Improved ERO modelling for spectroscopy of physically and chemically assisted eroded beryllium from the JET-ILW

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ContentslistsavailableatScienceDirect

Nuclear Materials and Energy

journalhomepage:www.elsevier.com/locate/nme

Improved ERO modelling for spectroscopy of physically and chemically assiste d erode d b eryllium from the JET-ILW

^✩

D. Borodinâ^,^∗, S. Brezinsekâ, I. Borodkina^b^,â, J.Romazanovâ,D. Matveevâ,A. Kirschnerâ, A. Lasa^c,K. Nordlund^d, C. Björkas^d, M.Airila^d, J.Miettunenê, M.Grothê,M. Firdaouss^f, JETContributors¹

a Forschungszentrum Jülich GmbH, Institut für Energie- und Klimaforschung - Plasmaphysik, 52425 Jülich, Germany

b National Research Nuclear University MEPhI, 31, Kashirskoe sh., 115409, Moscow, RF

c Oak Ridge National Laboratory, Oak Ridge, TN 37831-6169, USA

d VTT Technical Research Centre of Finland, P.O.Box 10 0 0, FIN-02044 VTT, Finland

e Aalto University, P.O.Box 14100, FIN-00076 Aalto, Finland

f CEA, IRFM, F-13108 St Paul-Lez-Durance, France

a rt i c l e i nf o

Article history:

Available online 18 October 2016 Keywords:

Beryllium Erosion JET ITER-like wall Spectroscopy

a b s t ra c t

PhysicalandchemicalassistedphysicalsputteringwerecharacterisedbytheBeIandBeIIlineandBeD bandemissionintheobservationchordmeasuringthesightlineintegratedemissioninfrontoftheinner berylliumlimiteratthetorusmidplane.The3Dlocaltransportand plasma-surfaceinteractionMonte- Carlomodelling(EROcode[18])isakeyfortheinterpretationoftheobservationsinthevicinityofthe shapedsolidBelimiter.Theplasmaparametervariation(densityscan)inlimiterregimehasprovideda usefulmaterialforthesimulationbenchmark.Theimprovedbackground plasmaparametersinput,the newanalyticalexpressionforparticletrackinginthesheathregionandimplementationoftheBeDre- leaseintoEROhashelpedtoclarifysomedeviationsbetweenmodellingandexperimentsencounteredin thepreviousstudies[4,5].Reproducingtheobservationsprovidesadditionalconﬁdenceinour‘ERO-min’

ﬁtforthephysicalsputteringyieldsfortheplasma-wettedareasbasedonsimulateddata.

ThisisanopenaccessarticleundertheCCBY-NC-NDlicense (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Introduction

Estimatingberyllium(Be)sputteringbyplasmaionsisakeyis- sueforITERaserosiondetermines thelife time ofplasma-facing components [1,2] and impacts on the tritium retention by co- depositionwithBe,whichmustbekept withinthenuclearsafety limitofITER.TheﬁrstexperimentalcampaignatJETequippedwith theITER-LikeWall (ILW)[3],withBelimitersandW divertor,in- cludedseveralexperimentsdedicatedtothedeterminationofﬁrst wallerosion.InthepresentpaperwefocusonthreesolidBecom- ponents(‘tiles’)ofthepoloidalguardlimiter(GL)positionedatthe innerwall(IW)closetothemidplane.Thelimiterplasmasshifted

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

∗ Corresponding author.

E-mail address: d.borodin@fz-juelich.de (D. Borodin).

1 See Appendix of F. Romanelli et al., 25th IAEA Fusion Energy Conference (2014, St. Petersburg, Russia)

towardstheIWwereusedtohaveasingleinteractionpointuseful forthedeterminationofBeyields.Themagneticconﬁgurationand plasmacurrentwaskeptunchanged,justtheDfuellingwasvaried leadingtotherespectiveincreaseofelectronicdensitywithanop- positeeffectforitstemperatureandcorrespondingimpactenergy ofsputtering ions.Passive spectroscopyofBeatoms, Beionsand BeD moleculeswere used forthe characterization oferosionand itscontributors.Thisworkisacontinuationandsigniﬁcantupdate ofpreviousstudies[4,5].

