The role of SOL plasma in the confinement of NBI fast ions in W7-X

Plasma Physics and Controlled Fusion PAPER • OPEN ACCESS The role of SOL plasma in the confinement of NBI fast ions in W7-X To cite this article: T P Kiviniemi et al 2025 Plasma Phys. Control. Fusion 67 025034 View the article online for updates and enhancements. You may also like Cross-scale turbulence in space plasmas: old concepts, recent findings, and future challenges Tommaso Alberti, Simone Benella, Mirko Stumpo et al. - Probabilistic theory of the L-H transition and causality Eun-jin Kim and Abhiram Anand Thiruthummal - Two-dimensional inference of divertor plasma characteristics: advancements to a multi-instrument Bayesian analysis system D Greenhouse, C Bowman, B Lipschultz et al. - This content was downloaded from IP address 193.147.173.203 on 29/04/2025 at 09:59 Plasma Physics and Controlled Fusion Plasma Phys. Control. Fusion 67 (2025) 025034 (12pp) https://doi.org/10.1088/1361-6587/adaa14 The role of SOL plasma in the confinement of NBI fast ions in W7-X T P Kiviniemi1,∗, T Kurki-Suonio1, S Lazerson2,4, S Äkäslompolo1, P Ollus1, L Sanchis3, D Kulla4and the W7-X Team4 1Aalto University, Espoo, Finland 2Gauss Fusion, 85748 Garching bei München, Germany 3University of Seville, Sevilla, Spain 4Max-Planck-Institut für Plasmaphysik, 17491 Greifswald, Germany E-mail: timo.ki[email protected] Received 2 October 2024, revised 12 December 2024 Accepted for publication 14 January 2025 Published 30 January 2025 Abstract The impact of the scrape-off layer (SOL) plasma on deposition, confinement and losses of neutral beam injected fast ions was investigated in W7-X plasma. The effect of SOL width, density, temperature profiles, radial electric field, and charge–exchange reactions (CX) was explored. Ionization and slowing down partly counterbalance each other, as slowing down in cold SOL plasma compensates for ionization effects in radially decaying model profiles. However, the effect of SOL plasma on more vulnerable steel components is mitigated over a wide range of different profiles, because for those components the collisionality effect overrules the effect of SOL on ionization. The effect of the radial electric field is mitigated for steel components in the experimentally observed direction of the field. The effect of CX reactions is shown to lead to a widely spread low power load distribution with no clear effect on peak load. Statistical challenges caused by hugely varying triangle sizes in the discretization of walls are discussed. Keywords: NBI, fast ions, Wendelstein 7-X, stellarator, ASCOT 1. Introduction Losses of neutral beam injected (NBI) fast ions can pose a significant challenge to stellarator first walls. Highly localized heat fluxes can cause sublimation of carbon and melting of steel components when peak loads are of the order of 10 MW m−2or more [1]. In Wendelstein 7-X (W7-X) this is especially true, where the overheating of the steel plasma facing components (PFCs) from lost fast ions can result in significant damage. In previous simulations of neutral beams ∗Author to whom any correspondence should be addressed. Original Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. in W7-X, the ionization probability has traditionally been evaluated only after the beam neutrals have crossed the last closed flux surface (LCFS). However, experimental evidence for edge-born fast ions exists [2]. Similarly, when a beam ion exits the plasma and enters the scrape-off layer (SOL), it is assumed to be collisionless. While sophisticated wall modeling has been conducted for different magnetic configurations (e.g. [3] where eight configurations, including the standard configuration, were investigated), the effect of SOL plasma and charge–exchange reactions have not been considered in those studies. In the present study, we address this limitation by introducing a finite plasma at finite temperature in the W7-X SOL for the standard configuration. The goal is to assess the impact of partially ionized SOL plasma on the beam deposition, beam ion confinement, and losses of beam ions when the plasma extends beyond the LCFS. This is possible using BBNBI5 [5] for the beam deposition and ASCOT5 [4] for the collisional 1 © 2025 The Author(s). Published by IOP Publishing Ltd Plasma Phys. Control. Fusion 67 (2025) 025034 T P Kiviniemi et al processes, including charge exchange (CX) reactions, for the beam ions. In the worst-case scenario, the SOL plasma can lead to a significant increase in power loads via premature beam ionization and/or CX reactions. On the other hand, since SOL plasma provides an additional region for the beam to slow down, it could mitigate the power loads. Determining the net effect of SOL plasma can only be achieved through meticulous simulation. In the present work, we concentrate on investigating the integrated effects due to different physical phenomena. In addition, the statistical challenges due to the discrete 3D wall structure when estimating the peak loads are discussed and means to avoid numerical anomalies are