Impact of gas injection location and divertor surface material on ITER fusion power operation phase divertor performance assessed with SOLPS-ITER

The ITER divertor design and performance assessment, primarily based on the SOLPS-4.3 burning plasma database (Pitts R. et al 2019 Nucl. Mater. Energy 20 100696), assumes the use of beryllium (Be) as the divertor surface material and the injection of gas from the main chamber top. However, the current ITER baseline favors gas injection from the more toroidally symmetric sub-divertor region. This paper evaluates the implications of these assumptions for divertor performance in the ITER fusion power operation phase. The impact of the divertor surface material and the gas injection location on the main ions mirrors the hydrogen only low power phase scenario shown in Park J.-S.et al (2020 Nucl. Fusion 61 016021). However, during burning plasma operation, extrinsic impurity seeding will be required. In the case of neon (Ne), studied here, impurity retention is influenced by both the divertor surface material and the fueling location. Neon leakage increases due to more energetic reflection from tungsten than beryllium, but equivalent divertor performance can be achieved by adjusting the neon seeding rate. While the impurity seeding location does not affect the distributions of impurity or radiation, the fueling location does. Top fueling provides local ionization sources mainly in the mid-SOL under detached conditions, enhancing divergences of the flux there (source-driven flow), bringing stagnation points close to the fueling location, and equilibrating flows towards both targets. In contrast, the global flow pattern (in the absence of fluid drifts) in the case of sub-divertor fueling is biased towards the inner target. Impurity flows, driven by force balance, largely mirror those of the main ion flow, including the stagnation point. The case with top fueling enhances Ne retention and corresponding radiation in the outer divertor, effectively reducing the total and peak target heat fluxes by 20%–40%, compared to the case with divertor fueling. Meanwhile, the case with outer target fueling also achieves similar reductions by enhancing plasma-neutral interactions. These results suggest the possibility that the selection of the fueling location and throughput can be used as an actuator to control impurity divertor retention and divertor radiation asymmetry.


Introduction
The design and performance assessment of the ITER tungsten (W) divertor have been primarily based on the SOLPS-4.3 burning plasma database [1].Nevertheless, this database rests on two key assumptions: the use of beryllium (Be) as the divertor surface material and the injection of gas (including both fuel and impurities) at the main chamber top.In the current ITER baseline [2], minimal Be deposition near the strike point is expected, with gas injection projected to occur from the more toroidally symmetric sub-divertor region, offering improved accessibility for divertor control.Moreover, in the context of some very recent studies at the ITER Organization examining the possibility of exchanging Be for W in the main chamber, it is of some importance to evaluate the implications of these material and gas injection assumptions on the performance of the ITER divertor.
Previous SOLPS-ITER investigations into a pre-fusion power operation-1 (PFPO-1) scenario, involving a scrape-off layer (SOL) power of P SOL = 20 MW using hydrogen (H) fuel, indicated that the choice of divertor surface material (Be vs. W) mainly influenced the ratio of thermally reflected H 2 molecules and fast reflected H atoms, but did not substantially affect overall divertor performance [3].This balance arises from the compensatory interactions between atom-plasma and molecule-plasma in terms of momentum and power losses.Due to high opacity, the impact of gas puff locations on near SOL plasmas was negligible.However, fueling from the main chamber top enhanced detachment in the mid-far SOL by increasing local ionization sources.
In this paper, we evaluate the impact of the gas injection location and the divertor surface material on the ITER baseline fusion power operation (FPO) scenario (Q DT = 10), with P SOL = 100 MW using deuterium (D) fuel, and including helium (He) fusion ash and neon (Ne) seeding [2].We utilized SOLPS-ITER [4,5] to conduct fueling throughput scans for several gas injection locations and two divertor surface materials (Be and W).The simulation results have been incorporated into the ITER Integrated Modeling and Analysis Suite (IMAS) [6] public database.
Unlike in the PFPO-1 simulations, the SOLPS-ITER FPO runs incorporate a seeded Ne impurity, which profoundly influences divertor performance.Our analysis therefore centers on the variation in divertor impurity retention.The choice of target surface materials does not notably influence divertor performance, and equivalent conditions can be achieved by modifying the Ne seeding rate.However, our findings reveal that Ne retention in the divertor and the radiation asymmetry much more influenced by the fueling location than the impurity seeding location.These results imply that fueling can serve as an actuator to regulate impurity divertor retention and divertor in-out asymmetries.

Setup of SOLPS-ITER simulations
The simulations discussed in this paper were conducted using the SOLPS-ITER code (versions 3.0.6 and 3.0.8) to simulate ITER FPO scenario plasmas.As detailed in table 1, simulations were performed for two types of divertor surface materials (Be and W) at four different gas injection locations: the main chamber top (Top), below the divertor dome (Div), inner target (IT), and outer target (OT).Cross cases, where fueling and impurity seeding locations were not the same, were also considered.Even though gas injection from IT and OT is not considered in the ITER baseline, these locations were included in the simulations to provide a more comprehensive understanding of the underlying physics.
The overall simulation setup, including the simulation grid, was the same as that used for the SOLPS-4.3 burning plasma database [1].The simulation grid is depicted in figure 1, which highlights the four gas injection locations, the pump location, and primary areas of interest via color-coding.The pump surface albedo is set at 0.9928, in line with previous work [1].This grid was constructed based on the q 95 = 3, I p = 15 MA, B T = 5.3 T baseline magnetic equilibrium.The plasma species considered were D, He, and Ne, and the P SOL = 100 MW was equally distributed between electrons and ions.
Radial transport coefficients D ⊥ = 0.3 m 2 s −1 and χ i,⊥ = χ e,⊥ = 1.0 m 2 s −1 were utilized, yielding a near-SOL heat flux width of λ q = 3-5 mm at the outer midplane (OMP).These settings, similar to those used in most older SOLPS-4.3 cases [1], resulted in a larger λ q in SOLPS-ITER due to the enhanced near-SOL flow reversal, observed in comparison to that found in the SOLPS-4.3 simulations.As discussed in [1], this value of λ q falls roughly in the range of values found by recent turbulence code simulations [7] of the ITER burning plasma at 15 MA, but is considerably larger than the value (λ q ∼ 1 mm) expected from the most recent experimental scalings [8].However, since the majority of the main findings of the present study are not strongly influenced by λ q , the adequacy of this value is not considered as a major focus.
Table 1.List of SOLPS-ITER simulation discharges featured in the main content of this paper.This simulation database is publicly available as part of the ITER IMAS database.IMAS shot numbers consist of six digits, beginning with a two-digit prefix corresponding to the main fuel species (10: hydrogen, 11: helium, 12: deuterium), followed by a unique four-digit identifier.All cases in the table have beryllium main chamber walls and semi-transparent iron dome supports, along with iron sub-divertor structures (iron is used as a proxy for the stainless steel from which these structures are manufactured).The colors in the legend correspond to various plasma regions, the separatrix, and gas injection locations.

