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The heat flux width (λq) is a key parameter determining the heat load at divertor targets. In recent years, drifts have been found to play a remarkable role in the edge plasma transport, while its influence on λq has not been well understood. Investigations of the influence of drifts on λq, systematic simulations using the SOLPS-ITER code are performed in this work. The statistics of the simulation results show that the drift under favorable/unfavorable B T tends to increase the λq in the outer/inner side and decrease the λq in the other side, which is consistent with the experiment observations. At the upstream and the target, the mechanisms of the influence of the drifts on λq are different. The upstream λq (λq,u) is directly affected by the drift-induced convective heat flux, while λq at the target (λq,t) is indirectly influenced through heat conduction (in the high-recycling regime) and the sheath (in the detached regime) due to the change of plasma parameters there. Furthermore, the synergetic effect of geometry and drift under favorable B T leads to an anomalously large λq,t in the inner side at high density. [ABSTRACT FROM AUTHOR]

The processes in far scrape‐off layer (SOL) and the plasma interaction with the first‐wall (FW) elements may notably affect the tokamak discharge, since they define fuel and impurity recycling, material erosion and redeposition, wall surface heating, etc. For a long time, the far SOL description in most plasma edge transport codes was insufficient or absent at all, and so particle and heat fluxes onto the FW (except divertor plates) were out of consideration. Recently some codes, for example, SOLEDGE and SOLPS‐ITER are upgraded allowing for the extension of the computational grid up to real walls and for corresponding account of the vacuum vessel shape and all in‐vessel elements. The new release of SOLPS‐ITER (the version 3.2.0) required a development of a new code data structure and new approach to numerical approximation of fluid equations compatible with unstructured non‐orthogonal computational grid. Intensive testing of the new code in different conditions is still required. In the present contribution, such a testing is performed for the EAST disconnected double null (DDN) L‐mode discharge. For the first time, the SOLPS‐ITER 3.2.0 modeling results with drifts and currents turned on are presented, and a comparison to former SOLPS‐ITER version (3.0.8) is performed. The far SOL transport and its effects on the discharge performance are studied by comparing the computational results obtained on several meshes which differ by their width in equatorial midplane. A single null (SN) one (with mesh width limited by distance to the secondary separatrix) was examined versus two DDN meshes (one with actual and one with artificially extended targets to make mesh wider) and a true unstructured (the widest) mesh. The notable difference in results obtained on different meshes appears in those places where plasma density does not vanishes at the computational domain boundaries. For the cases on true unstructured (the widest) mesh, the particle and heat fluxes onto central column, limiters, far SOL part of targets, dome umbrella and other EAST far SOL in‐vessel structures are calculated for the first time by SOLPS‐ITER, allowing assessment of the plasma interaction with those surfaces. [ABSTRACT FROM AUTHOR]

An optimized divertor design is crucial to maximize the lifetime of plasma‐facing components and reduce costs of future fusion power plants. Numerical shape optimization could be a powerful tool to obtain improved designs in an automated way. However, it is not trivial to apply due to the need of a field‐aligned and boundary‐fitted grid for simulating the plasma and quantifying the heat load. This paper shows how a grid deformation tool can automate the gridding process while safeguarding the grid quality. Additionally, sensitivities of shape parameters are computed using finite differences and compared to those obtained by remeshing using standard tools such as CARRE2. The plasma and neutral behavior is simulated using the unstructured SOLPS‐ITER code with the latest advanced fluid neutrals model for an ASDEX Upgrade test case. The comparison shows that, contrary to the remeshing strategy, the grid deformation approach yields smoother sensitivities. Furthermore, it is shown that the deformed grids have better mesh quality in terms of poloidal cell size ratio compared to the grid generated with CARRE2, which improves the accuracy of the simulation. This supports the use of the grid deformation tool for automated shape design in future work. [ABSTRACT FROM AUTHOR]

Only recently, plasma edge simulations up to the wall have been enabled with SOLPS‐ITER. This requires dedicated gridding techniques to reconcile grid alignment with the magnetic field and refinement toward the wall as grid quality is primordial to ensure fast and reliable convergence. Therefore, the gridding approach for the grids up to the wall is analyzed and improved. A truncation error analysis is performed on the discrete operators of the discretization scheme in SOLPS‐ITER, resulting in indicators of grid properties that are undesired. Based on these indicators, grid adaptation and grid smoothing algorithms are developed to reduce truncation errors and improve the overall grid quality. The resulting methods are applied on an AUG single‐null case. Here, the impact of the new gridding strategy is examined on the divertor heat load, a typical quantity of interest for plasma edge simulations. The new gridding methods allow to mitigate spurious numerical spikes in the target heat load profiles, reduce the convergence time with a factor 30, and improve the accuracy of the heat load with a factor 3 compared to original grids with similar total number of cells. [ABSTRACT FROM AUTHOR]

A grid refinement study is performed for mean‐field plasma boundary simulations with fluid neutrals in an EU‐DEMO geometry. In general, grid convergence of the simulations is achieved, with differences between the finest and second‐finest grid of <5% for the majority of the quantities of interest. The estimated discretization errors for the original 96 × 36 grid are mostly in the 4%–25% range. However, it is also shown that exceptions are possible due to the non‐linear nature of plasma boundary codes. Hence, it is advised to regularly perform grid refinement studies on subsets of cases. [ABSTRACT FROM AUTHOR]

The effect of differential biasing of the divertor plates in a tokamak is analyzed using SOLPS‐ITER modeling with account of drifts and currents in the SOL. The ASDEX‐Upgrade like geometry and transport parameters adjusted for modeling of the semi‐detached nitrogen‐seeded plasma of shot #28903 are used in analysis. The additional voltage is applied to the outer divertor plate with respect to the grounded vacuum chamber and the inner divertor plate. When high negative voltage is applied, the high field side high density region almost disappears and the divertor plates become more symmetrical than without biasing, while in the case with positive voltage, the formation of the X‐point radiator begins, and both divertor plates become more detached. The results are qualitatively consistent with the experiments conducted on the JFT‐2 M and DIII‐D tokamaks. In addition, both signs of the applied voltage lead to a significant redistribution of the nitrogen within the SOL. Therefore, the possibility of edge plasma control by biasing is demonstrated. [ABSTRACT FROM AUTHOR]

The SOLPS‐ITER3.0.8 code with new Grad‐Zhdanov module was applied for predictive modeling of tritium plasma and deuterium‐tritium mixture in tokamak JET. The moderate power scenario of shot JPN #85278 modeled earlier for deuterium plasma was taken as a starting point. Effect of puffing increase, which was applied in experiment, on divertor conditions and inter‐ELM tungsten sputtering for both working gases and on isotope separation in their mixture is analyzed. Both for attached and for semi‐detached outer targets, the tritium plasma shows moderate increase in SOL width compared to deuterium one. The tungsten sputtering at the outer target in the inter‐ELM period for tritium is an order of magnitude bigger than that for deuterium. The D–T separation in the D–T mixture is moderate. [ABSTRACT FROM AUTHOR]

Formation of a high-field-side high-density (HFSHD) regime and the role of the high-field-side (HFS) poloidal electric field in the scrape-off layer of the spherical tokamak Globus-M2 are analyzed using SOLPS-ITER edge plasma simulations. The dependence of the HFS poloidal electric field sign and, consequently, radial drift fluxes on the discharge density is discussed. It is demonstrated that the HFS poloidal electric field is the key element in the formation of a HFSHD regime in the Globus-M2 tokamak as in ASDEX Upgrade. It is demonstrated that the physics of HFSHD formation in a small spherical tokamak is similar to that suggested by Kaveeva et al (2009 36th EPS Conf. on Plasma Physics) and is in line with experimental observations and modeling, performed later on ASDEX Upgrade. [ABSTRACT FROM AUTHOR]

