Possible influence of near SOL plasma on the H-mode power threshold

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Nuclear Materials and Energy

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Possible influence of near SOL plasma on the H-mode power threshold

A.V. Chankina^a,∗, E. Delabie^b, G. Corrigan^c,C.F. Maggi^c,H. Meyer^c, JET Contributors^a,b,c,1

a Max-Planck-Institut für Plasmaphysik, Boltzmannstr.2, Garching bei München 85748, Germany

b Oak Ridge National Laboratory, Oak Ridge, TN, USA

c CCFE, Culham Science Centre, Abingdon, UK

a rt i c l e i n f o

Article history:

Available online 26 October 2016 Keywords:

Plasma-materials interaction Plasma properties H-mode SOL Divertor JET

EDGE2D-EIRENE

a b s t r a c t

AstrongeffectofdivertorconfigurationonthethresholdpowerfortheL-Htransition(P_LH)wasobserved inrecentJET experimentsinthenewITER-likeWall(ILW)[1–3].FollowingaseriesofEDGE2D-EIRENE codesimulationswithBe impurityand drifts apossible mechanismfor thePLH variation withthedi- vertorgeometryisproposed.Bothexperimentandcodesimulationsshowthatintheconfigurationwith lowerneutralrecyclingneartheouterstrikepoint(OSP),electrontemperature(Te)peaksneartheOSP priortotheL-Htransition,whileintheconfigurationwithhigherOSPrecyclingTepeaksfurtheroutin thescrape-off layer (SOL)andthe plasmastaysintheL-modeatthe sameinputpower. Coderesults showlargepositiveradialelectricfield(Er)inthenearSOLunderlowerrecyclingconditionsleadingtoa largeE×Bshearacrosstheseparatrixwhichmaytriggerearlier(atlowerinputpower)edgeturbulence suppressionandlowerP_LH.SuppressedT_e‘satOSPinconfigurationswithstrikepointsonverticaltargets (VT)wereobservedearlierandexplainedbyageometricaleffectofneutralrecyclingnearthisparticular position,whereasinconfigurationswithstrikepointsonhorizontaltargets(HT)theOSPappearstobe moreopenforneutrals(seee.g.reviewpaper[4]).

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1. Introduction

There is growing experimental evidencefor a strong effectof divertor configurationon thethresholdpower fortheL-H transi- tion(P_LH) (seee.g.[1–3] andrefs.therein).Recent experimentsin JETintheITER-like(Be/W)wallshoweda factoroftworeduction ofP_LH inaconfigurationwiththeouterstrikepoint (OSP)onthe horizontaltile5(hence,‘HT’configurationofpulse#81883) com- paredtothatwiththeOSPontheverticaltarget(hence,‘VT’con- figurationofpulse#84727),seeFig.1,observedinthehighdensity branch where P_LH increases withplasma density. The two mag- netic configurationswiththeplasmacurrent2.0MAandtoroidal field 2.4T, aswell as plasmaparameter profiles, were similar in thecore,insideofthemagneticseparatrix.Sometimestracesfora pulsesimilar tothe #81883pulseintheVTconfigurationcan be foundin[5].

R EUROfusion Consortium, JET, Culham Science Centre, Abingdon, OX14 3DB, UK.

∗ Corresponding author.

E-mail addresses: Alex.Chankin@ipp.mpg.de , avc@ipp.mpg.de (A.V. Chankina).

1 See the Appendix of F.Romanelli et al., Proceedings of the 25th IAEA Fusion Energy Conference 2014, Saint Petersburg, Russia.

With no significant difference between global parameters in these two pulses, it wasconcluded that the explanation for the differenceinP_LHmayberelatedtoadifferenceofplasmaparame- tersintheextremeedge:inthescrape-off layer(SOL)anddivertor.

EDGE2D-EIRENE[6–8]simulationsreproducedalargedifferencein experimentaltargetprofileswhicharedescribedbelow,leadingto alargedifferenceisradialelectricfield(E_r)which,inturn,mayin- fluenceplasmaturbulencearoundtheseparatrixlocationviaE× B shear[3].