Species
Following [1], the FPO scenario divertor condition is characterized hereby two main parameters: divertor neutral pressure (p div ) and the average Ne concentration near the separatrix (c Ne ).The definition of both quantities may be found in [1].Throughout this paper, c Ne was fixed at 0.8%.Scans of p div in the range of 2-11 Pa were performed by altering the fueling throughput.Note that the Ne seeding rate required to maintain c Ne = 0.8% varied depending on factors such as gas injection location and divertor material, a detail discussed later.
A more generalized form of thermal and friction forces ('b2sigp_style = 2' in the code) [9,10] was applied to the most detached cases (p div ∼ 10 Pa) of Be top, Be div, Be IT, and Be OT, ensuring improved force balance for impurities.
Cross-field drift terms were not included to better align the study with the SOLPS-4.3 database.The potential effects of including drifts are discussed in section 3.
Finally, the EIRENE reaction set used in [3] was expanded to include additional He and Ne atomic reactions such as electron impact ionization, charge-exchange, and neutral-neutral elastic collisions, maintaining consistency with the SOLPS-4.3 burning plasma database.

Results
In this section the effect of the divertor surface material and the gas injection location on the divertor plasma conditions are explored.The gas injection location has a significant impact, while changing the divertor surface material has a more modest effect.

Influence of divertor surface material on impurity retention
The choice of divertor surface material significantly affects properties related to reflection and sputtering.In the absence of sputtering, the parameters that are affected by the surface material within the SOLPS code are the fast particle reflection coefficient R F and the fast energy reflection coefficient Ēref /E 0 , defined in the TRIM database [11].The influence of variations in the reflection probabilities of the main ions on the divertor condition was discussed in [3].In this paper, we also examine the effects of changes in impurity reflection properties according to the material.
As with the main ions, the ionization source of Ne impurities is also predominantly from recycled impurities, which is several orders of magnitude larger than the source from gas puff seeded atoms.Therefore, the reflection properties of impurities recycled from the target can influence impurity retention or divertor conditions.Neon ions and atoms can be reflected in two forms: as fast reflected Ne atoms or as thermalized Ne atoms.The total recycling coefficient, which is the sum of the two, is set to 1. Figure 2 displays R F and Ēref /E 0 for Ne incident on Be and W surfaces at the most probable angle of incidence of 60 • .
At the divertor targets, 60%-70% of the incident Ne ions are Ne + and 20%-30% are Ne 2+ , with the remainder being negligible, resulting in Z values of ~1.3-1.6.The incident energy E 0 is computed as 2T i +3ZT e , which is ~6.4T e assuming T e = T i .The binding energy of Ne incident on both Be and W surfaces in the TRIM database is 0 eV, so a minimum cutoff energy limit of 1 eV is applied.
In common with the main ions, both R F and Ēref /E 0 are much larger for Ne incident on W than on Be.As a result, it is predicted that a greater proportion of Ne atoms and ions incident on W will be recycled as fast-reflected Ne atoms, and will be reflected with more energy compared to when they are incident on Be.This observation originates from the fact that the fast reflection coefficient of impurities is also affected by the target material, particularly the mass ratio.Neon atoms that are thermally reflected are dispersed with a Maxwellian energy distribution of thermalized particles, with an average energy twice that of the plasma facing boundary surface temperature.The surface temperature is set to 0.1 eV at the target and 0.05 eV for the main chamber walls.
The energy flux carried by emitted Ne atoms from divertor target surface segments, E emit Ne , is depicted as a function of the average energy of impinging Ne atoms on surface segments, E imp Ne , in figure 3. The Ne ion flux and Ne atom flux exhibit similar orders of magnitude on both targets for all four combinations of surface material and gas injection locations.Given the similar incidence rates of Ne ions and atoms, the reflection tendencies are also comparable.This figure thus serves as one measure of how the energy distribution of recycled atoms varies with the target material.For all cases, irrespective of the gas injection location, the points form distinct clusters corresponding to the material.As predicted from the earlier explained

TRIM results, the cases involving W target surfaces result in larger E emit
Ne values for a given E imp Ne .The difference in reflected Ne energy depending on the surface material can ultimately lead to variations in Ne retention.This disparity in retention arises because the mean-freepath (mfp) of Ne ionization is proportional to the square root of the recycled Ne atom temperature.The degree of impurity retention tends to increase when the Ne atom ionization location is downstream relative to the Ne ion stagnation point [12].Consequently, there is a tendency for Ne atom retention to decrease when reflected from W compared to Ne with reflection from Be.Therefore, as shown in figure 4, in order to achieve a Ne concentration of 0.8% for a given p div , a higher Ne seeding rate is required for a Be target than for a W target.
The trends observed in the figure 4 suggest that the location of gas injection also influences the seeding rate required to achieve c Ne =0.8%.This effect appears to be more pronounced in the case of Be compared to W. This aspect will be further explored in the following subsection.

Effect of gas injection location on radiation
The most pronounced difference observed across various gas injection locations is found to be in the radiation fraction and its spatial distribution.Figure 5 shows the ratio of the total radiated power to P SOL (f rad,tot , unfilled markers) and the divertor radiation fraction (f rad,div , filled markers) as functions of p div .Approximately 90% of the radiation comes from the divertor region, which includes the inner divertor SOL, outer divertor SOL, and PFR, as defined in figure 1.While f rad,div is largely unaffected by the gas injection location, f rad,tot shows a strong dependence.Divertor injection and IT injection cases display f rad,div ∼ 0.4 in the most detached conditions, whereas top and OT injection cases exhibit values ranging from 0.5 to 0.6.
The results depend both on the target material, and on the form of the thermal and friction forces used in the fluid equations, controlled by the numerical settings ('b2sigp_style' '1' vs. '2', see section 2).The new form for the friction and thermal force ('b2sigp_style' '2') leads to a greater impurity content in the upper SOL and a reduced impurity content in the divertor compared to the older form ('b2sigp_style' '1'), and the disparities between the old and new forms become more pronounced as the impurity seeding rate increases [10].As a result, an equivalent c Ne of 0.8% results in a lower divertor impurity content with the new form compared to the old form.Consequently, this leads to a reduction in total radiation, given that 90% of impurity radiation originates from the divertor.
Variations in the SOLPS code version also introduce discrepancies in f rad,tot as it approaches detached conditions (higher p div ), and these differences can be ascribed to variations in the atomic database concerning radiation and excitation.The SOLPS-4.3 points in figure 5 employ STRAHL [13] for Ne radiation, while the SOLPS-ITER points use ADAS (using the Year 96 data for Ne line radiation, which remains the default in SOLPS version 3.0.8)[14].The electron cooling rate of the main Ne radiators, Ne 3+ − Ne 7+ , can differ by a factor of 2-3 within the primary radiation temperature ranges (figures 6(a)-(c)), which results in differences in the radiated powers (figure 6(d)) per species.Ne 6+ and Ne 3+ radiation is more substantial for STRAHL, while Ne 4+ , Ne 5+ , and Ne 7+ are higher for ADAS.The radiated power per species is highest for Ne 6+ , followed by Ne 5+ and Ne 4+ .Hence, while the differences are balanced out per species, the total radiated power for STRAHL is generally higher than the ADAS cases by up to 20% when the contributions are summed up [15].
The two-dimensional radiated power distribution for the most detached conditions is shown in figure 7 across four different gas injection locations.From this point forward, our focus is primarily on the impact of the gas injection location with the target material set as Be, and the new form of friction and thermal forces ('b2sigp_style' '2') in place.The divertor, IT, and OT gas injection cases exhibit a similar radiation pattern, with radiation localized in the downstream SOL, along the separatrix legs.The radiation near the target is asymmetric, with the IT radiation being more pronounced compared to the OT, which is localized in a radially narrow region, along the separatrix.However, the top injection case is unique, showing pronounced outer SOL radiation that extends further radially outward, and poloidally towards the outboard midplane in the near-SOL.The inner SOL radiation pattern remains similar to the other three cases.
To quantify the radiation asymmetry and its dependence on the gas injection location, the radiated power summed along the SOL flux tubes from the target to the X-point is plotted as a function of radius at the OMP in figure 8.As anticipated from the 2D distribution, the top injection case exhibits the most pronounced in-out asymmetry, characterized by the smallest radiated power at the inner SOL and the largest at the outer SOL.In contrast, the divertor injection case demonstrates the opposite trend, with the radiated power at the inner SOL larger than the outer SOL.
The cases with injection at the target, however, do not demonstrate a consistent trend.The IT injection case shows a decrease in inner SOL radiation and a slight increase in outer SOL radiation compared to the divertor injection case.Conversely, for OT injection radiation at both inner and outer SOL is enhanced compared to the divertor injection case.
Comparing the sum of the radiated power in the inner and outer SOL (sum along the radial direction in figure 8) for the most extreme cases-top injection and divertor injectionreveals a significant shift.The sum of the radiated power in the inner SOL decreases by 25% from the divertor injection case to the top injection case (from 19.83 MW to 15.36 MW), while there is a 130% increase in the outer SOL (from 10.95 MW to 25.02 MW).This dramatically increased outer SOL radiation in the top injection case is not localized to the near SOL but extends over several λ q .
Lastly, cross-injection cases (meaning that the fueling and Ne seeding locations differ (marked as dashed lines in figure 8)), closely follow the results where the seeding and fueling are co-located (solid lines of the same color).This implies that the radiation distribution is not significantly impacted by the impurity seeding location, but that it is strongly dependent on the fueling location.