Self-healing liquid metal divertors (LMDs) based on the Capillary Porous Structure (CPS) concept are currently being considered among the possible solutions to the power exhaust problem in future fusion reactors. Indeed, the passive replenishment of the plasma-facing surface by capillary forces and the self-shielding of the target via vapor emission can potentially improve the divertor lifetime and its resilience to transient loads. On the other hand, the LMD target erosion can be significant due to evaporation and thermal sputtering, on top of physical sputtering, possibly leading to unacceptable core plasma dilution/power losses (for a low-Z/high-Z metal such as Li and Sn, respectively). For this reason, it is necessary to assess whether an LMD is compatible with an European DEMO (EU-DEMO) plasma scenario. This requires a self-consistent model of the impurity emission from the target, the plasma in both the scrape-off layer (SOL) and the core regions and the transport of impurities therein. In this paper, an an integrated modelling approach is proposed, which is based on SOLPS-ITER and includes its coupling with a target erosion model written in FreeFem++ and a core plasma model (ASTRA/STRAHL). An application of the coupled SOL-target model to simulate experiments performed in the Magnum-PSI linear plasma device with a CPS target filled with Li is also included to provide a first demonstration of the capabilities of the approach. Results are promising, being in good agreement (within a few degrees) with the measured target temperature distribution. In perspective, the modelling framework presented here will be applied to the EU-DEMO with an Sn divertor. [ABSTRACT FROM AUTHOR]

Reliable diagnostics that measure the detached state of the ITER divertor plasma will be necessary to control heat flux to the divertor targets during steady state, burning plasma operation. This paper conducts an initial exploration into the feasibility of the divertor shunt diagnostic as a lightweight, robust, and real-time detachment sensor. This diagnostic is a set of shunt lead pairs that measure the voltage drop along the divertor cassette body, from which the plasma scrape-off layer (SOL) current is calculated. Using SOLPS-ITER simulations for control-relevant ITER plasma scenarios, the thermoelectric current magnitude along the SOL is shown to decrease significantly with the onset of partial detachment at the outer divertor target. Electromagnetic modelling of a simplified divertor cassette is used to develop a control-oriented inductance-resistance circuit model, from which SOL currents can be calculated from shunt pair voltage measurements. The sensitivity and frequency-response of the resulting system indicates that the diagnostic will accurately measure SOL thermoelectric currents during ITER operation. These currents will be a good measure of the detached state of the divertor plasma, making the divertor shunt diagnostic a potentially extremely valuable and physically robust sensor for real-time detachment control. [ABSTRACT FROM AUTHOR]

The predicted divertor conditions for the SPARC tokamak are calculated using SOLPS-ITER for a range of scrape-off-layer (SOL) heat flux widths λ _q , input powers, and particle fueling locations. Under H-mode scenario conditions with an upstream separatrix density of 1 $\times \mathrm{10}^{20}\:$ m ^−3 , the most conservative range of λ _q extrapolations ( ${\approx}$ 0.15 mm) results in extremely high unmitigated particle and energy fluxes to the divertor, both under full field (12.2 T) and power ( $P_{\mathrm{SOL}}$ = 29 MW) conditions, and 2/3 field with $P_{\mathrm{SOL}}$ = 10 MW. Increasing the cross-field SOL diffusivities by 2–10× reduces the magnitude of the mitigation challenge, however strategies such as impurity seeding or strike-point-sweeping will likely still be required. A combination of steady-state and time-dependent SOLPS-ITER simulations are used to map out phase space diagrams of upstream and divertor conditions. The simulations include parallel currents but neglect cross-field drifts. At low upstream density the inner and outer divertor conditions are highly asymmetric, with a large temperature difference and significant heat fluxes driven by parallel currents. The solution has sharp bifurcations with a region of hysteresis, depending on whether the initial state is at a low or high density. This behavior is observed even when the fueling location, cross-field diffusivity, and impurity level is changed, although the density window with asymmetry is reduced with increasing diffusivity. The addition of neon impurity seeding reduces the divertor heat fluxes, but also causes a drop in the upstream electron density with fixed particle throughput. This drop can be counteracted by increased main ion throughput, however too much neon results in a back transition into the asymmetric divertor regimes suggesting a need for control of both main ion and impurity seeding levels to achieve a desired divertor state.

For the first time, an X -point radiating (XPR) regime using neon (Ne) seed impurity has been obtained in ITER modelling with the SOLPS-ITER code, including fluid drifts. The highly radiating pattern is qualitatively similar to those observed experimentally in ASDEX Upgrade and JET. Comparison of the simulation results with those obtained from modelling of the same regime, with the same approach, in ASDEX Upgrade is used to analyse the difference between the XPR in large and medium-sized machines. Analysis demonstrates that the cold X -point formation is controlled principally by the Ne radiation. The simulation results for the poloidal scale of the intense radiating zone are in good agreement with analytic estimates.

The highly radiating nitrogen-seeded H-mode plasmas in unfavorable B _T has been characterized in the ASDEX Upgrade tokamak (AUG). Three levels of nitrogen puffing rates have been injected into a fully detached H-mode plasma, which is run in lower single null configuration with the ion $B\times\nabla B$ drift away from the X-point. A cold ( ${\sim}1-2$ eV) highly radiating ( ${\sim}13.0 \mathrm{MW\,\,\,m}^{-3}$ ) region forms close to the X-point immediately after nitrogen seeding, as evidenced by measurements of the divertor Thomson scattering (DTS) and the two-dimensional bolometry reconstructions. In addition, the radiator moves further upwards above the X-point along the separatrix at the high-field side (HFS) with increasing nitrogen puffing rates, as evidenced by the Absolute eXtended UltraViolet (AXUV) measurements. The formation of the highly radiating regime is closely correlated to the modifications of the divertor plasma conditions. Along the line of sight of the DTS measurement, the electron temperature reduces down to a few eV, which initials near the X-point and further extends to the HFS scrape-off layer (SOL) simultaneously with the upward movement of the radiator, however, the electron temperature sustains ( ${\sim}30-50 $ eV) at the low-field side (LFS) SOL with slightly decreased electron density. The highly radiating regime shows LFS/HFS divertor asymmetry, in contrast to that for H-mode plasmas in favorable B _T , suggesting that the drifts play an important role for the formation of the highly radiating X-point regime at AUG. The neutral particle flux increases significantly (factor of ${\sim}2$ ) in the private flux region, while it increases slightly ( $ \lt\!20\%$ ) in the main chamber, thus suggesting an enhanced sub-divertor neutral compression with the formation of the highly radiating regime. Furthermore, a degradation of the pedestal electron density was observed with an enhancement of the electron temperature further inside the pedestal, and complete divertor detachment was achieved by nitrogen seeding with sustained plasma confinement. Finally, particle sources and flow patterns of deuterium and nitrogen ions have been analyzed by SOLPS-ITER modelling, confirming that the $E \,\times\,B$ drift plays an important role for the formation of the highly radiating regime in unfavorable B _T at AUG.

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.

The SOLPS-ITER code is utilized to analyze the boundary plasma associated with a fast-flow lithium (Li) divertor configuration in the fusion nuclear science facility (FNSF) tokamak and identify operational regimes with acceptable divertor and core conditions. Plasma transport from the SOLPS-ITER code has been coupled with a liquid metal (LM) MHD/heat transfer code to model a Li open-surface divertor design and assess its impact on the scrape-off-layer (SOL) and core plasma performance. Simulations with only Neon (Ne) impurity seeding have been conducted to evaluate its impact on meeting FNSF design demands for the divertor and upstream plasma parameters. Simulation results indicate that Ne seeding significantly mitigates divertor heat flux but potentially reduces both upstream electron and main ion density due to fuel dilution. The combined application of Ne seeding and deuterium (D _2 ) puffing is required to satisfy the FNSF design requirements on upstream density ( $n_{e,\textrm{sep}}^\textrm{OMP}$ ∼1× 10 ^20 m ^−3 ) and divertor energy flux ( $q_{\perp,\textrm{max}}^\textrm{Odiv}$ $\lt $ 10 MW m ^−2 ). D _2 puffing plays a role in counteracting upstream density drops and augmenting energy and momentum losses through atomic and molecular processes. The inlet Li flow velocity is systematically varied across a wide range to identify acceptable flows and corresponding LM surface temperatures. This comprehensive analysis identifies the acceptable Li flow parameters, LM surface temperature, and emitted Li fluxes necessary to meet the major design constraints. The emitted Li fluxes exhibit minimal impact on the main plasma at surface temperatures up to approximately ∼525 ^∘ C, corresponding emitted Li fluxes of up to φ _Li ∼2 $\times 10^{23}$ atoms s ^−1 . Uncertainties in the Li emission processes from the surface are also investigated, primarily influencing Li loss in the lower surface temperature range ( ${\lt}525\,^{\circ}$ C), with simulation results indicating a minor impact on the divertor and upstream plasma. Conversely, evaporation predominantly drives the Li loss processes at higher surface temperature ranges ( ${\gt}525\,^{\circ}$ C), contaminating both the divertor and upstream plasma.

