Gonzalez J.

Nallo G. F.

Westerhof E.

English

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)

18 September 2024POLITECNICO DI TORINORepository ISTITUZIONALESelf-consistent simulation of Magnum-PSI target in SOLPS-ITER with a Finite Element Wall model / Gonzalez, J.; Nallo,G. F.; Westerhof, E.. - 46 A:(2022). (Intervento presentato al  convegno 48th European Physical Society Conference onPlasma Physics, EPS 2022 nel 2022).OriginalSelf-consistent simulation of Magnum-PSI target in SOLPS-ITER with a Finite Element Wall modelPublisher:PublishedDOI:Terms of use:Publisher copyright(Article begins on next page)This article is made available under terms and conditions as specified in the  corresponding bibliographic description inthe repositoryAvailability:This version is available at: 11583/2981131 since: 2023-08-18T10:28:56ZEuropean Physical Society (EPS)Self-consistent simulation of Magnum-PSI target in SOLPS-ITER with aFinite Element Wall modelJ. Gonzalez1, G. F. Nallo2, E. Westerhof11 DIFFER, Dutch Institute for Fundamental Energy Research, Eindhoven, The Netherlands2 NEMO group, Dipartimento Energia, Politecnico di Torino, ItalyIntroductionSolving the power exhaust problem in tokamaks is one of the milestones along the pathtowards fusion electricity production [1]. In this context, accurate simulation of plasma-surfaceinteraction is of great importance for the determination of heat and particle fluxes towards thedivertor of a tokamak. For example, it is expected that during slow transients ITER divertorwill have to stand between 10 and 20MWm−2 [2] and orders of magnitude higher during fasttransients. These fluxes are in the thermal limit of known materials, thus the design of coolingsystems and divertors to sustain this load is determinant for future reactors.To support these design activities, the availability of a model which can self-consistentlysimulate the impinging plasma and the target temperature, accounting for the divertor cooling,would be beneficial. Moreover, it should be mentioned that in the case of a liquid metal di-vertor [3] a self-consistent coupling is essential, since the plasma and target mutually interactvia target evaporation and the consequent plasma cooling [4]. This work presents the couplingbetween SOLPS-ITER, a widely used code in the fusion community, and a Finite Element Wallmodel to self-consistently simulate the target behavior in terms of, e.g, surface temperatureand/or liquid metal evaporation rate.In this paper, the first results from the coupling mentioned above to the simulation of Magnum-PSI, a plasma linear device that can reproduce ITER relevant divertor fluxes, are discussed.These simulations will allow to validate the plasma solution provided by SOLPS-ITER withthe surface temperature obtained by the target model, increasing the reliability of the code andimproving our capability to simulate Magnum-PSI.SOLPS-ITER for Magnum-PSI simulationsSOLPS-ITER [5, 6] is widely used in the fusion community. However, validation and com-parison with experiments is often complicated by the limitations to experimental access in toka-maks. Magnum-PSI [7] is a plasma linear device that can reproduce heat and particle fluxes ofthose expected at the ITER divertor. Thus, there is an interest in using SOLPS-ITER to simulateMagnum-PSI, as this will allow for validation of the code and to extract information that can48th EPS Conference on Plasma Physics P4b.112Figure 1: 2D mesh of the tungsten target employed in the simulations. The bottom wall is set toa constant temperature of 180◦C (453K) to represent an active cooling.be easily translated to a tokamak divertor, like the relevant atomic and molecular processes nearthe target.Nevertheless, the application of SOLPS-ITER to a linear device like Magnum-PSI is notstraightforward and requires several aspect to be careful considered. Apart from the obviouschange in geometry respect to a tokamak, for Magnum-PSI the parallel direction represents theaxial coordinate z, a new set of boundary conditions to represent the plasma source need tobe incorporated. Experimental data from Thomson Scattering (TS) measurements are used asinput profiles for plasma density and temperature. The electric potential at the source, whichin Magnum-PSI controls the amount of Ohmic heating in the plasma beam, is adjusted so thattemperatures in the target chamber remain close to experimental data [8].Finite Element Target ModelCurrently, SOLPS-ITER is being coupled with a FreeFem++ [9] finite element model to self-consistently compute the target properties, accounting for the target material, its shape and thecooling system. This provides a flexible, fast running 2D transient heat conduction solver. Themodel receives the heat fluxes towards the target computed by SOLPS-ITER and returns thetarget temperature. The surface temperature can be then extracted and passed back to SOLPS-ITER. This cycle is repeated until plasma, neutrals and target temperature reach a convergedstate.For the case presented here, a solid tungsten target is employed, and the active cooling isimposed by setting a constant temperature at the bottom surface of 180◦C (453K). The targettemperature is recalculated at each time step taking into account the plasma heat flux towardsthe target and this value is passed back to SOLPS-ITER. The 2D model employed to representa Magnum-PSI target can be found in Fig. 1.Future