Flow patterns driven by fueling source locations
In the last part of the preceding subsection, it was demonstrated that while the fueling location significantly impacts the radiation distribution, the impurity seeding location has minimal influence.Given these findings, the remainder of this paper will focus on the effect of the fueling location.Differences in the radiation distribution suggest variations in impurity retention or T e distribution.Consequently, the focus is shifted towards the examination of impurity retention and the impurity flow influencing it, contingent on the fueling location.
Impurity flow generally mirrors the main ion (D + ) flow pattern, due to strong frictional coupling and the dominant source of neutrals arising from recycling at the divertor, although deviations can result from other forces on the impurity ions.Since the flows near the target are predominantly governed by the local recycling sources, the flow pattern in this region remains consistent across cases with varying fueling locations.
In contrast, the upstream flow patterns and main ion sources vary significantly with fueling location and are shown in figure 9 for two cases with notable variation: Be top and Be div.The primary contributors to the main ion source are electron impact ionization (EI) and radial transport by anomalous diffusion.Other sources, such as molecules and molecular ions, generally counterbalance each other, while recombination is only pronounced near the target.They therefore have a negligible impact on the overall distribution, and the EI source closely aligns with the total D + source distribution.
In the most detached condition for the Be top case (figure 9(a)), the D + source peaks midway between the separatrix and the radially most outward position of the grid, the region we refer to as mid-SOL (corresponding to (r − r sep ) OMP ∼ 0.04 − 0.06 m), and is poloidally near the gas injection location.The flow patterns stagnate in each flux tube at the points marked with yellow circles leading to flows that are directed only towards the OT for the SOL flux tubes with the strongest source.
The most detached condition of the Be div case (figure 9(b)) exhibits negligible ionization sources in the upstream SOL, and the upstream flows are solely directed towards the IT.The neutrals from divertor fueling are trapped in the PFR and the majority ionize near the target due to the V-shaped corners and divertor dome baffling [16].The divertor ion source is dominated by the target recycled neutrals, which are 2-3 orders of magnitude higher than the fueling rate.Therefore, in the case of upstream top injection, the main ion sources induced by gas injection can become locally strong new ionization sources, thereby influencing the flow patterns.
In the attached condition, fueling sources from upstream affect the flow pattern in a similar manner.In the most attached Be top case (figure 9(c)), the main ion sources are more radially and poloidally dispersed compared to the detached condition.This dispersion occurs because the detached plasma has higher n e and lower T e in the upstream SOL, particularly for the Be top case, leading to a higher ionization rate and a lower neutral mfp there [17,18].Consequently, in the attached case, the fueling neutrals penetrate farther into the plasma and closer to the separatrix.
The radial distribution of the ionization source, illustrated in figure 10 for a poloidal grid index of 46 (closest to the upstream top fueling location), further supports these observations.In the detached case (figure 10(a)), top fueling cases exhibit a peak ionization source around the mid-SOL area, reaching levels of 10 22 -10 23 m −3 s −1 .This is 2-3 orders of magnitude higher than the sources at this position for cases with other fueling locations, which have their peak ionization closer to the separatrix.The outward shift of the ionization peak for the top fueling case is attributed to enhanced neutral opacity, resulting from ionization of local neutral sources introduced by top fueling, which in turn increases the electron density in that region.
In the attached case, as shown in figure 10(b), the ionization source level is significantly lower due to a combination of reduced fueling rate and lower neutral opacity.This results in a more uniform distribution of ionization sources from the top fueling along the radial direction, without an opaque barrier.Despite this, the ionization sources in the upstream SOL near the top fueling location are still 1-3 orders of magnitude higher than in the divertor fueling case, significantly influencing the flow patterns.
The parallel distribution of the ionization source is presented in figure 11 at the 13th SOL ring ((r − r sep ) OMP = 0.0465 m, where the ionization sources peak radially) along the normalized parallel coordinate s ∥ , from the IT (s ∥ = 0) to the OT (s ∥ = 1).The IT, OT, and divertor injection cases display negligible ionization sources in the upstream region, with much higher ionization sources in the divertor SOL region between the target and the X-point, ranging from 10 21 − 10 24 m −3 s −1 .However, the top injection cases show a peak of the ionization source near the cells closest to the top injection locations (marked as the green region), and this is comparable to the ionization sources near the target.Around this peak, the sources still maintain a high level (>10 22 m −3 s −1 ) towards the IT (s ∥ = 0.4 − 0.6), while it decays much faster towards the OT (s ∥ = 0.63 − 0.67).This is attributed both to the biased gas injection direction of the top injection slot towards the IT, and the wall geometry that results in molecules and atoms being reflected and distributed further towards the IT.This neutral distribution of the FPO Be top case is similar to the PFPO-1 top injected case, as shown in figure 11 of [3].
The IT and OT injection cases have 1-2 orders of magnitude higher ionization sources in the inner divertor SOL and outer divertor SOL, respectively, within the mid-SOL flux tubes as shown in the lower part of figure 11, which magnifies those regions.In both IT and OT injection cases, the mid-SOL ring at (r − r sep ) OMP = 0.0465 m does not hold a specific significance.Nevertheless, these cases show additional ionization sources that are primarily effective in the mid-SOL (and far SOL), where direct fueling sources from the target are comparable to recycled neutral sources, unlike in the near-SOL.Therefore, the ionization sources in these cases are consistently shown at the mid-SOL ring in the lower part of figure 11.The peak location is further away from the target compared to other cases.This is attributed to the enhanced neutral sources leading to more volumetric power losses, consequently lowering T e in the mid-SOL flux tube.As a result, the mfp of the neutrals becomes longer and the ionization source peaks further away from the target compared to the cases with other fueling locations.
The parallel velocity distribution u ∥ is illustrated in figure 12 for the main ion and the Ne impurity ion for the same (13th) flux tube as depicted in figure 11.Since the flow pattern of Ne impurity between each charge state is similar, only the most radiating charge state (Ne 5+ ) is shown.As shown previously in figure 9, in the upstream region, the main ion flows are directed towards the IT (u D + ∥ > 0) for the div, IT and OT fueling cases.However, the top fueling case (as well as the cross case with top fueling) is significantly influenced by the strong ionization source near the top injection location (green shaded region in the figure), and the stagnation point is precisely located there.This resembles the effect of sources accumulated at the injection location, spreading in both directions.The IT and OT injection cases are distinct in that they do not involve radial injections, but instead result in neutral fueling from poloidal direction at each end of the flux tube.The stagnation point of the OT fueling cases is closer to the OT compared to other fueling locations.In contrast, the inner divertor SOL flow velocity in the IT cases is reduced relative to other cases but still cannot overcome the strong incoming flux towards the target, thus, stagnation points are not formed in the inner divertor SOL.The general flow pattern for the mid-SOL area indicates that one stagnation point exists along the flux tube, and a larger fraction of the flux tube has flow towards the OT for the top injection case due to the stagnation point being drawn closer to the top fueling location.
The impurity flow pattern in the mid-SOL flux tube is similar to the main ion flow pattern.Unlike the main ion fueling result, the impurity seeding location does not significantly affect the impurity flow pattern (solid lines and dashed lines are nearly identical).This is expected since the seeded impurity source (as shown in figure 4) is 2-3 orders of magnitude smaller than the main ion sources.Instead, the impurity flow pattern is primarily governed by the force balance and the recycled impurity sources.
Although they are not switched on in the simulations described here, the inclusion of drifts also influences the flow pattern.However, in the case of ITER in detached conditions, the drifts only slightly counteract the source-driven flow, but they can have a significant effect in the attached condition for both main ions and Ne ions (see figure 10 of [19]).In contrast, in smaller devices such as ASDEX Upgrade, the influence of drifts on the flow pattern cannot be easily dismissed, largely due to the important role played by the E × B and Pfirsch-Schlüter flows [12].