proposed. The ASCOT suite of codes is a comprehensive and wellestablished tool for fast ion studies in both current and future tokamaks. Its initial application in 3D stellarator geometry was to predict beam power loads for sensitive PFCs in the first operating phase of W7-X. The simulation results proved to be of immense value, leading to improved safety of the first wall [3]. Subsequently, ASCOT has also been employed to investigate the impact of W7-X magnetic configuration on neutron production rates [6] and the effect of NBI ion power load on the ICRH antenna [7]. The present study on power loads is an extension of the OP2 phase, which not only involves higher heating power but, more importantly, includes the physical processes previously overlooked. In addition to collisional processes, the effect of a SOL radial electric field is also included. To date, the effect of a radial electric field on fast particle confinement in W7-X has only been studied in the region inside the LCFS [8]. Here the fast particle confinement is found to be significantly improved by the associated E×Bdrift. In tokamaks, the SOL Erhas been found to have a clear impact on the fast ion power load distribution [9]. In dedicated experiments on W7-X, local power loads due to bulk plasma were measured by a system of infrared (IR) video cameras and revealed asymmetries that could not be explained other than by assuming a SOL radial electric field with the associated E×Bdrift [10]. This effect should thus also be studied for beam ions. In the absence of adequate measured data, we test the potential effect of SOL Er on beam power load distribution using model profiles. Beam ion power loads in W7-X were recently studied experimentally with thermographic measurements and simulated using BEAMS3D and ASCOT5 codes [11]. This work explicitly pointed out the lack of SOL physics in the simulations, a situation which we now wish to remedy. Therefore, even charge exchange (CX) reactions are included here: the new atomic reaction module in ASCOT5 enables the incorporation of CX reactions in the SOL plasma [12,13]. The model has been applied to TJ-II stellarator plasma in [14]. This article is organized as follows. The relevant features of the ASCOT5 and BBNBI5 simulation codes and W7-X setup are described in section 2. In section 3, the effects of both slowing down and ionization on beam power loads are investigated. The relevance of the SOL width is also tested. Ad hoc SOL radial electric fields are included in the simulations in section 4, and the effect of charge exchange in section 5. Finally, the conclusions are presented in section 6. 2. Tools and methods 2.1. ASCOT5 and BBNBI5 In this work, the main tools are ASCOT5 and BBNBI5. ASCOT5 [4] is the latest development version of ASCOT, which is a Monte Carlo code for simulating markers in a magnetically confined plasma, including collisional processes with a fixed background plasma. The code has two different options for orbit-following: (i) gyro orbit method, where the markers follow the trajectories of physical particles in electric and magnetic fields Eand B, respectively. The equations of motion, derived from the Hamiltonian dynamics: ˙ x=p γm ˙ p=q(E+˙ x×B) are solved using the volume-preserving algorithm [15], which can be thought of as a relativistic variant of the Boris scheme. Here, xand pare the position and momentum of the particle with mass m, and γ=√1−(p/mc)2is the Lorentz factor. In SOL, the gyro orbits are always followed. (ii) the guiding center method, which is faster but more inaccurate in evaluating power loads. The guiding-center equations of motion can be solved with either fourth-order Runge–Kutta method (fixed time step) or Cash–Karp [16] (adaptive time-step). These methods do not conserve the marker energy, but by choosing a sufficiently small timestep the resulting error remains insignificant. In the present work, most of the simulations are carried out using the so-called hybrid method in which the guidingcenter approach is used inside the LCFS, while gyro orbits are followed once the marker has crossed the LCFS. The hybrid method is cost-efficient for evaluating power loads since the role of the slowing-down simulations inside the LCFS is only to identify the markers reaching the LCFS. A notable exception to this is a simulation including the CX reactions since, in the present code version, the CX model is only applicable for full orbit simulations (for an example of the guiding-center approach on CX reactions see, e.g. [17]). The CX reaction between a fast hydrogen ion H+ fand a hydrogen neutral H(similarly for other isotopes) is based on the equation H+ f+H→Hf+H+, which, in the Monte Carlo simulation, is modeled assuming neutralization probability Pn=1−e−R∆t, with the reaction rate R=n0⟨σCXv⟩. Here, n0is the neutral density, ⟨σCXv⟩is the CX reaction rate coefficient and ∆tis the time step. In [12], this fast-ion CX model using atomic reaction data from the ADAS database [18,19] was implemented in ASCOT and verified by estimating the reaction mean free paths. Subsequently, the model has been used in simulations of beam-ion confinement in the MAST Upgrade [13]. 