660 × 10<sup>14</sup></td><td>0</td><td>1.385 × 10<sup>16</sup></td></tr></tbody></table>

<table><caption>**Table 2.** Comparison of simulated and experimental total integrated photon brightness at the WEST Q2 antenna.</caption><thead><tr><th rowspan="2">Phase</th><th>Sim. Brightness</th><th>Exp. Brightness</th></tr><tr><th>I<sub>φ, total</sub> (STRIPE)</th><th>I<sub>φ, total</sub> (Expt.)</th></tr></thead><tbody><tr><td>Ohmic</td><td>1.39 × 10<sup>15</sup></td><td>1.32 × 10<sup>15</sup></td></tr><tr><td>ICRH</td><td>4.35 × 10<sup>16</sup></td><td>3.38 × 10<sup>16</sup></td></tr></tbody></table>

dominate the W sputtering response due to their high sheath-accelerated energies, particularly under RF-enhanced sheath conditions.

Under RF sheath conditions, the total gross erosion flux reaches $4.35 \times 10^{17}$ particles/s-over 13 times higher than under thermal sheath conditions during ICRH and 31 times greater than during the ohmic phase. $O^{8+}$ ions alone contribute more than 50% of the total erosion flux in this case. The contribution from $D^{+}$ remains negligible across all scenarios, confirming that erosion is almost entirely impurity-driven, and depends heavily on charge state and sheath potential.

To further assess the model fidelity, $I_{φ, total}$ was calculated from the simulated $G_{gross, W}$ using the known S/XB. These synthetic $I_{φ, total}$ (STRIPE) values are compared with experimental measurements in table 2.

The simulated $I_{φ, total}$ values show strong agreement with experimental observations. In the ohmic phase, the model underpredicts the experimental brightness by only 5%, while in the ICRH phase with RF sheath, the simulated $I_{φ, total}$ is within 30% of the measured value. The factor-of-30 increase in both modeled $G_{gross, W}$ and $I_{φ, total}$ between ohmic and ICRH phases aligns well with spectroscopic trends, validating the role of RF sheath rectification and high-charge-state impurity acceleration as the primary erosion mechanisms during ICRH operation.

## 6.5. Validation with experimental observations

To further validate the modeled $Γ_{gross, W}(O^{x+} → W)$, STRIPE predictions-assuming a plasma composition of 99% $D^{+}$ and 1% oxygen-are compared with spectroscopic measurements from WEST discharge #57877 during both the ICRH and ohmic phases. Using charge-resolved sputtering fluxes and appropriate S/XB coefficients, STRIPE's synthetic diagnostic framework (section 5) converts $Γ_{gross, W}(O^{x+} → W)$ into brightness profiles $I_φ$, enabling direct comparison with experimental $W-I$ line emission.

The spectroscopic data were acquired along a set of vertical LOS intersecting the left Q2 antenna limiter at the following positions: $z = 0.4$ m, 0.3473 m, 0.1689 m, 0.0749 m, 0.0106 m,

-0.0851 m, -0.2 m, -0.3042 m and -0.4 m. As indicated by green lines in figure 4.

### 6.5.1. ICRH phase validation.
Figure 15 compares the simulated and experimental $I_{φ, W-I}$ of the W-I 400.9 nm line emission along the Q2 antenna left limiter during discharge #57877 ($t = 8$ s). The simulated $I_{φ, W-I}$, are derived from STRIPE by charge-resolved $Γ_{gross, W}(O^{x+} → W)$, weighted by the corresponding photon emission coefficients (S/XB) and averaged over the focal width of LOS, for both RF and thermal sheath scenarios.

Panel (a) of figure 15 shows the RF sheath case in ICRH phase. STRIPE reproduces the overall magnitude and trend of the experimental $I_{φ, W-I}$ reasonably well, though some spatial discrepancies are observed. In particular, the simulation predicts a sharp peak at $z = 0.3473$ m, which corresponds to a localized hotspot in the rectified RF sheath potential computed by COMSOL (see figure 6). This region also exhibits the highest simulated $Γ_{gross, W}(O^{x+} → W)$, driven by elevated sheath voltages that strongly accelerate high-charge-state oxygen ions (notably $O^{6+}-O^{8+}$), resulting in enhanced sputtering.

