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The coupling of transport code SOLPS with the turbulence code BOUT++ was reported in Reference [D. R. Zhang et al., Phys. Plasmas 26, 012508 (2019)], while the grids of SOLPS and BOUT++ are not completely consistent with each other, especially in the divertor region. In the present work, a method of replacing the grids of BOUT++ with the grids of SOLPS is proposed to make the simulation region fully consistent with each other for the SOLPS/BOUT++ coupling. A SOLPS grid file is generated with an MHD equilibrium and used in BOUT++ code to simulate the profiles of plasma density, ion temperature, and electron temperature with the six‐field two‐fluid model. The profiles of the main plasma parameters simulated with the SOLPS grids are similar with the profiles simulated with the BOUT++ grids at the midplane, while the profiles are deformed compared with the profiles simulated with the BOUT++ grids at the outer divertor target because of the differences of the distributions of SOLPS grids and BOUT++ grids in the divertor region. The radial particle transport coefficient and heat transport coefficients are also calculated by using the BOUT++ code with the two grids, and the comparisons of the radial particle transport coefficient and heat transport coefficients simulated with the two grids at the midplane and outer divertor target plate are discussed. [ABSTRACT FROM AUTHOR]

Partially detached H‐modes are the baseline regime for the future ITER operation. The ASDEX Upgrade partially detached H‐mode is modeled using the SOLPS‐ITER code with drifts enabled and compared with experimental data. For the first time, boron (B) impurity is simulated in the Scrape‐off layer (SOL) and divertor. A comparison between divertor diagnostics and discrepancies between Langmuir probe and Divertor Thomson scattering/Stark broadening diagnostic are discussed. In the modeling, experimental target profiles are reproduced if the experimental level of radiation in the SOL and divertor is achieved using nitrogen (N) impurity seeding. Bolometry measurements detect substantial radiation from the partially detached outer strike point. With B radiation, this maximum in bolometry data is reproduced in the modeling, which is not possible with N alone. [ABSTRACT FROM AUTHOR]

Featured Application: The research was carried out within the framework of the federal project Development of technologies for controlled fusion and innovative plasma technologies of the comprehensive program of the State Corporation Rosatom, Development of equipment, technologies and scientific research in the field of the use of atomic energy in the Russian Federation for the period up to 2030. The developed methodology and the results obtained can be used in the design of fusion neutron sources and hybrid reactor facilities. Modeling the D and T fluxes in Fusion Neutron Source based on a tokamak fuel cycle systems was performed consistently with the core and divertor plasma. An indirect integration of ASTRA, SOLPS4.3, and FC-FNS codes is used. The feedback coupling is realized between the pumping and puffing systems in the form of changes in the isotopic composition of the core and edge plasma. In the ASTRA code, instead of electrons, ions were used in the particle transport equations. This allows better estimates of the flows of the D/T components of the fuel that have to be provided by the gas puffing and processing systems. The particle flows into the plasma from pellets, required to maintain the target plasma density e> = (6–8) × 1019 m−3 are 1022 particles/s. In the majority of the working range of parameters, additional ELM stimulation is necessary (by ~1-mm3-size pellets from the low magnetic field side) in order to maintain the controlled energy losses at the level δWELM~0.5 MJ. For the starting load of the FC and steady-state operation of the facility, up to 500 g of tritium are required taking into account the radioactive decay losses. [ABSTRACT FROM AUTHOR]

Self-replenishing liquid metal coatings are considered as a perspective divertor design able to withstand challenging particle and power loads of a fusion tokamak-reactor. Numerical modeling of the scrape-of-layer (SOL) plasma with advanced 2D codes, such as SOLPS, is necessary for developing of the ‘liquid-metal’ divertor. In this work we report on upgraded version of SOLPS 4.3 code liquid metal erosion module implemented earlier in our group and present results of simulations of T-15MD tokamak with Li-covered divertor plates. The erosion model includes all main processes Li erosion, i.e. physical sputtering, thermal sputtering, evaporation, and prompt redeposition. Unlike some other available implementations, Li atoms are considered in kinetic approximation in our version. A detailed analysis of Li erosion and flow in T-15MD configuration for various powers (6–12 MW) and H content in the SOL is presented. It is shown that the most of eroded Li particles are redeposited on the divertor targets, however, in some regimes absolute Li flow from the divertor is still large and might lead to significant main plasma dilution with Li. Vapor shielding effect is pronounced on both divertor targets in the most reasonable regimes providing low peak heat flux values at the target plates, less than 10 MW m ^−2 . The target erosion rate and surface temperatures are within limits of the most target designs. Moreover, in strongly shielded cases the target temperature can be even lower than the Li melting temperature meaning that external heating is required to keep Li flowing. Sensitivity analysis shows that our results are most sensitive to the target heat conduction parameters, i.e. the target thickness, outer surface temperature. It means that controlling the target cooling rate can be a useful tool for controlling the liquid Li divertor regime. Variation of the Li erosion rate parameters has little effect on the divertor performance.

