ERO and PIC simulations of gross and net erosion of tungsten in the outer strike point region of ASDEX upgrade

ERO and PIC simulations of gross and net erosion of tungsten in the outer strike point region of ASDEX Upgrade ARTICLE IN PRESS JID NME [m5G; October 8, 2016;6 24 ] Nuclear Materials and Energy 0 0 0[.]

ERO and PIC simulations of gross and net erosion of tungsten in the

outer strike-point region of ASDEX Upgrade

A Hakolaa ,∗, M.I Airilaa , N Melletb , M Grothc , J Karhunenc , T Kurki-Suonioc ,

T Makkonenc , H Sillanpääc , G Meisld , M Oberkoflerd , ASDEX Upgrade Team

a VTT Technical Research Center of Finland Ltd., P O Box 10 0 0, 02044 VTT, Finland

b CNRS, Aix-Marseille Université, PIIM, UMR 7345, 13397 Marseille, France

c Aalto University, Department of Applied Physics, P O Box 1110 0, 0 0 076 Aalto, Finland

d Max Planck Institute for Plasma Physics, Boltzmannstr 2, 85748 Garching, Germany

a r t i c l e i n f o

Article history:

Available online xxx

Keywords:

ASDEX Upgrade

Tungsten erosion

ERO modelling

PIC simulations

Particle drifts

Cross-field diffusion

a b s t r a c t

WehavemodellednetandgrosserosionofWinlow-densityl-modeplasmasinthelow-fieldsidestrike pointregionofASDEXUpgradebyEROandParticle-in-Cell(PIC)simulations.Theobservednet-erosion peakatthestrikepointwasmainlyduetothelightimpuritiespresentintheplasmawhilethenoticeable net-depositionregionssurroundingtheerosionmaximumcouldbeattributedtothestrongE ×Bdriftand themagneticfieldbringingerodedparticlesfromadistanceofseveralmeterstowardstheprivateflux region.Ourresultsalsoimplythattheroleofcross-fielddiffusionisverysmallinthestudiedplasmas Thesimulationsindicatenet/grosserosionratioof0.2–0.6,whichisinlinewiththeliteraturedataand whatwasdeterminedspectroscopically.Thedeviationsfromtheestimatesextractedfrompost-exposure ion-beam-analysisdata(∼0.6–0.7)aremostlikelyduetothemeasuredre-depositionpatternsshowing theoutcomesofmultipleerosion-depositioncycles

© 2016TheAuthors.PublishedbyElsevierLtd ThisisanopenaccessarticleundertheCCBY-NC-NDlicense (http://creativecommons.org/licenses/by-nc-nd/4.0/)

1 Introduction

Thelimitedlifetimeofplasma-facingcomponents(PFCs)canbe

a potential showstopper in future fusion reactors including ITER

andDEMO[1] Therefore,onehastofullyunderstandthedamage

mechanismsanderosionbehaviorofdifferentPFCsuponexposure

to variousplasmascenarios Furthermore,quantifying theerosion

ratesrequiresdistinguishingbetweengrossandnetcontributions:

thesecandifferconsiderablyasalargefractionoftheeroded

ma-terialwillbelocallyre-deposited[1]

Tungsten (W) has proven to be a suitable PFC material as

demonstrated in several tokamaks like ASDEX Upgrade (AUG)

[2] and JET [3] Its main advantages are small erosion yield by

plasma bombardment,good power-handlingcapabilities, and low

accumulation of tritium in the material [4] Re-deposition of W,

foritspart,isgenerally>50%ofgrosserosion[5] andapproaches

100%inhigh-densityplasmas[6]

Here,weinvestigatesteady-stategrossandneterosionof

tung-sten and restrict our considerations to the low-fieldside (outer)

∗ Corresponding author

E-mail addresses: antti.hakola@vtt.fi , ahhakola@gmail.com (A Hakola)

strikepointregionofAUG.Wenumericallymodelthe experimen-talnet-erosionandre-depositionpatternsbytheEROcode[7] and

byParticle-in-Cell(PIC)simulations[8] ,withthegoalofidentifying thecontributionofvariousphysicalfactorsontheerosion charac-teristics.Thestartingpointisanexperiment,carriedoutatAUGin