2 Plasma Phys. Control. Fusion 67 (2025) 025034 T P Kiviniemi et al The magnetic configuration and plasma profiles are used to generate the beam ion birth profile with BBNBI5. The time evolution of the ensemble of beam ion markers is then modeled with the ASCOT5 code until they either collide with the 3D wall or are slowed down close to the local thermal energy. The energy and pitch collisions with the static hydrogen-electron plasma background, defined by the input profiles, are modeled with Monte Carlo collision operators. BBNBI [5] generates the ions from beam neutrals for ASCOT simulations. BBNBI5 is an ASCOT5 native implementation of BBNBI with identical physics. Here, the ionization cross-sections of the Suzuki model [20] are used. The NBI beam is modeled as realistic, injector-specific beamlets of markers. Beam neutrals are advanced until their ionization probability exceeds a random threshold λ, after which the exact ionization location is calculated and a new beam ion is recorded. 2.2. W7-X setup W7-X will be equipped with two NBI Boxes (for balanced injection), each with four sources [21]. Half of the sources have not yet been included in the OP2 campaign but, in this work, all planned sources are included. In BBNBI5 simulations, these eight NBI sources are set to inject hydrogen with a nominal power of 1.7 MW. BBNBI5 uses a detailed model of the NBI injectors, with 774 beamlets per source, each with a given divergence value of 0.0125 rad. The maximum particle energy for hydrogen injection is 55 keV, and realistic fractions for 1/2 and 1/3 energy particles are 39% and 28%, respectively. The equilibrium, corresponding to the W7-X discharge 20180920.17, was reconstructed using the equilibrium solver STELLOPT [22,23] which is interfaced to the VMEC 3D equilibrium solver. This was an ECRH discharge in the standard magnetic configuration with added NBI [24]. Equilibrium magnetic fields and flux surface coordinates were then placed onto the cylindrical ASCOT5 background grids using the BEAMS3D code [25]. The bootstrap current and the radial electric field inside the equilibrium boundary were obtained using the NEOTRANSP [26,27] transport solver. As VMEC is an inverse code, only fields inside the VMEC domain can be interpolated from the VMEC flux-aligned grid to the cylindrical grid. Outside the VMEC domain, the same methods were used to extrapolate the flux surface coordinates into the SOL, and the magnetic fields were obtained by Biot– Savart integration over the W7-X coils set, with a virtual casing principle for the plasma response [28]. The SOL plasma profiles can then be specified as a function of the extrapolated flux surface coordinate only. In figure 1, the extrapolated radial grid, VMEC equilibria, vacuum Poincaré, and wall structure are plotted in the region of the NI21 neutral beam line. A solid blue line is used to denote the ρ=1.1 and 1.2 surfaces which define the maximum extent of our profiles. The detailed 3D wall is acquired from CAD models by exporting them as triangular surface meshes with roughly 7.8 million triangles [29]. In this work, we mainly focus on the total load arriving at different wall components consisting of Figure 1. Plot of the various radial grid quantities for the W7-X standard magnetic configuration. The color map shows the radial gridding used in this work (extrapolated outside the VMEC domain). White solid lines depict the VMEC flux surfaces with the magnetic axis denoted by a white cross. A vacuum Poincaré plot is included showing the edge island structure (not considered in radial gridding). Solid blue lines are drawn at the ρ=1.1 and 1.2 surfaces for reference to the edge profiles considered. A cross section of the first wall structures is depicted in black. Figure 2. A view of the W7-X internal wall as seen by ASCOT. Wall components relevant for this work are color coded. these triangles. Such components, as seen by ASCOT markers, are illustrated in figure 2. Since the beam ion weights correspond to a source, they are in units of s-1, and the power load (in Watts) is calculated simply by summing up the energy contribution of all markers arriving at a particular wall component/triangle. The power loads can then be obtained by dividing the power by the surface area. As shown in figure 3triangle sizes vary a lot which, together with a finite number of markers, causes statistical problems for the smallest triangles as discussed later in section 3. In figure 4the extrapolated ρ-values of wall components are shown. This value indicates how close to the core plasma and LCFS the components are. Due to the ad hoc nature of much of the SOL input data, these simulations do not aim at quantitative estimates of the 3 Plasma Phys. Control. Fusion 67 (2025) 025034 T P Kiviniemi et al Figure 3. Number of wall triangles as a function of triangle size. Small triangle sizes are required at some parts of the wall to accurately discretize the wall but this also causes