The simulation also shows a dip in $I_{φ, W-I}$ near the OMP ($z \approx 0.1$ m), associated with reduced normal ion flux. This reduction is attributed to the combined effects of a plasma flow stagnation point-where parallel plasma flow along magnetic field lines vanishes-and the local tangency of the magnetic field to the limiter surface. While this dip is consistent with sheath-driven erosion physics, it is not observed in the experimental brightness profile. The absence of this feature in the measured data may be due to line-of-sight integration effects, spatial averaging over unresolved small-scale structures, or diagnostic limitations in vertical resolution.

Panel (b) shows the thermal sheath case. Here, simulations shows significantly lower $I_{φ, W-I}$-approximately one order of magnitude below the RF case-due to reduced sheath potentials and lower ion impact energies. The modeled $I_{φ, W-I}$ still captures the general increasing trend toward the upper limiter region, although a spatial shift is observed in the peak location. This offset could be attributed to geometrical asymmetry
<figure><img src="image_18.png" /><figcaption>**Figure 15.** Comparison of modeled and experimental $W-I$ 400.9 nm line brightness $I_{\phi,W-I}$ at the WEST ICRH antenna left limiter during discharge #57877 ($t=8$ s). (a) RF sheath case: STRIPE predictions for $O^{5+}-O^{8+}$ show reasonable agreement with experimental brightness magnitude with some spatial disagreement near OMP and at $z=0.3473$ m, aligned with a COMSOL-predicted RF sheath hotspot. (b) Thermal sheath case: Emission levels are approximately ten times lower. The model captures the overall trend but exhibits a spatial offset relative to the observed brightness peak.</figcaption></figure>

of the ICRH antenna, localized variations in plasma parameters, sheath conditions not captured in the model.

Although the total STRIPE-modeled $I_{\phi,\text{total}}$, shows good agreement with experimentally observed values, some spatial discrepancies in $I_{\phi,W-I}$ remain. In particular, the model predicts a dip in $I_{\phi,W-I}$ near the OMP, attributed to suppressed ion flux resulting from plasma flow stagnation and the tangential alignment of magnetic field lines at the limiter surface. This feature is not apparent in the current experimental dataset. At the same time, the model identifies highly localized erosion hotspots that align closely with regions of elevated incident ($\Gamma_O$) and COMSOL-predicted rectified sheath voltages at the antenna limiters.

Interestingly, recent WEST campaigns-such as discharge #61698-featuring improved vertical resolution and better-aligned spectroscopic lines of sight have observed midplane

<figure><img src="image_19.png" /><figcaption>**Figure 16.** Comparison of modeled and experimental $W-I$ 400.9 nm brightness, $I_{\phi,W-I}$, at the WEST ICRH antenna left limiter during the ohmic phase of discharge #57877 ($t=3$ s). STRIPE results assume thermal sheath conditions and show quantitative agreement with experimental brightness within error bars. A slight spatial offset is observed in the peak location.</figcaption></figure>

erosion suppression and brightness dips, along with asymmetric erosion hotspots concentrated near the upper portion of the limiter. These features are consistent with STRIPE's predictions [36]. Similar poloidal localization of RF-induced tungsten erosion has also been observed in AUG ICRH discharges [37]. The similarity between WEST and AUG observations supports the physical interpretation that such emission peaks result from real, localized RF sheath rectification rather than solely modeling artifacts. In earlier WEST datasets, the absence of these features could likely be due to limitations in spatial resolution, LOS integration effects, or imperfect alignment between diagnostics and the 3D antenna geometry. Ongoing experimental and modeling efforts are aimed at resolving these discrepancies more systematically.