2014whereWsampleswereexposedtoaseriesofl-modeplasma discharges[9]

2 Review of experimental results

Theexperimentaldatabaseisbasedonadedicatedexperiment

in which special W marker samples were exposed to 13 identi-cal plasma discharges in deuterium in the outer strike point re-gion of AUG [9] A full poloidal rowstarting from about50mm belowthestrikepoint,intheprivatefluxregion(PFR),and extend-ing∼150mmin thescrape-off layer (SOL)ofthedivertorplasma wascovered.Thelocationofthesamplesandthestrikelineofthe experimentareshownintheinsetofFig 1 Allthesampleshada 20-nmthickWmarkerongraphiteaswellasa0.2-mmdeep, un-coatedtrenchmagneticallydownstreamofthe markerandfinally

aninclinedMomarker(thickness20nm)

Low-density l-mode plasmas were used such that the elec-tron temperatures around the outer strike point were 20–40eV http://dx.doi.org/10.1016/j.nme.2016.09.012

2352-1791/© 2016 The Authors Published by Elsevier Ltd This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ ) Pleasecitethisarticleas:A.Hakolaetal.,EROandPICsimulationsofgrossandneterosionoftungstenintheouterstrike-pointregion

Fig 1 (a) Experimentally determined poloidal net deposition/erosion profile of the W marker as well as poloidal re-deposition profiles for W on the graphite and Mo

markers Negative values denote net erosion, positive net deposition and PFR corresponds to the poloidal distance being negative Inset shows schematic illustration of the AUG divertor and the target tile (red) The magnetic field points towards the viewer (b) Photograph of the marker samples on the target tile after their exposure to plasma discharges together with a schematic drawing of one of the samples and its geometry (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig 2 (a,b) Experimental Langmuir-probe data and simulated OSM profiles for the poloidal profiles of (a) electron density and (b) electron temperature around the strike

point (c) Poloidal profiles for the two electric field components ( E x and E z ) used in the ERO simulations together with the definitions for the ERO co-ordinate system

ThepoloidalprofilesofneandTe,asmeasured byfixedLangmuir

probes,are shownin Fig 2 a and btogether withtheir modelled

counterparts that were used in subsequent ERO and PIC

simula-tions.The neterosion ofthe W markersaswell asre-deposition

ofW onthe trenchandon the Momarkerwere determined

us-ingRutherfordbackscatteringspectroscopy(RBS)andtheresulting

erosionanddepositionrates(nm/s)arecollectedinFig 1

The mainobservationsareanoticeablenet-erosionzone,

coin-cidingwiththelocationofthestrikepoint,andclearly

distinguish-able deposition-dominated regions on both sides of the erosion

maximum.OntheSOLside,thedepositionpeak isalmost40mm

wideandmatches withthelocation ofthemain depositionpeak

oflightimpuritiesboron(B),carbon(C),andnitrogen(N)(see[9] )

Theseobservationshinttowards astronginflux ofmaterial,

how-ever,intheabsenceofdirectmeasurementsofthefluxesof

differ-entimpurityionsintheplasma(B,C,N,W)thishypothesiscannot

beexperimentallyverified

The shape of theW re-deposition profile on thegraphite and

MomarkersinFig 1 is,unexpectedly,quitesimilartothenet

ero-sion/depositioncurve fortheW marker IfgraphiteandMowere

efficientlyshadowed from direct contactwith plasmaduringthe

experiment, the deposition rate should peak close to the most

prominentsource,i.e.,thestrikepoint,andgraduallydiminish

fur-therawayfromit.AccordingtoFig 1 thisisnotthecase

Ifweestimatetheratiobetweenneterosion,N,andgross

ero-sion,G,close tothe strikepoint, assuming that G=N+R, where

Rstandsforre-deposition,weobtainN/G∼0.6–0.7.However,

liter-aturevaluesindicate muchlarger re-deposition,corresponding to

N/G<0.5(see [3 ,6] ) Thus, especially the trench and Mo marker

appearto show the outcomes ofmultiple erosion-deposition

cy-cles.An independent estimate forgross erosionby spectroscopic

measurements of the neutral WI line at 400.9nm supports the conclusion: a relatively sharp erosion profile with N/G=0.4–0.6 aroundthestrikepointemerges[9]

