# Plasma heat load in the toroidal gaps of the ITER-like plasma facing units in WEST tokamak

Q. Tichit, M.H. Aumeunier, Y. Corre, R. Dejarnac, L. Dubus, J. Gaspar, J. Gerardin, A. Grosjean, J.P. Gunn, A. Juven, et al.

► To cite this version:

Q. Tichit, M.H. Aumeunier, Y. Corre, R. Dejarnac, L. Dubus, et al. Plasma heat load in the toroidal gaps of the ITER-like plasma facing units in WEST tokamak. Nuclear Materials and Energy, 2025, 42, pp.101899. 10.1016/j.nme.2025.101899. cea-04976181

HAL Id: cea-04976181

https://cea.hal.science/cea-04976181v1

Submitted on 4 Mar 2025

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# Plasma heat load in the toroidal gaps of the ITER-like plasma facing units in WEST tokamak ☆

Q. Tichit<sup>a, *</sup>, M.H. Aumeunier<sup>a</sup>, Y. Corre<sup>a</sup>, R. Dejarnac<sup>b</sup>, L. Dubus<sup>a</sup>, J. Gaspar<sup>c</sup>, J. Gerardin<sup>a</sup>, A. Grosjean<sup>d</sup>, J.P. Gunn<sup>a</sup>, A. Juven<sup>a</sup>, K. Krieger<sup>e</sup>, A. Podolník<sup>b</sup>, E. Tsitrone<sup>a, 1</sup>

## ARTICLE INFO

Keywords:

Divertor

ITER-like PFUs

Toroidal gaps

Heat loading

Infrared thermography

Cavity effect

Optical hot spot

Photonic simulation

Ray tracing

## ABSTRACT

The heat load deposited in the toroidal gaps between two tungsten monoblocks remains an open problem to prepare safe and powerful experiments in ITER. An experiment has been carried out on the WEST tokamak aiming to study the power deposition on the toroidal surfaces with various monoblock and heat loading configurations. The very high spatial resolution (0.1 mm/px) infrared camera of WEST has been used to monitor the temperature distribution on the blocks. Few actively cooled ITER-like plasma facing units have been misaligned in the vertical and poloidal direction to maximize the heat loading and temperature on specific block areas. This paper shows the experimental results obtained during high power plasma experiment (4.5 MW injected power) performed with the outer strike line located precisely in the toroidal gap. The experimental IR images exhibit complex pattern with strong signal into the gap (greater than measured on the top surface) and shifted hot spot on the poloidal chamfer of the downstream component featuring poloidal misalignment (where optical hot spot are expected). Thermal and photonic modelling have been used to mimic the infrared thermal scene an try to provide a better understanding of the heat loading on the toroidal edge and on the optical hot spots. The importance of specular reflection is highlighted in the two cases because the reflective facets of the block facing each other.

## 1. Introduction

The divertor is a critical component for every tokamak-like fusion device. As it ensures the power exhaust it should withstand extreme thermomechanical stresses as heat fluxes in the range of 10 MW.m⁻² in steady state and up to 20 MW.m⁻² during slow transient events (time scale up to 10 s) expected in ITER operation [1]. With a divertor fully equipped with the ITER-like actively cooled components, the WEST tokamak (CEA Cadarache) provides a relevant environment to carry out experiments on plasma facing components [2].

Nowadays, the technology chosen by ITER for the plasma facing units (PFUs) of the divertor, consist of centimetric bulk tungsten monoblocks (MBs) bounded along a copper cooling pipe. Pressurized

water circulating into the copper pipes ensures the active cooling. On the WEST divertor, a PFU is made of 35 tungsten MB, and each of the 12 sectors of the divertor counts 38 PFUs. MBs of a same PFU are separated by 0.5 mm gaps called toroidal gaps (TG). Likewise, 0.5 mm poloidal gaps (PG) separate two neighboring PFUs (poloidal gaps can be wider on ITER divertor between two cassette) [3]. More recently, this design has been modified to introduce a 1° (~ 0.5 mm height) toroidal bevel of the top surface in order to protect the leading edge (LE) (Fig. 2) from extremely high heat fluxes [4]. With unshaped MBs or in case of strong vertical misalignment between two consecutive PFUs (> 0.5 mm) with shaped components, the magnetic field lines (MFLs) can strike the poloidal LE of a MB with quasi-normal incidence, which makes these tiny surfaces vulnerable to damaging processes such as cracking and

<footnote><sup>a</sup> CEA, Institute for Research on Fusion by Magnetic confinement 13108 St-Paul-Lez-Durance, France</footnote>

<footnote><sup>b</sup> Institute of Plasma Physics of the CAS, U Slovancy 2525/1a, 182 00 Prague 8, Czech Republic</footnote>

<footnote><sup>c</sup> Aix Marseille Univ, CNRS, IUSTI, Marseille, France</footnote>

<footnote><sup>d</sup> Department of Nuclear Engineering, University of Tennessee, Knoxville, TN 37996, USA</footnote>

<footnote><sup>e</sup> Max-Planck-Institut für Plasmaphysik, 85748 Garching b. München, Germany</footnote>