Role of thermal and friction forces in shaping impurity flow patterns
Understanding the nature of plasma flow patterns is a challenging task due to the coupled nature of particle and force balances.The particle source impacts the divergence of the particle flux, creating a 'source-driven flow' and establishing specific flow patterns.This effect is particularly noticeable in regions with a high source concentration, where stagnation points can even be formed.
Force balance also plays a crucial role, notably in the presence of a net force that can influence the divergence of momentum flux, thereby impacting flow patterns.However, many steady-state cases-impurity species in particularachieve nearly perfect force balance.This near equilibrium can make it challenging to delineate the effect of force balance on flow patterns.Nonetheless, examining the constituent forces and their interactions, can offer insights into how force balance affects flow patterns, even when the overall net force is nearly zero.
We examine first the force balance of impurities.The parallel forces on the Ne main radiator (Ne 5+ ) along the flux tube are shown in figure 13 (see the appendix for a more detailed discussion of the parallel momentum balance equation as it is formulated in SOLPS-ITER).In accordance with the well known impurity transport behavior [20], the impurity force balance is largely dominated by friction and thermal forces, while the other terms such as pressure gradient, plasma-neutral interaction, and electric force become negligible, even close to the target where impurity sources are primarily driven by recycling.
To better comprehend the distribution of thermal force, the parallel distributions of T e , T i , and n e are displayed in figure 14 for the cases with four distinct fueling locations.The T e distributions for div, IT, and OT fueling cases are nearly identical, with noticeable reduction in the temperature near each target for IT and OT fueling cases.However, the T e distribution for the top fueling case exhibits cooling between IXpt and OXpt, which is most pronounced between the IMP and top injection location (s ∥ = 0.25 − 0.65).This area precisely coincides with the n e accumulation location, when considering pressure balance.
Even though molecules and atoms from top fueling deposit closely to the top injection location, along with D + sources, the actual peaks in electron density are poloidally shifted towards the IT direction.This shift acknowledges the main ion flow patterns across the entire upstream SOL, with only a narrow area in the mid-SOL flowing towards the OT from the stagnation point.In contrast, most flows, both in the nearand far-SOL, are directed towards the IT.An analogous observation can be made in the PFPO-1 case, as demonstrated in figure 11 of [3].
In regions characterized by high n e and low T i (T i < 20 eV, n e > 2 × 10 19 m −3 ), T i closely aligns with T e , due to enhanced heat exchange between electrons and ions.Given that the thermal force is proportional to the temperature gradient, it peaks between the local minimum temperature location (s ∥ ∼ 0.5) and the OMP, which is characterized by a local maximum in temperature.This region roughly corresponds to the top injection location, though this correlation appears to be coincidental, since the location of the thermal force peak (representing the steepest temperature gradient) is slightly off towards the OT, failing to align with either the peak of the D + source or the stagnation point.
Returning to the discussion of parallel impurity force balance, the implications of the ion/electron temperature distribution in the divertor region (from IT to IXpt and from OXpt to OT in figure 13) are considered.The thermal forces are always directed from the target to the upstream, following the temperature gradients.These upstream oriented forces in the divertor are balanced by the friction force directed towards the target.
Near the top injection location, both forces peak strongly: thermal forces are directed towards the OT while the friction forces are directed towards the IT.This behavior is a consequence of the strong temperature gradients in the mid-SOL, as previously discussed.Impurities near the top fueling location are primarily driven towards the OT by thermal forces, not by friction forces.It might seem counterintuitive, but friction does not drag impurity ions near the top injection location towards the OT-instead, it acts against the impurity flow towards the OMP, contributing to the synchronization of the main ion flow velocity and impurity flow velocity (figure 12).This synchronization occurs because the friction force is proportional to the differences in flow velocity between species.
Considering the parallel distribution of T e and T i in the mid-SOL (figure 14), the peak generally occurs between the upstream top (near the top gas injection location) and the OMP, regardless of the gas injection location.Therefore, the point where the direction of the thermal force changes is also located there.Consequently, in the divertor region, the T e and T i distributions are largely monotonic, resulting in the thermal force always being directed upstream, while the friction force is directed towards the divertor target.
In the steady-state solutions presented in table 1, the forces generally maintain a stable balance, with no significant outlier net forces.However, dynamics can be observed when the gas injection location is shifted from the divertor to the top, using the divertor gas injection case as an initial condition.This transition allows us to trace the process of how the force evolves after a transition to top fueling and observe its eventual stabilization over time.The forces that serve as sources in the momentum equation (equation ( 1) in the appendix), excluding the time derivative term and the divergence of momentum flux, acting on the main ion and main Ne radiator (Ne 5+ ) are compiled in figure 15.The timestamp t = 1 × 10 −6 s (first row) corresponds to the Be div solution, since changes within this brief timeframe are negligible.On the other hand, t = 1 × 10 −2 s (last row) corresponds to the fully converged Be top solution.
Contrary to impurity force balance, which primarily results from the interaction between friction and thermal force, the main ion force balance involves additional factors such as pressure gradient and electric forces.This derives from the considerably higher density of the main ions compared to the impurities (see equation (1) in the appendix).
Starting with the timestamp at 1 × 10 −6 s, friction on the main ions generally acts in the direction moving away from the target (opposite to that of the impurities), which is counterbalanced by other forces.Compared to the Be top case (as represented by t = 1 × 10 −2 s), the overall magnitude of forces is relatively smaller, indicating minimal changes in temperature and pressure gradient profiles in the parallel direction.
The most significant deviation in the main ion force is observed near the top injection location.Here, pressure gradient forces begin to rise and reach a peak around t = 1 × 10 −4 s.These forces exhibit a positive peak (IT-directed force) and a negative peak (OT-directed peak).Both peaks are close to the top injection location, with the center of the two peaks corresponding to this location.This positioning implies a push away from the top injection location towards each target, resembling the source-driven flows due to localized ionization sources.Interestingly, during this timeframe, the net force aligns closely with the pressure gradient force, underscoring it as the primary driver of the momentum flux.
The aforementioned positive/negative peak around the top fueling location persists until 1 × 10 −3 s.Subsequently, the pressure gradient force and the electric force start contributing similarly to the net force.After 2 × 10 −3 s, the net forces appear to stabilize.The pressure gradient force after 1 × 10 −3 s displays a drastic reduction in its negative peak while the positive peak (acting in the IT direction) maximizes almost exclusively near the top injection location.This pattern suggests minimal changes in the parallel distribution of the main ion pressure beyond this point.
However, other forces, such as the electric force and electron thermal force, start to dominate, implying that the electron temperature (T e ) gradient continues to evolve while pressure gradients stabilize, up until reaching 1 × 10 −2 s.The electron temperature maintains strong gradients in the region where a high-density zone forms near the top injection location, slightly biased towards the IT side (see figure 14).This suggests that the main ion force balance is initially dominated by pressure gradients, but once the pressure profile stabilizes, the force balance is dominated by the T e gradientdriven forces.These forces originate from the formation of high-density zones by particle sources from the top injection.These forces gradually intensify, eventually surpassing other forces in dominance and demonstrating a pattern of mutual cancellation.
From t = 1 × 10 −3 s onwards, a notable trend is the consistent increase in friction and thermal forces near the OT.Although not fully depicted here, this trend can be attributed mainly to the forces acting on the main ions as a counter reaction to the increases in friction and thermal forces on Ne impurities.These forces can rise by up to 20 times in the outer divertor SOL region.
The impurity force balance is dominated by thermal and friction forces.These forces are always well balanced, ensuring that the impurity flow velocity cannot deviate from the main ion flow velocity by an arbitrarily large value.The differences are proportional to the ratio of the thermal force to the friction force coefficient, i.e.T 3/2 •∇T n D + , considering the force balance [21].This holds true even in dynamic situations, as shown in figure 15, where the net forces are maintained at nearly zero for all the timestamps shown.The evolution of the impurity force balance is discussed below, segmented by parallel location.See the appendix for an explanation of the source multiplier √ g appearing on the y-axis.The electron density peak and corresponding T e , T i cooling occur most significantly slightly away from the top injection location, towards the high field side, around s ∥ = 0.5.This results in the formation of T e and T i gradient peaks around the top injection location, along with thermal force peaks.The alignment between the top injection location and the thermal force peak is a consequence of the biased gas injection direction towards the high field side.This bias, coupled with the overall flow velocity trends also skewed from OT to the IT direction (figure 12), creates an electron density peak (and T e , T i minima) around s ∥ = 0.5 (figure 14).The direction of the thermal forces is towards the OT, with the friction force in the opposite direction.Therefore, unlike at the targets where friction enhances impurity retention and the thermal forces counteract it, near the top injection location, the thermal forces tend to increase outer SOL impurity retention and the friction forces counteract it.In fact, the OT-directed flow velocity of the impurities around s ∥ = 0.65 is larger than that of the main ion velocity (figure 12), and this is compensated by the friction forces to make the velocities between the main ion and impurity similar.