3 Simulation setups

3.1 ERO modelling of net and gross erosion

To understand the physics behind the features observed in Fig 1 ,wehavemodelledtheerosionanddepositionprocesses us-ingERO.EROisa3DMonteCarlocodethatsimulatesthetransport

oftestparticlesintheSOL[7] Weusedthedivertorversionofthe codeandcarriedoutthesimulationsinacomputationalvolume il-lustratedinFig 3 a.Theentiretoroidal(y=70mm)andpoloidal (x=300mm)extentofthetargettilewerecovered,andthebox wasz=50mmhighinthedirectionnormaltothesurface.A

5-mmspacingwasusedforthesimulationgrid,andinthetoroidal directionperiodicalboundary conditionswere establishedto pre-ventunphysicallossesofparticles.ThisisinlinewithfullW cov-erageoftheAUGdivertorinthetoroidaldirection.Thesolidblack linein Fig 3 a denotes thesimplified wall geometry ofAUG that wasusedinbackground-plasmacalculations

Forsimplicity, onlythe W marker wasconsidered and imple-mented asbulk material The overall simulation time was 1 at 0.01 stepsandthenumberoftestparticleswas104pertimestep This was enough for equilibrium to be reached and accumulate enough statistics forreliable profiles.Losses through thepoloidal andperpendicular sidefacesofthesimulationboxweregenerally

<0.1%oftheprimarilysputteredatoms

The background deuterium plasma was produced by the DI-VIMP codewith its Onion SkinModel (OSM, SOL option 22)

ac-Fig 3 (a) Schematic illustration of the ERO simulation box and the applied co-ordinate system (b) ERO results for the poloidal net deposition/erosion profile in the base case

(blue circles, c W = 0.005%, c B = c C = c N = 0.5%) and in the cases with c W = 0.01%, c B = c C = c N = 0.5% (red rectangles) and with c W = 0.01%, c B = c C = c N = 1.0% (black asterisks) Also the experimental profile has been reproduced (c) Poloidal gross erosion (blue circles) and re-deposition (red rectangles) profiles for the base case (For interpretation

of the references to colour in this figure legend, the reader is referred to the web version of this article.)

tivated[10] Thecodereturnsvaluesforelectrondensity,electron

andiontemperatures, andflow velocityalong magnetic flux

sur-faces of the OSM grid, which were then interpolated to obtain

corresponding plasmadatainthe EROvolume.The resulting

pro-files for ne andTe along the target surface( =0) are shown in

Fig 2 a and btogether withthe experimental ones Different fits

fortheexperimentalprofileswereusedasinputfortheOSM

sim-ulations Deep in the private flux region, where the OSM

back-groundwas missing, a coldplasma approximation withne=1017

m−3 andTe=Ti=0.1eVwasused.TheTeprofilehasa somewhat

longerdecaylengthintheSOLsideandthepeakislowerthanthe

Langmuir-probedatasuggests,whilethenepeak isoverestimated

atthestrikepoint.Thesemayhavehadaninfluenceontheshape

and absolutelevels ofthe simulated erosionand deposition

pro-files

In thesimulations, the type andconcentration oftypical light

impurities inthe AUG divertor plasma(hereB, C, andN) andW

originatingfromother partsofthetorus than thesimulationbox

were varied such that the effectivecharge, Zeff, remained within

reasonable limits (between 1.5 and 2.6) and that the

concentra-tions of individual impurities agreed withprevious measurement

resultsfromAUG, i.e., B, C,and N<1.0%and W<0.01%[11 ,12]