It has to be noted that large differences between target pro- filesindivertorconfigurationswithstrikepointsonhorizontaland vertical tiles were observed earlierin differentmachines andat- tributed to different neutral recycling patterns: in VT configura- tions, neutralsrecycling fromthetarget had largerprobability to beionisedonfluxsurfaceshittingthetargetnearthestrikepoint, compared with HT configurations, which appeared to be more open to neutrals (see e.g. review paper [4]). Consequently, mea- suredelectrontemperature(Te) hadatendency topeak nearthe strikepoint inHT configurations,while beinglower atthe strike pointinVTconfigurations.One expectssimilarbehaviour incon- figurations showninFig.1, justthat thisdifference shouldapply

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Fig. 1. Magnetic configurations of the HT (#81883) and VT (#84727) discharges in the divertor.

onlytoOSP, sinceinner strikepoints(ISP)areon verticaltiles in bothconfigurations.

2. SetupofEDGE2D-EIRENEcases

EDGE2D-EIRENE grids were built using magnetic equilibria of JETpulsesshowninFig.1.Thegridswereoptimisedfornumerical stabilityofthecoderunsinthepresence ofparallel currentsand drifts. The optimisation wasmainly aimed at avoiding very nar- rowseparationbetweenradial‘rows’insomepartsofthegrid,e.g.

alongtherowconnectingtheX-pointwiththeinner targetalong theseparatrix,whichresultedinverysmallcellsizes. Sincesharp switchingofdriftsoftenleadstonumericalinstabilities,theywere switchedongraduallyacrosstheentirecomputationaldomain.All drifts velocities were multipliedby the coefficient α^{, which was}

raisedlinearlyfrom0to1over1mstimeperiod,whichisastan- dard drift-relatedoption in EDGE2D-EIRENE. Material surfaces in the coderuns were assumed as in the ITER-likewall (ILW), and ionspecies included deuterium (D) and beryllium (Be) withthe latterbeingphysicallysputteredfromthewall.Tungsten (W)was not included in the ion mixture, as W concentrations inside of theplasmacoveredbytheEDGE2D-EIRENEgridwerefoundtobe negligible.A neoclassicalself-consistent model for Er wasimple- mented in the core which impeded surface averaged radial cur- rents.

TheEIRENEversionwithKotov-2008model[9]wasusedtode- scribeneutralbehaviour.The plasmadensitywascontrolledby a combinationofgaspuff fromthePFRandwallrecycling(‘puff+re- cycling’optioninEDGE2D-EIRENE),aiming atmaintainingaspec- ifiedelectrondensityattheoutermidplane(OMP)positionofthe separatrix,ne,sep. Dueto some difference inline averageelectron density(largerby∼8.5%intheHTpulse),asomewhathigherelec- tronseparatrix densityatOMP intheHTcase,ne,sep=1.2e19m⁻³, comparedto 1.0e19m⁻³ in VT,wasspecified.Thesechoiceswere partlymotivatedby theknowneffectofa non-lineardependence ofne,sep online-averagedensityatlow to medium densities,and partlybythedesiretomatchtargetprofilesmeasuredbyLangmuir probes.

Theinputpowerintothegridwassetat2.7MWinbothcases, tomatchexperimentalpowerbalance.Inthecode,theinputpower wasequallysplitbetweenionandelectronchannels.

Divertor andtarget plateparameters in EDGE2D-EIRENEcases are strongly influenced by arbitrarily specified anomalous trans- portcoefficients.Betweenionandelectronheatconductivities,and particlediffusioncoefficient,oftenthe relationχe,i=2/3D_⊥ isas-

sumed.Atthesametime,inrecentEDGE2D-EIRENEsimulationsof JET -L-mode plasmas itwas found that better matchwith target Langmuirprobemeasurements canbe achievedifχ^e≈ D⊥ across mostoftheSOLandPFRisassumed,withD_⊥beingreducedinthe outercoreandSOLregionsaround theseparatrix position[10].In thesimulationsdescribedhere,thefollowingtransportcoefficients were assumed:D_⊥=1m²s⁻¹ andχi=2m²s⁻¹ across thewhole grid, χ^e=1m²s⁻¹ everywhere except forthe main SOL (notin- cludingthedivertor)whereitwasreducedto0.5m²s⁻¹.

Physical sputteringmodelforBeimpurity wasassumed.In all EDGE2D-EIRENE cases, however, Be radiation represented only a fewpercent ofthe totalradiatedpowerwhichwasdominatedby thedeuteriumLymanalpharadiation.Thesameresultcomesfrom theexperiment[11].Also,target T_e,i andneprofiles incaseswith Bewerequiteclosetothosewithpuredeuterium.

Catalogued EDGE2D-EIRENE cases can be found in: alexc/edge2d/jet/81883/nov1015/seq#1 for HT and alexc/edge2d/jet/84727/nov1015/seq#1forVTconfigurations.

