Carvalho, I.

Dunne, M.

Frassinetti, L.

Frigione, D.

Garzotti, L.

Labit, B.

Lomanowski, B.

Maslov, M.

Radovanovic, L.

Rimini, F.

Schneider, P.

Sergienko, G.

Sheikh, U.

van Eester, D.

Vianello, N.

Wolfrum, E.

English

MPG.PuRe

Ideal ballooning modes in the ASDEX-Upgrade, JET and TCV pedestalsM. G. Dunne1, L. Frassinetti2, B. Lomanowski3, U. Sheikh4, N. Vianello5, E. Wolfrum1,L. Radovanovic6, I. S. Carvalho7, D. Frigione8, L. Garzotti9, B. Labit4, M. Maslov9,F. G. Rimini9, G. Sergienko10, P. A. Schneider1, D. van Eester11, The ASDEX UpgradeTeam∗, The EUROfusion MST1 Team†, JET contributors††, the TCV Team‡1Max Planck Institute for Plasma Physics, Boltzmannstr. 2, 85748 Garching, Germany, 2Division of FusionPlasma Physics, KTH Royal Institute of Technology, Stockholm SE, 3Oak Ridge National Laboratory, Oak Ridge,TN 37831, USA 4Ecole Polytechnique Fédérale de Lausanne (EPFL), Swiss Plasma Center (SPC), Lausanne,Switzerland, 5Consorzio RFX, Padova, Italy 6Institute of Applied Physics, TU Wien, Fusion@ÖAW, 1040 Vienna,Austria, 7Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, Universidade de Lisboa, 1049-001Lisboa, Portugal, 8Università di Roma Tor Vergata, Via del Politecnico 1, Roma, Italy, 9United Kingdom AtomicEnergy Authority, Culham Science Centre, Abingdon, Oxon, OX14 3DB, UK, 10Forschungszentrum Jülich GmbH,Institut für Energie- und Klimaforschung, Plasmaphysik, 52425 Jülich, Germany, 11Laboratory for PlasmaPhysics LPP-ERM/KMS, B-1000 Brussels, Belgium, ∗See author list of H. Meyer et al. 2019 Nucl. Fusion 59112014, †See author list of B. Labit et al. 2019 Nucl. Fusion 59 086020, ††See the author list of ‘Overview of JETresults for optimising ITER operation’ by J. Mailloux et al. to be published in Nuclear Fusion Special issue:Overview and Summary Papers from the 28th Fusion Energy Conference (Nice, France, 10-15 May 2021), ‡Seeauthor list of S. Coda et al. 2019 Nucl.Fusion 59 112023A complete understanding of pedestal structure and limits remains an open question in fusionresearch. Research in this direction generally makes use of some generalised version of theEPED model[1]; transport mechanisms (which can have different drives for the particles andheat, and for ions and electrons) determine, in combination with the heat and particle sources,the profile gradients. In the ”standard” case, the profiles continue to extend radially furtherinwards away from the separatrix until there is enough free energy in the pressure gradient (andassociated driven edge current density) that a large magnetohydrodynamic (MHD) instabilityoccurs, the so-called edge localised modes (ELMs). The onset of the ELM then determines thesteepest and widest pedestal pressure profile.The onset of the ELM is often rather sudden, which has inspired the use of ideal MHD to de-scribe the critical pre-ELM profiles. Many publications have shown good agreement betweenthe peeling-ballooning (PB) model (coupled modes driven by the current density and pres-sure gradient) and experimental observations. More recent work on ASDEX Upgrade (AUG),JET-ILW, and TCV have shown the importance of the location of the pressure gradient profilerelative to the separatrix; experiments shifting the density profile peak radially outwards show47th EPS Conference on Plasma Physics P4.1038significantly reduced performance, which is reproduced by the models).Despite the general success of the PB model, there are some notable exceptions. Many, thoughby no means all, cases in JET with the ITER-like wall (Be main chamber and W divertor)do not agree with the predictions of PB, indicating that some physics must be missing[2]. Inaddition, recent work investigating the parameter space of no/small-ELM regimes[3] proposesa transport-limited pedestal, where a radially small mode close to the separatrix creates enoughtransport to hold the pedestal short of the PB limit. With these exceptions in mind, the aim ofthis work is to examine pedestal transport in combination with PB stability for the three devices,AUG, JET, and TCV.While the determination of the active transport mechanism in the pedestal via gyrokinetic sim-ulations remains open, there are two main hypotheses for modes which are expected in thepedestal: the kinetic ballooning mode (KBM), as proposed in the EPED model and; the electrontemperature gradient (ETG) mode. Evidence for the latter was presented by Schneider et al.