Measurements are presented, alongside corresponding interpretative SOLPS-ITER simulations, of the first MAST-U experiments comparing ohmically heated L-mode fuelling scans in Conventional divertor (CD) and Super-X divertor (SXD) configurations. In experiment, at comparable outer mid-plane separatrix electron density, $n_{e,\textrm{sep,OMP}}$ , the maximum lower outer target heat load was found to be a factor 16 $\,\pm\,7$ lower in SXD compared to CD. In simulation, a factor 26.8 reduction was found (slightly higher than the experimental range), suggesting an additional reduction in SXD compared to the factor 9.3 expected from geometric considerations alone. According to the simulations, this additional reduction in the SXD is due to a net radial transport of the energy remaining downstream of the $T_e = 5$ eV location. This energy is carried out of the critical (highest heat load) flux tube by deuterium atoms, demonstrating the importance of a longer legged divertor which provides space for this to occur. Importantly, in both simulation and experiment, the SXD has minimal impact on the upstream n _e and T _e profiles. Spectral inferences of detachment front movement in SXD compare well between simulation and experiment. In regions of high magnetic field gradient, the parallel movement of the front towards the X-point becomes less sensitive to increasing $n_{e,\textrm{sep,OMP}}$ , in qualitative agreement with simplified models and previous predictive simulations. Additional aspects, regarding the target ion flux rollover, upstream separatrix temperature and drift effects, are also presented and discussed.

Commercial fusion reactors will be faced with extremely high divertor target heat fluxes that will require mitigation. Simulations of detachment in an NSTX-U scenario projected to have 92 MW m ^−2 unmitigated peak target heat flux are presented, which reaches sub-10 MW m ^−2 target heat flux using a highly dissipating lithium vapor box divertor design. The lithium vapor box is a detached divertor design which employs lithium vapor evaporation and condensation to contain lithium below the X-point. Previous SOLPS modeling has indicated a lithium vapor box can reduce the heat flux down to 10 MW m ^−2 via simultaneous evaporation from the Private Flux Region (PFR) and the Common Flux Region (CFR) sides of the vapor box. It is found here that PFR evaporation has improved access to the separatrix leading to significantly more efficient power dissipation than CFR evaporation. Simulations of target evaporation with an evaporation distribution that is self-consistent with the temperature of a Capillary Porous System with Fast flowing liquid lithium could reach $n_\textrm{Li}$ / $n_\textrm{e} \sim$ 0.025–0.030 at the Last Closed Flux Surface (LCFS) depending on the liquid metal flow speeds and lithium sputtering yield, while PFR-side evaporation can reach acceptable heat fluxes with $n_\textrm{Li}$ / $n_\textrm{e} \sim$ 0.038 at the LCFS. However, PFR evaporator performance can be improved if the target is allowed to be hot enough such that it reflects lithium, reaching $n_\textrm{Li}$ / $n_\textrm{e} \sim$ 0.028 and reducing required lithium evaporation. Ultimately PFR evaporation and target evaporation are found to have similar ability to produce acceptable heat flux solutions with minimal upstream concentration.

One of the major design limitations for tokamak fusion reactors is the heat load that can be sustained by the materials at the divertor target. Developing a full understanding of how machine or operation parameters affect the conditions at the divertor requires an enormous number of simulations. A promising approach to circumvent this is to use machine learning models trained on simulation data as surrogate models. Once trained such surrogate models can make fast predictions for any scenario in the design parameter space. In future such simulation based surrogate models could be used in system codes for rapid design studies of future fusion power plants. This work presents the first steps towards the development of such surrogate models for plasma exhaust and the datasets required for their training. Machine learning models like neural networks usually require several thousand data points for training, but the exact amount of data required varies from case to case. Due to the long runtimes of simulations we aim at finding the minimal amount of training data required. A preliminary dataset based on SOLPS-ITER simulations with varying tokamak design parameters, including the major radius, magnetic field strength and neutral density is constructed. To be able to generate more training data within reasonable computation time the simulations in the dataset use fluid neutral simulations and no fluid drift effects. The dataset is used to train a simple neural network and Gradient Boosted Regression Trees and test how the performance depends on the number of training simulations.