The vapor-box, a liquid metal design for the divertor, utilizes lithium recirculation through evaporation and condensation. Safety concerns arise from Li-D/T formation and co-deposition on vapor-box walls and the first wall, affecting tritium retention. Additively manufactured tungsten capillary porous structure (CPS) samples with Li were exposed to high heat flux D plasmas in the linear plasma device Magnum-PSI, to study D retention in Li–D co-deposition dependence on substrate temperature (200 ${^\circ}$ C–428 ${^\circ}$ C) and distance from the plasma beam center (25–85 mm). The D:Li ratio was determined via in-situ ion beam diagnostics with simultaneously analyzed Nuclear Reaction Analysis and Elastic Backscattering Spectroscopy spectra to maximize the precision. Experimental results approach close to the theoretical maximum at 40:60 D:Li ratio and deposited film thickness ranging from 0.02 to 3.2 µ m. Witness plate temperatures above 400 ${^\circ}$ C yielded Li films under 150 nm in thickness with lower D:Li ratios (5:95 D:Li ratio). At this temperature LiD decomposition pressure is comparable with vessel pressure during plasma. SOLPS-ITER simulations narrowed CPS surface temperature to 650 ${^\circ}$ C–700 ${^\circ}$ C, indicating Li ^+ plasma dominance near the target surface. Redeposition ratio of lithium on the CPS surface was determined to be around 80 $\%$ , matching quartz crystal microbalance results. However, SOLPS-ITER simulations lacked accuracy in recreating observed Li and D deposition layers on WPs, improvements are needed to model plasmas with significant Li quantities. Extension of SOLPS-ITER simulations to include LiD molecules and enhance heat flux accuracy is crucial for better alignment with experimental data.

This paper presents the application of full time-dependent SOLPS-ITER simulations for actuator design in the SPARC tokamak. This study employs both the EIRENE module, a neutral solver, and the B2.5 plasma module in a time-dependent mode. This is in contrast to most SOLPS simulations, which focus on steady-state solutions, where the neutral distribution is evolved without any time limit or for a time step of 1 $\cdot10^{-3}$ second, which is several orders of magnitude larger than the fluid plasma time step. The time-dependent EIRENE was tested with a fixed B2.5 background and compared with a simple conductance based model in a simplified pump chamber geometry. This comparison aimed to verify the reliability of the neutral relaxation timescale derived from the time-dependent EIRENE. Subsequently, a full time-dependent simulation was performed in a realistic geometry, with the Monte-Carlo neutral time step synchronized with the plasma fluid time step. The numerical setup of the code, including relative time steps and the size of the census data used to store Monte-Carlo particle information is considered. The full-time dependent simulations are then applied to inform the design of the SPARC louver structure, which affects divertor plasma parameters by regulating the neutral conductance from the divertor to the pump. The response of the plasma and neutral parameters was captured on a timescale that enables the design of the actuator to consider time-dependent control capability. It was found that changing the louver opacity has an equivalent effect as varying the gas throughput via puff actuation. Therefore, equivalent divertor plasma conditions can be obtained from both actuators, while the neutral pressure distribution in the pump and divertor differs for each actuator.

In order to achieve a compatible solution between the divertors and the core, SOLPS-ITER simulations were performed in a Spherical Tokamak for Energy Production (STEP) connected double-null geometry to investigate the possibility of using deuterium ( $\mathrm{D}_2$ ) puff locations as an actuator for divertor argon (Ar) compression/enrichment. It was found that puffing ${\mathrm{D}}_2$ from the inner-midplane (IMP) ${\mathrm{D}}_2$ puff enhanced Ar compression and enrichment on the high-field-side (HFS) and lowered the required upstream Ar fraction to achieve acceptable target conditions. An interesting link was found between argon compression and the number of stagnation points of the middle-charge-state Ar ions in the HFS SOL, $N_{\mathrm{st}}$ ; significantly improved compression and enrichment were obtained for $N_{\mathrm{st}} = 1$ (corresponding mostly to the cases with IMP puff) compared to $N_{\mathrm{st}} = 3$ (corresponding mostly to the cases without IMP puff). An intermediate compression and enrichment was obtained when $N_{\mathrm{st}} = 5$ . The change of $N_{\mathrm{st}}$ from 3 to 1 (or 5) was achieved by a combination of $\mathrm{D}^+$ outflow, high collision frequency, and flipped temperature gradients around the IMP. Given a possible drawback of ${\Gamma}_{\text{D}}^{{\text{OMP}}+{\text{IMP}}}$ , that is a direct effect on the upstream main plasma density and temperature, we propose ${\Gamma}_{\text{D}}^{{\text{PFR}}+{\text{IMP}}}$ as the best solution, balancing the negative and positive effects of private-flux-region and IMP ${\mathrm{D}}_2$ puffs. Further studies will be carried out both experimentally and numerically.

Introduction of cross-field drifts in SOLPS-ITER simulations of connected double-null plasmas in STEP with the ion $\nabla B \times B$ drift towards the upper divertors was found to enhance the detachment of the inner divertors with decreased target densities and ion and heat fluxes, while simultaneously complicating the access to detachment in the outer lower divertor by increasing the target temperature and heat loads to levels above the engineering limits. The $\nabla B \times B$ drift was observed to significantly affect the radial heat transport between the core and the scrape-off layer (SOL), altering the poloidal temperature and pressure profiles and, consequently, the poloidal conductive and convective heat transport in the SOL. As a result, up-down asymmetries of 52:48 and 58:42 biased towards the outer lower and upper inner divertors, respectively, were observed to arise in the unmitigated power entering the divertor regions, breaking the up-down symmetry seen in simulations without the drift terms and contradicting with earlier experimental observations on the low-field side. Moreover, the upstream electron density was found to decrease noticeably in the core and separatrix regions following the activation of the drifts due to an increased share of the neutrals arriving from D _2 injections near the upper and lower X-points ionizing already in the private flux regions.

The heat flux width ( λ _q ) is a key parameter determining the heat load at divertor targets. In recent years, drifts have been found to play a remarkable role in the edge plasma transport, while its influence on λ _q has not been well understood. Investigations of the influence of drifts on λ _q , systematic simulations using the SOLPS-ITER code are performed in this work. The statistics of the simulation results show that the drift under favorable/unfavorable B _T tends to increase the λ _q in the outer/inner side and decrease the λ _q in the other side, which is consistent with the experiment observations. At the upstream and the target, the mechanisms of the influence of the drifts on λ _q are different. The upstream λ _q ( λ _q _,u ) is directly affected by the drift-induced convective heat flux, while λ _q at the target ( λ _q _,t ) is indirectly influenced through heat conduction (in the high-recycling regime) and the sheath (in the detached regime) due to the change of plasma parameters there. Furthermore, the synergetic effect of geometry and drift under favorable B _T leads to an anomalously large λ _q _,t in the inner side at high density.