[4];a constant average gradient length in the pedestal in three devices of ca. 2 cm.The methodology followed here starts with fetching the pedestal profiles from each of the ma-chines. Due to different data gathering, storage, and fitting methods at each machine, this is han-dled on a case-by-case basis. Once this is done, ”a self-consistent path” is created, following thestrategy described in[5]. A single equilibrium representative of the time window in which theprofiles are fitted is loaded (an exact equilibrium is not necessary at this point, as only the plasmaboundary, an approximate q-profile, and the total stored energy are required). Using these ex-perimental data as a base, the pedestal Te and Ti profiles are scaled up and down (assuming aconstant density profile and fixed temperature pedestal width) to create a range of pedestal pres-sures. 0 0.5 1 1.5 2 2.5 3 0.2  0.3  0.4  0.5  0.6  0.7  0.8  0.9  1Te,ped/Ip (keV/MA)ne,ped/(nGW)AUGJETTCVFigure 1: Normalised temperature vs normaliseddensity for the three devices; AUG (purple), JET-ILW (green), and TCV (blue). The dashed lines de-pict lines of constant βθFor TCV and JET, the core profiles are scaledto match the experimental beta, for AUG thefast-ion content is calculated using the RAB-BIT code and added to the thermal profiles(which are well known for both ions and elec-trons across the full radius). Next, the edgecurrent density is calculated self-consistentlyusing the Redl model[6] and a parabolic corecurrent is created to match the experimental plasma current. Finally, the range of pressure andcurrent density profiles are used along with the plasma boundary as input to the HELENAequilibrium code (which also calculates the n=∞ stability profile) and finally to the MISHKA47th EPS Conference on Plasma Physics P4.1038ideal-MHD stability code for global pedestal stability.To give an impression of the data set used for this study, a plot showing the pedestal top tem-perature normalised to the plasma current as a function of the pedestal top density normalisedto the Greenwald density is shown in figure 1. This normalisation has the benefit of allowinglines of constant βθ ,ped to be over-plotted, demonstrating that the normalised pedestal heightfrom the three machines overlaps reasonably well (though the JET-ILW data in this data settend towards lower values than AUG or TCV; future extensions will attempt to remedy this). 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0.6  0.8  1  1.2  1.4  1.6  1.8  2  2.2pped,exp / pped,critFmarg,αmaxAUGJETTCVFigure 2: pped,exp/pped,crit,PB vs Fmarg,αmax for AUG,JET-ILW, and TCV. A clear trends of higher Fmargand increasing gap to the PB stability boundary canbe seen for JET-ILW.A starting hypothesis of this work centeredaround the idea that second stability accesswas necessary for good confinement; an ex-ample of this has already been presented forJET-ILW plasmas[7], showing that only plas-mas with second stability access reached thePB boundary. We examined this here by com-paring the peak value of Fmarg (the ratio of then=∞ critical α to the experimental one) to thedistance to the PB boundary for all three devices. The result of this is shown in figure 2. 