One should note thatthe measurements are fromthecorewhile

in the divertor region the concentrations can locally be much

larger From coronal equilibrium [13] , we obtain for the average

charge states oftheimpurities qB=3, qC=4,qN=5,andqW=13

inthesimulationvolume.Theanomalousdiffusioncoefficientwas

varied from0 to 1.0 m2/s withD⊥=0.2m2/s being the nominal

value No pre-calculated, integrated sputtering yields existed for

theprojectile-targetcombinationsathigherchargestates(q >2)to

describebackgroundplasmasputtering.Instead,weestimatedthe

missingdatabytheBohdansky-Yamamuraformalism(see[14 ,15] )

TheeffectofE × Bdriftwasinvestigatedbyincludingthe

elec-tricfieldintheplasmabackground[16 ,17] SincetheOSMsolution

didnotcontaintheelectricfield,northeplasmapotential,we

cre-atedplausibleprofilesforthepoloidal(Ex)andnormal(Ez)

compo-nentsofthefieldby assumingthepotential beingdirectly

pro-portionaltoTe,i.e.,=3kBTe/e;theelectricfieldisthenevaluated

by E= ∇ [18] By assuming that the plasma potential remains

the same along all the lines that are parallel withthe magnetic

fieldinthexzplane,oneobtainsaprofileshowninFig 2 c

3.2 PIC simulations

To further study the role of re-deposition on the

ero-sion/deposition behaviour of tungsten we carried out

simula-tions based on the magnetic sheath potentials calculated

self-consistentlywitha1DPICcodeintroducedin[19] Impuritieswere

injectedintotheplasmaastestparticlesandassumednotto

influ-encetheevaluated electricfield asdescribedin [8] The required profilesforplasmaparameterswereagaintakenfromtheOSM so-lution(see Section 3.1 ) and alsothe impurity mix of theplasma wasvariedsimilarlytothecaseoftheEROruns

The 2D profiles forthe normal (Ez) and poloidal(Ex) compo-nentsof thecalculated electric field are shownin Fig 5 a andb Thefieldwasdeterminedbyinterpolatingthepotentialsresulting fromPICcalculationsforasetofparametersthatincludethe den-sity, the angle ofthe magnetic field withrespect to the surface, andtheion/electron-temperatureratio.ThecomponentE z reaches muchlarger valuesthan E x andthe profiles usedin ERO simula-tions (seeFig 2 c),butonly inthe immediatevicinityof the sur-face, within the magnetic sheath; further away, the two compo-nentsare comparable Notealso that thesheath electricfield to-wardsthesurfaceextendsthefarthestintotheplasmawherethe temperatureisthehighest.Acorrectionforthepotentialdropwas introduced to compensate for the drift induced by the poloidal fieldsothatambipolaritywasmaintained

PhysicalsputteringwastreatedaccordingtotheEckstein’s for-mulas[20] or, inthecaseofB andC,to therevised Bohdansky– Yamamuraformalism [14 ,15] Re-depositionwascomputedby in-jecting atomswith cosineangular andThomson energy distribu-tions.Altogether106tungstenatomswereinjectedineachrun.We also used atleast 1000 iterationsfor each Larmor gyration once theparticle wasionised.The simulationdomain coversthe same size boxas theone used in ERO, which ismuch larger than the regionshowninFig 5 aandb

4 Results

4.1 ERO modelling

Light impurities are responsible for almost all the observed neterosion inthe vicinity ofthe strike point(see Fig 3 b) Here, poloidalneterosion profiles resultingfromERO simulations with

cB, C,and Nvariedfrom0.5–1.0%andtheWconcentrationwithin therange W=0.005–0.01%areshown.Forcomparison,the exper-imentalneterosionprofileofFig 1 isreproducedinthefigure.If onlyWwasincludedinthesimulations,neterosionwouldbe al-mosttwoorders ormagnitudesmaller unlessunrealisticallyhigh