Impurity stagnation point and divertor retention
The impurity flow velocity ultimately follows a trend that closely mirrors that of the main ion flow velocity.Moreover, the pattern of the main ion flow, especially the location of the stagnation point, is predominantly influenced by the particle source.It can be observed that the location of the impurity stagnation point aligns closely with that of the main ions (figure 12). Figure 16 illustrates the impurity stagnation point not only in the mid SOL but also throughout the entire SOL.
The stagnation point depicted here corresponds to that of u mean ∥,Ne ions , which represents the flow velocity of Ne ions averaged over all charge states.There can be several stagnation points in a single flux tube.
In the near-SOL flux tubes (i.e.(r − r sep ) OMP = 0 − 0.01 m), the stagnation points are located near both targets due to the strong recycling sources.Given that the gas injection is small compared to the near-SOL recycling sources (as seen in figure 11, it is only comparable in the mid-SOL flux tube), the location of the stagnation points remains similar across different gas injection locations.Some flux tubes are also associated with additional stagnation points upstream, attributable to the non-negligible sources from radial transport in this region.
In contrast, the mid and far-SOL regions (where (r − r sep ) OMP > 0.01 m) display distinct trends in the location of stagnation points across different gas injection cases.Notably, the Be top case shows stagnation points closest to the top injection location (marked by the blue dotted line, indicating the poloidal cells nearest to the top gas injection location).Some flux tubes in this region have multiple stagnation points, a result of the slow flow velocity along the flux tube over a wide range (e.g.see figure 12 Be div case at outer upstream SOL (OMP-OXpt)).
The Be div case has two or more stagnation points in most of the mid-SOL (red shaded region), within the range of (r − r sep ) OMP = 0.01 − 0.05 m.This suggests that the global flows are from OT to IT, with flow velocities nearly zero between OMP and OXpt.The OT-directed flows are limited to the outer divertor SOL.However, the Be top case has a clear stagnation point (or points) upstream near the top gas injection location, resulting in OT-directed impurity flows distributed over a much larger portion of the outer SOL compared to the other cases.These trends are observed throughout the mid-and far-SOL regions where the additional particle sources from the top gas injection can compete with target recycling sources and other particle sources.The IT and OT injection cases show stagnation points shifted closer to their respective injection locations, i.e. each target, compared to the div injection case, due to the direct addition of particle sources from these locations.
The location of impurity stagnation points influences impurity divertor retention [12] and the impurity distribution.In this study, c Ne = 0.8%, measured at the 1st SOL ring in the upstream SOL.However, the impurity distribution can vary across different gas injection locations, leading to variations in the number of Ne particles and the Ne concentration in each region.This variability also extends to the divertor impurity retention.Figure 17 illustrates the impurity concentration averaged in the upstream SOL, inner divertor SOL, and outer divertor SOL, as well as the Ne retention in each of the inner and outer divertors.Here, the Ne retention in the divertor is defined as the ratio of the number of Ne particles in the inner-/outer divertor SOL (below the X-point) to the number of Ne particles in the upstream SOL (above the X-point).
The Ne concentration in each region aligns with the distribution of impurity stagnation points.The cross-injection cases closely mirror those of the synchronized injection cases with the same fueling locations.The choice of 'fueling' location significantly influences the Ne concentration in each region, while the impurity seeding location provides a minor adjustment.The cross case, which involves divertor fueling and top Ne injection, presents an enhanced inner divertor Ne concentration.This enhancement is due to additional Ne sources from the top seeding and the corresponding flow pattern, which is primarily determined by the fueling location and in this case, flows are mainly directed towards IT.Considering the div case as a reference, the concentration changes are as follows: OT case: c ids Ne (see figure 17 for the meaning of 'ids', 'ods', 'upsol') increases as the mid-SOL stagnation points move closer to the OT, adding more Ne flows towards the IT (See figure 12).However, c ods Ne remains at a similar level since the mid-SOL stagnation points are still above the outer X-point.
IT case: The mid-SOL stagnation points shift towards the IT but are located in the upstream SOL, reducing c ids Ne (See figure 12).c ods Ne remains at a similar level to the OT case.Top case: As the mid-SOL stagnation points shift closer to the top injection location, the flow velocity 'strongly' enhances towards the OT direction (see figure 12).Consequently, c ids Ne decreases and c ods increases.The trend in Ne retention, measured as a particle number ratio in the upstream SOL and divertor, is similar to the Ne concentration in each region.While the OT, IT, and div cases show asymmetric divertor Ne retention, top cases display the most symmetric retention with enhanced outer divertor Ne retention.Thus, top fueling effectively balances Ne retention between the inner and outer divertor SOL.It is important to note that the upstream Ne distribution (or content), which varies across different gas injection locations even for fixed c Ne = 0.8% in the 1st flux tube, also influences retention.Therefore, the typical definition of retention may not be an appropriate metric in this study.