The influence of the input power (IP), puffing rate and neutral pressure on the fuel (hydrogen isotopes) inventory of the WEST and ITER divertors is investigated. For the chosen range of parameters (relatively low temperature at the strike points), the inventory of the WEST divertor evolves as the power 0.2 of the puffing rate and as the power 0.3 of the IP. The inventory at the strike points is highly dominated by ions whereas it is dominated by neutrals in the private zone. Increasing the fuelling rate increases the retention in the private zone and decreases slightly the retention at the strike points. Increasing the IP increases the inventory at the strike points and does not affect much the inventory at the private flux region. The inventory of the ITER divertor is not strongly dependent on the divertor neutral pressure. The inventory increases from 0Â Pa to 7Â Pa and then decreases slightly from 7Â Pa to 10Â Pa. After 107Â s of continuous exposure, the maximum inventory in the ITER divertor was found to be 14Â g. The inventory is not maximum at the strike points due to the high surface temperature of the monoblocks in this region. The maximum accumulation of H in the ITER divertor is below 5 mg per 400Â s discharge and below 2 mg per 400Â s discharge after 200 discharges. [ABSTRACT FROM AUTHOR]

Comprehensive studies of energy and particle balances in the transition to plasma detachment in an alternative divertor configuration with long outer legs are shown. Numerical simulations are performed with the 2D code suite SOLPS 4.3, using a disconnected double null grid with narrow, tightly baffled long poloidal leg divertors at the outer lower target and outer upper target. A particle count scan is performed using the ‘closed gas box’ model, where the tunable parameter in the simulations is the total number of deuterium particles in the simulation space and all other parameters are held fixed, including a constant input power and trace neon impurity radiation, to assess the physics of the transition to detachment in the system as the particle count increases. Three main aspects of the physics of divertor detachment are addressed: the criteria for the local onset of divertor detachment in each of the divertors, the distribution of heat flux and other plasma parameters between the four divertors as each divertor transitions to detachment, and the role of perpendicular transport in the transition to the detached regime. A synergistic mechanism by which the cross-field transport is reduced by factors associated with the onset of plasma recombination effects is identified. These results are compared to the existing understanding of the physics of the transition to plasma detachment in standard divertors.

Through SOLPS-ITER simulations of DIII-D and MAST-U, an X-divertor (XD) on DIII-D and a super X-divertor (SXD) on MAST-U were shown to have increased carbon emissivity ( P _Rad / n _e n _I ) over corresponding standard divertors (SD) at similar degrees of partial detachment. The reasons behind the increased emissivity in the DIII-D XD and SXD are analyzed using a simple 0D transport model. From the transport model, it is seen that a major cause of the increased emissivity in the XD and SXD over the SDs is a shorter impurity confinement time. An additional cause (for the SXD) is an increase in the ratio of neutral hydrogen to electron density. The input power ( P _in ) was varied and the XD had a higher emissivity at the higher P _in , unlike the SDs which had the emissivity decrease with increasing P _in . A basic geometrical reason is given to explain both the benefits of the XD over the SD as well as the increase in the XD’s emissivity with P _in .

SOLPS modelling has shown that divertor plasma detachment occurs at a lower upstream separatrix density in the more closed DIII‐D upper divertor than the open lower divertor, demonstrating the utility of the divertor closure in widening the range of acceptable densities for adequate heat handling. To achieve reduced heat flux and erosion at the plasma‐facing components, future devices will need to operate in at least partially detached divertor conditions . Two‐dimensional fluid plasma models coupled to Monte Carlo neutral transport simulations, such as SOLPS, have been widely used to predict the onset of detachment. In modelling the DIII‐D discharges, the cross‐field transport coefficients are constrained to reproduce the experimental upstream profiles. The closed divertor has been modelled with the same input parameters of the open divertor, allowing a direct comparison of the target conditions in both geometries. SOLPS simulations indicate that a higher molecular density correlates strongly with lower electron temperatures. The increased closure of the upper divertor improves the trapping of neutrals, thereby reducing the power density deposited at the target and facilitating detachment, in agreement with experimental observations. [ABSTRACT FROM AUTHOR]