Investigations of parametric scaling of power exhaust in the alternative divertor configuration (ADC) SOLPS-ITER simulation database of the EU-DEMO are conducted and compared to predictions based on the Lengyel model. The Lengyel model overpredicts the necessary argon concentrations for LFS divertor detachment by about a factor of 5–10 relative to the SOLPS-ITER simulations. Therefore, while the Lengyel model predicts that plasmas with acceptable divertor heat loads in EU-DEMO would exceed the tolerable upstream impurity concentrations by a large margin, there are several SOLPS-ITER solutions within an acceptable operational space. The SOLPS-ITER simulations indicate that, unlike assumed by the standard Lengyel model, there are significant heat dissipation mechanisms other than argon radiation, such as cross-field transport, that reduce the role of argon radiation by a factor of 2 to 3. Furthermore, the Lengyel model assumes that the radiation front is powered by parallel heat conduction only, which tends to lead to a narrow radiation front as the radiative efficiency increases strongly with reducing thermal conductivity. As a result, the radiative volume and total impurity radiation are suppressed for a given impurity concentration. However, the SOLPS-ITER simulations indicate that other mechanisms, such as cross-field transport, can compete with parallel heat conduction within the radiative front and increase the radiative volume. As a result, the standard Lengyel model provides a very pessimistic estimate for the necessary concentration for impurities with strong radiative capability in low temperatures around 10 eV, such as argon. However, parametric scaling relations are needed for fast scoping of the operational space without having to run a complex, numerical code, such as SOLPS-ITER. In these applications, the Lengyel model might still be useful to provide guidance on the relative scaling of the exhaust characteristic of the various points in the operational space. The aim of this work is to provide evidence to avoid overconfidence on these simple model predictions.

The main goal of the Divertor Tokamak Test facility (DTT) is to operate with a high value of power-exhaust-relevant parameter PSOL/R in plasma scenarios similar to those foreseen for the Demonstration Fusion Power Plant (DEMO) in terms of low collisionality and neutral opacity. For these unique characteristics, accurate modelling of the principal scenario is necessary for machine designing.In edge numerical codes, cross-field transport profiles have a high impact on modelling results. This work aims at providing a coherent set of transport parameters for DTT full-power (FP) single-null (SN) scenario edge modelling. To evaluate such parameters for DTT, a transport analysis on the current machine has been performed using SOLEDGE2D-EIRENE and SOLPS-ITER.The transport parameters to be used in the simulations of the DTT single-null scenario were selected using two complementary methods. The first is the modelling of JET and Alcator C-Mod (C-Mod) with SOLEDGE2D-EIRENE and SOLPS-ITER, validating transport parameters by comparing modelling results to experimental data from pulses which are considered DTT-relevant. JET pulses were selected with the highest auxiliary input power (from 29 to 33 MW), plasma current and toroidal field to better match DTT parameters; nitrogen and neon seeded pulses were selected to check possible seeding material dependencies. The considered C-Mod pulse better matches DTT plasma density and neutral opacity. Transport parameters are then scaled to DTT according to scaling laws. The second method derives the transport parameters by tuning their values inside the DTT separatrix to reproduce the pedestal profiles predicted by the EPED model via the Europed code and applied in DTT.The derived set of DTT transport parameters is consistent with the results obtained by modelling present machines, reproduces the expected heat flux decay length in detached conditions and, inside the separatrix, reproduces the predicted pedestal using transport parameters which are coherent with what is predicted by the quasi-linear turbulent model QuaLiKiz.

In this paper SOLPS-ITER simulations of Ar and N seeded discharges are presented for H-mode conditions on ASDEX Upgrade and for burning plasmas on ITER. These discharges are additionally compared with Ne seeded cases for both tokamaks. It is demonstrated that Ar and N are retained in the divertor, and that the amount of seeded impurity (measured both by the seeding rate in atoms/s and the averaged separatrix density) necessary to achieve the same divertor conditions is lower for Ar than for N. This is attributed to almost the same values of first ionization potential of Ar and N (if compared to e.g. Ne) and to higher Ar radiation efficiency. If the radiated power fraction within the numerical simulation grid is of the order of 50%, which is sufficient to achieve partial detachment at the outer target in both devices, radiation losses from the confined region remain small for Ar seeded ITER cases (about 6% of power from the outer core region included in the SOLPS-ITER computational domain with total volume 135 m3). The fuel dilution by Ar remains lower than that by N and Ne, which corresponds to an Ar averaged separatrix concentration of 0.4%. From the point of view of target power handling, the boundary simulations thus demonstrate that Ar may be a suitable alternative seed impurity on ITER.

A staged divertor program is currently under discussion to advance DIII-D research on core-edge integration. One phase could address optimization of power and particle exhaust, and supporting modeling of several slot divertor options is underway, including variations in wall baffling, slot depth and divertor leg length. This paper focuses on the role of slot depth to achieve highly dissipative (detached) divertor conditions, in both BT directions. For ion B×∇B into the divertor and PSOL= 4 MW, SOLPS-ITER finds that increasing the slot depth from 18 to 50 cm reduces the upstream separatrix electron density needed to detach by 15%, due to increased divertor radiation. A dedicated run of the EIRENE neutral transport code, in which neutrals are launched from the outer target and followed until ionization, finds that neutral leakage is strongly reduced in the deep slot compared to the shallow slot, explaining the increased divertor radiation and, thus, lower detachment density threshold. Reversing the BT direction cools and densifies the plasma in the slot, such that both slot options are detached at all simulated densities. As for the opposite BT direction, the deep slot has lower target temperature compared to the shallow slot, as a result of lower neutral leakage. Increasing the depth of a slot divertor is, therefore, beneficial to achieve highly dissipative divertor conditions for both field directions. Additional modeling will build on these results to evaluate whether an increased slot depth can also improve trapping of low-Z radiating impurities.

SOLPS calculations of lithium vapor box divertor designs on NSTX-U are presented. Predictive high power simulations (Pheat=10 MW, qpeakunmitigated∼65 MW/m2) are used to compare and contrast two divertor designs. Specifically a baffled “box” divertor, where a region of neutral density is allowed to build up, is compared to a more typical slot divertor geometry. It is found that significant differences in lithium containment lead to profoundly different viability of the two designs. These differences are seen to be due to far SOL flow patterns that change based on the presence of baffling as well differences in efficiency of the lithium evaporator. Outer-midplane (OMP) separatrix lithium content is found to be strongly detrimental to upstream temperature when nLi/ne>0.1 is reached. This regime of high upstream contamination is avoided via baffling. The reduction in upstream lithium allows access to low heat flux solutions below 5 MW/m2 with very little reduction to upstream temperature from the unmitigated, 65 MW/m2 solution. The slot is able to reach sub-10 MW/m2 heat fluxes though raising the evaporation rate much further reduces the upstream temperature, such that the range of stable evaporation rates with low heat flux to the target is small. Higher performance solutions (low heat flux and low upstream lithium content) are accessible by controlling recycling coefficients of deuterium on the walls above the box.

The X-point radiator (XPR) is an attractive scenario that may contribute to solving the power exhaust problem in future fusion devices. The 2D transport code SOLPS-ITER was applied to reproduce the experimentally measured plasma condition with an XPR in the ASDEX Upgrade tokamak and to compare with a reduced model. Neutrals penetrating from the adjoining cold divertor region and the large connection length near the X-point play an important role in initiating an XPR. However, once such a radiator is created, it persists even if the fueling and impurity seeding rates were reduced. The redistribution of plasma density and radiation near the X-point caused by fluid drifts at the XPR was studied in the simulation. [ABSTRACT FROM AUTHOR]

The SOLPS-ITER code has been applied to the analysis of the scrape-off layer (SOL) plasma associated with the fast flow Lithium (Li) divertor design for Fusion Nuclear Science Facility (FNSF). Two divertor configurations are investigated to determine puff levels that provide robust operational windows that meet the FNSF design requirements on upstream density and divertor flux with a flat divertor for flowing liquid metal (LM). Neon (Ne) is introduced to control the heat flux to the divertors while Deuterium (D2) puffing is performed to maintain sufficiently high upstream density. We found that a simplified open geometry presents challenges for neutral control and impurity retention, but a balanced geometry with baffling is found to have acceptable puff operational windows. Lithium (Li) is sourced into the balanced configuration uniformly along the divertor surfaces and scanning over a large range to understand what level of Li emission is needed to influence the divertor and upstream plasma conditions. At low sourcing level (ϕLi≤1×1023/s), the Li shows a minor effect on the plasma and is well confined in the private flux region (PFR) and divertor surfaces. At moderate sourcing level (1×10231×1024/s), the Li strongly affects the upstream and divertor plasma conditions and leads to strong detachment by increasing momentum and power losses. At high sourcing level, Li reaches above the x-point that can result in a substantial Li radiation in the core and sufficient dissipation to strongly affect the divertor and upstream plasmas.