<footnote>* This article is part of a special issue entitled: 'PSI-26' published in Nuclear Materials and Energy.</footnote>

<footnote>* Corresponding author.
E-mail address: Quentin.TICHIT@cea.fr (Q. Tichit).</footnote>

<footnote n="1">1 http://west.cea.fr/WESTteam.</footnote>
melting [5,6,7]. The assembling tolerances foreseen in ITER are (±0.3 mm) smaller than the height of the bevel [4], such as no LE should be exposed to the perpendicular heat flux, except in front of the TG were MFLs can still penetrate and strike the LE (also called “optical hot spot”). In addition, in WEST, most of the PFUs have a little 45° chamfer (1 × 1 mm) of the LE. However, the toroidal bevel does not protect the toroidal edges, and due to the MFLs inclination, heat flux can be deposited onto the toroidal lateral face of the MBs. Numerical predictions indicate possible high heat fluxes, especially during transient events, which can lead to damages [8].

In this context, it is important to characterize the heat flux deposited in toroidal gaps and understand the underlying physics in order to estimate the impact for the thermomechanical handling of the component and their lifetime during plasma operations. For this, the very high spatial resolution infrared camera (VHR) installed in WEST [9] represents an ideal tool for temperature monitoring and studies at the MB scale.

This paper presents the results of the toroidal gap loading experiments performed in WEST (section 2) and the modelling (section 3) developed to improve the interpretation of the VHR images and assess the heat flux distribution in the toroidal gaps. Conclusion and perspectives are discussed in section 4.

## 2. Toroidal gaps loading experiment

The toroidal gap loading experiments in WEST aim to maximize the heat flux deposited in the toroidal gaps between two ITER-like monoblocks and study the effects on these components.

## 3. Experimental set-up

### 2.1.1. Temperature monitoring

During the two experimental sessions, the surface temperature of the MBs of interest was monitored by infrared (IR) thermography, using the VHR camera of WEST. With a spatial resolution of about 0.1 mm/px, this diagnostic is well adapted for studies at the MB scale, and in the 0.5 mm PG and TG as well. The typical field of view (FoV) is 64 × 51 mm (3MBs × 2PFUs), and it can be moved between pulses over a 360 × 420 mm area (MB7 to 35, PFU#5 to #22–23). See Fig. 1 below, which also shows the ripple modulation of the incident angle of the magnetic field lines on the MB surfaces on a whole WEST divertor sector.

The VHR camera provides measurement of the black body spectral

<figure><img src="image_3.png" /><figcaption>Fig. 2. Illustration of vertical ($\delta_v$) and poloidal ($\delta_p$) misalignments.</figcaption></figure>

radiance emitted by the components: $L_{BB,\lambda}$ in equation (1). It could be expressed as the sum of the emission coming from the W surface with the reflection of the ambient radiation coming from the first wall:

$$L_{IR,\lambda}(T_{MB}) = \varepsilon_{W,\lambda}(T_{MB})L_{BB,\lambda}(T_{MB}) + (1 - \varepsilon_{W,\lambda}(T_{BG}))L_{BB,\lambda}(T_{BG}) \quad (1)$$

$L_{IR,\lambda}$ being the spectral radiance measured by the VHR at the wavelength $\lambda$, $L_{BB,\lambda}$ the black body (BB) spectral radiance, $\varepsilon_{W,\lambda}$ the tungsten emissivity, $T_{MB}$ the MB temperature and $T_{BG}$ the temperature of the background (actively cooled and considered at 70 °C). Here, self-reflection of the tungsten component is neglected.

The VHR uses a medium wavelength infrared (MWIR) filter centered on $\lambda = 3.9 \pm 0.1$ µm and it is calibrated using a black body source. With this filter the BB temperature threshold is about 250 °C [10]. The VHR is further described in [9].

### 2.1.2. WEST divertor configuration

Since the end of the year 2022, WEST operates with a full actively cooled tungsten divertor equipped with ITER-like PFUs. Before running the plasma experiment, the test sector of the WEST divertor has been modified locally, only in the field of view of the VHR IR camera, with misaligned PFUs in both poloidal ($\delta_p$) and vertical ($\delta_v$) directions (Table 1 and Fig. 2) to assess the effect of such misalignments on the heat flux distribution (cf. §-3). For $\delta_v$, a positive value means that the $MB_n$ is higher than the $MB_{n-1}$ (maximizing the wetted surface on $MB_n$), and a negative value means it is lower than the $MB_{n-1}$ (minimizing the wetted

<figure><img src="image_4.png" /><figcaption>Fig. 1. Map of magnetic field lines incident angle over the WEST test sector (Q3B), showing the toroidal modulation of the angle (ripple effect). MB are counted from the inner side to the outer side (MB1 to MB35, see white arrow), and PFUs from the left to the right (see # numbers). The observable area with the VHR camera is represented with the dashed back square. The solid line square delimit the scanned area during the toroidal edge experimental session. See 2.2.</figcaption></figure>
**Table 1**

Misalignments values for PFUs of interest. For $\delta_p$, values are expressed for PFU\#n regarding the upstream one (PFU\#n-1). For $\delta_v$, a positive value mean that the MBn is higher than the MBn-1, and a negative value mean it is lower than the MBn-1.