challenges in statistics of the simulation. Figure 4. The extrapolated ρ-values of wall structure show that the carbon components getting most of the load are much closer to the core plasma when compared to steel components. peak power but, rather, at obtaining a qualitative understanding of the relative role of different SOL mechanisms affecting the beam ion confinement and power loads. Consequently, 1.2 million markers is considered sufficient in all addressed cases. The input profiles for density n(ρ)and temperature T(ρ), together with the radial electric field Erand the beam ion birth profile, calculated from the density and temperature values, are shown in figure 5. The input profiles are based on a stereotypical W7-X standard magnetic configuration discharge with mixed ECRH and NBI [24]. The electron density profile and electron temperature profiles are based on fits to Thomson data [30], while the ion temperature is based on XICS measurements [31] (inside of ρ=1). The radial electric field is derived from neoclassical estimates based on these profiles and magnetic configuration. No edge transport modeling Figure 5. Plasma background used in the simulations: (a) density, (b) temperature, and (c) radial electric field. In (d), the NBI source distribution, calculated with BBNBI5 using these profiles, is shown. Notice that the SOL profiles are varied along the study in an attempt to determine the importance of different physical processes. was considered in this work, instead edge profile shapes were chosen to help scope the effect of including such profiles in the future. 3. The effect of slowing down and ionization in SOL In this section, the effect of slowing down and ionization due to the SOL plasma are studied. The profiles inside LCFS are kept intact throughout this study, while we experiment with the SOL profiles to obtain a qualitative understanding of the relative importance of different processes. The electron temperature at LCFS is about 150 eV, which implies that the critical energy (Ecrit ≈14.8·Te) in the SOL will be approximately equal to or less than 2 keV. Therefore, pitch scattering will play no role in SOL and, consequently, we refer to collisional processes in SOL as slowing down only. First, we use constant SOL density and temperature profiles to examine if the SOL width plays an important role. This is followed by investigations with more realistic profiles. 3.1. Constant profiles and SOL width We start our work on the effect of SOL plasma with sanity checks that also address the significance of the SOL width. Since the magnetic islands in the standard configuration can 4 Plasma Phys. Control. Fusion 67 (2025) 025034 T P Kiviniemi et al Table 1. Change in the number of ions lost to the wall (∆parts) and in the power load (∆P), caused by introducing a SOL plasma. Numbers written in italics correspond to cases where constant SOL density of nLCFS and constant temperature at two different values (TLCFS/10 and TLCFS/3) were assumed, while numbers written in bold have linearly decaying SOL profiles. The two bottom lines correspond to cases where either density or temperature was kept constant at the given value, while the other decayed linearly (‘linear n’, ‘linear T’). Both slowing down (SD) and ionization processes in SOL are included unless otherwise stated. Case ∆parts ∆P no SOL base base T/3 (ρmax =1.2), SD only −12.0% −30.0% T/10 (ρmax =1.1), SD only −37.3% −60.2% T/10 (ρmax =1.2), SD only −40.7% −66.3% T/10 (ρmax =1.2)−16.4% −27.6% linear n&T, SD only −1.5% −9.4% linear n&T, Ionization only +9.9% +19.8% linear n&T+8.3% +8.5 % linear n,T=TLCFS +8.7% +9.5% linear T,n=nLCFS +15% +9.3% be 10 cm wide and the effective minor radius of W7-X is of the order of 50 cm, as a preliminary check we compare plasmas extending to different radii: ρmax =1.0 (i.e. no SOL plasma), 1.1, and 1.2. Here, ρstands for the extrapolated radial coordinate, with ρ=1.0 corresponding to the LCFS. For clarity, these tests were done assuming a constant SOL plasma with nSOL =nLCFS and TSOL =TLCFS/10. These values probably overestimate SOL collisionality so the rationality of these simulations is to explore the upper limit of slowing down effects. The results, collected to table 1, show that there is very little difference between the plasmas extending to ρmax =1.1 and ρmax =1.2, indicating that the main slowing down effects of SOL are coming from the region between ρ=1.0–1.1. Extending the SOL further does not change the results, which is due to the divertor plates being close to the plasma (as shown later in figure 4). Another interesting observation from this simple simulation set is that the power load drops more significantly than the number of wall particles. For the ρmax =1.2 case, the SOL plasma reduces the power load by roughly 66% , while the number of wall particles drops by only 41% . This means that not only is the number of particles reaching the wall reduced, but those reaching the wall are less energetic due to the slowing down effect. The simulations were repeated for higher SOL temperature, TSOL =TLCFS/3, but keeping the same density. As expected, due to the inverse temperature dependence of the collision frequency, this leads to a more modest slowing down effect, i.e. the power load was reduced only by 30%, and the number of wall particles dropped by a mere 12%. The T/10, ρmax =1.2-case was then repeated including the effect of SOL also on ionization. Beam neutrals can be ionized already in the SOL which, for the wall loads, has an effect opposite to the slowing down. The power load, in particular, can be expected to even increase since the ions born in SOL do not necessarily slow down before reaching the wall. Indeed, both the reduction in the number of lost particles (−16.4%) and the power load reduction (−27.6%) are roughly a factor 2 smaller than with just pure slowing down. It can thus be concluded that, as far as wall loads are concerned, the beneficial effect of the slowing down in the SOL plasma can be largely reduced by the premature ionization of the beam ions. Next we shall further investigate the relative importance of slowing down and ionization using more realistic, decaying plasma profiles in the SOL. 3.2. Ionization and slowing down with experimentally motivated SOL plasma profiles Since the NBI ionization profile, in particular, depends strongly on the density but only weakly on the plasma temperature, we now take a closer look at the relative significance of ionization and slowing down using more realistic model profiles. We let ne,iand Te,idrop from their values at LCFS linearly to zero at ρ=1.15. For these profiles, the ionization in SOL is about 3% of the total injected particles, see figure 5(d) that shows the radial ionization profile with and without the SOL plasma. Table 1also lists the results of a set of simulations where the different processes were activated one at a time. It is immediately noticed that, compared to the constant profiles, the effect of decaying SOL profiles is detrimental—even in the absence of beam ions born in SOL, the slowing down effect on power loads is now only about a 10% decrease (compared to 66% with the constant profiles). In all other cases, the minus signs change to plus signs. Compared to the no-SOL case, ionization alone is found to increase the power load by almost 20%. Including SOL slowing down reduces this to below 10%. However, before drawing any conclusions on the severity of these observations, it is important to notice that the W7-X wall consists of steel and carbon components, with the steel components being significantly more vulnerable to power loads. Table 2lists the power received by various wall components, with red corresponding to steel components and blue to carbon ones (see figure 2for the meaning of the components). Cases with and without SOL plasma are presented, and for the SOL plasma, different processes were activated one at a time. According to the table, premature beam ionization in SOL mostly increases the target load, with a noticeable effect also on the baffle and shield. All three are carbon components, designed to receive significant loads, and including the slowing down process partly compensates for the increase. For the steel components including the SOL plasma either slightly reduced the arriving power or did not have a noticeable effect. Therefore, the net effect on power loads does not appear significant. In figure 4the ρ-values of load positions are shown. Even though we do not expect the extrapolation of ρbe accurate up to ρ=1.5, the values clearly indicate that the target in the figure showing ρ-values of ρ≈1.1 is much closer to the core plasma compared to the panel and other steel components in the figure. 5 Plasma Phys. Control. Fusion 67 (2025) 025034 T P Kiviniemi et al Table 2. Beam ion power loads (kW) on selected wall components with different physical mechanisms included: no SOL, SOL effect on beam ionization only, SOL effect on slowing down only, and effect of SOL on both. Carbon components are indicated in italics. Other components are steel components. case No SOL Ioniz. Slow.down Both Closure: 9 10 7 8 Closureside 82 85 75 77 Panel: 184 190 165 171 Slits: 2 3 3 2 Vessel: 3 3 3 3 Baffle: 309 353 289 326 Shield: 224 244 205 220 Target: 662 882 592 791 Totmetal: 281 291 252 261 Totcarbon: 1196 1479 1085 1337 Also, the relative importance of the density and temperature profiles was tested and is reported at the bottom of table 1: first the SOL temperature was kept constant at its LCFS value while the density dropped linearly, which is the lowest SOL collisionality case considered. The simulation was then repeated with profiles of the opposite behavior: the density was kept at its high LCFS value while the temperature dropped linearly. In these simulations, the effect of the SOL plasma on both ionization and collisional processes was included. Comparing the numbers, it is seen that with constant temperature but decreasing density profile we obtain results very similar to the case where both the density and temperature decay toward the wall. As expected, the case with constant, high density