It is clear that atomic physics rates are important for understanding the edge plasma — but how important is the uncertainty in these rates in contributing to the uncertainty in simulations of the edge plasma?Standard Uncertainty Quantification (UQ) methods are used to attempt to provide an answer: first to the charge state balance in a coronal plasma model, and, second, to the plasma profiles in 1D SOLPS-ITER simulations of the Scrape-Off Layer with deuterium and nitrogen.For the charge state balance, larger deviations are observed in using different atomic physics data sets, than assuming reasonable uncertainties in the rates. For the SOLPS-ITER simulations, assumed uncertainties in the upstream boundary conditions (D and N densities, electron and ion power inputs) are typically more important than the same level of assumed uncertainties in the atomic physics rates.

Linear plasma devices are the ideal devices to simulate the divertor conditions of tokamak experimentally. The Multiple Plasma Simulation Linear Device (MPS-LD) is under construction at Dalian University of Technology with a focus of studying the plasma-material interactions (PMIs) and edge plasma transport. Before the experiment, numerical modeling plays a crucial role in predicting the main plasma parameters and discharge performance. To this end, simulations are carried out by using scrape-off layer plasma simulation code SOLPS-ITER for the designing studies of MPS-LD in the present work. The effects of particle source simulation method, heating power, and device chamber length on the plasma are investigated systemically. The simulation demonstrates that the direct imposing particle source in the source region is suitable for handling the plasma source. The radiation region, recombination front region and recombination region are formed during plasma transport. Enhancing the plasma source strength can promote the achievement of plasma detachment. The helicon source with a 6 kW radio frequency power source can only obtain the maximum electron density of 5 × 1018 m−3 and electron temperature of 2 eV in the vicinity of the target. Raising the heating power and shortening the distance from the plasma source to the target can significantly increase the plasma parameters at the target.

A spatially hybrid fluid‐kinetic approach for the efficient simulation of plasma‐edge neutrals is extended with a kinetic‐fluid condensation process and an automated approach to select a fluid or kinetic treatment at each point along the divertor targets. With the proposed hybrid fluid‐kinetic methods, the dominant charge–exchange reaction can be largely removed from the kinetic neutral simulation. The hybrid methods achieve quantitative agreement with the standard kinetic approach, with relative errors on the peak target plasma density and peak target ion flux density of 5–30%, while the Central Processing Unit (CPU) time for the kinetic neutral solver is reduced by a factor 3–6. [ABSTRACT FROM AUTHOR]

The ad‐hoc description of anomalous transport through diffusive relations with manually tuned coefficients is currently one of the main limitations in mean‐field plasma edge codes, seriously restricting their interpretive and predictive capabilities. In this paper, we attempt to improve that description by relating the anomalous transport coefficients to the turbulent kinetic energy κ as a measure for the local intensity of the turbulence. Using RANS techniques from hydrodynamic turbulence and insights from their recent successful application to 2D electrostatic E×B drift turbulence modelling for the scrape‐off layer, we propose a transport equation for κ and discuss its coupling with the mean‐field transport equations. The main features of the model include (a) an analytically exact interchange source of κ which introduces the ballooning character of the transport; (b) fast parallel transport of κ through the connection with parallel current fluctuations; and (c) consistent transport reduction due to the impact of mean E×B flow shear. The resulting model has been implemented in the new extended grids version of SOLPS‐ITER, enabling for the first time mean‐field simulations self‐consistently combining classical parallel transport with mean‐field drifts and anomalous transport with the code. A first assessment of the model has been made for a representative C‐Mod case study, highlighting the promising features of the model. Further analysis is needed to investigate in detail the impact of the different new terms in the model across operational regimes, and determine the new closures constants based on larger sets of turbulence simulations and experimental data. [ABSTRACT FROM AUTHOR]

Radial anomalous diffusion coefficients are among the largest sources of uncertainty in mean‐field plasma‐edge codes such as SOLPS‐ITER. These coefficients are machine, scenario, and space‐dependent, thus hampering the predictive and interpretive capability of these codes. In fact, modellers usually adjust these coefficients manually, based on expert judgement or on large, computationally expensive, parameter scans. Matching data from various diagnostics, each with their own experimental uncertainties, additionally complicates the problem of finding a good parameter set. In addition, standard non‐linear regression techniques have shown to become prohibitive for expensive plasma‐edge simulations with many unknown parameters, as gradient calculation was based on finite differences. In this paper, we apply algorithmic differentiation (AD) as an efficient and more accurate alternative for gradient calculation in large, continuously developed codes as SOLPS‐ITER. In addition, the lack of uncertainty information and danger of data overfitting, key limitations of regression techniques, are overcome by combining data and uncertainties from different diagnostics in a Bayesian framework. We implement for the first time such a Bayesian inference framework into SOLPS‐ITER, using gradient‐based optimization with gradients obtained through tangent AD to find the maximum a posteriori (MAP) values of the parameters. The recently developed κ turbulence model is employed to limit the number of unknown parameters compared to full spatial profiles of diffusion coefficients. The Bayesian MAP‐estimation is compared to standard regression techniques on a small‐scale tokamak. We adopt fictitious experimental data obtained from a reference SOLPS‐ITER solution with artificial measurement noise. [ABSTRACT FROM AUTHOR]

A novel double‐peaked emission profile has been observed by the visible light imaging system in EAST. In the upper divertor region, two emission peaks in the high‐field side (HFS) scrape‐off layer (SOL) and near the X‐point are identified by tomographic reconstruction. In our previous SOLPS‐ITER simulation work, the emission peaks in the HFS SOL and near the X‐point are attributed to the carbon deposition on the HFS baffle and the dome of the upper tungsten divertor, respectively. The appearance of the emission peak near the X‐point when the outer target is attached was understood by analysing the carbon transport in the private flux region (PFR). However, the simulated intensity of the emission peak in the HFS SOL is lower by one order of magnitude than that in the PFR, while they are at the similar level in the experiment. In this work, the influence of the drifts is further studied by SOLPS‐ITER simulations. Under the favourable toroidal field condition, the HFS SOL plasma transits to the detachment regime. The chemical sputtering of the carbon deposited on the inner baffle increases significantly, as well as the emission intensity of the peak in the HFS SOL. Meanwhile, the C2+ density peak in the PFR decreases due to the E × B drift towards inner target. The emission intensity in the PFR near the X‐point, therefore, decreases moderately. As a result, the intensities of the two emission peaks become comparable, which matches better with the experiment. [ABSTRACT FROM AUTHOR]

New Grad–Zhdanov module is implemented in the SOLPS‐ITER code and applied to ITER impurity transport simulations. Significant difference appears in the helium transport due to improved parallel kinetic coefficients. As a result, 30% decrease of the separatrix‐averaged helium relative concentration is observed for the constant helium source and pumping speed. However, for the neon changes are less pronounce. Change of the impurity behaviour is discussed. For the first time the ion distribution functions are studied in the ITER scrape‐off layer conditions to reveal the origin of the kinetic coefficient improvements and theory limitations. [ABSTRACT FROM AUTHOR]

In ITER, tritium retention primarily occurs through co-deposition with beryllium. To avoid exceeding the strict tritium inventory limit, efficient tritium recovery techniques are essential. Baking is the ITER baseline for tritium recovery, but its effectiveness in removing tritium from thick beryllium layers is limited. A raised strike point scenario is considered an alternative method for removing tritium from the ITER inner vertical divertor target by heating components via plasma flux. This paper presents SOLPS-ITER code simulations conducted under various conditions, assessing the divertor performance and tritium outgassing of the raised strike point scenario. As the strike point is raised, recycled neutrals are not efficiently baffled by the dome and scrape-off layer, significantly changing the neutral trajectory and ionization source distribution. This improves detachment accessibility but worsens core-edge compatibility compared to the baseline scenario. However, in the partially detached condition, the impact of raising the strike point, perpendicular transport, and q _95 on target heat flux is not significant, as it primarily scales with the input power. Target heat flux is translated to target surface temperature using a simplified heat transfer model that considers the 3D target monoblock geometry and active cooling condition, excluding Be layer thermal properties. For partially detached divertor conditions, the bulk tungsten monoblock surface temperature remains below the baking temperature, which is insufficient for efficient tritium outgassing under the actively cooled ITER divertor condition. However, considering the potential thermal contact resistance between the beryllium and tungsten layers, which may significantly impact temperature distribution, the temperature of the beryllium layer can be raised to a level sufficient for efficient tritium outgassing. Therefore, the raised strike point scenario can be considered as an alternative in-vessel tritium removal technique.