<table><thead><tr><th colspan="6">Poloidal misalignments</th></tr><tr><th>PFUs</th><th>#9/#8</th><th>#10/#9</th><th>#11/#10</th><th>#12/#11</th><th>#13/#12</th></tr></thead><tbody><tr><td>δ<sub>p</sub>(mm)</td><td>-1.5</td><td>0</td><td>+3</td><td>0</td><td>-1.5</td></tr><tr><th colspan="6">Vertical misalignments</th></tr><tr><td>PFUs</td><td>#8/#7</td><td>#9/#8</td><td>#10/#9</td><td>#11/#10</td><td>#12/#11</td></tr><tr><td>δ<sub>v</sub>(mm)</td><td>+0.08</td><td>+0.08</td><td>-0.47</td><td>0.00</td><td>-0.09</td></tr></tbody></table>

surface on MBn). The assembling of the PFU is controlled by surface metrology. The measured misalignments are then included in the CAD model of the PFUs on the test divertor sector. The detection threshold of the VHR camera is relatively high (250 °C), it is useful to maximize the wetted areas in order to increase the temperature of the block of interest.

### 2.1.3. Plasma scenario

The objective during the toroidal gap sessions was to maximize the deposited power in the toroidal gaps to get accurate VHR IR measurement. For this, the X-point height was set between 67 and 69 mm, reaching MB16 in the inner strike point (ISP) and the gap between MB 25 and 26 in the outer strike point (OSP) to maximize the temperature on MB26. The total lower hybrid power injected was from 4 up to 4.7 MW over 15 s to reach the thermal equilibrium of the MB, with a radiative power around 50–55 %. The plasma current and the total toroidal magnetic field were respectively set to 500kA and 3.7 T.

## 4. Main achievements of the experimental sessions

During the experimental sessions, the OSP has been successfully put in the TG between MB25 and MB26 with a good and quite stable control of the position over the pulse duration (lasting at least 10 s to reach the thermal equilibrium of the MB). A scan was performed with the VHR on the low field side (LFS), moving the FoV from PFU#7/#8 to PFU#11/#12, centered on MB26, over 8 repetitive pulses. This PFUs are located at a maximum of the ripple modulation on the low field side (LFS) (see Fig. 1). The VHR FoV was also moved on the high field side (HFS) of the divertor, looking at MB16 (ISP), PFU#11, #12, and #19 (maximum of the ripple modulation on the inner side). But due to the HFS/LFS power asymmetric repartition (1/4 HFS, 3/4 LFS [11]), the surface temperature on the HFS is lower than the VHR detection threshold ( 250 °C).

<figure><img src="image_5.png" /><figcaption>**Fig. 3.** VHR view, pulse #57544. The zoom box highlight the optical hot spot observed on the MB26 PFU#9 LE.</figcaption></figure>

The Fig. 3 presents the VHR view during the pulse #57544, with VHR camera looking at PFU8 and PFU9 featuring 1.5 mm radial misalignment as shown in Fig. 2. The OSP is well positioned right into the toroidal gap between MB25 and MB26 (black dashed line on Fig. 3). The parallel heat flux ($q||$) comes from the left (pink arrow). The magnetic shadowing induced by the toroidal bevel appears clearly on the MBs top surface (cold part on the left of the MB surface, see dashed area in Fig. 3). The signal collected by the VHR appears higher into the TG and PG than on the MB top surface. Note that PG is supposed to be cold in theory because of the magnetic shadowing of the LE. This phenomenon could be attributed to the multiple reflections which occur between the two faces of the gaps. The result is a local enhancement of the collected signal and then of the estimated temperature. This effect is known as the cavity effect. In the same way, the poloidal chamfer of MB26 PFU#9 which is magnetically shadowed, seems to be hotter than the shadowed areas (350 °C versus < 200 °C black body). This should be due to specular reflections. Finally, looking at the corner of MB between the two PFUs, one can observe a small hot spot on the poloidal chamfer of MB26 PFU#9, but shifted regarding the TG axis.

The aim of this study is to explain these observation by means of detailed simulations of all the physical phenomena involved in the measurement chain.

## 5. Modelling of the heat flux in the toroidal gap and making of the synthetic IR VHR images

In order to correctly interpret the IR images and understand the underlying physics of the hot patterns, a detailed simulation package was carried out. The simulation involves two main steps: (1) modeling of IR thermal scene observed by the camera which includes modeling of the heat load on 3D castellated surfaces and calculating the resulting surface temperature (2) modeling the 2D IR images taking into account the low emissivity of materials and the multiple reflections occurring between the MB surfaces.