3D local transport modelling of eroded Be has been shown previously to be absolutely essential for the interpretation of sightline-integrated spectroscopy [6]. Similar to previous studies we utilize the Monte-Carlo (MC) code ERO for thispurpose. The codeappliesphysicalsputteringdatabasedonmoleculardynamics (MD)[7]andbinary-collision approximationcalculations[8].This dataisbeingbenchmarkedbycomparisonoftheEROsyntheticre- sultswiththeexperimental observations.It shouldbe mentioned thataverysimilarworkgoesinparallelfortheOWofJET[9]. http://dx.doi.org/10.1016/j.nme.2016.08.013

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Fig. 1. The connection lengths simulated by the PFCFlux code [12] along the IWGL limiter surface part (3 tiles) included into the ERO simulation volume.

A numberofimprovements havebeencarried out incompar- ison tothe previous studies. Thebackground plasma(EROinput) wasrevisedincludingplasmaconditionsdeducedfromembedded Langmuirprobes[10].Moreover,theanalyticalexpressionsforthe electric field inthe sheath andforthe very last part ofthe par- ticletrajectory justbefore theioncollisionwiththesurfacewere incorporated [11] providing moreprecise distributions ofion en- ergies and angles withthe surface on deuteron (D) impact. This affects the effectivesputtering yieldat each point ofPFC surface withvarying localB-fieldanglewithit andlocalplasmatemper- ature.Theinfluenceoftheinitialmetastablepopulation [12]after the physicalsputteringonthelight emission isstudied.The con- tributionsofself-sputteringandchemicallyassistedphysicalsput- tering[7]areassessedanddiscussed.

The inclusionof theabove mentionedeffects shallreduce un- certaintiesandgivefurtherconﬁdenceinthemodelsandunderly- ingdata,includingtheﬁtusedfortheBesputteringyields.

Passivespectroscopyand3Dlocaltransportsimulation

Particleseroded fromPFCs, includingthe IWGL considered in the present paper, are released into the plasma, dissociated (for molecules),and ionizedorexcited ata certain distance fromthe surface.Thepenetrationdepthisdeterminedmostlybytheioniza- tionrates,plasmaparameterdistribution,initial directionandve- locityoferodedparticles.Theerosionbythebackgroundplasmais calculatedasmultiplicationoftheDandBeimpurityfluxesbyre- spectiveeffectiveyields(seebelow)forphysicalsputtering.Forthe D-fluxadditionallythechemicallyassistedreleaseofBeDisconsid- ered. Beions arebeing trappedby themagnetic field anddriven bytheplasmaflowandelectricfield.Theseeffectsareeasytode- scribe in a deterministic way. However, the ions alsoexperience stochasticprocesses,forinstance,furtherionizationoranomalous transportoftentreatedlikecross-fielddiffusion.The3DMC simulations of the mentioned processes are proved to be an efficient way to obtain the resulting species density and light emission plumes.TheEROcodefollowsarepresentativeamountofMCtest particles on their waythrough the plasma, calculates their spec- troscopiclightemission(forthelinesormolecularbandsofinter- est,mostlytheonesobservedintheexperiment)andintegratesit withintheobservationchordofthediagnostics.

ItshouldbenotedthatthesurfaceoftheIWGLisonlypartially plasma-wettedduetoshadowingofneighboredlimiterstoroidally separatedfrom the observed one included in the simulations by thefieldtracingPFCFluxcode[13]whichcontainsthedetailedILW geometry(Fig.1).Inafirstapproximationitispossibletoassume that the erosion in the shadowed areas is negligible. In such an approachvariationsalong thelimiter surfacebetweenconnection lengthsbelowthecertainvaluecharacteristicforthelimiterridge isneglected. However, later on,thisapproach can be refinedfol- lowingtheprocedurecarriedoutin[14].

InFig.2thesideviewsoftheEROsimulatedemissionpatterns are shown. The cylindricalsightline (in fact conical,however the

Fig. 2. Be I and Be II light emission in the close to the solid Be shaped IW limiter. ERO simulations for Be sputtered from the wall physically alongside with the simulations for chemically released BeD. Be II plume is determined by the shadowing local transport and ionization/dissociation.