Despite some remaining localized discrepancies, these findings indicate that STRIPE provides a physically consistent and reasonably accurate prediction of tungsten erosion and optical emission behavior. Continued improvements in diagnostic resolution and full 3D PMI modeling will be critical for refining quantitative agreement between simulation and experiment, as further discussed in section 7.

### 6.5.2. Ohmic phase validation.
Further validation of the STRIPE framework is performed using spectroscopic measurements from WEST discharge #57877 during the ohmic phase. In this regime, plasma parameters were relatively cooler and sheath potentials were lower than during ICRH as shown in figure 10. Background plasma profiles are obtained from SolEdge3x simulations with $P_{\text{sep}} = 0.4$ MW, and thermal sheath conditions were assumed throughout.

Using STRIPE's synthetic diagnostic module (see section 5), the charge-resolved $\Gamma_{\text{gross},W}(O^{x+} \rightarrow W)$, was converted into $I_{\phi,W-I}$, using appropriate S/XB. Figure 16 presents
a comparison between the modeled and experimental $I_{\phi}$ along
vertical LOS intersecting the left limiter.

The modeled $I_{\phi, W-I}$ shows quantitative agreement with the
experimental measurements, generally remaining within the
experimental uncertainty bounds. A modest peak in bright-
ness is predicted around $z = 0.2$ m, consistent with the experi-
mental trend, although a slight spatial shift is evident between
the model and the measured peak. This offset may be attrib-
uted to antenna geometrical asymmetry, local variations in
plasma parameters-such as edge density gradients, magnetic
field shaping, or temperature asymmetries-not fully captured
in the modeling. Furthermore, the signal-to-noise ratio in the
ohmic phase is close to 1, resulting relative large fluctuations
in signal and corresponding large error bars in this regime as
can be noted in figure 16.

As expected, the overall $I_{\phi, W-I}$ during the ohmic phase are
significantly lower than those observed during ICRH oper-
ation. This reduction reflects the decreased sheath potential
and correspondingly lower incident ion energies under purely
thermal sheath conditions. As discussed earlier, the lower
energy of both background $D^{+}$ and oxygen ions results in sput-
tering rates that are substantially reduced compared to the RF-
enhanced ICRH phase.

The relatively good agreement between modeled and
observed brightness profiles in this regime reinforces the
validity of the STRIPE framework under low-power, thermal
sheath-dominated conditions. The small spatial discrepancies
motivate further refinements in input profile resolution, sur-
face geometry fidelity, and possible 3D effects, which are
explored in detail in sections 7.2–7.4.

## 7. Discussion

The results presented in this study provide a comprehens-
ive understanding of W-erosion at ICRH antenna limiters in
WEST, highlighting the distinct effects of thermal vs. RF
sheath conditions during the ICRH phase. Validated against
experimental data, this study emphasizes the critical role of
RF-induced sheaths in amplifying erosion at PFCs. This dis-
cussion addresses implications for PMI in fusion devices,
potential STRIPE enhancements, and considerations for future
fusion reactor designs.

### 7.1. RF sheath-driven W erosion

A key finding of this study is the significant enhancement in
$\Gamma_{\text{gross},W}$ driven by RF sheaths. STRIPE simulations indicate
a ~30 times increase in $\Gamma_{\text{gross},W}$ when transitioning from the
ohmic phase to the ICRH phase, where elevated impurity ion
energies and sheath potentials dominate sputtering dynamics.
Within the ICRH phase itself, a further ~10 times increase in
$\Gamma_{\text{gross},W}$ is observed when comparing thermal vs. RF sheath
conditions, driven by rectified sheath potentials. These trends
are consistent with spectroscopic observations from WEST
discharge #57877.

As shown in figures 15(a) and (b), RF sheath potentials sub-
stantially elevate the impact energies of high-Z ions, notably
$O^{6+}$ and higher, thereby enhancing sputtering yields and W
erosion rates [14, 38]. STRIPE results suggest a near-linear
scaling between $\Gamma_{\text{gross},W}$ and the local sheath voltage.