## 6. Modelling of the IR thermal scene

### 3.1.1. Expected heat flux distribution under optical approximation

The heat loads on ITER-like PFU are computed under the optical approximation (OA) on a full 3D MB surfaces geometry. Under OA the gyro motion of the ions and electrons is neglected, assuming then that the particles strictly follow the MFLs. In the toroidal gap, this means that the heat load is deposited only on one side, regarding the pitch angle of

<figure><img src="image_6.png" /><figcaption>**Fig. 4.** Heat flux distribution on MBs. PFU9 is shifted by 1.5 mm compared to PFU#8.</figcaption></figure>
the magnetic field line with the toroidal gap. For the MBs in the LFS (OSP), the heat loading is expected on the HFS toroidal edge of the MB (Fig. 4).

Another feature related to the toroidal gap is observed when PFUs are poloidally misaligned ($\delta_p \neq 0$). In this case, MFLs penetrating the toroidal gaps can strike the LE of the downstream PFU with a 90° incidence on sharp LE geometry and 45° on chamfered geometry (Fig. 4). This leads to extreme heat flux density, especially during transients ($\geq 200$ MW.m$^{-2}$ [8]), on a very localized area, potential source of thermal stress and damages due to the very steep temperature gradient [6,8]. These localized areas receiving the high heat flux are called optical hot spot (OHS).

### 3.1.2. Heat flux estimation under optical approximation

A magnetic field line tracing code, called PFCflux [12], is used to calculate the heat loads under the OA approximation. PFCflux code is based on magnetic equilibrium data and uses a 3D model of the castel-lated divertor configuration, including the misalignments to calculate the plasma wetted and shadowed areas. It provides incident angle, magnetic fields and heat flux maps on the divertor, including ripple effect. The heat flux shape along the scrape-off layer (SOL) at the OMP is computed using the expression (3) [13,14]:

$$q\| (x) = \frac{q_0}{2} \exp \left[ \left( \frac{S^{OMP}}{2\lambda_q^{OMP}} \right)^2 - \frac{\bar{x}}{\lambda_q^{OMP}} \right] \times \text{erfc} \left( \frac{S^{OMP}}{2\lambda_q^{OMP}} - \frac{\bar{x}}{S^{OMP}} \right) + q_{BG} \quad (3)$$

where $q\|$ is the parallel heat flux on the OMP at radial position $x$, $\bar{x} = x - x_0$ is the radial distance at the OMP between the separatrix ($x_0$) and the considered radial position ($x$). $q_0$ is the maximum parallel heat flux when $S \to 0$ and $x \to x_0$. $\lambda_q^{OMP}$ and $S^{OMP}$ are respectively the heat flux decay length in the SOL, and the spreading factor (diffusion in the private flux region) taken at the outer midplane.

Under the OA, the heat flux projection on the MB surfaces is computed as follows:

$$\begin{align*} q_{top} &= q\|\sin\alpha \\ q_{LE} &= q\|\sin(\alpha + \beta) \\ q_{toro} &= q\|\sin\theta\| \end{align*} \quad (4)$$

With $q_{top}$, $q_{LE}$, $q_{toro}$, respectively the heat flux densities on the top surface, the poloidal LE and the toroidal lateral surfaces. The angle $\alpha$ is the incident angle of the MFL on the top surface, meaning that it counts the +1° on the top surface ($\alpha = \alpha_{flat} + 1°$, $a_{flat}$ beeing the incident angle regarding a flat surface). $\beta$ is the inclination of the poloidal LE, equal to 90° in case of sharp LE, and 45° for chamfered LE. $\theta\|$ is the angle between the projection of the MFL onto the plane parallel to the MB top surface, and the toroidal surface.

The heat flux map is extracted from PFCflux calculation given the magnetic equilibrium of the studied pulse (#57544), and manually setting parameters such as $\lambda_q^{OMP}$ and $S^{OMP}$, a mesh size for the 3D model of the components and the power entering the SOL ($P_{SOL}$). The mesh size is about 0.1 mm. For this study, $P_{SOL}$ is arbitrarily set to 1 MW in PFCflux, and the calculated heat flux on MBs surfaces is normalized. The heat flux amplitude will be determined using an iterative loop between simulation and experiment.

### 3.1.3. Estimation of the surface temperature and heat flux densities

This study attempts to reproduce the thermal scene observed during WEST pulse #57544 and the IR images captured by the VHR. The first step is to estimate the heat flux densities on the MB surfaces, from the surface temperature.

The surface temperature is the result of the heat transfer deposited at the surface down to the cooling pipes. It depends therefore of the heat flux distribution profile: peak heat flux amplitude and position, as well as the heat flux decays in the poloidal directions ($\lambda_q^{OMP}$ and $S^{OMP}$). The temperature distribution are computed with the 3D FEM ANSYS code. The input plasma parameters ($\lambda_q^{OMP}$, $S^{OMP}$ and $P_{SOL}$) are adjusted, step by step, to match the experimental data. The experimental temperature profiles are extracted from the IR images in the wetted areas, first because it leads to the maximum of surface temperature (less sensitive to parasitic light from the first wall) and secondly, because it shows a relatively uniform emissivity because of the erosion process which is dominant here. (i.e. high temperature).