Reliable diagnostics that measure the detached state of the ITER divertor plasma will be necessary to control heat flux to the divertor targets during steady state, burning plasma operation. This paper conducts an initial exploration into the feasibility of the divertor shunt diagnostic as a lightweight, robust, and real-time detachment sensor. This diagnostic is a set of shunt lead pairs that measure the voltage drop along the divertor cassette body, from which the plasma scrape-off layer (SOL) current is calculated. Using SOLPS-ITER simulations for control-relevant ITER plasma scenarios, the thermoelectric current magnitude along the SOL is shown to decrease significantly with the onset of partial detachment at the outer divertor target. Electromagnetic modelling of a simplified divertor cassette is used to develop a control-oriented inductance-resistance circuit model, from which SOL currents can be calculated from shunt pair voltage measurements. The sensitivity and frequency-response of the resulting system indicates that the diagnostic will accurately measure SOL thermoelectric currents during ITER operation. These currents will be a good measure of the detached state of the divertor plasma, making the divertor shunt diagnostic a potentially extremely valuable and physically robust sensor for real-time detachment control.

To mitigate the issue of plasma exhaust in reactor scale tight aspect ratio tokamaks such as Spherical Tokamak for Energy Production (STEP), a double-null (DN) configuration is thought to be advantageous over a single-null (SN) configuration. However, practical control of the plasma vertical stability will likely lead to an oscillation around the symmetry point, which may lead to transient loading of the divertors. In this work we investigated the impact of disconnection of the two separatrices $\delta R_{\mathrm{sep}}$ on the power-sharing between the divertors in disconnected-double-null configurations for the initial iteration of STEP design using the SOLPS-ITER code without drifts. The power fraction to the primary divertor increased with $\delta R_{\mathrm{sep}}$ , reaching ∼95% at the highest $\delta R_{\mathrm{sep}}$ which is representative of SN. The total power fraction to the inner divertors (upper + lower), however, did not show an increase with $\delta R_{\mathrm{sep}}$ for $\delta R_{\mathrm{sep}}/\lambda_q \leqslant 2$ , where λ _q is the parallel heat flux decay length, and even at the highest $\delta R_{\mathrm{sep}}$ it showed only ∼30% increase from connected-double-null (CDN), unlike the experimental results for current conventional aspect ratio machines. We found two underlying mechanisms that could explain this result—the total flux compression from the outer midplane to the primary inner divertor target and the parallel current in the primary SOL (between the two separatrices). This work implies that the benefit of DN over SN in power load onto the inner divertor in STEP may be less than found experimentally in conventional tokamaks due to its tight aspect ratio. Further investigations through experiments, especially on STs and simulations with additional physics such as drifts, are the subject of a future investigation.

Numerical simulations explore a possible tightly baffled, long-legged divertor (TBLLD) concept in a future upgrade of the tokamak à configuration variable (TCV). The SOLPS-ITER code package is used to compare the exhaust performance of several TBLLD configurations with results from unbaffled and baffled TCV configurations. The investigated TBLLDs feature a range of radial gaps between the separatrix and the divertor baffles, with a smaller gap resulting in tighter baffling. All modeled TBLLDs are predicted to lead to a denser and colder plasma in front of the targets and increase the power handling by factors of 2–3 compared to the present, baffled, divertor and by up to a factor of 12 compared to the original, unbaffled, configuration. This improved TBLLD performance is attributed to an increased neutral confinement with more plasma–neutral interactions in the divertor region. Both power handling capability and neutral confinement increase with tighter baffling. The core compatibility of TBLLDs with nitrogen seeding is also evaluated and the detachment window, with acceptable core pollution, for these TBLLDs is explored, showing a reduction of the required upstream impurity concentration to achieve detachment by up to 18% with tighter baffling.

The lithium vapor box divertor is a proposed divertor design that will minimize contamination of the upstream plasma in a fusion device, while also ensuring protection of the target. In this design lithium is evaporated near the target by high temperature lithium surfaces, dissipating the plasma heat flux. The lithium vapor box has been predicted via the fluid-kinetic code scrape off layer plasma simulator (SOLPS-ITER) to achieve low ( $n_\mathrm{Li}$ / $n_\mathrm{e}\sim\ $ 0.05) upstream concentrations of lithium and low target heat fluxes. Here we compare two choices of deuterium gas puff location using SOLPS-ITER, the private flux region (PFR) and the common flux region (CFR), and find significant differences in the contamination level required to reach an acceptable target heat flux (defined here as q $^\mathrm{max}_\mathrm{tar}\leqslant$ 10 MW m ^−2 ). Deuterium gas puffing from the PFR is seen to better reduce upstream lithium contamination. The difference in puffing location is seen to cause changes in the upstream flow of lithium ions. The PFR puff, having better access to the separatrix, can better reduce the upstream-directed flow of lithium near the separatrix which is the primary source of contamination due to a large thermal force in this region. Puffing from the CFR, partially due to inefficacy at reducing separatrix lithium flow, has higher lithium concentration within the plasma. Solutions that reduce the heat flux to below 10 MW m ^−2 have a range of lithium concentrations between $n_\mathrm{Li}$ / $n_\mathrm{e}\ \sim\ $ 0.01–0.12 depending on puff intensity, location, evaporator temperature and recycling at the various plasma facing components. The efficacy of the puffs is tested for sensitivity to deuterium recycling coefficient at the target, evaporators, and main chamber walls. A CFR located puff is found to be more dependent on the recycling coefficients used than a PFR located puff. regardless of the set of recycling coefficients chosen, PFR puffing achieves lower lithium contamination than CFR puffing for a given heat flux.

The SOLPS-ITER code has been utilised to study the movement of the detachment front location from target towards the X-point for MAST-U Super-X plasmas. Two sets of detached steady state solutions are obtained by either varying the deuterium ( D _2 ) fuelling rate or the nitrogen ( N ) seeding rate to scan the corresponding ‘control’ parameters of outboard midplane density, $n_\mathrm{u}$ , and the divertor impurity concentration, $f_\mathrm{I}$ . At seeding and fuelling rates ∼10× and ∼5× that required to start detachment at the divertor target, the detachment front only reaches ∼50% of the poloidal distance to the X-point, $l_\mathrm{pol}$ , corresponding to a region of strong parallel gradients in the total magnetic field B . The region of strong total field gradients correlates with where the detachment front location becomes less sensitive to control parameter variation. This result is qualitatively consistent with the predictions of a simple, analytic detachment location sensitivity (DLS) model (Lipschultz et al 2016 Nucl. Fusion 56 056007) which is based in a scaled parallel-to- B space, z . While the DLS model predictions are in agreement with SOLPS-ITER results in terms of where the front location becomes less sensitive to controls (i.e. in the region of strong parallel gradients in B ), the DLS model predicts a higher sensitivity in the region of weak parallel gradients in B downstream as compared to the simulation results. Potential sources of differences between the SOLPS-ITER and DLS model predictions were explored: The DLS model does not include energy sinks beyond radiation from a single impurity nor cross-field energy transport. Momentum and particle balance are also not included in the DLS model. The tight opening into the divertor for flux surfaces could lead to variations in plasma-neutral pressure balance as the detachment front reaches that region, exactly how this affects the front movement needs further investigation.