brings the largest changes in the number of lost ions due to increased ionization, but the change in power load is modest due to the stronger slowing down with the decaying temperature profile. The information in tables 1and 2is combined in figure 6 for visual inspection. The effect of collisionality clearly has higher relative importance for the loads on steel components. This is probably due to the fact that, on average, the distance to these components is larger, which enhances the effect of collisions. In all cases where slowing-down is taken into account, the power load to steel components is lower than in the absence of SOL. Thus it can be concluded that the effect of SOL plasma in most cases (over a wide range of different profiles) is to mitigate the power load on steel components even if it would increase the total load. Figure 7shows a histogram of the ρ-distribution of the power load for the different physics cases. This distribution gives an indication of the distance at which the beam ions reach the wall component. The two divertor plates (in each of the five segments, here summed over) are clearly visible as two humps at around ρ=1.07 and ρ=1.11, with the one closer to the plasma receiving a larger power load. It is also at these components that the difference between the assumed physics cases becomes noticeable: only with ionization included do we get enhancement in power loads. Figure 6. Power loads on steel (red) and carbon (blue filled markers) components. Here, first four cases are no SOL; linearly decaying SOL profiles; linearly decaying n, constant T=TLCFS; constant n=nLCFS, linearly decaying T. All cases included both ionization and slowing down effects in SOL. Last two cases both have linearly decaying profiles but reduced SOL physics i.e. only slowing down or only ionization. 3.3. Statistics of hot spots Most of the analysis in this work is done for integrated wall loads, which is sufficient to give insight into the relative importance of the effects of different physics processes on wall loads. Thus, the large number of small triangles, as shown in figure 3, does not play a significant role as results are weighted by their small area. We have numerically tested that leaving out small triangles (<2 mm2) can be up to 2% for closure sides, but for other elements it is <1% being negligible for targets and baffle. Also, in 3D visualizations, all the triangles are included but possible high peak loads caused only by pure statistics in small triangles naturally get the weight they deserve as small triangles are difficult to see by eye. However, in machine safety 6 Plasma Phys. Control. Fusion 67 (2025) 025034 T P Kiviniemi et al Figure 7. Number of markers reach the wall as a function of the radial coordinate ρfor the different cases: no SOL, only SOL slowing down, only SOL beam ionization, and including SOL mechanisms. The two divertor plates show up as distinct humps. Figure 8. Test on statistical significance of small wall elements: the number of wall triangles receiving a given peak power load, in MW m−2, including all elements or leaving out those receiving only one, two or three markers. The distribution is found to converge after leaving out triangles receiving only two markers. the highly localized peak loads are of special interest, so we here take a closer look at the statistical challenges in evaluating them, although this is not the main scope of the present paper. In order to identify possible hot spots, it is necessary to look at the power densities, in units of MW m−2. Here, the discrete nature of our approach becomes an issue: not only do we have a finite number of markers, representing the beam ions, but also deciding the size of the surface area to be used in the calculation matters: a very small surface area receiving a single marker can result in an excessive, artificial peak load. To avoid such anomalies, we calculated the power densities on each wall triangle keeping track of cases where the triangle receives only one, two or three markers. The results of this analysis are presented in figure 8, illustrating that the high-end of Table 3. Results from the statistical test. The number of wall triangles receiving more than 2 MW m−2or 10 MW m−2(total number of triangles almost 8 million). Top: no triangles excluded. Bottom: triangles receiving only one or two markers excluded. >2 MW m−2>10 MW m−2 No sol effects 4237 1445 Ionization in SOL 4454 1526 Slowing down in SOL 4035 1352 Both effects in SOL 4268 1384 >2 MW m−2>10 MW m−2 No sol effects 667 126 Ionization in SOL 694 134 Slowing down in SOL 606 117 Both effects in SOL 641 109 the power density distribution is indeed strongly affected by this filtering. This is an indication of the suggested anomaly and is confirmed by the fact that if we do the filtering based on the size of the triangles instead of the number of markers received, i.e. by excluding triangles with a size of less than 2×10−6m2, we get very similar results. Furthermore, when looking at the effect of the chosen selection criteria on different