At high enough temperature ($T \ 10 \times T_{BG}$), the second term of equation (1) can be neglected, and the spectral radiance of the component appears directly proportional through its emissivity, to its black body radiance at the same temperature (Planck law). The BB spectral radiance, measured by the VHR can then be corrected assuming constant emissivity correction based on post-exposure measurements [15,16]. Radiance and temperature are link through equation (2).

$$L_{BB,\lambda}(T_{MB}) = \frac{c_1 \lambda^{-5}}{\exp(\frac{\epsilon_2}{\lambda T}) - 1} \quad (2)$$

where $C_1 = 2hc \approx 1.19 \times 10^{-16} \frac{W}{m^2 \cdot sr}$ and $C_2 = \frac{hc}{k_B} \approx 1.44 \times 10^{-2} m \cdot K$.

Temperatures used in the following will be labelled as follows: $T_{BB}$, the black body temperature, $T_\epsilon$ the temperature with constant emissivity correction by replacing $\epsilon$ by its value (e.g. $T_{0.15}$), $T_{FEM}$ the simulated temperature from ANSYS calculation. An iterative loop was established to minimize the discrepancy between simulation (providing 3D temperature maps) and experiment (forward calculation). This heat flux map generated by the PFCflux simulation is then mapped on a ANSYS 3D model of the MB of interest for the FEM calculation. The ANSYS mesh size varies from 0.1 mm on the MBs of interest (MB26) up to 1 mm elsewhere. An appropriate scale is set in ANSYS parameters. The heat flux is approached by matching experimental temperature profiles and FEM simulated profiles. See Fig. 5 where the red curve is the raw black body temperature profile from IR VHR images.

The magenta one is the same profile but corrected assuming an emissivity of 0.15 (value extrapolated from the post-mortem measurements and temperature dependence found in laboratory). The magenta solid lines delimit the error bars associated to the emissivity variation that is established in laboratory ($\pm 0.05$). Magenta and green profiles

<figure><img src="image_7.png" /><figcaption>Fig. 5. Poloidal temperature profiles (measured and simulated) along MB25 to 27 PFU#8, about 3 mm away from the LE. #57544.</figcaption></figure>
delimit the error bars associated to the emissivity variation that is established in laboratory (±0.05). The black profile represents the simulation (output from ANSYS). For the pulse #57544, the best match was obtained with $\lambda_q^{OMP} = 3.333$ mm, $S^{OMP} = 0.333$ mm, i.e., assuming $f_x = 3$, target values ($\lambda'_q$ and $S'$) around 10 mm and 1 mm respectively. For this pulse, surface temperature is found to be ≈600 °C near the strike line and 450 °C on the opposite part of the MB. The required heat flux on the top surface to match $T_{0.15}^{MAX}$ is $q_{top} = 9MW.m^{-2}$, corresponding to $q$ close to $180MW.m^{-2}$ for a mean incident angle of 2.9° on MB26 PFU#8 top surface (calculated with PFCflux). On the top surface, the agreement is not perfect (experimental and simulated slopes are slightly different) but still satisfying using a minimum number of input. A strong discrepancy is found in the toroidal gap as mentioned earlier.

## 7. Modelling of the IR images (synthetic data)

Photonic modeling is then required to take into account both, the finite size of the IR pixels and also the multiple reflection of the light emitted in the gaps (from the different MB facets). The resulting surface temperature computed by FEM is used as input to a Monte Carlo Ray Tracing code [17,18]. The input surface temperature is provided on top face and over the first 4 mm (along vertical direction) of the lateral faces (poloidal and toroidal) to take into account the multiple reflections within gap. It should be noted that the accuracy of the simulation data is also dependent on the mesh size.

To solve (spatially) the OHS, the mesh size is about 0.5 mm on the neighboring MBs (MB25 and MB27 PFU#8 and #9), 0.2 mm on MB26 PFU#8 and 0.1 mm on MB26 PFU#9, the MB of interest. Optical properties are set for each surface, considering their emissivity and the reflection model. The reflection model (also known as the Bidirectional Reflectivity Distribution Function or BRDF), describes the behavior of reflected photon for a given incident angle and is related to the emissivity value by the Kirchhoff Law. The Table 2 presents the two reflection models used here: one dominated by specular reflections, and one purely diffuse. Geometrical parameters of the virtual camera (position, orientation, focal view) are chosen in order to match the real VHR view. The resulting simulated IR scene is a numerical twin of the real VHR view aligned with an accuracy under 5 pixels. The temperatures obtained from the photonic modelling will be called “synthetic temperatures” ($T_{synth}$).