Assessing momentum and power balances in relation to fueling location
This subsection presents an analysis of the volumetric momentum and power balance to understand the resultant divertor conditions in relation to the fueling locations.The momentum loss factor (1 − f mom ), which is the fraction of total pressure loss from the upstream (selected as OMP here to account for volumetric momentum source/sink beyond the X-point) to the target, has been found to be strongly correlated with T et in 2D fluid divertor SOL plasma simulations [22].This behavior is consistent across ITER FPO scenarios, irrespective of the fueling location (figure 18).
Given the efficient detachment in the near-SOL of ITER, the 1st-3rd SOL rings are located in the low T et branch below 1 eV.Meanwhile, the 4th-15th SOL rings, which are mostly mid-SOL rings, are located above 1 eV and are clustered by the same fueling locations.These clusters follow the T et order (or This ordering originates from the fact that the primary momentum loss (in terms of plasma, or momentum transfer if including neutrals in the system) is due to plasma-neutral interactions.This results in the OT ion particle flux (summed over these clusters, 4th-15th SOL rings), i.e. the recycled neutral source, following the exactly reversed order of OT T et (figure 19): OT > top > IT > div.This is also consistent with the ionization sources near the OT (figure 11).However, the shape of the curve (1 − f mom ) − T et does not change with the fueling location.Therefore, changes in impurity retention, radiation asymmetry, etc do not fundamentally alter the relationship of momentum loss with T et .
While high outer divertor SOL impurity retention was most effectively achieved in the top fueling case, the resulting T et was lowest in the OT fueling case.This suggests that power loss and momentum loss do not always align, since the dominant loss mechanism can differ and vary significantly depending on the operational scenario (e.g.impurity driven detachment, whether through seeding or sputtering, vs. fueling driven detachment [23,24]).Figure 20 presents a radial plot of (1 − f mom ) for each flux tube in the outer SOL.This includes all species, including impurities, and uses the new form of friction and thermal force ('b2sigp_style = 2' in the code).Additionally, the momentum loss factors are decomposed to illustrate the contributions from each major mechanism (see appendix for details).
Momentum losses are predominantly governed by perpendicular transport (limited to the 1st-3rd SOL rings), atom-plasma interactions, and molecule-plasma interactions.The drag effect of molecules is the dominant factor in momentum loss for the low-temperature regime (~few eV), where molecules begin to accumulate [24].Across all four fueling locations, the 1st-3rd SOL rings exhibit significant momentum loss due to perpendicular transport and molecular drag, resulting from highly efficient cooling in these regions.While impurity retention and the corresponding impurity radiation do not directly contribute to momentum losses, they indirectly enhance plasma-neutral interaction driven momentum losses by cooling the plasma.Consequently, the top injection case (figure 20(a)), which is associated with the most enhanced outer divertor SOL radiation, demonstrates increased momentum losses in the 4th-15th SOL rings compared to the divertor fueling and IT fueling cases (figures 20(b) and (c)).However, the OT fueling case (figure 20(d)) shows a much more pronounced momentum loss at the 4th-15th SOL rings than the other cases, primarily enhanced by plasmaneutral interaction.This is due to direct fueling (additional molecule source) from the OT, an effect that is stronger than the enhanced outer divertor SOL radiation from top fueling.
Analogous to the momentum losses, the power loss factors (1 − f cool ) are shown by the SOL flux tubes radially across four different fueling location cases in figure 21.Slightly deviating from the definition of the power loss factor in [22], we used the power loss fraction of the internal energy equation (electron + ion) instead of the total energy equation.This approach simplifies the decomposition of power losses into contributions from different mechanisms.
Power losses in the 1st-3rd SOL rings are the most significant among all the flux tubes for all four cases, similar to the momentum loss.This is a result of perpendicular transport and plasma-neutral interaction (mostly neutral ionization cost) and electron cooling (mostly impurity ion line radiation).The term denoted by ∇u represents the contribution of the heating source due to the divergence of flow velocity.This corresponds to the conversion between internal energy and kinetic energy (work done by plasma compression (positive divergence), which increases its internal energy and thus heats it up).This term would be eliminated if expressed in terms of the total energy equation, so it has been excluded from the discussion.The remainders are denoted as 'etc', and they are negligible for all four cases.
The divertor fueling and IT fueling cases (figures 21(b) and (c)) show similar trends, with electron cooling and plasmaneutral interaction inducing moderate power loss in the 4th-15th SOL rings.However, the IT case has additional plasmaneutral interaction loss in the region (r − r sep ) OMP > 0.01 m compared to the div case, due to increased outer divertor SOL radiation (figure 8) and the consequent additional electron cooling.In the top fueling case (figure 21(a)), electron cooling is significantly increased due to the enhanced impurity radiation in the outer divertor SOL.This electron cooling is most pronounced in the region (r − r sep ) OMP = 0.01 − 0.05 m, as evidenced by the increased 'total' radiation shown in figure 8.This also leads to an increase in the contribution from plasma-neutral interaction due to the reduced background temperature.
On the other hand, in the OT fueling case (figure 21(d)), most of the power loss increase originates from plasma-neutral interaction.This is due to the direct supply of additional neutral sources from the OT, which is significantly increased in the far SOL where the recycled neutral is relatively small or similar to the fueling rate.
In conclusion, both increasing impurity radiation in the outer divertor SOL by top fueling and enhancing plasmaneutral interaction by direct OT fueling effectively induce power loss.However, their radial distributions differ, and increasing impurity radiation is more advantageous for reducing peak target heat flux.