3. ComparisonbetweenEDGE2D-EIRENEoutputand experimentalresults

Fig.2showsexperimentalLangmuirprobeandEDGE2D-EIRENE simulated target profiles of Te, ne and ionsaturation current jsat

along inner and outer targets in both configurations, mapped to radial positionsatOMP.Theprofiles areplottedvs.distancefrom the separatrix (strikepointson both targets)which are indicated by horizontaldash-dotted linesmapped to positions atthe OMP.

Duetouncertaintiesintheequilibriumreconstructionexperimen- talprofileswerearbitrarilyshifted(ITprofilesby0.5cminbothHT andVTcases,andOTprofilesby1.2cmintheHTand1.7cminthe VTcase,all shiftstowards thehighfieldside)andtheir positions on the targetswere converted intodistances from theseparatrix usinglinearinterpolationbasedonEDGE2D-EIRENEpositions.

Themostimportantfeatureofthecoderesultsisamuchmore peaked Te at OT in the HT configuration, obtainedfor the same input parameters asin VT (even, in the more challenging setup, witha 20% higherne,sep). This isrelatedto the recycledneutrals beingionised morestronglyalong the separatrix intheVT,com- paredtoHTconfigurations,whichisapurelyballisticeffectofre- cyclingneutrals[4].Thisresultsinlowertarget Teandhighertar- getn_e nearstrikepointsatoutertarget (OT)intheVTcompared tothe HTconfiguration.Atthe innertarget (IT),the situationre- gardingcodetotheexperimentcomparisonissimilarforthetwo configurations,sincetheconfigurationsarealmostthesameonthe inner(high field)side.It hastobenotedthat resultsanalyzedin [4] were obtainedin machineswith carbon walls, while experi- mental andcode results presented hereare obtained in theILW environment on JET. One of the consequences of this change is the lossof the intrinsicradiator(C) in ILW: W concentrationsin theSOLanddivertorarenegligible,whilesomeBesputteringfrom themainchamber (Be)walldoesn’tleadtohighenoughradiation losseswhichwouldstronglyinfluencetheradiationpatternestab- lishedby themain workinggas (usuallyD)radiation.Asa result, anintroductionofnon-intrinsicimpurities(N,Neetc.gases)isre- quiredtoincrease radiationintheSOLanddivertor.All theseas- pects,focusingonthedifferencebetweentheCandILWenviron- mentsarediscussedinthereviewpaper[12].

In the HT configuration, all code OT parameters are more peakednearthestrikepointandlargerthanexperimentalonesin the commonfluxregion (CFR), onthe main SOLrings. According to the probes, there exists the plasmain the private flux region (PFR),especiallyattheoutertarget,whichisnotseeninthecode output. The reasonforthisstrong discrepancymay be relatedto deficiencies of the transport model used in the code or the ne- glectofneutralleakagesfromdivertorstructures(see[12]andrefs.

Fig. 2. Experimental (triangles) and EDGE2D-EIRENE (dots) target profiles of electron temperature (T e ), electron density (n e ), and ion saturation current density (j sat ) in HT (a) and VT (b) configurations. Note the inverted X-scale for the left target.

Fig. 3. Measured (blue dotted line) and simulated (red solid line) D αemission profiles in the divertor in HT (a) and VT (b) configurations. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

therein).Theprobepointwiththelargestj_satatOTisunreliable.At ITprobetargetTe‘snearthestrikepointandinthePFRaremuch greater thanthe codevalues.Itis knownhoweverthat Langmuir probeT_e‘sbelow∼5eVareunreliable.Thismaypartlyexplainthe discrepancyinITne,aslowerexperimentalTewouldimplyhigher ne,closer tothe code values(notethat jsat valuesare fairly well matched atIT).AtOT inboth cases,thecodeneis muchgreater thanexperimentalvalues,whichcanbeattributedtoanunderesti- mateofthedegreeofdetachmentinthecode,evidencedbyfactor two higherjsat inthecodethanintheexperiment.Thedegree of detachmentatthetargetisoftenunderestimatedin2Dfluidcodes (seee.g.[13]).

A bettermatch betweenthecode andexperimentisachieved in the VT configuration. Still, at OT j_sat is overestimated by the code, and due to somewhat lower code Te, ne is overestimated evenstronger.Again,asinthecaseoftheHTconfiguration,probe T_e’sdonotfallsignificantlybelow10eVand,ascommentedabove, such relativelyhighvaluescan’tbetrusted, especiallydeepinthe PFR.