cW,oftheorderofafew%,wasused

One should note that it is mainly the effective charge, Zeff, that influences the maximum of the main erosion peak: the ex-act impurity composition plays a minor role The peak scales roughly as Zeff−1 within the investigated range of Zeff=1.5–2.6 According to [11] , the typical impurity content of the AUG SOL plasmawouldresultinZeff∼1.5–2.0,albeitZeff>2.0canlocally ex-ist in divertor plasmas This leads us to select a base case with

cB= C= N=0.5%and W=0.005%forfollow-upsimulations,

cor-Fig 4 (a) ERO results for the poloidal net deposition/erosion profile in the base case both with (red triangles) and without (blue circles) the electric field (b) Poloidal

gross erosion (blue circles) and re-deposition (red rectangles) profiles for the case with the electric field being switched on (c) Influence of cross-field diffusion on net deposition/erosion: D ⊥ = 0 (black diamonds), D ⊥ = 0.2m 2 /s (red triangles), and D ⊥ = 1.0m 2 /s (orange stars) In (a) and (c) also the experimental profile has been reproduced (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

respondingtoZeff=1.81 Accordingto Fig 3 b,maximum net

ero-sionwouldthenbeunderestimatedbyaboutafactorofthree

In-creasingZeff improves the match but the simulated erosion rate

is still off by ∼25% Besides the net-erosion peak, the

simula-tionsqualitativelypredicttheformationofabroadnet-deposition

plateauontheSOLsideofthestrikepoint,thoughthedeposition

ratesare3–5timessmallerthantheexperimentalvalues.In

addi-tion,adeposition notchisseen toemerge inthePFR butthe

re-markablenarrowpeakaroundx=−20mmremainsfarfrombeing

reproduced

TheneterosionregionclearlycoincideswiththepeakoftheTe

profile(seeFig 2 b),whiletheoccurrenceofnetdepositionzones

isbestexplainedbyalargefractionoftheerodedparticles

return-ing on the surfacea few mm off from the location from which

they were sputtered This we can see in Fig 3 c where poloidal

gross erosion and re-deposition profiles of W are illustrated for

thebase case The simulated erosion andre-deposition rates are

2–5timeslargerthanthenet-erosionrates,indicatingthatindeed

thenet/grosserosionratiowouldbeN/G∼0.2–0.5incontrastwith

N/G∼0.6–0.7reported in[9] This gives supportfor the

hypothe-sisthatthemeasuredamountsofWatthebottomofthegraphite

trenchandon the Momarker havebeen subjectedto significant

plasma-surfaceinteractionsduringtheexperiment

Besides the discrepancies discussed above, the simulated net

erosionpoloidallyfar awayfromthestrikepoint approacheszero

independentoftheappliedimpurity contentofthe plasmawhile

experimentally it should saturatetowards a value of∼0.04nm/s

Thereasonmaybe connectedwiththeOSMsolutions forTe and

nedeviatingfromthemeasuredprofiles(seeFig 2 aandb),which

mayfurthercontributetotheerosion/deposition balance.In

addi-tion,theapproximationswemadetoobtainthemissingintegrated

sputteringyielddata(seeSection 3.1 )mayhaveledto

underesti-matedgrosserosionatlowTe.However,alsootherfactorsthanthe

impuritycontentneedtobeconsidered

The clearest contribution comes from the E × B drift To this

end,we ran simulations usingthefield profile ofFig 2 c andthe

impurity content of the base case above The net erosion peak

atthe strikepointbecomesmorepronounced andthedeposition

maximasurrounding it more peaked such that a relatively good

qualitative matchwiththe experimental curve within the

strike-zone region x=−30…20mm is obtained This is illustrated in

Fig 4 awheretheresultingneterosion/depositionprofilesforERO

simulationswith andwithoutthe drift termare shown, together

withtheexperimentalones.Especially,thedepositionpeakinthe

PFRhasbecomemuchmorenoticeablethanintheno-driftcaseof

Fig 3 b.Thisis causedby alteredtransportof theparticles: gross

erosionisnotaffectedbythefieldbutthere-depositionprofileis

largelyshiftedtowardstheSOLinthepoloidaldirectionaswe

no-tice fromFig 4 b However, both gross erosion andre-deposition

remain at the same level as in Fig 3 c, which sets the net/gross erosionratiotoN/G∼0.5–0.6.Thisisclosetotheexperimental val-uesin[9] butstillsmallerandsubjecttolargeerrorbars induced