## 8. Analysis of experimental data in comparison with simulated data

As shown in the synthetic images on Fig. 6, both diffuse (Fig. 6 (b)) and specular (Fig. 6 (c)) models, allow to reproduce the emission in the gaps (PG and TG), as well as on the magnetically shaded chamfer observed on the IR image (Fig. 3). The specular model also predicts the radially shifted hot spot on the poloidal chamfer of the MB26 PFU#9. This shifted hot spot appears neither on the true temperature map from FEM calculation (Fig. 6 (a)) nor with the diffuse model (Fig. 6 (b)), but only on the synthetic images from the specular case (Fig. 6 (c)). This proves that the shifted hot spot is a “false hot spot” (FHS) resulting from the specular reflection of the hot corner of the upstream MBs. In the same way, the signal on the magnetically shadowed chamfer, originates from the TE of the upstream MB. As a whole, the IR VHR images are

<table><caption>**Table 2**
BRDF applied on each surface of the MB (see Fig. 2 for surfaces nomenclature).</caption><thead><tr><th>BRDF</th><th>Specular model</th><th>Diffuse model</th></tr></thead><tbody><tr><td>S<sub>top</sub></td><td>25 % diffuse + 75 % Gaussian specular</td><td>100 % diffuse</td></tr><tr><td>S<sub>chamfer</sub></td><td>10 % diffuse + 90 % Gaussian specular</td><td>100 % diffuse</td></tr><tr><td>S<sub>toro</sub></td><td>15 % diffuse + 85 % Gaussian specular</td><td>100 % diffuse</td></tr></tbody></table>

better reproduced assuming a reflection model dominated by specular reflections.

In a quantitative way, the Fig. 7 presents poloidal temperature profiles along the chamfers of MBs 25 (in the private flux area), MB26 (OSP) and MB27 on PFU#9. FEM and synthetic profiles are compared to the experimental IR black body profile (dashed red line). The best match between $T_{synth}$ and $T_{FEM}$ is obtained by considering the emissivity settings sum-up in Table 3. Only the specular case allows to provide a good agreement with the IR experimental profile (in red). As observed on the chamfer in the IR images, the diffuse case does not reproduce neither the OHS nor the FHS. Regarding the specular case, the discrepancy between the synthetic profile (dashed blue line) and the FEM profile (in black) on MB26 (see ① on Fig. 7), is due to the flux coming from parasite reflections, from the upstream MB trailing edge. On the MB25 and 27 surface, the discrepancy is quite important between the experimental profile and the synthetic ones (see ② on Fig. 7). On these MBs, the difference comes from not taking into account the temperature detection threshold of the VHR camera which is about 250 °C (black body), and the contributions of flux coming from the environment (IR emission from other PFCs in the machine).

Another challenging point is the adjustment of the geometrical parameters of the camera model, with the IR VHR view. The accuracy of the final adjustment is about 5 pixels, which explains the slight shift between experimental and synthetic profiles on Fig. 7, visible on the HFS edge. By correcting this shift, the synthetic profiles will move on the HFS direction, and the FHS will be even further away from the real OHS.

Concerning the OHS, the FEM calculation predicts a maximum temperature around 400 °C on the chamfer. The poloidal profiles presented on Fig. 7 are extracted at the middle of the chamfer surface, where the true temperature of the OHS is $T_{FEM}^{360}$ °C, close to the maximum, while synthetic data give $T_{synth}^{350}$ °C, considering specular reflections and 0.1 emissivity for the chamfer surface. This is close to the black body temperature measured on the OHS (red dashed curve) $T_{BB}^{330}$ °C (ΔT 6%). The apparent temperature of the chamfer at the vicinity the OHS is also about 320 to 330 °C. On the synthetic image with specular surfaces, the OHS is still barely visible with a ΔT around +20 °C.

Regarding the reflection of the hot corner on the chamfer (the FHS), the experimental value is around 370 °C (ΔT 50°C compared to the chamfer black body temperature), where the specular case predicts 420 °C (ΔT 100°C). The specular case overestimates the apparent temperature of the reflection (+14 %), probably because of the emissivity assumptions in the BRDF model.

The Fig. 8 presents poloidal temperature profiles extract along MB25 to 27 top surface on PFU#8, about 1 mm away from the trailing edge. On the top surface, diffuse and specular models, provide similar results, with a good agreement with the IR profile (red). Into the toroidal gap, once again, the specular model provide a better agreement with the measurements (about 100° higher temperature on the TG compared to the temperature measured on the flat top surface). As on Fig. 7, the discrepancy between synthetic and experimental profiles on cold MB25 and 27 (②) could be explained by the VHR temperature threshold and the surrounding. It is interesting to note that on the chamfer, which is more sensitive to the contribution of reflections (because of its low temperature and its proximity with the hot surface of the upstream block), we overestimate the temperature with the IR VHR compared to the FEM values (Fig. 7), whereas on the top surface (Fig. 8), the experimental temperature is underestimated due to the low emissivity.