Target loads and detachment: the influence of fueling location
The radiation and power balance analyses discussed earlier were solely focused on the plasma.However, the target heat load is composed of contributions from plasma, neutrals, and radiation.Figure 22 presents the total target heat load, along with the individual contributions from plasma, neutrals, and radiation, radially for both the IT and OTs.
Starting with the IT (top row of figure 22), the radiated power in the inner divertor SOL only varies by about 25% depending on the fueling location, as can be seen in figure 8. Therefore, the target heat flux does not vary significantly with the fueling location.
In contrast, for the OT (bottom row of figure 22), the change in the outer divertor SOL radiated power can be as high as 130% depending on the fueling location.In addition, the power carried by the plasma is significantly affected by direct fueling at the OT, as shown in figure 21.The resulting plasma load is significantly reduced for both the outer and top fueling cases.The neutral load is highest with OT fueling, where the target particle flux is highest and the electron temperature is lowest in the mid-SOL.The radiation load follows the order seen in figure 8, but shows a broader profile due to the dispersion of localized radiation.Despite the significant differences in plasma load, the neutral and radiation loads do not vary significantly with the fueling location.Therefore, the total target heat load is largely determined by changes in the plasma heat load.The top fueling case, including the cross case, results in the lowest OT heat load, demonstrating a reduction of several MW/m 2 in the heat flux in the mid-SOL region, including the peak.

Interpretation of the ITER simulation results in the current experimental context
The impact of fueling locations on divertor impurity retention aligns with previous experimental observations and studies on the puff-and-pump technique conducted in DIII-D [25][26][27].These studies, conducted mostly with argon (Ar) impurity seeding, demonstrated enhanced impurity enrichment throughout the entire divertor region, from the nearto far-SOL.This significant finding suggests that controlling the SOL flow can influence impurity behavior in the divertor region.
However, these studies also highlighted the complex interplay of factors that can influence the effectiveness of this technique.For instance, the location of impurity injection, the nature of the impurity species, and the characteristics of the background plasma all play crucial roles.Moreover, UEDGE modelling results [27] suggest that core contamination by neutral Ar could potentially offset the effectiveness of the puffand-pump technique.Argon atoms, when injected into the divertor, are largely confined to the PFR.Their distribution within the PFR, influenced by the E r × B drift, can affect the locations of significant leakage.Furthermore, Ar atoms which leak directly into the core and subsequently engage in radial transport in the SOL can further counteract the effects of the puff-and-pump technique.
The DIII-D experiment and SOLPS-ITER simulations with the pronounced closure of the SAS divertor results in highly localized ionization, which leads to a reversal of flow [28,29].This flow reversal, coupled with plasma drift, significantly affects the impurity stagnation point and leakage, underscoring the critical role of divertor geometry and drifts in SOL impurity transport, and the effectiveness of the puff-and-pump technique in medium-sized tokamaks.While these insights provide valuable understanding of the puff-and-pump technique in the context of DIII-D, it is important to consider the potential implications for ITER.Given the high neutral opacity in ITER, the effectiveness of flow control deep into the near-SOL is likely to be limited.With recycling dominated impurity flux in ITER, the PFR distribution affected by E r × B drift is expected to be insignificant.Furthermore, the background temperature distribution in ITER is expected to be significantly different from that in DIII-D, so the core contamination by Ar is also expected to be much smaller than in DIII-D.Therefore, the effectiveness of the flow induced by fueling is not expected to be significantly affected by the core contamination of the seeded impurities.Consequently, the interplay of factors influencing the puff-and-pump technique, as observed in DIII-D, might manifest differently in ITER.Further research is needed to elucidate these dynamics and optimize impurity control strategies for ITER and future fusion devices.

Conclusions
In this study, the effects of gas injection location and the choice of divertor surface material on an ITER fusion power operation scenario have been investigated.It was found that the choice of divertor surface material influenced properties related to reflection and affected Ne retention in the divertor.However, it was observed that the same divertor performance could be regained by adjusting the Ne seeding rate.
The effect of main ion fueling and impurity seeding locations have also been disentangled.The seeding location was observed to have a minimal effect on divertor performance.However, the choice of fueling location significantly influenced impurity retention and radiation asymmetry, consistent with [30].This is attributed to the shaping of the main ion flow pattern driven by the source, and the corresponding impurity flow pattern, which is governed by the force balance between thermal and friction forces.
Among the four fueling location cases studied, top fueling was found to demonstrate the most symmetric radiation pattern between the inner and outer divertor SOL by equilibrating flows from the main chamber top fueling location in the mid-SOL under detached conditions.This resulted in an enhanced volumetric power loss in the outer SOL and a 20%-40% reduction in target heat load compared to the divertor fueling case, which displayed the most asymmetric radiation pattern.
Fueling directly from the OT was observed to reduce the OT heat flux comparably to top fueling by increasing volumetric power loss due to plasma-neutral interactions.Since the radial distribution of impurity radiation and plasma-neutral interaction differ from each other, the power loss distribution was also observed to change as a result of different driving mechanisms.
Momentum losses are found to be dominated by plasmaneutral interactions, with impurity radiation having only an indirect effect, resulting in a radial distribution distinct from that of the power losses.However, since the main factors contributing to momentum losses are found to be consistent across fueling locations, the correlation of the momentum loss factor with the target electron temperature is observed to remain universal.
This study suggests that the selection of an appropriate fueling location and the regulation of its throughput can serve as effective actuators for controlling impurity divertor retention and divertor in-out asymmetry, and consequently, divertor heat loads, which are largely determined by changes in the plasma heat load.
The findings of this study are consistent with prior experimental observations and research on the impact of fueling locations on divertor impurity retention.However, it is also emphasized that the interplay of factors, as observed for example in DIII-D, might manifest differently in ITER.Given the high neutral opacity in ITER, the effectiveness of flow control deep into the near-SOL is likely to be limited.Furthermore, the background temperature distribution in ITER is expected to be significantly different from that in DIII-D, suggesting that core contamination of impurities counteracting flow-driven retention control could be significantly lower in ITER.
Finally, it is critical to consider the influence of drifts on the flow pattern to accurately simulating changes in impurity retention induced by fueling.In the detached ITER condition examined in this study, the influence of drifts is expected to be limited [19].However, in the attached regime or in smaller devices, the impact of drifts on flows is significant, necessitating a detailed analysis including drifts.

