Arnoux, G.

Benkadda, S.

Beurskens, M.

Devaux, S.

Eich, T.

Frassinetti, L.

Huysmans, G.

Kirk, A.

Pamela, S.

English

MPG.PuRe

Simulation of ELMs in JETS.J.P. Pamela1, G.T.A. Huysmans1, M.N.A. Beurskens2, G. Arnoux2,A. Kirk 2, T. Eich3, S. Devaux3, S. Benkadda4, L. Frassinetti5 and JET EFDA contributors∗1 Association EURATOM-CEA, F-13108 Saint-Paul-lez-Durance, France.2 JET-EFDA, Culham Science Centre, Abingdon, OX14 3DB, UK.3 Max-Planck Institut fur Plasmaphysik, EURATOM Association, Garching, Germany.4 PIIM,CNRS - Univ.Provence, Centre St.Jérôme, Case321, 13397 Marseille Cedex20,France.5 Association EURATOM-VR, Royal Institute of Technology KTH, Stockholm, Sweden.∗ See the Appendix of F. Romanelli et al., Proc. 22nd Int. FEC Geneva, IAEA (2008)1. IntroductionThe future tokamak ITER is expected to run routinely in type-I ELMy H-mode confinementregime. The ELMs are necessary in order to rid the plasma of its impurities. However, it isexpected that ELMs in ITER could release up to 20MJ, which is not bearable for the presentlydesigned tungsten divertor [1,2]. Hence, some techniques have been developed to control ELMs(RMPs, pellets, kicks), but there is at present poor understanding of how these tools provoke ormitigate the ELMs. In fact, the ELMs themselves are not fullynderstood. The linear stabilityof ELMs has been well established in the last two decades [3],but the understanding of thenonlinear properties of ELMs still requires some effort.The nonlinear simulation of ELMs is already in reasonable qualitative agreement with ex-perimental observation [4,5]. In particular, simulationsshow a filamentation of the plasma edgeinto the Scrape-Off Layer, and large amounts of energy arriving on the divertor in the form ofsmall heat-flux structures near the strike point. In sight ofusing the simulations to obtain somepredictions of ELMs in ITER, the MHD code JOREK [4,5] should first undergo a quantitativevalidation against experimental data. This paper aims at a first step towards this validation, bypresenting simulations of ELMs for a given plasma pulse fromJET. The long term goal beingto extend the simulations to multiple shots analysis, both fr JET and for other tokamaks.2. From Experimental Data to Numerical SimulationsThe JET pulse #73569 has been chosen as a first simulation basis because it is a type-I ELMyH-mode with good HRTS profiles (High-Resolution Thomson Scattering diagnostic [6]), and agood view of the Infra-Red camera on the outer divertor. For this pulse, the field was 2T, thedensityne= 6.1019m−3 at the magnetic axis and the temperatureTe= 3keV. In order to producea simulation, one needs to solve the Grad-Shafranov equilibri m, so that three ingredients areneeded: the pressure profilep, the current profilej, and the poloidal fluxψ on a closed boundaryΩ around the plasma.The pressure profile is obtained from HRTS, which gives the electron density and tempera-ture. Since JOREK solves the two-fluid MHD equations with separate variablesρ, Ti andTe, theion temperature profile is assumed to be identical to the electron temperature profile. The HRTSprofiles are all taken before the ELMs (80-99% of the ELM-period), and a fit is done over theprofiles. This way, using multiple profiles ensures a good resolution in the pedestal, so that thepressure profile is reliable (see Fig.1b).The global current profile is obtained from EFIT, with an additional bootstrap current calcu-lated from HELENA, according to the pressure profile, following the Sauter method [7].37th EPS Conference on Plasma Physics O2.106(a) (b)Figure 1:a) compares the initial EFIT flux (right) with the JOREK equilibrium reconstruction (left). b) showsthe density and temperature profiles from HRTS (circles) together with the profiles used in simulations (lines)The flux ψ at the boundary is also taken from the EFIT reconstruction. Si ce there is yetno resistive wall boundary conditions in JOREK, this contourhas been taken just outside thevacuum vessel wall, and close to the divertor. The resultingreconstruction ofψ is shown inFig.1a next to the EFIT flux. Also shown in Fig.1b are the temperature and density profiles usedin simulations, compared to the HRTS profiles. The reconstruction of equilibrium with JOREKis in reasonable agreement with the EFIT reconstruction andthe HRTS diagnostic.3. JET SimulationsThe resulting JET equilibrium has a pressure profile very close t ideal ballooning stabilitylimit, which is highly unstable with respect to resistive ballooning, so that the perturbation oftoroidal mode numbers results in a pedestal collapse, whichmay be compared to an ELM. Thesimulations have been run for different mode numbers, varying the main plasma parameters(resistivityη , parallel thermal conductivityκ‖ etc...).One first observes the distinction betweenTi andTe during the ballooning crash. The theoret-ical κ‖ for each species (implemented in the code) depends on the corr sp nding temperatureand has a coefficient which depends on the species’ mass, resulting in a faster conductivity forTe. Namelyκe,‖κi,‖≈ 40. As a consequence, and as can be seen on Fig.2a,Te is rapidly conductedto the divertor, where distinct stripes are observed near the strike point. This is not the case forTi, which is convected into filaments like the density.Te filaments are also observed, but lessdistinctively thanTi filaments.TheseTe stripes are important, because they are responsible for most of the energy arrivingon the divertor. Similar stripes are observed in JET during ELMs. The common procedure to de-termine the dominant mode number of an ELM in JET relies partly on the signals from MirnovCoils, but also on the number of stripes observed on the outer div tor tile. Simulations clearlyshow a relation between the mode number and the number of stripe , as seen from Fig.2b, al-though the number of divertor