## 9. Conclusion and prospects

The WEST VHR IR camera is a highly effective diagnostic tool for studying surface temperature at the MB scale, but the interpretation of the images must be treated with caution, particularly on the PG, TG, and chamfers, which are sensitive to reflections (cold surfaces in the shaded
<figure><img src="image_8.png" /><figcaption>Fig. 6. A) 3d temperature map from fem calculation, used as input for the ray tracing code. b) synthetic image for the diffuse case. c) synthetic image for the specular case.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 7. Poloidal temperature profile along the chamfer of the MB25 to MB27 PFU#9. Profiles are extracted at the middle of the chamfer.</figcaption></figure>

<table><caption>**Table 3**

Emissivity settings for each surface for diffuse and specular models.</caption><thead><tr><th colspan="2">Emissivity values set for each surface</th></tr></thead><tbody><tr><td>S<sub>top</sub></td><td>0.15</td></tr><tr><td>S<sub>chamfer</sub></td><td>0.1</td></tr><tr><td>S<sub>lateral</sub></td><td>0.2</td></tr></tbody></table>

<figure><img src="image_10.png" /><figcaption>Fig. 8. Poloidal temperature profiles along the top surface of the MB26 PFU#9. Profiles are extracted about 1 mm away from the trailing edge.</figcaption></figure>

areas, close to the hot surfaces in the plasma wetted areas). It has been shown that the complex pattern observed on the VHR IR images, involves specular reflections. These reflections lead to the local apparent temperature enhancement into the gaps (PGs and TGs), named cavity effect, and to the apparition of a shifted “false” hot spot on the poloidal chamfer in front of the TGs of the upstream MB. This feature is the consequence of a specular reflection of the hot corner of the upstream MB. Due to the reflections on the poloidal chamfer, the OHS is not measurable (the surface emission is drowned in the reflected flux). The specular reflection of the hot corner is clearly visible, with a ΔT around +50 °C. Finally it has been shown that the specular contribution in the BRDF model does not influence the signal on the top surface (similar results with the purely diffuse surface). Nevertheless a model widely dominated by the specular contribution (75 to 90 % Gaussian specular (Table 2)), is required to reproduce the observations into the gaps and on the chamfers.

Further step should include the plasma contributions and camera dynamic to improve the reflection model and provide better agreement with the experimental images.

Lastly, the optical approximation looks sufficient to provide a decent agreement with the experimental observations, and temperatures on both the top surface and the chamfer. However, numerical predictions, show a strong impact of the ion gyro radius and the $E \times B$ drift (local fields), on the heat flux distribution, particularly during transient events like ELMs (edge localized modes), where the ion gyro radius increase dramatically [19,20]. The ion gyration effect is particularly important into the gaps, as the Larmor radius of the ions is typically the same order of magnitude as the gaps in WEST plasma with $T_i$ expected around tens of eV at the target location. Ion orbit model (IO) [21] -which takes into account the ion gyro motion-, and particle-in-cell (PIC) model [22]- which takes into account also the plasma sheath effects and the $E \times B$ drift.

<figure><img src="image_11.png" /><figcaption>Fig. 9. Comparative scheme between heat flux distributions from AO and IO models in the toroidal gaps.</figcaption></figure>
drift-, predict heat flux deposition from ions on the opposite face of the gap regarding the MFLs impact side (Blue surface on Fig. 9) [8,19,20]. Then, while the optical approximation predicts flux deposition only on one side of the gap, the IO and PIC models predict flux deposition on both sides. This effect is only expected on the outer strike point, due to the reverse field line on the ISP. Heat flux estimation with the IO and PIC models will depend as well on the $T_i/T_e$ ratio. The impact of ions gyro radius on the deposited heat flux into the TG should be then quantified. IO and PIC (particles-in-cell) modelling are ongoing to provide proper heat fluxes estimation for FEM calculations and photonic modelling.

### CRediT authorship contribution statement

Q. Tichit: Writing – original draft, Software, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. M.H. Aumeunier: Writing – review & editing, Software, Investigation. Y. Corre: Writing – review & editing, Supervision, Project administration, Methodology, Investigation, Conceptualization. R. Dejarnac: Software. L. Dubus: Resources. J. Gaspar: Investigation, Data curation. J. Gerardin: Writing – review & editing, Software, Investigation. A. Grosjean: Investigation, Data curation. J.P. Gunn: Software. A. Juven: Writing – review & editing, Software. K. Krieger: Software. A. Podolník: Software. E. Tsitrone: Supervision.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgements

"This work has been carried out within the framework of the EUROfusion Consortium, funded by the European Union via the Eurotom 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."

### Data availability

Data will be made available on request.

### References

[1] T. Hirai, et al., ITER full tungsten divertor qualification program and progress, Phys. Scr. T159 (Apr. 2014) 014006, https://doi.org/10.1088/0031-8949/2014/ T159/014006.

[2] J. Bucalossi, M. Missirlian, P. Moreau, F. Samaille, E. Tsitrone, The WEST project: Testing ITER divertor high heat flux component technology in a steady state

tokamak environment, Fusion Eng. Des. 89 (2014) 907–912, 10.1016/j. fusengdes.2014.01.062.

[3] T. Hirai, et al., Design optimization of the ITER tungsten divertor vertical targets, Fusion Eng. Des. 127 (Feb. 2018) 66–72, https://doi.org/10.1016/j. fusengdes.2017.12.007.

[4] M. Missirlian, M. Firdaouss, M. Richou, P. Languille, S. Lecocq, M. Lipa, The WEST project: PFC shaping solutions investigated for the ITER-like W divertor, Fusion Eng. Des. 88 (9–10) (2013) 1793–1797, https://doi.org/10.1016/j. fusengdes.2013.03.048.