Appendix. Total pressure balance with impurities
The total pressure balance, introduced in [31] for a pure deuterium case without drifts and currents, is extended here to incorporate impurities and a new form of friction and thermal forces ('b2sigp_style' '2' in the code [9,10]).This generalized form is employed for 1 − f mom calculations in this paper.In this equation, each of the source terms corresponds to the divergence of the momentum stress tensor, centrifugal force, friction force, thermal force, ionization, recombination, charge exchange, anomalous contribution, and EIRENE (plasma-neutral interaction) contribution, respectively.Detailed expressions for these terms can be found in [32].The parameters h x , h y , and h z are the geometric factors corresponding to the lengths in the poloidal, radial, and toroidal directions, respectively.The term √ g is the square root of the determinant of the metric tensor, which, in these orthogonal curvilinear coordinates, is given by √ g = h x h y h z .The symbols Γ m ax and Γ m ay denote the parallel momentum fluxes of species a in the poloidal and radial directions, respectively.
The dynamic pressure of species a is denoted as p dyn,a = m a n a u 2 ∥a , which can be obtained by expanding the first term of the equation ( 1 where S m ⊥,a is the second term of equation (1).
Summing over ion species a provides: h ∥ = h z A ∥ , where A ∥ is the cell area normal to the parallel direction, and integrating from target (t) to upstream (u), we obtain: By dividing equation ( 5) by p tot,u , the momentum loss factor f mom can be obtained.If an individual source term is used instead of the total momentum source in the integration, the loss factor can be decomposed by mechanism.This is illustrated in figure 20, where EIRENE plasma-neutral interaction sources are further decomposed into contributions from each EIRENE neutral species (atom, molecule, test-ion, bulk ion).

Figure 2 .
Figure 2. Fast particle reflection coefficient and energy reflection coefficient of Ne incident on Be and W surfaces, with an incident energy of E 0 .Note that the fast particle reflection model is deactivated in the SOLPS-ITER code for E 0 < 1 eV.

Figure 3 .
Figure 3. Scatter plot representing the average energy of impinging Ne atoms (E imp Ne ) versus the energy flux carried by emitted Ne atoms from target surface segments (E emit Ne ) for four distinct cases: Be top, Be div, W top, and W div.Each point denotes a surface element from both the IT and OT regions (36 radial grid points each), with different colors and markers signifying the separate cases.The diagonal black line shows a 1:1 correlation between impinging and emitted energy fluxes.[IMAS shot numbers (run number): 123135-123162 (3)].

Figure 6 .
Figure 6.(a)-(c) The ratio of the electron cooling rate Pe for Ne ions, with the rate derived from STRAHL relative to that from the ADAS (Year 96 data) database, for Te = 1, 10, 100 eV, respectively.(d) The ratio of Ne radiated power, obtained from STRAHL relative to that from ADAS, for the main Ne radiators (Ne 3+ − Ne 7+ ) as a function of p div .[IMAS shot numbers (run number): 123135-123162 (3)].

Figure 8 .
Figure 8. Radiated power summed along the flux tubes from the target to the X-point, mapped to the OMP for the regions (a) Inner divertor SOL (b) Outer divertor SOL, as marked in figure 1.The range of increase and decrease between the div and top cases indicated by arrows is based on the total radiated power within the region.[IMAS shot numbers (run number): 123141 (4), 123148 (4), 123293-123296 (1)].

Figure 9 .
Figure 9. 2D distribution of total D + particle sources (including ionization and radial transport) per volume with D + flow velocities indicated by colored arrows.Magenta and cyan arrows indicate flows towards IT and OT respectively.The stagnation points of the D + flow in each flux tube are shown as yellow circles.The dotted orange line is plotted along the radial direction at the poloidal index = 46, which is the reference for figure 10.(a) Be top (most detached, IMAS shot number (run number): 123141 (4)); (b) Be div (most detached, IMAS shot number (run number): 123148 (4)); (c) Be top (most attached, IMAS shot number (run number): 123135 (3)).

Figure 11 .
Figure 11.Ionization sources of D + along the normalized parallel coordinate s ∥ at (r − rsep) OMP = 0.0465 m.The location of top gas puff is marked as the green band considering variation of s ∥ along the radial coordinate.Areas near both targets where the peak of the ionization source is located are enlarged and shown in the lower row.[IMAS shot numbers (run number): 123141 (4), 123148 (4), 123293-123296 (1)].

Figure 13 .
Figure 13.Parallel force exerted on Ne 5+ along the normalized parallel coordinate s ∥ at (r − rsep) OMP = 0.0465 m for the most detached Be top case (IMAS shot number (run number): 123141 (4)).Sign convention is the same as figure12.See the appendix for an explanation of the source multiplier √ g appearing on the y-axis.

( 1 )
OXpt-OT (s ∥ = 0.95 − 1): The peaks of the thermal forces (away from OT) and the friction forces (towards OT) grow as a function of time.The increased thermal force is due to the reduction in the temperature at the OT which exceeds the drop in the X-point temperature, (figure14) caused by the radiation asymmetry shown in figure8.(2)OMP-OXpt (s ∥ = 0.8 − 0.95): In this region the forces are largely unchanged, since the temperature gradients are similar between the cases, although the temperature itself decreases.(3) Near the top injection location (s ∥ = 0.65): The most significant changes occur in this region.However, since the impurities are not sensitive to the pressure gradient forces, they only meaningfully respond to the temperature gradient development timescale, e.g. after 1 × 10 −3 s.Note that SOLPS-ITER solves an ion energy equation assuming a single ion temperature for all species.

Figure 15 .
Figure 15.Temporal evolution of the parallel force exerted on D + ions (left column), Ne 5+ ions (right column) along the normalized parallel coordinate s ∥ at (r − rsep) OMP = 0.0465 m.The initial condition is taken as the most detached Be div case (IMAS shot numbers (run number): 123 148 (4)).The gas injection location for both D 2 and Ne was changed from div to top at t = 0.The force balances at t = 1 × 10 −6 , 1 × 10 −4 , 1 × 10 −3 , 2 × 10 −3 , 1 × 10 −2 s are shown in consecutive rows.The sign convention is consistent with figure 12.See the appendix for an explanation of the source multiplier √ g appearing on the y-axis.

Figure 16 .
Figure 16.Stagnation points of the mean Ne ion flow velocities along radial coordinates mapped to OMP on the s ∥ coordinate for four different gas injection location cases.The colored regions correspond to (r − rsep) OMP = 0 − 0.01, 0.01 − 0.06, 0.06 − 0.1 m, respectively.A reference line with a poloidal index of 46 (shown in figure 10) is represented by a blue dotted line in the figure.The radial position of the 13th SOL ring is marked by a red vertical dotted line in the figure.[IMAS shot numbers (run number): 123141 (4), 123148 (4), 123293-123294 (1)].
+ p stat,e + p stat,i ) The steady-state parallel momentum balance equation for ion species a in SOLPS-ITER can be expressed as follows: In this context, vis represents non-parallel components and viscosity terms.The static pressure for electrons and ions is defined as p stat,e = n e T e and p stat,i = ∑ a n a T i , respectively.Equation (1) is rearranged and bx