simulations of the target will include self-consistent calculated recycling parameter or48th EPS Conference on Plasma Physics P4b.112ne (×1020 m-3)Radial Position (mm)0.46Pa4.30Pa0.01.02.03.04.05.06.0-20 -15 -10 -5  0  5  10  15  20Te (eV)Radial Position (mm)0.46Pa4.30Pa0.00.20.40.60.81.01.2-20 -15 -10 -5  0  5  10  15  20Figure 2: Electron density (left) and temperature (right) at the Thomson Scatering (TS) tar-get position for two neutral pressures at the target chamber. SOLPS-ITER results (solid line)agree with experimental TS data (data points), although discrepancies in the temperature for the4.30Pa case appear.Heat Flux (MW m-2)Radial Position (mm)0.46Pa4.30Pa  0  2  4  6  8 10 0  5  10  15  20Wall Temperature (K)Radial Position (mm)0.46Pa4.30Pa400500600700 0  5  10  15  20Figure 3: Target heat flux (left) and surface temperature (right) provided by the finite elementwall model. For the high pressure case, surface temperature is reduced to the cooling tempera-ture as plasma heat flux has been mitigated upstream by interaction with neutral particles.the evaporation flux when a porous material filled with a liquid metal is used as a target.Coupled simulationsTo test the coupling between SOLPS-ITER and the FreeFem++ target model a high densitycase is used. In this plasma scenario, density close to the target are around 1021 m−3 and tem-peratures around 1eV. Two different neutral pressures in the target chamber are analysed, low(0.46Pa) and high (4.30Pa), representing attached and detached plasma scenarios, respectively.Figure 2 presents the comparison of SOLPS-ITER simulations and experimental TS data forthe cases described above. SOLPS-ITER captures the temperature reduction observed exper-imentally when the amount of neutrals near the target is increased by gas puffing. However,discrepancies appear between the simulations and experiments, particularly for the electrondensity in the high pressure case. Although the cause of this discrepancy is not clear yet, itis expected that the coupling with the target finite element model will provide a much morerealistic scenario.Figure 3 depict the heat flux hitting the target and the surface temperature provided by theFreeFem++ model. For the low pressure case, a Gaussian-like heat flux profile impacts the48th EPS Conference on Plasma Physics P4b.112target, which results in a temperature profile with an increase of more than 100K near theplasma beam peak. However, when the Magnum-PSI plasma beam is mitigated by gas puffing,target temperature drops to the one set by the bottom cooling system.ConclusionsThe widely use edge plasma code SOLPS-ITER has been successfully applied to the plasmalinear device Magnum-PSI. Results are in qualitatively agreement with experimental data al-though some discrepancies still appear. The code has been successfully coupled with a finiteelement target model based on the open-source FreeFem++ language. The target temperaturehas been self-consistently computed based on the heat fluxes in two scenarios: low and high neu-tral pressure. For a high pressure case, which represents a detached plasma, the temperature ofthe target drops to the temperature set by the cooling system. Further work is currently ongoingto close the self-consistent loop passing multiple parameters from FreeFem++ to SOLPS-ITER.AcknowledgementThis work has been carried out within the framework of the EUROfusion Consortium, fundedby the European Union via the Euratom Research and Training Programme (Grant AgreementNo 101052200 — EUROfusion). Views and opinions expressed are however those of the au-thor(s) only and do not necessarily reflect those of the European Union or the European Com-mission. Neither the European Union nor the European Commission can be held responsiblefor them. This work was carried out on the Dutch national e-infrastructure with the support ofSURF Cooperative and the EUROfusion High Performance Computer Marconi-Fusion hostedat Cineca (Bologna, Italy). This work is part of the research programme "The Leidenfrost diver-tor: a lithium vapour shield for extreme heat loads to fusion reactor walls" with project numberVI.Vidi.198.018, which is (partly) financed by NWO.References[1] T. Donné, W. Morris, X. Litaudon, et al., European Research Roadmap to the Realisation of Fusion Energy(long version), (2018).[2] J. P. Gunn, S. Carpentier-Chouchana, F. Escourbiac, Nuclear Fusion, 57, 4, (2017)[3] G. F. Nallo, G. Caruso, F. Crisanti, et al., Fusion Eng. Des., 125, 206–15 (2017)[4] G. F. Nallo, G. Mazzitelli, M. Moscheni, et al., Nuclear Fusion 62, 3 (2022)[5] S. Wiesen, D. Retlev, V. Kotov, et al., Journal of nuclear materials, 463, 480-484, (2015)[6] D. V. Borodin, F. Schluck, S. Wiesen, et al., Nuclear Fusion, Accepted Manuscript, https://doi.org/10.1088/1741-4326/ac3fe8, (2021)[7] G. de Temmerman, M. A. van den Berg, J. Scholten, et al., Fusion Engineering and Design 88, 6-8, (2013)[8] R. Chandra, H. J. de Blank, P. Diomede, et al., Plasma Physics and Controlled Fusion 63, 9, (2022)[9] F. Hecht, Journal of numerical mathematics 20.3-4, 251-266 (2012)48th EPS Conference on Plasma Physics P4b.112

Self-consistent simulation of Magnum-PSI target in SOLPS-ITER with a Finite Element Wall model

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Self-consistent simulation of Magnum-PSI target in SOLPS-ITER with a Finite Element Wall model

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