[5] Y. Corre, et al., Sustained W-melting experiments on actively cooled ITER-like plasma facing unit in WEST, Phys. Scr. 96 (12) (Dec. 2021) 124057, https://doi.org/10.1088/1402-4896/ac326a.

[6] M. Diez, et al., In situ observation of tungsten plasma-facing components after the first phase of operation of the WEST tokamak, Nucl. Fusion 61 (10) (2021), https:// doi.org/10.1088/1741-4326/ac1dc6.

[7] Q. Tichit, et al., Infrared detection of tungsten cracking on actively cooled ITER-like component during high power experiment in WEST, Nucl. Mater. Energy 37 (Dec. 2023) 101537, https://doi.org/10.1016/j.nme.2023.101537.

[8] J.P. Gunn, et al., Thermal loads in gaps between ITER divertor monoblocks: First lessons learnt from WEST, Nucl. Mater. Energy 27 (100920) (2021), https://doi.org/10.1016/j.nme.2021.100920.

[9] M. Houry, C. Pocheau, M.H. Aumeunier, C. Balorin, The very high spatial resolution infrared thermography on ITER-like tungsten monoblocks in WEST Tokamak, Fusion Eng. Des. 146 (Part A) (2019) 1104–1107, https://doi.org/10.1016/j. fusengdes.2019.02.017.

[10] A. Grosjean, et al., Very high-resolution infrared imagery of misaligned tungsten monoblock edge heating in the WEST tokamak, Nucl. Mater. Energy 27 (Jun. 2021) 100910, https://doi.org/10.1016/j.nme.2021.100910.

[11] J. Gaspar, Y. Corre, N. Fedorczak, J.P. Gunn, C. Bourdelle, Divertor power loads and scrape off layer width in the large aspect ratio full tungsten tokamak WEST, Nucl. Fusion 61 (9) (2021), https://doi.org/10.1088/1741-4326/ac1803.

[12] M. Firdaouss, V. Riccardo, V. Martin, G. Arnoux, C. Reux, Modelling of power deposition on the JET ITER like wall using the code PFCFLux, J. Nucl. Mater. 438 (Jul. 2013) S536–S539, https://doi.org/10.1016/j.jnucmat.2013.01.111.

[13] T. Eich, et al., Inter-ELM Power Decay Length for JET and ASDEX Upgrade: Measurement and Comparison with Heuristic Drift-Based Model, PhysRevLett. 107 (21) (Nov. 2011) 215001, https://doi.org/10.1103/PhysRevLett.107.215001.

[14] F. Wagner, A study of the perpendicular particle transport properties in the scrape-off layer of ASDEX, Nucl. Fusion 25 (5) (May 1985) 525–536, https://doi.org/10.1088/0029-5515/25/5/002.

[15] J. Gaspar, C. Pocheau, Y. Corre, N. Ehret, D. Guilhem, Emissivity measurement of tungsten plasma facing components of the WEST tokamak, Fusion Eng. Des. 149 (2019), https://doi.org/10.1016/j.fusengdes.2019.111328.

[16] J. Gaspar, et al., Overview of the emissivity measurements performed in WEST: in situ and post-mortem observations, Nucl. Fusion 62 (096023) (2022), https://doi.org/10.1088/1741-4326/ac6f68.

[17] M.-H. Aumeunier, et al., Infrared thermography in metallic environments of WEST and ASDEX Upgrade, Nucl. Mater. Energy 26 (Mar. 2021) 100879, https://doi.org/10.1016/j.nme.2020.100879.

[18] A. Juven, M.-H. Aumeunier, J. Marot, U-Net for temperature estimation from simulated infrared images in tokamaks, Nucl. Mater. Energy 38 (Mar. 2024) 101562, https://doi.org/10.1016/j.nme.2023.101562.

[19] J.P. Gunn, et al., Surface heat loads on the ITER divertor vertical targets, Nucl. Fusion 57 (4) (2017), https://doi.org/10.1088/1741-4326/aa5e2a.

[20] R. Dejarnac, J.P. Gunn, P. Vondracek, M. Komm, R. Panek, R.A. Pitts, Physics of toroidal gap heat loading on castellated plasma-facing components, Nucl. Mater. Energy 19 (May 2019) 19–27, https://doi.org/10.1016/j.nme.2019.02.010.

[21] J.P. Gunn, S. Carpentier-Chouchana, R. Dejarnac, F. Escourbiac, Ion orbit modelling of ELM heat loads on ITER divertor vertical targets, Nucl. Mater. Energy 12 (2017) 75–83, https://doi.org/10.1016/j.nme.2016.10.005.

[22] M. Komm, J.P. Gunn, R. Dejarnac, R. Pánek, R.A. Pitts, A. Podolník, Particle-in-cell simulations of plasma interaction with poloidal gaps in the ITER divertor outer vertical target, Nucl. Fusion 57 (12) (2017), https://doi.org/10.1088/1741-4326/ aa5e2a.