Density ramps with ion grad B drift directed into lower single null KSTAR L-mode plasmas are associated with a simultaneous and abrupt reduction of the divertor particle flux on both low- and high-field-side targets when the mid-plane line averaged electron density reaches a given level. Target embedded Langmuir probe signals show a clear ‘cliff edge’ behavior similar to that observed in the divertor target electron temperature in DIII-D H-mode plasmas (Eldon et al 2017 Nucl. Fusion 57 066039; McLean et al 2015 J. Nucl. Mater. 463 533–6). The collapse of the particle flux is observed along the whole divertor target area (from private flux region to the far scrape-off layer (SOL)). The critical upstream density of this target flux cliff is invariant under fuel gas throughput modulation. The transition along the cliff occurs in tens of milliseconds. With the cliff, carbon impurities and deuterium neutrals transported through the X-point to the core produce a strong radiation spot near the X-point, seen on bolometric signals, and increase the upstream density. The experimental observations are consistent with time-dependent SOLPS-ITER simulations, which also demonstrate an abrupt transition of the target flux and upstream density with the increase in X-point radiation. The timescale of the cliff predicted by SOLPS-ITER is consistent with the experiment, although, it is influenced by gas throughput or time-dependent numerical methods. In the L-mode phase space of separatrix electron density and temperature, branches are divided based on target temperature, because the latter is strongly coupled to the radiation front and ionization front due to the monotonic characteristic of the parallel electron temperature distribution. Since the H-mode condition operates at a much higher upstream density and electron temperature in phase space, dissipation from sputtered carbon alone leads to the density limit before reaching the X-point radiation condition. This is therefore consistent with the fact that cliffs have never been observed in H-mode KSTAR experiments.

Tungsten (W) is used as the plasma-facing material in the divertor region of future fusion reactors, such as ITER; however, its concentration in the core plasma must be maintained at an extremely low level. W transport in the scrape-off layer (SOL), which is related to the source of core W contamination, has been extensively studied. In this study, the influence of E × B drift on the transport of W impurity in the SOL is studied via numerical simulations of a model case based on EAST upper single-null configuration with high recycling divertor plasma. W transport is simulated using DIVIMP on the background plasma obtained from scape-off layer plasma simulation-ITER simulation including drifts. The E × B drift of W ions is introduced based on the background electric field. Therefore, both the direct E × B drift effect of W ion and the indirect effect via background plasma on W transport in the SOL are studied. The influence on the flux of W impurities entering confined plasma across the last closed flux surface Γ _enter is focused on, which is expected to be proportional to the core W concentration. Results reveal that Γ _enter is mainly from the outer (inner) target under a favorable (unfavorable) toroidal field B _T and can be increased by more than one order of magnitude compared with the case without drifts; this reflects the significant effect of E × B drift. The effects due to the background plasma and the poloidal and radial E × B drift of W ion, as well as the related mechanisms, are analyzed in detail for three stages of W transport in the SOL: effective sputtering from the target, leakage from the divertor, and entry into the confined plasma.

Time-dependent SOLPS-ITER simulations have been used to identify reduced models with the sparse identification of nonlinear dynamics (SINDy) method and develop model-predictive control of the boundary plasma state using main ion gas puff actuation. A series of gas actuation sequences are input into SOLPS-ITER to produce a dynamic response in upstream and divertor plasma quantities. The SINDy method is applied to identify reduced linear and nonlinear models for the electron density at the outboard midplane $n_\mathrm{e,sep}^\mathrm{OMP}$ and the electron temperature at the outer divertor $T_\mathrm{e,sep}^{\,\mathrm{div}}$ . Note that $T_\mathrm{e,sep}^{\,\mathrm{div}}$ is not necessarily the peak value of T _e along the divertor. The identified reduced models are interpretable by construction (i.e. not black box), and have the form of coupled ordinary differential equations. Despite significant noise in $T_\mathrm{e,sep}^{\,\mathrm{div}}$ , the reduced models can be used to predict the response over a range of actuation levels to a maximum deviation of 0.5% in $n_\mathrm{e,sep}^\mathrm{OMP}$ and 5%–10% in $T_\mathrm{e,sep}^{\,\mathrm{div}}$ for the cases considered. Model retraining using time history data triggered by a preset error threshold is also demonstrated. A model predictive control strategy for nonlinear models is developed and used to perform feedback control of a SOLPS-ITER simulation to produce a setpoint trajectory in $n_\mathrm{e,sep}^\mathrm{OMP}$ using the integrated plasma simulator framework. The developed techniques are general and can be applied to time-dependent data from other boundary simulations or experimental data. Ongoing work is extending the approach to model identification and control for divertor detachment, which will present transient nonlinear behavior from impurity seeding, including realistic latency and synthetic diagnostic signals derived from the full SOLPS-ITER output.

Plasma–wall interaction (PWI) is a great challenge in the development of a nuclear fusion power plant. To investigate phenomena like erosion of plasma-facing components, impurity transport and redeposition, one needs reliable numerical tools for the description of both the plasma and the material evolution. The development of such tools is essential to guide the design and interpretation of experiments in present and future fusion devices. This contribution presents the first global simulation of PWI processes in a linear plasma device mimicking the boundary plasma conditions in toroidal ones, including both the description of plasma and impurity transport and of plasma-facing material evolution. This integrated description is obtained by coupling two of the state-of-the-art numerical codes employed to model the plasma boundary and the PWI, namely SOLPS-ITER and ERO2.0. Investigation of helium plasma is also of primary importance due to the role helium will have during ITER pre-fusion power operation, when it is planned to be used as one of the main plasma species, as well as fusion ash in full power operation. The plasma background is simulated by SOLPS-ITER and the set of atomic reactions for helium plasmas is updated, including charge-exchange and radiative heat losses. ERO2.0 is used to assess the surface erosion in the GyM vessel, using different wall materials (e.g. carbon, iron or tungsten) and applying different biasing voltage. Eroded particles are followed within the plasma to assess their redeposition location. The ionization probability of the different materials in the GyM plasma is inferred through the energy distribution of impacting particles and its effects on migration are investigated.

A new Grad–Zhdanov module is implemented into the SOLPS-ITER code for calculation of the parallel kinetic coefficients. A complete, multi-ion generalization is performed, relaxing the heavy impurity assumption. A JET-like D+T+Ne test simulation is conducted to demonstrate the ability to model a 50/50 deuterium (D) and tritium (T) mixture in SOLPS-ITER. More than 30% T build-up with respect to D is observed in different parts of the simulation domain, in particular at the high field side. A T predominance over D is also observed near both the inner and outer targets. It is a result of the different effective diffusion, dominated by charge-exchange processes, for the D and T neutral species. A simple 1D model is proposed to describe this phenomenon. The contribution to the differing D and T distribution in different regions from the Grad–Zhdanov thermal force is also studied. Due to the thermal force and the D/T poloidal flow from the low field side to the high field side, the prevalence of the T species over D is found at the high field side at the X-point level. The latter leads to an inner–outer divertor asymmetry of $n_T/n_D$ . However, the effect is relatively small due to the close D and T masses. It is further shown that the infinite ion mass difference limit, which is used for the derivation of the Zhdanov-Yushmanov analytical expressions and applied for the thermal force coefficient calculation previously used in the SOLPS-ITER code, overestimates $n_T/n_D$ significantly. Thus, the old SOLPS-ITER model should not be applied for D–T simulations. Finally, possible experimental studies of the D and T spatial separation due to the new effects revealed by this modelling are discussed.