We employ the SOLPS5.1 code to analyse different impurity choices and injection methods as possible drivers for highly radiative scenarios in the European DEMO (EU‐DEMO). We aim at assessing the existence of a suitable parameter region to safely operate the divertor in H‐mode discharges. It turns out that such an operational region exists, and that puffing is strongly preferred to pellet as the impurity injection method. It also appears that many different impurity mixtures can meet the divertor survival requirements, with a low level of W sputtering. This provides an additional degree of freedom, which will be exploited in the future to optimize the overall reactor performance. [ABSTRACT FROM AUTHOR]

As part of a scoping study for an ITER‐sized tokamak, more than 50,000 simulations have been performed of the edge plasma with SOLPS5.0‐B2 using aggressive charge state bundling, fluid neutrals, and constant‐in‐time boundary conditions. These simulations have 40, 80, 100, 125, and 250 MW crossing into the simulation domain from the core region, and a range of D/T (deuterium/tritium) and impurity gas puffs giving a variation of electron density and Zeff. Most of the simulations are steady‐state, but about 10% show oscillations where the range of peak power flux densities to the outer target exceed 1% of the average value, and about 1% where the normalized range exceeds 10%. These oscillating cases present a challenge in determining whether a particular case has converged, or needs to be continued. The oscillations seem to have a physical origin because: the frequency of oscillations changed by less than a factor of two despite the time‐step for one case being varied by a factor 100; doubling the grid‐resolution resulted in similar oscillations; at least in some cases, a physically plausible limit‐cycle is present. [ABSTRACT FROM AUTHOR]

The three-dimensional (3D) edge Monte Carlo code coupled with EIRENE (EMC3-EIRENE) was recently successfully implemented to the double null of EAST. The SOLPS5.0 code package has been used to investigate the validation and consistency of the 3D edge EMC3-EIRENE code on EAST. These two codes show a good agreement with each other with the average error less than 20%. However, there exist discrepancies for ne and Te profiles along target between calculations and measurements. The evaluation of kinetic corrections by heat flux limiters which is not included in EMC3-EIRENE has been presented in a low density discharge. With considering the correction of heat flux limit, the upstream ion density is strongly affected and the target parameters slightly increase and get closer to the experimental measurements. Our previous analysis of parameters sensitivity showed the most possible reason is uncertainty of the separatrix position [J. Huang et al., Plasma Phys. Control. Fusion 56 (2014) 075023]. Agreement is achieved in both Te and ne at targets when the innermost separatrix shift ∼7 mm inward at outer midplane for both codes. [ABSTRACT FROM AUTHOR]

China Fusion Engineering Test Reactor (CFETR) is now in conceptual design phase. CFETR is proposed as a good complement to ITER for demonstrating of fusion energy. Divertor is a crucial component which faces the plasmas and handles huge heat power for CFETR and future fusion reactor. To explore an effective way for heat exhaust, various methods to reduce the heat flux to divertor target should be considered for CFETR. In this work, the effect of extended out divertor leg on the peak heat flux is studied. The magnetic configuration of the long leg divertor is obtained by EFIT and Tokamak Simulation Code (TSC), while a hypothetical geometry is assumed to extend the out divertor leg as long as possible inside vacuum vessel. A SOLPS simulation is performed to study peak heat flux of the long leg divertor for CFETR. D 2 gas puffing is used and increasing of the puffing rate means increase of plasma density. Both peak heat flux onto inner and outer targets are below 10 MW/m 2 is achieved. A comparison between the peak heat flux between long leg and conventional divertor shows that an attached–detached regime transition of out divertor occurs at lower gas puffing gas puffing rate for long leg divertor. While for the inner divertor, even the configuration is almost the same, the situation is opposite. [ABSTRACT FROM AUTHOR]

Heat exhaust is a challenge for ITER and becomes even more of an issue for devices beyond ITER. The main reason for this is that the power produced in the core scales as R3 while relying on standard exhaust physics results in the heat exhaust scaling as R1 (R is the major radius). ITER has used SOLPS (B2-EIRENE) to design the ITER divertor, as well as to provide a database that supports the calculations of the ITER operational parameter space. The typical run time for such SOLPS runs is of the order 3 months (for D+C+He using EIRENE to treat the neutrals kinetically with an extensive choice of atomic and molecular physics). Future devices will be expected to radiate much of the power before it crosses the separatrix, and this requires treating extrinsic impurities such as Ne, Ar, Kr and Xe - the large number of charge states puts additional pressure on SOLPS, further slowing down the code. For design work of future machines, fast models have been implemented in system codes but these are usually unavoidably restricted in the included physics. As a bridge between system studies and detailed SOLPS runs, SOLPS offers a number of possibilities to speed up the code considerably at the cost of reducing the fidelity of the physics. By employing a fluid neutral model, aggressive bundling of the charge state of impurities, and reducing the size of the grids used, the run time for one second of physics time (which is often enough for the divertor to come to a steady state) can be reduced to approximately one day. This work looks at the impact of these trade-offs in the physics by comparing key parameters for different simulation assumptions. (© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