20 40 60 80 100 120 140 0  10  20  30  40  50  60  70  80R / LTeR / LneAUGJETTCVFigure 3: R/LTe vs R/Lne for AUG, JET-ILW,and TCV. While AUG and TCV overlap, JET-ILWpedestals exist at higher values of R/LTe .While the AUG and TCV data sets lie with-ing a reasonable distance to the PB bound-ary, it has already been seen that the JET-ILWdata are relatively far away. One can also seethat the JET-ILW plasmas have high values ofFmarg, and the higher the value of Fmarg, thefurther away these plasmas are from the PBboundary. A value of Fmarg close to one (orsecond stability access) appears to be a nec-essary criterion for PB instability (one sees at high values of pexp/pcrit an increase of Fmargagain; this is due to local second stability access in the middle of the pedestal). This impliesthat if the pedestal transport is not governed by MHD-like mechanisms that it will not reach thePB boundary. This result may not be surprising, but the analysis here highlights the differencesbetween JET-ILW and AUG/TCV for both PB stability and potential transport mechanisms.Given the lack of PB instabilities or KBM/ideal-ballooning transport in the analysed JET-ILWplasmas, it is interesting to investigate other transport mechanisms, as already suggested in[2]. To this end, the gradient lengths of electron temperature and density averaged over the47th EPS Conference on Plasma Physics P4.1038pedestal width are shown for the three devices in figure 3. The gradients for this plot are takenas a function of rminor,OMP; the general relations shown here do not change when taking thegradients against ΨN or any other normalised radius. While the AUG and TCV data lie on topof one another in this space, the JET data are notably shifted to higher R/LTe , implying highertransport (particularly for a given value of Lne). It should be noted in addition that although ahigh separatrix density (or high Lne , see figure 4, which is strongly correlated) is observed ineach device to degrade confinement, it does not necessarily provide a correlation to the departurefrom the PB boundary.In conclusion, the implemented workflow allows a comparison of pedestal stability across mul-tiple devices. The study has highlighted key areas in which the AUG and JET-ILW data sets pre-sented here could be easily extended to improve overlap (notably towards higher ne,sep/ne,pedin AUG and lower ne,sep/ne,ped in JET-ILW); the present data sets were chosen simply for prac-tical reasons of an established data set in AUG and divertor diagnostic coverage in JET-ILW.These data exist on both devices, but have not yet been included in the analysis. 0 10 20 30 40 50 60 70 80 0.1  0.2  0.3  0.4  0.5  0.6  0.7  0.8  0.9  1R / Lnene,sep/ne,pedAUGJETTCVFigure 4: ne,sep/ne,ped vs R/Lne for AUG, JET-ILW,and TCV.The comparison of distance to the PBboundary with the local ballooning stabilitymargin highlights the importance of under-standing the transport in the pedestal not onlyfor predictive purposes, but also for max-imising performance. The JET-ILW data set,which exhibits higher transport when com-pared to AUG and TCV, exists at lower βθ ,pedand further away from the stability boundary. Given the strong link between divertor conditionsand the ne,sep/ne,ped ratio (or, alternatively, and perhaps more importantly, the density gradientlength) known from all three devices, this indicates that the density pedestal is key to under-standing the overall pedestal structure and stability.References[1] P. B. Snyder, et al. Physics of Plasmas, 16(5), 2009.[2] L. Frassinetti. IAEA FEC, 2021.[3] G F Harrer, et al. Nuclear Fusion, 58(11), 2018.[4] P.A. Schneider, et al. Plasma Physics and Con-trolled Fusion, 56(2), 2014.[5] S. Saarelma, et al. Physics of Plasmas, 22(5), 2015.[6] A. Redl, et al. Physics of Plasmas, 28(2), 2021.[7] C. Bowman, et al. Nuclear Fusion, 58(1), 2018.This work has been carried out within the framework of the EUROfusion Consortium and has received fundingfrom the Euratom research and training programme 2014-2018 and 2019-2020 under grant agreement No 633053.The views and opinions expressed herein do not necessarily reflect those of the European Commission. This workwas supported in part by the Swiss National Science Foundation.47th EPS Conference on Plasma Physics P4.1038

Ideal ballooning modes in the ASDEX-Upgrade, JET and TCV pedestals

http://hdl.handle.net/21.11116/0000-0009-AA9E-6

Ideal ballooning modes in the ASDEX-Upgrade, JET and TCV pedestals

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