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Fig. 3. D spectroscopy (Balmer- αа nd Balmer- β) characterizing the plasma ion ﬂux to the surface. Experimental results are multiplied by 2 to account for the mostly molecular D release as D 2 which dissociates preferably through the channel with ionization of one of the atoms; this way every second released D atom is lost for the observation.

difference for the small fraction inside the simulation volume is negligible)projectionislabeledintheFigure;itsimpactanglewith thelimiterisalsoindicated.Theobservationgeometryaffectsthe fractionof the emission entering the volume of integration. This fractionvaries withdistance of the plasma withthe limiter due to changing plasmaparameters, species ionization state and MS population.As it can be seen inFig. 2, the emission pattern for the BeD band varies from the one for BeI line emission due to thelargerpenetrationdepthofthemolecules.Botharealsoessen- tiallydifferentfortheBeionswhichareproduced bydissociation ofmoleculesandassociatedionization,aswellasdirectlyionized afterphysicalsputtering.

Improvedplasmaparameters

Ascan beinferredfromtheprecedingsection,ERO resultsare very dependent on the local 3D distribution of plasma parame- ters.For the currentstudies they are reconstructed from theex- perimental data (effective radius profiles), in 2D, for a poloidal cross-section, applyingthe 2-point(onion skin) model[5].More- over,toroidal symmetryisassumedto translatethe dataintothe 3DsimulationboxaroundtheBelimiter.Thenewplasmaparam- etersetwasdevelopedusingthedatafromtheembeddedprobes andre-interpretedspectroscopy.Therevisedelectrontemperature in the plasma background is abouta factor 2 smaller than previously used (Te∼15eV at the separatrix).In addition, theD-flux duringtheplasmadensityscan wasenforcedtofollowtheexper- imentalrampcharacterizedbyD_γ spectroscopymeasuringthere- cyclingflux atthe limiter (Fig.3). The figure showsthat the re- visedplasmabackgroundreproduceswell theD_β/ D_γ ratioanda verysatisfactorysimulationoftheabsolutevaluesintheobserva- tionchord(sightline).

Anothertest forthe plasmaparameters andatomicdata used [15]aretheBeIIlineratios(Fig.4)usedearlierin[6]forTedeter- mination.All3lineratiosarereproducedwell.TheBeIIlevelsys- temdoesnotcontainsignificantmetastables,thusthebehaviourof the lineratios is determined by the photon-emission coefficients presented onthe righthand sideof Fig.4. Thoughthe ratiosin- dicate that the assumed Te is slightlyinsufficient, the deviations (∼20%) are well within the measurement uncertainties. It should be notedthat in Fig. 4 the ratios for physically eroded particles arepresented.ThefractionreleasedasBeDpenetratesdeeperinto theplasmaduetothedissociationandsubsequentionizationand emitslightatlargeTe,soitcanonlyreducetheratiodeviations.

Alast interesting parameter forabenchmark isthe branching ratiobetweenBeDdissociativeionizationtoBeD⁺anddissociation to Be neutrals deduced from the lineintensity drops during the surfacetemperaturescanin[6].Itwasshownthatonly25%ofthe moleculesaregoing throughthe channelBeD+e→BeD⁺+e+e‘.

Fig. 4. Line ratios in Be II sputtered from the IW GL (left) and the relevant photon eﬃcient coeﬃcients from ADAS (right) [14] .

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Fig. 5. Branching rates for the BeD decay reactions contained in ERO databank [15] . At marked T e = 15 eV the fractions are really close to the observed [6] 75%:25% val- ues.

Fig. 6. The effective sputtering yields in ERO and S/XB method measurements [6] (using Be II 527nm line). The influence of the physical sputtering fits for pure Be (‘ERO-max’) and Be with 50%D in the interaction layer (‘ERO-min’) [3] . The influence of the recently implemented analytical expressions [10] is shown (‘analytic’) as well as influence of the intrinsic Be impurity concentration and respective self- sputtering.

The rates for thesereactions have already been implemented in ERO [16]. The branching ratio obtained from these data comes really close to the experimental observations in particular at Te=15eV(Fig.5).Asmentionedearlier,thisisthecorrectedvalue at theseparatrix. The limiter ridge stays about2cm inwardsthe scrape-off-layer. As most penetration depths in the modelled experiment areaboutfew cm,mostlight emissionanddissociation shouldhappencloseby.

Effectivesputteringyieldsbenchmark

As itwasshownin[5],theionimpactangleαimp andenergy E_im_pdistributionsareofimportanceforphysicalsputteringincase of the shallow angle between the PFC surfaceand the magnetic field. Thereforewe haveto calculatetheeffective valuesforeach surfacelocation, which areproved to vary withtheB-fieldangle tothesurfacenormalηând^local^Tê^.În^Fig.⁶^theêffective^yields

YÊff(η^, ^Tê⁾ întegrated ^from ^the ^basic ^fits ^Y⁽Êimp, αimp) e.g. ‘ERO- min’,with the (E_imp, αimp) distributions on impact are depicted.