To facilitate the design of the China Fusion Engineering Testing Reactor (CFETR), predictive modeling for the assessment and optimization of the divertor performances is an indispensable approach. This paper presents the modeling of the edge plasma behaviors as well as the W erosion and transport properties in CFETR with ITER-like divertor by using the B2-Eirene/SOLPS 5.0 code package together with the Monte Carlo impurity transport code DIVIMP. As expected, SOLPS modeling of divertor-SOL plasmas finds that the peak heat flux onto the divertor targets greatly exceeds 10 MW/m, an engineering limit posed to the steady-state and/or long-pulse operation of the next-step fusion devices, for a wide range of plasma conditions, and thus modeling of Ar puffing by scanning the puffing rate for radiative divertor is performed. As the increase of the Ar puffing rate, the peak target heat fluxes and plasma temperature decreases exponentially,reflecting that Ar puffing is highly effective at power exhausting. Based on the ion fluxes from SOLPS, the W erosion is calculated by taking into consideration the bombardment of both D and Ar ions, and then the W plasma concentrations are calculated based on the W erosion fluxes using DIVIMP. The calculations show that if the Ar puffing only being used to reduce the divertor heat load, the W plasma contamination in the core plasma exceeds the tolerable value (<10), which demonstrates that some further upgrading of the divertor geometry is still needed. [ABSTRACT FROM AUTHOR]

Impacts of particle and energy fluxes during edge localized modes (ELMs) on the divertor targets were particularly studied through Langmuir Probes in EAST (Wang et al., 2012); however, no attempt has been made to model the time-dependent ELMy H-mode of EAST yet by the edge plasma code package SOLPS. This paper aims to model the type-III ELMy H-mode discharge in EAST using SOLPS. Firstly, we adjust the perpendicular anomalous transport coefficients (PATCs) by matching the experimental upstream radial electron density and temperature profiles under given type-III ELMy H-mode discharge conditions (shot #33266) to obtain the steady-state H-mode, and then, ELMs are modeled by periodically enhancing PATCs with the parameters, such as the repetition frequency and the energy expelled from the core plasma, taken directly from the experimental data of the given EAST discharge. In this way, many experimentally inaccessible upstream parameters can be evaluated through the simulation; meanwhile, many input parameters can be provided from such simulations to other codes for understanding the damage of plasma-facing materials caused by plasma irradiation. [ABSTRACT FROM AUTHOR]

A density scan is performed in SOLPS5.0 for two divertor configurations of MAST Upgrade: (i) a short divertor silimiar to configurations in present-day tokamaks, (ii) the Super-X divertor. In the simulation, a clear roll-over of the ion flux and plasma density at the target is observed as the plasma detaches. The separatrix density at which the transition occurs is estimated. In addition, we investigate the ability of the long-legged divertor to reduce the target power loads and enhance the radiated power at higher collisionalities. We also study how distribution of power losses in the divertor region changes with the modification of geometry and we separately analyze neutral radiation and carbon ion line radiation. (© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

For the purpose of a consistent treatment of tungsten impurity together with background plasma, coupling of the IMPGYRO and SOLPS codes has been undertaken. The fluid part of SOLPS transfers the background plasma data to the IMPGYRO kinetic impurity code, while IMPGYRO transfers the effect of tungsten impurities to SOLPS as particle, momentum and energy source/sink terms. An initial test calculation has been performed under a simple model for impurity generation. The impurity content in the system reaches a quasi-steady state in the coupled calculation. The temporal history of the simulation shows that an initial impurity generation results in a relatively large radiation loss and plasma cooling. The cooler plasma suppresses further impurity generation, leading to a quasi-steady state in the coupled calculation (© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Abstract: The paper presents a review of the development of edge plasma modeling at ITER and of its interaction with the evolving divertor design. The SOLPS (B2-Eirene) code has been developed for, and applied to, the evaluation and the design of the ITER divertor for the last 15 years. With respect to the physics and engineering design, divertor modeling had started as an evaluation tool and has developed into essential design tool synthesizing information from theoretical analysis, experimental studies, and engineering intuition. Examples given in the paper illustrate this process. [Copyright &y& Elsevier]