Fig.3shows experimental and simulated D_α emission profiles alongverticalchannelslookingintothedivertor.Fairlyreasonable matchbetweenthe experiment andsimulations is seenat OT in bothconfigurations,takingintoaccountalluncertaintiesassociated with the neutral model and perpendicular transport coefficients adoptedin EDGE2D-EIRENE runs. A considerablediscrepancycan beseen atIT, withexperimentalD_α emission beingmuchhigher, indicatingamuchstrongerdegree ofdetachmentatthistarget in theexperimentcompared tothe codesimulations. The D_α radia- tionshortfallinthemodelinghasbeenreportedearlierandrelated toan insufficienttarget T_e dropinthe code,which,inturn,may berelatedtomolecularpowerlosstermswhicharepresentlynot properlyaccountedforinEDGE2D-EIRENE,seee.g.[14–16].

4. Radialelectricfield(Er)profilealongoutermidplanefrom EDGE2D-EIRENEoutput

ExperimentalErdata forthepulsesanalysed inthispaperare unavailable.Fig.4showsErprofilevs.distancefromtheseparatrix

Fig. 4. Simulated E r profiles along OMP for HT and VT configurations.

alongOMPcalculatedbyEDGE2D-EIRENE.Thecleardifferencebe- tweenthetwocasescanbeseen,withthecaseinHTconfiguration showingalargepositiveEr spikeneartheOSP,withlargepositive valuesalsoinafewother,adjacentpositionsinthenearSOL.This canberelatedtoaspikeinT_einthisconfigurationcausingpositive plasmapotentialupstreamofthetargetwhichistoalargeextent attributedtothe potential sheath dropat thetarget |eV_sh| ∼3Te. Sinceanelectrically conductingtarget (W)hasconstantpotential, positiveEr≡ −∇^rVsh inthe plasmaemerges forradially decaying TeintheSOL.Incontrast,intheVTconfigurationErisnegativein thenearSOL,sinceTerisesradially.IntheoutercoreEr<0,caused byionpressureandtemperaturegradients(notoroidalmomentum inputwasassumedinthecoderuns).Aparticularlylargeshearof poloidalEr× Brotationis thereforeformedneartheseparatrix in theHTconfiguration.

InFig.4ErvaluesatthefirstSOLringoutsideoftheseparatrix (ring‘s01’)arenot plotted.ThishastodowiththewayEriscal- culatedinthecode.Onthecore(poloidal)ringstheprimaryvalue isEr: the self-consistent neoclassicalsolution forEr ensures zero surfaceaveragedradialelectriccurrentsbetweenrings.Plasmapo- tentialsarecalculatedlaterusingE_rvalues.Incontrast,intheSOL electricpotentialistheprimaryquantity,calculatedassumingzero targetpotential andtakingintoaccountparallel electronmomen- tumbalanceequation andapossibility ofelectriccurrentstothe targetsurface. Er intheSOListhen calculatedbysubtracting po- tentialsbetween neighboringrings. Calculationof Er on ring s01 therefore requires subtraction of the potential on the outermost corering(c01)fromthat onrings02,whichisthesecond ringin theSOL.InEDGE2D-EIRENE nomodelisused toelectrically con- nectthetwotopologicallydisconnectedregions:coreandSOL,and anarbitraryvaluecanbeaddedtopotentialsinthecore.Forplot- tingthepotentialacrossbothcoreandSOL,potentialsareassumed equalonringsc01ands01attheOMPposition.Thisarbitraryelec- tricallinkbetweentheregionscreatesanuncertaintyintheE_rcal- culationatrings01. ForthisreasonErvaluesonringss01are ig- nored.Positions ofpointsc01, s01, s02 ands03 atthe equatorial planewithrespecttotheseparatrixpositionare:−0.07,0.04,0.11 and0.19cm,whichensuregoodspatialresolutionevenintheab- senceoftheErdataatpositions01.

5. Discussion

ThemainpurposeoftheEDGE2D-EIRENEmodelingactivitywas to compareHT andVTconfigurations forthe same modeling as- sumptionsaboutpowerflowintothecomputationaldomain,sepa- ratrixdensity,plasma-wallinteraction,neutralbehaviouretc.,since thefocus wason theeffectofneutralsinthe twodifferentmag- neticconfigurations.Atthesametime,coderesultsweretobeob- tainedunderconditionswhicharerelevanttoJETpulsesatpower levelswherethe plasmaintheHTconfigurationgoesintotheH- mode,whileinVTconfigurationitstaysintheL-mode.Thisdeter- minedthechoiceofseparatrixdensitiesandtransportcoefficients inEDGE2D-EIRENEsimulations.