bytheshapeoftheelectricfieldprofile

Thenormalcomponentofthefield, Ez,affectsthedistribution

of W atomson the surfaceby driving them poloidallyeither to-wards orawayfromthe strikepoint,e.g., inthegeometryofFig

3 adownwards ifEz<0.Theotherfield component, Ex,influences the erosion/deposition picture only indirectly The more negative

Ex is, themore particles will drift away from thesurface andin addition tobeingre-deposited furtheraway fromtheir origin es-capefromthesimulationbox;positivevaluesforExwillkeepthe erodedatomsmoretightlyclosetothesurface

The effect ofthermal gradient forces parallel to the magnetic field [17] on theerosion/deposition profiles (not shown)was ob-served tobe negligible butcross-field diffusionplayedan impor-tant role in the balance between erosion and deposition By re-ducingtheperpendiculardiffusioncoefficient,neterosionand de-positionpeakswerebothsharpenedwhereaslargervaluesforD⊥ re-distributed the particles on the surface, thus smearing out all theprominentfeatures oftheprofiles.Thisbecomesevidentfrom Fig 4 cwherethesimulationsatD⊥=0,0.2,and1.0m2/sare pre-sentedwiththeE × Bdriftswitchedon

We conclude that the locations and magnitudes of the depo-sition maxima are largely attributedto the poloidal transport of particles and diffusion across the field lines Since in our model the electric field is proportional to the gradient of the electron temperature, it is clear that even small changes in the Te pro-file can result in large changes in the E profile, when also inac-curaciesindeterminingthe exactvalueforthe Tepeak aretaken intoaccount Besides,alsothefield componentinduced by paral-lel Pfirsch-Schluetercurrentwouldneed tobe takeninto account [21] but this is beyond the scope of the present work

4.2 PIC modelling

ThreePICsimulations wereperformed:one withthe full elec-tricfield ofFig 5 aandb,thesecondwithonlytheEz component turned on, andthe last one without any electricfields.The case withonly Ez beingactive wasselected to study transport purely

in the poloidal direction, according to the discussion above (in Section 4.1 )

The poloidal erosion/deposition profiles are shown in Fig 5 c Additionally, Fig 5 d shows the comparison between the re-deposition and gross erosion profiles in the full electric field case Qualitatively, the PIC profiles have many similarities withtheEROresultsofFigs 3 and4 buttheneterosionmaximum

atthe strikepoint isdeeperandthe deposition peakon theSOL sideisalmostnon-existent.Thesituationwithouttheelectricfield

Fig. 5 (a,b) 2D profiles for (a) E z and (b) E x used in the PIC simulations The field had been generated by interpolating the magnetic sheath potentials calculated by the PIC code (c,d) PIC results for (c) net deposition/erosion computed using the test-particle in three cases: no electric field (blue), only the E z component activated (blue) and the full electric field (black) and (d) poloidal gross erosion (blue) and deposition (red) profiles in the full electric field case (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 6 PIC results for 2D re-deposition profiles of the prompt (a,c) and long-range (b,d) fractions Two models have been compared: only E z (a,b) and the full electric field (c,d) Superimposed in (d) is re-deposition taking place toroidally outside of the original box

