Korving, S.Q.

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 The influence of drifts in the ITER divertor in nonlinear MHDJOREK simulations with fluid and kinetic neutralsCitation for published version (APA):JOREK team, & Korving, S. Q. (2021). The influence of drifts in the ITER divertor in nonlinear MHD JOREKsimulations with fluid and kinetic neutrals. In 47th EPS Conference on Plasma Physics, EPS 2021 ArticleP4.1026 (Europhysics Conference Abstracts; Vol. 45A). European Physical Society (EPS).Document status and date:Published: 01/01/2021Document Version:Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers)Please check the document version of this publication:• A submitted manuscript is the version of the article upon submission and before peer-review. There can beimportant differences between the submitted version and the official published version of record. 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Oct. 2023The influence of drifts in the ITER divertor in nonlinear MHD JOREKsimulations with fluid and kinetic neutralsS.Q. Korving1,2, G.T.A. Huijsmans1,3, J.-S. Park2,4 and the JOREK team (see ref [1])1 Eindhoven University of Technology , Eindhoven, The Netherlands2 ITER Organization, St. Paul Lez Durance Cedex, France3 CEA, IRFM,F-13108 St. Paul Lez Durance Cedex, France4 Korea Advanced Institute of Science and Technology, Daejeon 34141, Republic of KoreaFor ITER operation, resonant magnetic perturbations (RMP) applied for ELM control will ergodisethe plasma-edge magnetic field. This will strongly influence the topology of the magnetic field atthe divertor, leading to 3D patterns in the energy and particles fluxes. This will influence impuritysputtering and transport across the separatrix. The aim is, using the nonlinear extended MHD codeJOREK [1], to simulate the MHD response of the plasma to the applied RMP fields, with a consistent3D description of the divertor. JOREK has previously been extended with a module for kinetic par-ticles (neutrals, impurities, fast particles), non-linearly coupled to the MHD fluid [2]. The extendedMHD model includes ExB drifts, diamagnetic drifts and neoclassical flows. These drift can have largeinfluences, on e.g. divertor asymmetries. Realistic divertor conditions are important for impurity sput-tering, transport and their effect on the plasma. In this contribution we look at the influence of poloidalflows on divertor conditions in the ITER PFPO-1 (1.8T/5MA) H-mode plasma scenario, and comparethe divertor plasma conditions and heat flux to the wall for both the fluid and kinetic neutral model(in JOREK) to the well-established 2D boundary plasma simulation code suite SOLPS-ITER [3].Fluid MHD plus fluid and kinetic neutral physics in JOREKJOREK is a fully implicit non-linear extended MHD code for realistic tokamak X-point plasmas[1]. Here, the visco-resistive reduced MHD is used as model where the time-evolved parameters areψ, j, u, ω, ρ, T, v‖, respectively the poloidal flux, the toroidal current density, the poloidal velocitystream function, the vorticity, the electron density, the ion plus electron temperature and the parallelvelocity. For fluid neutrals we introduce ρn, the neutral density, that we assume to behave fully diffu-sive. Then we only need the density equation, ∂ρn∂ t −Dn∇2ρn = S, to evolve the neutral density. Theneutrals are coupled to the plasma via ionisation, recombination and wall-assisted recombination (i.e.the outgoing ion flux equals the incoming neutral flux).Previously JOREK has been extended with a Monte-Carlo kinetic particle code [2]. Apart fromdiffusive fluid neutrals, JOREK is now able to use kinetic neutrals which consists of superparticleswith a weight representing the amount of physical particles and a position and velocity in three di-mensions. The physical coupling to the plasma is via ionisation, recombination, charge-exchange(CX), wall-assisted recombination and reflection. In both neutral models, line-radiation, recombina-tion radiation and Bremsstrahlung losses are included. For each superparticle in the domain, everytimestep, the probability of a physics event (i.e. ionisation and CX) is calculated based on the localplasma parameters. If this probability is higher than a uniformly distributed random value, the physicsevent is performed. For