Thesedistributionsaregenerated:

(a) numerically,asformerlydone,byaspecialEROpreliminaryrun [5];

(b)bythenewanalyticalexpressionsfortheE-ﬁeldandionveloc- ityinthesheath[11].

TheY^Eff varyalongthelimitersurface,howeverthevaluesare averaged byERO alongthe whole sightline-relevanterosionzone excludingtheshadowedarea.

The reliability of the analytical expressions havebeen proved [11]by a very good agreementwithparticle-in-cell (PIC) simulations.The onlyadvantage remaining yeton thenumeric EROap- proach(the directincorporation ofthe analyticalsolution inERO isongoing)isthatittracksthesputteringionsrightfromthestag- nationpoint, thus takesinto account their thermalization in the plasma.The analytical approachstartsfornow witha reasonable ionvelocitydistributionatthesheathentranceasinitialcondition.

It leadsto broader angle andenergy distributions than the ones simulatedbyERO.This,inparticulartheαimp distribution,results inan increase ofthe resulting effectiveyields of ∼30%for ‘ERO- min’(Fig.6).Fromthetechnicalside,theanalyticalapproachsuits betterforthattaskasthenumericapproachsuffersduetothene- cessitytodecreasethesimulationstepintherisingsheathE-ﬁeld downto10⁻¹³–10⁻¹⁵stoproducetheaccurateanglesonimpact.

Fig.6demonstrates theinﬂuenceofthe self-sputteringby the intrinsicBeimpurity inthe plasmacontributingto thetotal ero- sionyieldproportionallytoitsconcentrationf_Be:

Ytotal=Y^{E f f}Be←D∗(¹^{− f}^Be)⁺^Y^{E f f}^Be←Be∗(^f^Be)^, ⁽¹⁾

whereY^Eff_Be_←_D andY^Eff_Be_←_Be arethe effective sputteringyields forDandBe(‘self-sputter’)eroding species.Similar tothe previ- ousstudieswededucef_BefromthemeasuredeffectivechargeZ_eff. Beimpurity comes partially fromtheclosest PFCs,but alsofrom thecoreasBe⁴⁺(Z_Be=4),whichhowevercanalsorecombinee.g.

to Be³⁺ on its way. Self-consistent modelling would demand in- cludingamuchlargervolume,withallrelevantimpuritysinksand sources and self-consistent tracking of Be ions. For now we can justassumethat allBeionscomeforinstanceasBe⁴⁺ oralterna- tivelyBe³⁺.ThechargeZ_Behasnoinﬂuenceonthesputteringyield by itself,however it affectsthe charge-dependentacceleration in thesheath,thoughthe yielddependenceonenergyisstagnating.

Thus the erosionupon assumption of 3+ charge is largerdue to the amount ofatoms deduced from Z_eff (Fig. 6) matching better withtheexperiment.

The standard JET Z_eff diagnostics has no radial resolution, whereasitistoexpectthattheimpuritycontentattheradialpo- sitionscorrespondingtothemosteffectiveerosionlocationsatthe limiter ridge, islarger. It can be seen inFig. 6 that the assump- tionofZ_Be=3charge anddoubleconcentration attheerosion lo- cation leads to a perfect match with the experiment. This is of coursemorean indicationthanaproofthatweinterprettheself- sputteringcorrectly.Ontherightsideoftheplotscorrespondingto largeplasmadensitiesandlowtemperatures(lowenergiesofsput- teringions) theeffectofself-sputteringgoes tozeroasthemea- suredZ_eff∼1. In thisregion thecalculated curvesassuming ‘ERO- min’with analytic distributions are matching really well the ex- perimentalvaluesobtainedby theS/XBmethod[17] refinedwith theTe adjusted accordingto the lineratios observedin the very samesightline[6].On onehand,the uncertaintiesinintrinsicBe impuritychargeandconcentrationdonotallowtobenchmarkthe self-sputteringyieldsdirectly,butthedeviationswithexperiments areshowntobeexplainable.Ontheotherhand,thebasicdataand fitforself-sputteringisproducedinthesamewayandcanbeex- pectedtobe ofthesameaccuracy. The‘ERO-max’fiton thezero

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Fig. 7. ERO synthetic line intensities integrated inside the observation chord compared against the absolute experimental measurements during the density scan experiment.