The STRIPE simulations demonstrate the strong influence
of ICRH on PMI. RF-induced rectified potentials enable high-
energy impurity ion bombardment, accelerating material wear
at PFCs. These findings emphasize the necessity of incorpor-
ating RF sheath effects in predictive modeling for high-power
ICRH scenarios.

### 7.2. Spatial asymmetry in erosion

RF-driven erosion exhibits strong poloidal asymmetry, with
localized hotspots concentrated near the upper portion of the
limiter. As shown in STRIPE's 3D erosion maps, this asym-
metry arises from the interplay between local plasma condi-
tions, magnetic geometry, the RF field distribution (computed
using COMSOL), and spatial variation in rectified sheath
potentials $V_{\text{sheath}}^{\text{RF}}$.

As discussed in [8], while the magnitude of $V_{\text{sheath}}^{\text{RF}}$ is sensit-
ive to local plasma and geometric parameters, the spatial loca-
tion of erosion hotspots remains remarkably rigid across vary-
ing input conditions. The physical mechanisms behind this
rigidity are still under investigation. However, the modeled
erosion patterns align well with some recent observations in
WEST experiments. For example, WEST discharge #61698-
featuring improved vertical resolution and better-aligned lines
of sight-revealed brightness dips near the OMP and asymmet-
ric emission peaks near the upper limiter region, consistent
with STRIPE predictions [36]. Similar poloidal localization
of RF-induced W-emission has also been observed in AUG
experiments [37]. This experimental agreement further sup-
ports the interpretation that localized W erosion patterns are
driven by physical RF sheath rectification rather than numer-
ical artifacts or LOS effects.

An important geometric factor influencing these patterns
is the magnetic field angle relative to the surface normal. As
shown in figure 12, $\cos\theta_B$ is significantly greater than zero
on most front-facing limiter surfaces-particularly in regions
where erosion is strongest. This validates the use of the RF
sheath boundary condition in STRIPE, which assumes quasi-
normal field incidence. However, on the limiter sidewalls and
near the OMP, the magnetic field becomes nearly tangential,
and the sheath-equivalent dielectric model may be less accur-
ate. Notably, these regions already exhibit minimal erosion, so
any modeling inaccuracies are expected to have limited influ-
ence on the overall conclusions. The erosion dip near the OMP
is therefore likely due to both reduced ion flux-arising from
magnetic geometry and flow stagnation-and reduced model
fidelity in regions of tangential field-line incidence.

Currently, STRIPE uses 2D SolEdge3x profiles mapped
onto the 3D limiter geometry. Due to the vertical asym-
metry of the WEST ICRH antenna, this 2D-to-3D mapping
may underrepresent vertical variation in plasma exposure.
Future implementation of fully 3D SolEdge3x simulations will
provide improved resolution of local plasma conditions and field topology.

In addition, the present simulations do not yet incorporate **E** × **B** drifts or biased wall conditions. Even in the absence of external biasing, local **E** × **B** flows can arise due to the combined effects of sheath electric fields (thermal or RF) and the background magnetic field. These drifts can generate localized convective cells and modify impurity transport and erosion patterns near RF antennas. Prior experimental and theoretical studies [39–41] have shown that **E** × **B** flows can lead to cross-field displacement of ions and enhanced poloidal asymmetry in impurity deposition. In the presence of strong RF rectification, these effects may be further amplified due to non-uniform sheath potentials. Capturing these dynamics will require integration of drift terms in the background plasma model or kinetic treatment of cross-field impurity transport. Such enhancements are planned in future extensions of STRIPE.

Poloidal asymmetry in erosion remains a critical challenge for maintaining PFCs integrity in ICRH-heated plasmas. Accurate modeling of RF sheath behavior, magnetic field alignment, impurity dynamics, and drift-driven transport is essential for designing erosion-resilient antenna structures and optimizing future RF heating systems.