CX, a test particle is sampled from the local temperature distribution in a co-moving frame of reference, then shifted back to the laboratory frame to include macroscopic flow ofthe plasma. The recombination rate and associated lost plasma momentum are calculated from thelocal plasma parameters and the resulting kinetic neutrals are added in each element. This strategyensures good conservation properties between plasma and kinetic neutrals, regardless of the timestepand amount of superparticles chosen for sampling.Kinetic neutral modelling requires many kinetic time steps per fluid time step to resolve the physicscoupling on the collision time scales of the neutrals. Especially in the divertor region where densitiesare high and the temperatures are low, the ionisation and CX timescales are typically a few times 10−7seconds. From the ionisation and CX reaction rates an effective diffusivity can be calculated. Rangingfrom 0.03 m2/s at 1 eV to ∼ 1 m2/s at 1 keV at an electron density of ne = 1020 m−3.47th EPS Conference on Plasma Physics P4.1026SOLPS-ITER comparison for PFPO-1 H-mode plasmas with and without poloidal flowsThe recently published SOLPS-ITER simulations [4] for the ITER PFPO-1 scenario provide a goodstarting point for a comparison of JOREK to SOLPS-ITER. In this gas throughput scan, only hydro-genic species are present (atoms and molecules) with a tungsten divertor.SOLPS-ITER does not resolve the plasma core nor evolves the magnetic equilibrium. To obtain theself-consistent equilibrium close to the SOLPS-ITER solution, as required by JOREK, we take thepressure profile from the EQDSK equilibrium on which the SOLPS-ITER runs are based. The sameheating and transport parameters are used as in [4], Pheating = 20 MW, D⊥ = 0.3 m2s−1, χi,⊥ = χe,⊥ =1.0 m2s−1. Parallel heat transport is based on the Braginskii closure. The fluid neutral diffusivity waschosen to match the SOLPS-ITER neutral density decay from the strikepoint following the fieldlinesat low puffing. This resulted in Dn ≈ 2 ·102 m2s−1. To reach a quasi-steady-state JOREK simulationwere run between 11 ∼ 55 ms. To reduce the set of time-evolved physics, i.e. removing poloidalflows, to be consistent with SOLPS-ITER, we have removed the time evolution of ψ, j, u, ω . Thereduced model is the closest to SOLPS-ITER without drifts. Plasma wall interaction and neutral-ioninteraction strongly affect the profiles at the target and the onset towards detachment [4], it is notappropriate to compare the exact density, temperature and heat flux profiles at a single level of gaspuffing/sepatrix density value. Instead, the total heat load and peak heat flux to the divertor targetare compared as a function of increased neutral puffing in the divertor. To quantitatively compare theresults, the toroidally averaged values predicted by SOLPS-ITER are compared with JOREK withoutthe corrections required to account for tilting of divertor targets and shaping of monoblocks [6], whichare required to predict the surface temperatures of these elements on the basis of SOLPS-ITER results[4].0.0 0.5 1.0 1.5 2.0Puffing [atoms/s] 1e230.00.20.40.60.81.01.2Heatload[W]1e7Total [full]OT [full]IT[full]Total [reduced]OT [reduced]IT [reduced]Total [SOLPS]IT [SOLPS]OT [SOLPS]0.0 0.5 1.0 1.5 2.0Puffing [atoms/s] 1e2301234567Peakheatflux[W/m2 ]1e6OT [full]IT [full]OT [reduced]IT [reduced]OT [SOLPS]IT [SOLPS]Figure 1: Neutral puffing scan results for JOREK [Full], JOREK without poloidal flows[Reduced], andSOLPS-ITER [SOLPS]. (left) Plasma heat load on inner and outer divertor targets and their sum. (right) Peakheat flux on inner and outer divertor targetsAs puffing increases, the total heat load to the inner wall stays almost constant, and on the outer wallslowly decreases [4]. This contribution only looks at the plasma heat load. In figure 1(left) the plasmaheat load is in all cases higher on the outer target than on the inner target. The highest SOLPS-ITERpuffing, results in a plasma heat load reduction of 63% versus 66% for JOREK without poloidal flows.JOREK without poloidal flows is in very good agreement with SOLPS-ITER staying within 15%difference in total head load. Thus power balance estimations for this scenario can be produced withthe diffusive neutral approximation of JOREK. Furthermore, figure 1 shows poloidal flows