ThecleardifferenceinTe profilesatoutertargetsbetweenthe two configurations has beenobserved andinterpreted earlier,as explained in the Introduction section. In the present code simu- lations strongdifference intargetprofiles expectedinHTandVT configurationsisseeneventhoughne,sepwaschosentobehigher inHTcomparedtotheVTconfiguration,emphasisingaverystrong impact of the divertor configuration on neutrals behaviour and theirimpactontargetTeprofilesandErattheOMP.

Itisworthnotingthat thepeakTe valueatOT isprobablynot soimportant,fromtheviewpointofthemechanismofturbulence suppression by the E × B shear, if it is achieved farther in the

‘outer SOL’, where plasma densities and temperatures are much lower than in the ‘near SOL’. The main difference in Er profiles betweenthetwo configurations,withthemuch largerE×Bshear around the separatrix location in the HTconfiguration, isdue to differentneutralbehaviourattheOSPandimmediatelyupstream ofthisposition,whichseemtobethekeylocationsforthismech- anism.

In JET experiments it is observed that, as the input power is raised,the L-Htransitionisprecededby detachmentatthe inner target[3].EDGE2D-EIRENErunswereunabletosimulatetheinner targetdetachment,andtheinnertargetTewasconstantlyincreas- ing withtheinput power. Thismayindicate missingelementsin the plasmaorneutralmodels ofthe code,orthe need tohigher transport coefficients at highinput powers. Test EDGE2D-EIRENE caseswithtransportcoefficientsvariedproportionallytotheinput power have howeverfailed to simulatestronger inner target de- tachmentwithincreaseintheinputpower.

6. Summary

Thereisgrowingexperimentalevidencefromanumberofma- chinesforastrongeffectofdivertorconfigurationonthethreshold power forthe L-H transition (P_LH). Recent experiments in JET in theITER-like(Be/W)wallshowedafactoroftworeductionofP_LH inaconfigurationwiththeouterstrikepoint(OSP)onthehorizon- taltarget(HT)comparedtothatwiththeOSPontheverticaltarget (VT)observedinthehighdensitybranchwhereP_LH increaseswith plasmadensity(forthe ‘highdensitybranch’see e.g.linearlyris- ing partofP_LH vs. multi-machineMartin’sscaling forinputpow- ers above 2.5MWin [17]). The two magnetic configurations and plasmaparametersweresimilarinthecore.

In search of a possible explanation for the P_LH difference, EDGE2D-EIRENE code simulations withdrifts aimed atreproduc- ing Langmuirtarget profilesandD_α emissioninthe divertor,but havingthesame transportcoefficientsforthetwo configurations, were carried out. Bothin the experimentand inthe code simu- lated outer target T_e shows a spike at the OSP and then decay across the SOL in the HT configuration, whereas in the VT con- figuration Te is low at the OSPand rising in the near SOL (first

∼0.7cm),withpeaktargetTe‘sbeingsimilarinthetwocases(20–

25eV). TheeffectofrecyclingneutralsontargetTeprofilesindif- ferentdivertorconfigurationswasstudiedearlierandattributedto

the ionisationpatternof recyclingneutrals:whether theyare re- cycled towards the field linestriking the target at the separatrix locationorawayfromit.

ThedifferenceintargetT_eprofilesresultsinthedifferenceofE_r profilesintheSOL,duepartlytotheeffectofthepotentialsheath drop:|eV_sh|∼ 3Te,henceEr≡ −∇^rVsh>0fortheHTand<0forthe VTconfiguration,forconstanttargetpotential.WithnegativeE_rin theouter core,apositiveEr spikeinthenearSOL,justoutsideof the separatrix, generates a particularlylarge poloidal E× B shear inthe HTconfiguration.Itis hypothesisedthat theextremeedge E× B shear effect on the local turbulence suppression mayhave an impact onthe L-Htransition, leadingto lower P_LH indivertor configurationswithlessionisationofrecycledneutralsatthestrike pointandupstreamofit.

Acknowledgements

This project has received funding from the Euratom research andtrainingprogramme(grantNo633053)2014–2018.The views andopinionsexpressed herein donot necessarilyreflect thoseof theEuropeanCommission.

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