### 7.3. Validation with WEST diagnostics

**ICRH Phase:** STRIPE reproduces the overall magnitude of $W-I$ (400.9 nm) emission observed during the ICRH phase, with $I_{\phi, total}$ in good agreement with experimental data. However, the model predicts a significantly more localized and intense hotspot in $I_{\phi, W-I}$ near $z = 0.3473$ m, driven by the COMSOL-modeled $V_{\text{sheath}}^{\text{RF}}$ and elevated $\Gamma_O$, which is not observed in the experimental profile. This spatial discrepancy suggests that either the modeled sheath potential is overly localized or the diagnostic LOS integration smooths out such features. Additionally, the model predicts a midplane dip in brightness not captured by the measurements, indicating potential differences in local plasma or sheath conditions.

**Ohmic Phase:** Under thermal sheath-only conditions, STRIPE reproduces the expected reduction in $I_{\phi, total}$ magnitude, consistent with experimental observations. However, as in the ICRH case, a spatial offset exists between the modeled and measured $I_{\phi, W-I}$ peaks. This mismatch may be attributed to uncertainties in the mapped plasma profiles or geometric alignment differences between the modeled and actual diagnostic LOS.

### 7.4. Model sensitivity and uncertainty

STRIPE predictions depend on background profiles, $V_{\text{sheath}}$, and IEADs. Uncertainty in these parameters can have impact on the erosion patterns. Discrepancies during the ICRH phase likely arise from variations in COMSOL-predicted $V_{\text{sheath}}^{\text{RF}}$ as well as uncertainties in local plasma and sheath conditions.

It is important to note that while reflectometry data provides reliable measurements in the region near the antenna, it does not extend beyond the RF limiters into the region directly in

front of the FS bars. To ensure continuity in the COMSOL modeling, the density in this unmeasured region is extrapolated using a parameterized fit informed by nearby reflectometry data and typical scrape-off layer behavior, as described in [8]. This extrapolation is essential for calculating the full spatial distribution of sheath potentials. In future studies, the use of additional edge diagnostics such as He-beam spectroscopy systems [42] deployed on devices like DIII-D could help reduce uncertainty in far-SOL density estimates near the antenna structure.

Additionally, while the present WEST discharge (#57877) does not encounter a LHR in the antenna-facing region due to its relatively high electron density, this is not always the case. In other discharges, an LHR occurring just behind the FRs can strongly influence wave propagation and enhance local sheath voltages. These scenarios are challenging to model in COMSOL due to short wavelengths and slow wave propagation near the resonance. Full-wave solvers such as AORSA [43], which can resolve mode conversion, slow wave dynamics, and kinetic effects such as Landau damping, may offer a complementary path forward for modeling resonance-driven interactions and their impact on RF sheath formation. Incorporating such models remains an important goal for future work.

A 99% D+, 1% O composition was assumed. O is used as a proxy for light impurities in WEST #57877. However, recent WEST campaigns have employed boron powder conditioning [44, 45]. Future STRIPE simulations will incorporate boron and other impurity species to improve scenario fidelity.

More advanced kinetic or turbulence-sheath coupled models could further improve the predictive fidelity of STRIPE but remain computationally demanding. Balancing model accuracy with practical runtime will be essential for deployment in reactor-scale design studies.

### 7.5. STRIPE development pathways

STRIPE integrates SolEdge3x, COMSOL, GITR, and RustBCA to simulate gross and net erosion, re-deposition, and impurity transport. GITR supports global impurity migration and PFC interaction modeling, which is crucial for evaluating erosion and re-deposition over time.