Fig. 8. The BeD band emission simulated by ERO (total) and observed in experiment (right) using the ﬁts for the fraction of BeD release from obtained on the experimental (‘PISCES’, ‘JET’) and simulated (‘MD’) data from [6] . Measurements are multiplied by 3.5 to obtain the total band intensity whereas only a fraction of it depending on the vibrational and rotational temperatures is coming into the spectral window.

self-sputtering side of the curve leads to effective yields clearly largerthanmeasured onesevenifnumericalimpactdistributions (smalleryields)areusedfortheintegration.

Amorethoroughbenchmarkforthemodelanddataisthedi- rectcomparisonofthesyntheticlight inthesightline(ERO) with theexperiment.Simulationsinvolve,forinstance,thespatialdistri- butionoferosionalongthePFCsurface,localtransportandatomic processesinthecontextof3D plasmaparameters(Fig.7). Anin- terestingeffectistheinitialpopulationoftheMSstatesinBeIjust afterphysicalsputtering (seebelow).Ithasan essentialinﬂuence ontheBeIlineintensities.TheinﬂuenceofMSpopulationonion-

izationtoBe⁺isminimal,sotheBeIIlinescanbeusedforerosion characterization. Onthe left of the both graphs, inthe region of lowdensityandhightemperature,theself-sputteringbytheBe³⁺ content inplasmadeducedfromZ_eff isinsuﬃcient similarto the respectivecurveonFig.6.

Fig.8 showstheﬁrstattempt toreproducethe BeDA-X band (around∼500nm) emission by ERO.The wavelength spanin the experimentislimitedtothebandhead[6],whereasthemodelling considersthefullelectronictransition.Thus,theexperimentaldata must be corrected by inclusion the full spectrum which can be donebyspectramodellingincludinge.g.accountingforpopulation

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of vibrational statesresulting in a correction factor ofabout 3.5.

That means that all the synthetic results agree withexperiment within 20–30%(simulated curvesaremultipliedby 0.8togetthe perfectmatchfortheone basedontheexperimentalbasedﬁtfor the BeD releasefractionin comparisonto the ‘ERO-min’physical sputtering).Thelineartrendisalsoverywellreproduced.

Summaryandconclusion

A signiﬁcant update for modelling [5] of Be erosion at JET ILWcharacterized by thepassivespectroscopy iscarriedout. The plasmaparameters input wasrevisitedby inclusionof embedded Langmuirprobesinformation(mostsigniﬁcantisthecorrectionof formerly overestimated Te). New analytical expressions were ap- pliedtogeneratetheenergyandanglesputteringiondistributions onimpactdeterminingtheeffectivesputteringyields.Atlargeden- sities(Z_eff ∼ 1)thetrendsforbothBeIandBeII linesarewell reproduced. Still,thesimulations overestimate theBeII light nearly byafactorof2.Partiallyitcanbeexplainedbytheremainingun- certaintiesintheplasmabackgroundsandBeDdataandassump- tionse.g.iswassupposedthatBeDreleasedoesnotaffectphysical sputtering. The BeD band intensity trendis reproduced well and theabsolutevaluewithin20%.

Thisbenchmarkincreasestheconﬁdenceintheresultsofmore general and less detailed S/XB approach, which clearly indicates that ‘ERO-min’ﬁtaveragedovertheimpactangleandenergydis- tributionsestimatedusingtheanalyticalexpressionsfrom[11]can be recommendedforplasma-wettedareas asthe GL surfacecon- sideredinthiswork.

The ERO modellingofBeDrelease,localtransport andrespec- tivesurfaceandreactiondatashouldbefurtherimproved.Forthat a detailedsimulation ofthesurfacetemperaturescanexperiment

[6]wouldbeuseful. Theshadowingtreatmentandself-sputtering assumptionsshouldalsobereﬁned.

Acknowledgements

This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Eu- ratom research and training programme 2014–2018 under grant agreement No 633053.The views and opinionsexpressed herein donotnecessarilyreﬂectthoseoftheEuropeanCommission.Com- putertimeonJURECAwasprovidedbytheJülichSupercomputing Centre.

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