mechanisms, it turns out that the individual hits on random, tiny elements are due to the slowing down process, while the ionization process is quite insensitive to it. Figure 8shows that the results seem to converge when triangles receiving only two markers are excluded, so in table 3we summarize the cases where either 2 MW m−2or 10 MW m−2is exceeded. The number of such triangles is found to be quite limited and is expected to get even smaller if the CX reactions, to be investigated in section 5, are also included. However, at the present level of uncertainties in all SOL parameters, a more extensive study is not meaningful but will have to wait until experimental data is available. The merit of the present work is merely to identify the importance of different SOL processes. 4. Effect of SOL electric field In this section, the effect of a radial electric field is tested. In the absence of accurate data for the SOL potential and keeping in mind that even the values for the flux surface coordinate ρ are extrapolated, the purpose of this section is only to give a qualitative picture of possible effects of the SOL fields. Other SOL effects, such as beam ionization or slowing-down, are not included here. In experiments, for good core confinement, the radial electric field Ercan be either negative (ion-root) or positive (electron-root) inside ρ=0.5. At the edge (inside the LCFS), negative Eris always observed, and a shear flow layer at the LCFS has been clearly measured, implying that the SOL radial electric field is always positive. This is also intuitive: the electron temperature typically drops when moving deeper in the SOL, as is the corresponding electric potential. Based on these observations we constructed simplistic Erprofiles in the region 7 Plasma Phys. Control. Fusion 67 (2025) 025034 T P Kiviniemi et al Figure 9. Model profiles for Er= (−dΦ/dρ)/aminor used for testing the effect of radial electric field in SOL. ρ=1–1.15. The variation of the field strength is piece-wise linear, with varying peak values of Er,max =0, ±15, ±30 and ±60 kV m−1as illustrated in figure 9. The profiles depicted with solid lines in are thus in qualitative agreement with experiments, and our core Ercorresponds to the ion-root. The negative field values, shown with dashed lines, are included out of curiosity since these simulations could shed light on the situation when the magnetic field direction is reversed. In the ASCOT simulations, we assume that the electrostatic scalar potential Φis constant on a flux surface and plot the results as a function of Er(ρ)=(−dΦ/dρ)/aminor which, with this simplification, is also only a function of the extrapolated radial coordinate. Here, aminor is the effective minor radius. Pre-sheath or sheath (or any other E∥) electric fields which could accelerate the ions near targets are not taken into account in the present study. The overall effect of a SOL radial electric field is summarized in figure 10, separately for carbon (blue) and steel (red) components. A non-zero radial electric field is found to lower the power load on the steel components, particularly the panel, with the effect being significantly larger for the positive Er,max and removes the hot spots observed on the panel for the standard configuration in [3]. On the contrary, the power lost on carbon components has a strong dependence on the direction of the radial electric field: a positive Er,max increases the power load, the effect being most dramatic for the target. A negative Er,max, on the other hand, has a mitigating effect on all but the load on the target. This kind of change of target load asymmetry due to SOL E×B-drift is a well-known phenomenon in tokamaks (see e.g. [9,35,36]). However, this has not been Figure 10. Effect of a radial electric field on steel (red) vs carbon (blue) components. Here, ‘steel other’ includes loads on closure, slits and vessel which are not relevant for the realistic direction of SOL Er. Figure 11. A 3D illustration of the effect of SOL radial electric field on peak power load near the AEF20 port, panels (a) and (b), and around the lower target, panels (c) and (d). In (a) and (c), Er,max =−30 kV m−1, while in (b) and (d) Er,max = +30 kV m−1, which is the more realistic direction. greatly studied in stellarators. The present work suggests that similar phenomena also exist in stellarators but should be further verified with a 3D potential background, e.g. from EMC3EIRENE. The main effect here is that drifts lead the particles carrying the heat load to the targets and other carbon components which are closer to the core plasma compared to steel components as shown in figure 4. Figure 11 shows synthetic camera views of the power load with Er,max =±30 kV m−1for two specific locations: around the port AEF20, which hosts some immersion tubes (not included in this simulation), and the target. A positive Er,max is found to increase the load on the target although the peak loads seen in the figure are lower. Near the AEF20 port the load is higher with positive Er,max. In figure 12, we show the 8