should betaken into account as they result in a different distribution of the heat load, even at high puffing rates.From the MHD equations and transport coefficients, one might expect the heat flux profiles tobe the same width for JOREK and SOLPS. Figure 1(right) shows a much lower peak heat flux forSOLPS-ITER, and thus much broader profiles. The plasma and neutral wall interactions and mo-mentum exchange strongly affects the density (neutral and plasma) profiles close to the strike point.SOLPS-ITER uses the TRIM-Code database for its Monte Carlo kinetic neutral transport code[7],which includes e.g. reflection of fast neutrals. CX and neutral reflection change the density and mo-mentum balance strongly. Figure 1(right) clearly shows these effects. This means the effective Dn andmomentum exchange do not strongly affect the total power balance. The heat flux profiles are sensitive47th EPS Conference on Plasma Physics P4.1026to Dn; suggesting our assumption on effective Dn was too low, or the diffusive neutrals approximationis not sufficient to produce correct heat flux widths indicating the need of kinetic neutrals.Influence of poloidal ExB flowsAs a first application of more realistic heat flux profiles in JOREK, we investigate the influence ofpoloidal flows on the heat flux. ExB drifts cause an asymmetry between the inner and outer divertors.They broaden and drive the density in inner leg upwards and, compresses and drives the density inouter leg towards the strike point. This results in an asymmetric response to gas puffing. The heat fluxdepends on the ion flux and the temperature, the latter gives it a different response to ExB flows. Thepushing effect of ExB drifts is clearly visible on the OT in figure 2 between the upper (without pol-oidal flows) and the lower (with poloidal flows) plots. The peak heat flux moves from just right of theseparatrix (physically above) to just left of the separatrix (physically below). On the IT, as the densityis pushed upwards, the temperature rises on the separatrix, resulting in a higher peak heat flux at lowpuffing rates, but a stronger decrease. The results in figure 2 do not include the diamagnetic drift.0.02 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14s ssep [m]0123456Heatflux[W/m2 ]1e6 JOREK no poloidal flows IT2.15E+22 atoms/sec4.29E+226.44E+228.58E+221.07E+231.29E+231.50E+231.72E+231.93E+230.02 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14s ssep [m]0123456Heatflux[W/m2 ]1e6 JOREK no poloidal flows OT2.15E+22 atoms/sec4.29E+226.44E+228.58E+221.07E+231.29E+231.50E+231.72E+231.93E+230.02 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14s ssep [m]0123456Heatflux[W/m2 ]1e6 JOREK IT1.18E+22 atoms/sec3.33E+225.48E+227.62E+229.77E+221.19E+231.41E+231.62E+231.84E+230.02 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14s ssep [m]0123456Heatflux[W/m2 ]1e6 JOREK OT1.18E+22 atoms/sec3.33E+225.48E+227.62E+229.77E+221.19E+231.41E+231.62E+231.84E+23Figure 2: Heat flux profiles from the strike point vertically along the divertor contour with several gas puffingrates. Effect of poloidal flows on heat flux flux profiles and detachment dynamics. (Upper left) JOREK withoutpoloidal flows on inner target. (Upper right) JOREK without poloidal flows on outer target. (Lower left) JOREKwith poloidal flows on inner target. (Lower right) JOREK with poloidal flows on outer target.Figure 1 shows the peak heat flux and total heat load diminishes faster on the IT for both with andwithout poloidal flows; however, the poloidal flows distribute signifcantly more heat to the IT at lowpuffing rates. Figure 3 demonstrates the displacement of plasma density due to the poloidal flows.The white contours show the poloidal flow directions, where plasma above the separatrix is pushedupwards on the inboard side and downwards on the outboard side. Deviations of the plasma para-meters from the magnetic field line structure result in the changing heat flux profiles shown in figure2. Preliminary simulations including diamagnetic drift show an opposite effect to the ExB flows.Comparing kinetic and fluid neutrals in high recycling regimeKinetic neutrals including simple reflection physics can strongly broaden the profile. Momentum ex-change between neutrals and ions is a driving mechanism for profile broadening. In