Plasma-molecular interactions generate molecular ions which react with the plasma and contribute to detachment through molecular activated recombination (MAR), reducing the ion target flux, and molecular activated dissociation (MAD), both of which create excited atoms. Hydrogenic emission from these atoms has been detected experimentally in detached TCV, JET and MAST-U deuterium plasmas. The TCV findings, however, were in disagreement with SOLPS-ITER simulations for deuterium, indicating a molecular ion density ( $D_2^+$ ) that was insufficient to lead to significant hydrogenic emission, which was attributed to underestimates of the molecular charge exchange rate ( $D_2 + D^+ \rightarrow D_2^+ + D$ ) for deuterium (obtained by rescaling the hydrogen rates by their isotope mass). In this work, we have performed new SOLPS-ITER simulations with the default rate setup and a modified rate setup where ion isotope mass rescaling was disabled. This increased the $D_2^+$ content by ${\gt}{\times} 100$ . By disabling ion isotope mass rescaling: (1) the total ion sinks are more than doubled due to the inclusion of MAR; (2) the additional MAR causes the ion target flux to roll-over during detachment; (3) the total $D\alpha$ emission in the divertor increases during deep detachment by roughly a factor of four; (4) the neutral atom density in the divertor is doubled due to MAD, leading to a 50% increase in neutral pressure; (5) total hydrogenic power loss is increased by up to 60% due to MAD. These differences result in an improved agreement between the experiment and the simulations in terms of spectroscopic measurements, ion source/sink inferences and the occurrence of an ion target flux roll-over. Extrapolating simplified scalings of divertor molecular densities (TCV & MAST-U) to reactor-relevant densities suggests the underestimation of molecular charge exchange could strongly impact divertor physics (neutral atom density, ions sinks) and hydrogen emission (which has implications for detachment control) in deeply detached conditions, warranting further study.

Plasma edge simulations with codes like SOLPS-ITER are widely employed to interpret fusion experiments. However, numerical errors appearing in such simulations are rarely investigated, despite their potential large impact on simulation results. These errors consist of the statistical error and the bias, both resulting from the finite number of employed EIRENE Monte Carlo particles and incomplete convergence, and the discretization error due to the finite resolution of the computational grids. In this contribution, the resulting numerical errors on simulations of pure deuterium and neon seeded H-mode EAST discharges are examined. The statistical error can be kept small compared to other numerical error contributions by averaging the plasma profiles. This allows investigating the bias and discretization errors using Richardson extrapolation. It is shown that grid refinement and the number of employed Monte Carlo particles have the largest influence on the result, in agreement with similar studies of an ITER deuterium case. For the first time, numerical error bars on the entire simulated target profiles are determined showing that the largest numerical error is 17.9%, mainly due to the plasma grid discretization. On top, also numerical errors on simulated neutral pressures are investigated in detail, for which the statistical error is dominant. The analysis demonstrates which setup is needed to keep numerical errors limited: the SOLPS-ITER averaging procedure should be employed including enough EIRENE particles, and the involved grids should be sufficiently refined to reduce discretization errors.

Edge codes such as SOLPS coupled to neutral codes such as EIRENE have become so comprehensive and sophisticated that they now constitute, in effect, ‘code-experiments’ that, as for actual experiments, can benefit from interpretation using simple models and conceptual frameworks, i.e. reduced models. The first task is the identification of options for the reduced model control parameters that are best suited for control of the action of the divertor, i.e. for control of target power loading and sputter-erosion, primarily. A strong correlation between the electron temperature at the divertor target, T _e,t , and the neutral deuterium D _2 density at the target, n _D2,t , flux-tube resolved, has recently been reported for a number of code studies including SOLPS-4.3 modeling of a set of ∼50 ITER baseline cases: Q _DT = 10, q _95 = 3, P _SOL = 100 MW, metallic walls, and Ne seeding (Pitts et al 2019 Nucl. Mater. Energy 20 100696). This part A of the present study reports new results for largely the same ITER cases, confirming the strong correlations reported earlier between local values of T _e,t , and (i) n _D2,t , and (ii) normalized volumetric losses of power and pressure in the divertor. Strong correlations have now also been found, and are reported here for the first time, between T _e,t and all of the divertor target quantities of practical interest. A physical explanation for this surprising result has not been fully identified; nevertheless it has encouraging implications for reduced modeling of the ITER divertor. For such ITER conditions, (i) the global Ne injection rate, Inj _Ne (Ne s ^−1 ), and (ii) the electron temperature at the location on the target where the peak power deposition occurs, T _e,t @q _⊥,pk (eV), are found to be promising reduced model control parameters. In the companion report, part B, a reduced model for the ITER divertor is developed and described in detail, based on reversed-direction 2 point modelling, Rev2PM. The input to the reduced model is a value of the variable pair $\left({T}_{\text{e},\mathrm{t}}@{q}_{\perp ,\mathrm{p}\mathrm{k}},\mathrm{I}\mathrm{n}{\mathrm{j}}_{\text{Ne}}\right)$ and the output are values of the various target as well as divertor-entrance quantities of practical interest, e.g. q _⊥,pk , n _e,Xpt (the electron density at the poloidal location of the X-point), etc. In part B the reduced model is quantitatively characterized using one half of the code cases; it is then used to successfully predict (replicate) the code values of e.g. n _e,Xpt for the other half of the cases.

The X-point radiator (XPR) is an attractive scenario that may contribute to solving the power exhaust problem in future fusion devices. The 2D transport code SOLPS-ITER was applied to reproduce the experimentally measured plasma condition with an XPR in the ASDEX Upgrade tokamak and to compare with a reduced model. Neutrals penetrating from the adjoining cold divertor region and the large connection length near the X-point play an important role in initiating an XPR. However, once such a radiator is created, it persists even if the fueling and impurity seeding rates were reduced. The redistribution of plasma density and radiation near the X-point caused by fluid drifts at the XPR was studied in the simulation.

Edge codes such as SOLPS coupled to neutral codes such as EIRENE have become so comprehensive and sophisticated that they now constitute, in effect, ‘code-experiments’ that, as for actual experiments, can benefit from interpretation using simple models and conceptual frameworks, i.e. reduced models. The first task is the identification of options for the reduced model control parameters that are best suited for control of the action of the divertor, i.e. for control of target power loading and sputter–erosion, primarily. A strong correlation between the electron temperature at the divertor target, T _e,t , and the neutral deuterium D _2 density at the target, n _D2,t , flux-tube resolved, has recently been reported for a number of code studies including SOLPS-4.3 modeling of a set of ∼50 ITER baseline cases: Q _DT = 10, q _95 = 3, P _SOL = 100 MW, metallic walls, and Ne seeding (Pitts et al 2019). Part A of the present study reports new results for largely the same ITER cases, confirming the strong correlation reported earlier between local values of T _e,t , and (i) n _D2,t , and (ii) normalized volumetric losses of power and pressure in the divertor. Strong correlations have now also been found, and are reported here for the first time, between T _e,t and all of the divertor target quantities of practical interest. A physical explanation for this surprising result has not as yet been fully identified; nevertheless it has encouraging implications for reduced modeling of the ITER divertor. For such ITER conditions, (i) the global Ne injection rate, Inj _Ne (Ne s ^−1 ), and (ii) the electron temperature at the location on the target where the peak power deposition occurs, T _e,t @q _⊥,pk (eV), are found to be promising reduced model control parameters. In this part B, a reduced model for the ITER divertor is developed and described in detail, based on reversed-direction two point modeling, Rev2PM. The input to the reduced model is a value of the variable pair $\left({T}_{\text{e},\mathrm{t}}@{q}_{\perp ,\mathrm{p}\mathrm{k}},\mathrm{I}\mathrm{n}{\mathrm{j}}_{\text{Ne}}\right)$ for a chosen case and the output are values of the various target as well as divertor-entrance quantities of practical interest, e.g. q _⊥,pk , the electron density at the X-point, n _e,Xpt , etc. The reduced model was quantitatively characterized using one half of the code cases; it was then used to successfully predict (replicate) the code values of e.g. n _e,Xpt for the other half.