From a computational standpoint, full STRIPE simulations are resource-intensive due to the need to resolve multiple coupled physics domains using distinct codes. A typical end-to-end STRIPE workflow—including plasma background generation with SolEdge3x, RF field and sheath potential computations in COMSOL, surface sputtering response via RustBCA, and impurity transport modeling with GITR—requires approximately 9000 CPU-hours and 120–150 GPU-hours on ORNL computing clusters. The total computational cost depends strongly on factors such as spatial mesh resolution, the number of injected particles, complexity of the sheath voltage maps, and fidelity of limiter geometry representation. STRIPE leverages parallel CPU execution for SOL plasma transport (SolEdge3x), RF sheath calculations (COMSOL) and surface interaction modeling (RustBCA), while GPU acceleration is used for GITR-based IEADs and impurity
transport. This hybrid architecture enables tractable simula-
tions of realistic device-scale geometries with high physical
fidelity.

Future STRIPE simulations will incorporate GITRm [46],
an adaptive mesh version, to resolve full antenna geometries
and multi-species impurity transport.

Enhancements such as temperature-dependent $Y_{\text{eff}}$, crys-
tallographic dependence [47], and turbulence-informed edge
profiles [48] will refine predictive accuracy. Coupling to integ-
rated plasma simulator [49] will streamline STRIPE integra-
tion into broader reactor-scale modeling workflows.

7.6. Implications for reactor design

Findings have implications for future devices (ITER, SPARC, MPEX) where ICRH is prominent. Elevated $\Gamma_{\text{gross,W}}$ under RF sheaths can accelerate PFC degradation, emphasizing the need for RF-resilient materials.

Accurate modeling of $V_{\text{sheath}}^{\text{RF}}$ and IEADs is essential for erosion prediction and component lifetime estimates. These factors are critical for PFC design, maintenance planning, and overall fusion device performance.

8. Summary

This study demonstrates the dominant role of RF-induced sheaths in enhancing w-erosion at ICRH antenna limiters in WEST. STRIPE modeling shows that $G_{\text{gross,W}}$ during the ICRH phase under RF sheath conditions reaches $4.35 \times 10^{17}$ particles/s-over 13 times higher than under thermal sheath conditions during the same phase ($3.29 \times 10^{16}$ particles/s), and more than 30 times greater than the ohmic-phase value ($1.39 \times 10^{16}$ particles/s). These results confirm that RF sheath rectification significantly amplifies impurity-driven erosion in RF-heated plasmas.

High-charge-state oxygen ions ($O^{6+}$, $O^{7+}$, $O^{8+}$) are identified as the primary contributors to W sputtering, with $O^{8+}$ alone accounting for approximately 52% of the total erosion flux under RF sheath conditions. In contrast, $D^+$ ions contribute negligibly across all scenarios, emphasizing the importance of light impurity ion charge state and impact energy in driving material erosion. Spatially, erosion is strongly localized near regions of elevated RF sheath potential, as predicted by COMSOL, with peaks observed near the upper limiter and suppression near the OMP, where magnetic field lines intersect PFCs tangentially.

The STRIPE framework-integrating SolEdge3x, COMSOL, RustBCA, and GITR-enables self-consistent modeling of PMI by combining RF sheath physics, ion transport, and surface response. Validation against W-I (400.9 nm) spectroscopic data from WEST discharge #57877 shows good agreement in overall emission magnitude and trends. However, spatial discrepancies remain-notably at $z = 0.3473$ m, where STRIPE predicts a more localized and intense hotspot than observed-indicating the need for improved spatial resolution in plasma profiles and sheath geometry in future modeling.

While recent linear device studies (Proto-MPEX [12, 13, 50], PISCES-RF [51]) have demonstrated STRIPE-like workflows for whole-device impurity transport, net erosion, and re-deposition, the present study is focused specifically on validating gross erosion predictions and demonstrating STRIPE's core capabilities. The modeling of net erosion, re-deposition, and W self-sputtering effects originating from ICRH antenna limiters in WEST will be addressed in a forthcoming companion publication.

Despite these limitations, STRIPE provides robust insight
into impurity-driven erosion under RF conditions. Its ability
to capture 3D effects, charge-resolved ion contributions, and
sheath-enhanced erosion makes it a valuable predictive tool for
evaluating PFC performance. These results offer critical guid-
ance for mitigating PMI in next-generation fusion devices and
for informing the design of RF-resilient materials and antenna
geometries.