our diffusiveneutral fluid model, these momentum exchanges, e.g. CX, are not present. We thus expect the kineticneutrals to facilitate broader profiles on the divertor wall. CX does not per se significantly increaseenergy losses, as most fast neutrals created will ionize again.Figure 4 compares the heat flux profileson the outer target, showing a strongly reduced peak heat flux and a strong broadening of the profilein terms of Full-width-half-maximum. The profile broadening disputes the assumption of a very low47th EPS Conference on Plasma Physics P4.1026Figure 3: Comparison of plasma density in the poloidal plane with flow/potential contours in white and theseparatrix in lightblue. The density colorbar range is selected to make divertor profiles more visible. (Left)JOREK without poloidal flows. (Right) JOREK with poloidal flows.effective neutral diffusivity based on the collision rates. The total heat load remains approximatelythe same across the whole domain. On the outer target shown in figure 4 the hoat load is reduced from5.8 to 4.8 MW when switching to kinetic neutrals. The exact reason for the significant drop in heatloads just around the strike point in the simulation is not clear. However, the CX plays a dominantrole for energy and momentum exchange.ConclusionGood quantitative agreement (< 15% difference) has beenfound between the SOLPS-ITER and JOREK solutions forthe plasma heat load for a scan in neutral puffing. Heat fluxprofiles are sensitive to the plasma-neutral interactions. Ef-fective diffusivity is not a good description for the behaviorof kinetic neutrals, resulting in narrow heat flux profiles.As a first application, the JOREK code is applied to studythe effects of ExB drifts on the divertor solutions. Applyingthe extended MHD model yields a strong asymmetry in thebehaviour between low field and high field side. The innerdivertor detaches at a significantly lower gas puff rate com-pared to the outer divertor, generally consistent with resultsFigure 4: Comparison JOREK (with ExBflows) with fluid neutrals, and with kineticneutrals along the divertor contour.of SOLPS-ITER [5]. The asymmetries arise from the opposite flow directions of the poloidal flowsnear the separatrix on the low and high field sides. These effects are expected to be much lower forthe ITER FPO phase, as PFPO-1 is an operating scenario with high temperature and low densities.Kinetic neutrals will be needed to obtain broadened profiles at the strike points. Although CXplays a dominant role in the momentum exchange with neutrals in the divertor region, we still clearlyobserve the influence of poloidal flows. The peak heat flux remains at the same location as for theJOREK simulations with neutral fluid including the poloidal flows.The next step is improving reflection physics on the wall and achieving partially detached stateswith kinetic neutrals.Acknowledgements and DisclaimerThis work is part of the research programme of the Foundation forNederlandse Wetenschappelijk Onderzoek Instituten (NWO-I), which ispart of the NWO and has been carried out within the framework of theEUROfusion Consortium and has received funding from the Euratomresearch and training program 2014-2018 and 2019-2020 under grantagreement No 633053 and from the ITER Organization under Imple-menting Agreement 43-2174 with the Eindhoven University of Technol-References[1] M. Hoelzl et al., Nuclear fusion 61, 065001 (2021)[2] D.C van Vugt, PhD thesis, Eindhoven University ofTechnology, (2019)[3] Wiesen S. et al, J. Nucl. Mater. 463, (2015)[4] J.-S. Park et al, Nuclear fusion 61, (2021)[5] E. Kaveeva et al, Nuclear Fusion 60, (2020)[6] S. Carli, et al, Nucl. Fusion 58 (2018)[7] D. Reiter, The EIRENE Code User Manual. (2021)ogy. Computations were performed using the computer cluster Marconi-Fusion. The views and opinions expressed hereindo not necessarily reflect those of the European Commission nor the ITER Organization.47th EPS Conference on Plasma Physics P4.1026

The influence of drifts in the ITER divertor in nonlinear MHD JOREK simulations with fluid and kinetic neutrals

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The influence of drifts in the ITER divertor in nonlinear MHD JOREK simulations with fluid and kinetic neutrals

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