stripes is generally inferiorto the mode number itself. This showshow simulations could be used in return to reinforce the interpretation of IR diagnostics in orderto determine the mode number of an ELM in JET.37th EPS Conference on Plasma Physics O2.106(a) (b)Figure 2:a) shows Ti filaments together with density contours (white) on the left, and Te on the right. The redcircles show the stripes of Te on the divertor, which are less distinct for Ti . b) shows profiles of Te on the divertor fordifferent mode numbers. Different numbers of stripes are also observed for different ELMs in pulse 73569 (above).Figure 3:The density and temperature profiles from the HRTS(left) compared to simulation results (right) for shot# 73569.As another example of comparisonsbetween simulations and experiments,Fig.3 shows the HRTS profiles beforeand after ELMs from shot 73569, andthe profiles taken from simulation atthe same position as HRTS, beforeand after a crash. The main interestof such a comparison is to look atthe convective/conductive ELM losses,and the ELM-affected area, which givesthe penetration of the ELM into thepedestal. As seen from Fig.3, the sim-ulations are in reasonable agreementwith experiments.4. Collisionality ScanIn the multi-machine collisionalityscan done by Loarte [1], the ELMs size is shown to increase with decreasing collisionality.This result is most important for ITER, which should run at even lower collisionality than JET.It is therefore of interest to produce a collisionality scanwith simulations, in order to check ifsimulated ELMs can reproduce the experimental scaling. Furthermore, such a scan could helpunderstand why the ELMs size is increasing at lowerν∗.To get such a scan with simulations, density and temperatures are varied together such thatthe total pressure profile does not change. This way, the ideal MHD stability properties of theplasma remain identical, but collisionality changes. The principal parameters that are affectedby this scan are the resistivityη and the parallel thermal conductivityκ‖, which vary asη ∼ ν∗16andκ‖ ∼ ν∗−1. It is not yet possible to use the proper experimental valuesfor η andκ‖, dueto limited numerical resolution, but recent progress in parallel computing, as with the HPC-FF,enables simulations withη andκ‖ values closer and closer to experimental conditions.37th EPS Conference on Plasma Physics O2.106Figure 4:A collisionality scan done for two dif-ferent regimes. A resistive regime (blue) and amore ideal regime (red) with lower resistivity. Thedifferent signs stand for different mode numbers.A first scan has been done with collisionalityvarying from 1.4× 10−2 to 0.9, with a resistivityvarying from 5.10−8 to 10−7. The result is that theELMs size is decreasing with decreasing collision-ality, which is mainly due to the fact the resistivityhas a strong influence on the growth rates of the bal-looning modes. Hence, in this resistive regime, theresistivity dominates the collisionality scan, and theresult is opposite to that expected.A second collisionality scan was then run withlower (a factor 10) resistivity (which comes a fac-tor 20 from the theoretical Spitzer resistivity). How-ever, at lower resistivity, the ballooning modes arestable to the pressure profile, so the pedestal widthwas reduced from 2.8cm to 1.5cm. The results ofthis second scan are closer to experiments, and theELMs size is seen to increase with decreasing col-lisionality. Furthermore, the growth rates show that resistivity does not have such a strong ef-fect anymore, so that the parameter of merit becomesκ‖, which evacuates more temperaturefrom the pedestal at low collisionality. Hence, as collisionality decreases,∆TELM/Tped increaseswhile ∆ρELM/ρped remains almost constant.5. ConclusionsSimulations of ELMs were obtained for the JET pulse # 73569. The transition from exper-imental data to numerical simulations was presented, and basic features of ELMs simulationswere analyzed. The stripes observed on the targets in simulat ons are similar to those seen inexperiments. As an example of comparisons with experimentsstood the fact that the number ofstripes on the divertor increases with increasing ballooning mode number.The second part of this paper presented a collisionality scan for ELMs for the base case ofpulse 73569. At relatively high resistivity (η ∼ 10−8 − 10−7) the ELMs size decreases withdecreasing collisionality, which is opposite to what is observed in experiments, at least forstandard type-I ELMs. At lower resistivity (η ∼ 10−9−10−8), the regime is more ideal, so thatthe ballooning modes are really destabilized by the pressurgradient, not by resistivity. In thiscase, the ELMs size does increase with decreasing collisionality. It should also be noted that aresistive regime is not necessarily an artifact from simulations, and that the ELMs simulated forhigh resistivity could correspond to ELMs other that type-I.AcknowledgmentsThis work, supported by the European Communities under the contract of Association between EURATOM and CEA, was carried outwithin the framework of the European Fusion Development Agreement. The views and opinions expressed herein do not necessarily reflectthose of the European Commission.[1] A. Loarteet al., Plasma Phys. Control. Fusion45 1549-1569 (2003)[2] B. Bazylevet al., Phys. Scr.T128 229-233 (2007)[3] J.P. Freidberg, ’Ideal Magneto-Hydro-Dynamics’ISBN-13: 978-0306425127[4] G.T.A. Huysmans and O. Czarny,Nucl. Fusion47 659-666 (2007)[5] G.T.A. Huysmanset al., Plasma Phys. Control. Fusion51 124012 (2009)[6] M.N.A. Beurskenset al., Nucl. Fusion49 125006 (2009)[7] O. Sauteret al., Phys. Plasmas6 2834 (1999)37th EPS Conference on Plasma Physics O2.106

Simulation of ELMs in JET

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Simulation of ELMs in JET

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