Acknowledgment

This material is based upon work supported by the U.S.
Department of Energy, Office of Science, Office of Advanced
Scientific Computing Research and Office of Fusion Energy
Science, Scientific Discovery through Advanced Computing
(SciDAC) program. This research used resources of the Fusion
Energy Division, FFESD and the ORNL Research Cloud
Infrastructure at the Oak Ridge National Laboratory, which is
supported by the Office of Science of the U.S. Department of
Energy under Contract No. DE-AC05-00OR22725. The work
from Princeton Plasma Physics Laboratory is supported by
the US Department of Energy under Contract No. DE-AC02-
09CH1146.

Appendix A. RF sheath model and dependent parameters

To complement the description in section 2, we summarize here the theoretical and computational framework used to model RF sheath boundary conditions via the sheath-equivalent dielectric layer technique [8, 12, 13].

A.1. Overview of RF sheath physics

RF sheaths form at material interfaces in contact with RF-
driven plasmas when a net time-averaged potential (rectified
sheath potential) develops due to oscillating RF fields. This
potential can accelerate ions toward the surface, increasing
sputtering and impurity release. Accurate modeling of these
sheaths is essential in RF-heated devices, particularly near
ICRF or helicon antennas.

A.2. Sheath-equivalent dielectric layer method

The sheath model implemented here approximates the phys-
ical sheath as a thin artificial dielectric layer with thickness *d*
such that $\lambda_D \ll d \ll \lambda_{RF}$, where $\lambda_D$ is the Debye length and
$\lambda_{RF}$ is the RF wavelength. The layer is thin in comparison
with the RF length scales and the geometry length scales, but still much thicker than the physical sheath length scale. This approach avoids the need for direct implementation of sheath boundary conditions by embedding the sheath physics into the material properties of the layer.

The complex dielectric constant $\varepsilon$ and conductivity $\sigma$ of this layer are derived from the local RF sheath admittance per unit area $y_{sh}$, following the impedance formalism in [25]

$$y_{sh} = \frac{\langle J\bar{V} \rangle}{\langle V^2 \rangle} - i\omega \frac{\langle J\dot{V} \rangle}{\langle \dot{V}^2 \rangle} \quad (A.1)$$

where $J$ is the RF current density, $V$ is the sheath voltage, and $\omega$ is the RF angular frequency. This admittance is a function of dimensionless quantities: ion mobility parameter, $\hat{\omega} = \omega/\omega_{pi}$, the ion magnetization parameter, $\hat{\Omega} = eB/m_i\omega_{pi}$, the normal component of the unit vector parallel to magnetic field, $b_n = \mathbf{B} \cdot \mathbf{n}/B$ and the 0 to peak amplitude $\xi = e\phi_{sh}/T_e$. Here $\omega_{pi}$ is the ion plasma frequency, $\mathbf{n}$ is the unit surface normal, $\mathbf{B}/B$ is the unit vector parallel to magnetic field, $\phi_{sh}$ is the RF potential across the sheath or the simulated sheath layer and $T_e$ is the electron temperature.

From these, the complex impedance $Z_{sh}$ and admittance $Y_{sh}$ are determined using analytical fits (e.g. from [25, 52]), and the effective dielectric properties are then computed as:

$$\sigma_{\text{eff}} = \varepsilon_0 \omega_{\text{pi}} \hat{y} \frac{d}{\lambda_{\text{de}}}, \quad \varepsilon_{\text{eff}} = i \varepsilon_0 \frac{\hat{y}}{\hat{\omega}} \frac{d}{\lambda_{\text{de}}} \quad (A.2)$$

where $\hat{y}$ is the normalized admittance and $\lambda_{de}$ is a fitting parameter related to sheath width.