is even more extreme – only large net erosion with rates more

than 2 times the experimental values is observed This we can

understand by noting that now only Larmor gyration influences

re-deposition, which will shift the entire re-deposition

distribu-tion poloidally upwards.In thePFR, the experimentally observed

net-deposition peak starts to be formed when the electric field

is switched on but only for the full electric-field case a good

correspondence with the experimental and simulated profiles is

obtainedinthisregion

The re-deposition picture is, however,more complicated than

what can be concluded from the analyses above To this end,

we separated re-deposition into two components: prompt

re-depositionwheretungstenionsenduponthesurfacewithintheir

first Larmor radius and long-rangere-deposition wherethey

un-dergoseveralgyrationsbeforereturningonthesurface.The2D

re-deposition profiles are displayed in Fig 6 a and b forboth these

contributions in the caseE x =0and inFig 6 c andd forthe full

model In both cases,prompt re-deposition (Fig 6 a andc) is

lo-cal,theprofileshaveanextentofsome10–20mmfromthestrike

point,andtheeffectofE x isweak.Thepattern,however,changes

drastically whenlong-rangedeposition is considered(Fig 6 b and

d) In the case E x =0, a significant part of re-deposition occurs

poloidallydownwardsofthestrikepointandcanbe attributedto

theE × B driftinducedbylargeandnegativeE z (seeFig 6 b).This

we alsonotice from Fig 5 c.In the full model,however, the

rel-ativelystrong E × B drift towardsthe plasmaduetoE x competes

withtheeffectofthemagneticfieldtobringtheparticlestowards

thewallandresultsinre-depositedWtravellingseveralmetersin

the toroidal direction This suggests that the peak in the PFR in

Fig 5 c couldoriginate frombulk divertormaterial orfrom

ma-terialoriginatingfromother PFCsofthe AUGtorus astheinset

ofFig 6 dillustrates.Simultaneously,thenumberofparticles

accu-mulating poloidallyupwards tothe strike point (whereE x is

op-positelyoriented)isincreased.UnlikethecaseE x =0,particlescan

bere-depositedinthe directionopposite tothemagnetic fieldas theprojectionofE x onBisorientedinthatdirection(Bbeingnot fullytoroidal)

5 Discussion and conclusions

Wehavenumericallymodelledthe experimentallydetermined net andgross erosion of W in the outer strike point of AUG by EROandPICsimulations.Thestrongnet-erosionpeakatthestrike point was reproduced by adding a realistic mixture of light im-purities (a few at.%) in the plasma while the noticeable deposi-tion peaks poloidally on both sides of the strike point could be explainedbythestrongE × Bdriftonthetargets

Thedeterminednet/grosserosionratiowas0.2–0.6,whichisto

be comparedwiththe experimentally determinedvalue of ∼0.6– 0.7.Thediscrepancyisattributedtothere-depositedmaterial hav-ingbeenincontactwithplasmaduringtherestoftheexperiment Indeed,independent,spectroscopicestimateforthenet/gross ero-sionratioof0.4–0.6supportsthishypothesis

The E × B drift is the most significant individual factor con-tributingtotheshapeoftheerosion/depositionprofile.ERO simu-lationsindicatethatboththeerosionanddepositionpeaksbecome sharperwhenthedrifttermsareactivated.Ontheotherhand,PIC simulationsindicatethatalsotransportofmaterialalongthe mag-neticfieldlineshastobetakenintoaccount:theparticles originat-ingfromotherregionsofthedivertorormainchambercantravel severalmetersinthetoroidaldirectionandincreasetheW inven-toryintheprivatefluxregion.Ontopofthedrifts,ourresults sug-gestaverysmallvalueforD⊥ inlow-densityplasmas,thus cross-fielddiffusionplaysaminorrole

Theremainingshortcomingsinthereproductionofthetwo ex-perimentally observed deposition peaks are currently being

ad-experimentswithmodifiedgeometryofthematerial samplesare

consideredtoeliminateonesourceofuncertainty

Acknowledgements

This work has been carried out within the framework ofthe

EUROfusion Consortium and has received funding from the

Eu-ratom research and training programme 2014–2018 under grant

agreement number 633053 The views and opinions expressed

herein donot necessarilyreflect those of theEuropean

Commis-sion.WorkperformedunderEUROfusionWPPFC

[13] https://www-amdis.iaea.org/FLYCHK/ (ref 10.05.2016)

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