## Coupling the sheath model to COMSOL

The model is implemented in COMSOL Multiphysics as a user-defined material property applied to a thin dielectric layer at plasma-facing boundaries as shown in figure A1 where the dielectric sheath layer is highlighted in blue color on top metallic gray color antenna structures.

An iterative coupling procedure is used as described below:

(i) Run initial COMSOL simulation with vacuum sheaths (i.e. $\sigma = 0, \epsilon = 1$ in the sheath layer) to estimate local RF fields and plasma parameters at the sheath.

(ii) Compute updated $Z_{sh}$ and thus $\varepsilon_{\text{eff}}, \sigma_{\text{eff}}$ using the sheath model and the RF fields.

(iii) Apply the updated material properties to the sheath layer in COMSOL.

(iv) Repeat until the RF sheath potential $U_{sh}$ converges (typically within 3–5 iterations).

This approach enables a physically consistent representation of RF sheath effects in complex geometries and magnetized plasmas. It has been validated in linear devices (Proto-MPEX [12]) and extended to tokamak ICRF antennas (WEST [8]), demonstrating its utility in capturing hot-spot localization, sheath-enhanced sputtering, and directional impurity transport.

<figure><img src="image_20.png" /><figcaption>Figure A1. WEST Q2 RF antenna with dielectric sheath layer in blue.</figcaption></figure>

## Appendix B. Global impurity transport (GITR) code

The GITR code [53] is a GPU-accelerated, three-dimensional Monte Carlo particle-tracking tool developed to simulate impurity transport, PMI, and material erosion in MCF plasmas.

GITR advances tracer particles (e.g. $O^{x+}$) by integrating their trajectories under the influence of external electromagnetic fields and collisional interactions. The particle dynamics are governed by the following equation of motion:

$$m \frac{d\mathbf{v}}{dt} = q(\mathbf{E} + \mathbf{v} \times \mathbf{B}) - \nu_S m \mathbf{U} \\ \pm m \sqrt{\frac{\nu_{\perp}}{2\Delta t}} \mathbf{U}_{\perp} \pm m \sqrt{\frac{\nu_{\parallel}}{\Delta t}} \mathbf{U}_{\parallel} \\ + \alpha_e \nabla_{\parallel} B(kT_e) + \beta_i \nabla_{\parallel} B(kT_i). \quad (B.1)$$

Here, $m$ is the particle mass, $q$ is the charge, $\mathbf{v}$ is the velocity, and $\mathbf{E}$ and $\mathbf{B}$ are the background electric and magnetic fields. The relative velocity between the particle and plasma flow is given by $\mathbf{U} = \mathbf{v} - \mathbf{v}_{\text{flow}}$. The terms $\nu_S$, $\nu_{\perp}$, and $\nu_{\parallel}$ are the collisional frequencies for dynamical friction, pitch-angle scattering, and parallel energy diffusion, respectively. The final two terms account for thermal force contributions along magnetic field gradients due to temperature variations, where $T_e$ and $T_i$ are the electron and ion temperatures.
Kinetic energy scattering due to collisional interactions is modeled as:

$$ KE = (1 - \nu_E \Delta t) \frac{1}{2}mv^2 \quad (B.2) $$

where $\nu_E$ is the energy relaxation frequency and $\Delta t$ is the simulation time step.

Anomalous cross-field diffusion is included through a stochastic displacement operator:

$$ \Delta \mathbf{r} = \mathbf{r} + \sqrt{4D\Delta t}\hat{b}_{\perp} \quad (B.3) $$

where $D$ is the anomalous diffusion coefficient and $\hat{b}_{\perp}$ is a randomly sampled unit vector perpendicular to the magnetic field direction.

Ionization and recombination processes are treated via a Monte Carlo approach, using Maxwellian-averaged reaction rates sourced from the ADAS database [54]. The probability of a reaction occurring in a given timestep is determined from the corresponding rate coefficients and local plasma conditions, allowing charge state evolution to be resolved during particle tracking.

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