Tokes studies of the thermal quench heat load reduction in mitigated iter disruptions

The positions of the three upper injectors and the midplane injector are shown in the left panel.. Examples of Ne flow from the midplane injector and from the upper injector are shown in

ARTICLE IN PRESS

Nuclear Materials and Energy 0 0 0 (2016) 1–8

ContentslistsavailableatScienceDirect

Nuclear Materials and Energy

journalhomepage:www.elsevier.com/locate/nme

TOKES studies of the thermal quench heat load reduction in mitigated

ITER disruptions

S Pestchanyia ,∗, M Lehnenb , R.A Pittsb , G Saibenec

a KIT, Hermann-von-Helmholtz-Platz 1, Eggenstein-Leopoldshafen, Germany

b ITER Organization, Route de Vinon-sur-Verdon, CS 90 046, 13067 St Paul Lez Durance Cedex, France

c Fusion for Energy, 08019 Barcelona, Spain

a r t i c l e i n f o

Article history:

Received 13 July 2016

Accepted 7 December 2016

Available online xxx

a b s t r a c t

Disruptionmitigationbymassivegasinjection(MGI)ofNegashasbeensimulatedusingthe3DTOKES codethat includesthe injectorsoftheDisruptionMitigationSystem(DMS)as itwillbeimplemented

inITER.Thesimulationshavebeendoneusingaquasi-3Dapproach,whichgivesanupperlimitforthe radiationheatload(notwithstandingpossibleasymmetriesinradialheatfluxassociatedwithMHD).The heatingofthefirstwallfromthe radiationflashhasbeen assessedwithrespectto injectionquantity, thenumberofinjectors,andtheirlocationforanH-modeITERdischargewith280MJofthermalenergy SimulationsforthemaximumquantityofNe(8kPam3)haveshownthatwallmeltingcanbeavoidedby usingsolelythethreeinjectorsintheupperports,whereasshallowmeltingoccurredwhenthemidplane injectorhadbeenadded.Withallfourinjectors,meltinghadbeenavoidedforasmallerneonquantity

of250Pam3thatprovidesstillasufficientradiationlevelforthermalloadmitigation

© 2016 Published by Elsevier Ltd ThisisanopenaccessarticleundertheCCBY-NC-NDlicense (http://creativecommons.org/licenses/by-nc-nd/4.0/)

1 Introduction

The ITERplasma control systemis designedto allow reliable

and stable operation throughout all discharge phases It will

re-act to any deviationfrom the predictedbehavior which includes

applicationof active disruptionavoidance schemes.Despitethese

efforts, disruptionscaused by plasma instabilities,loss of control

events or plant failures cannot be excluded Should a disruption

remainunmitigated,meltingandvaporizationoftheITERmetallic

plasma-facingcomponents(PFC)cannotbeexcluded[1] A

disrup-tion mitigation system(DMS) isbeingdesigned forITERto

miti-gatethethermalloadsdepositedduringunavoidabledisruptions

TheITERDMSisbeingdesignedbasedonacomprehensive

ex-perimental database collected from existing tokamaks The

miti-gation strategy relies on the injection of highZ noble gas (NG),

namelyneonorargon,possiblycombinedwithdeuteriumfor

pre-ventionofrunawayelectronsgeneration.Theinjectionaimsto

dis-sipatethe plasmastoredenergythrough an increaseinradiation,

therebyreducingdirectthermalloadstothefirstwallanddivertor

PFCs The systemconsistsof hybridinjectors that are ableto act

asshattered pellet injectors(SPI)orcan be used formassivegas

∗ Corresponding author

E-mail address: serguei.pestchanyi@kit.edu (S Pestchanyi)

injection(MGI).Theseinjectorsaresituatedinthreeoftheupper portplugsandinoneequatorialport,seeFig 1

DisruptionmitigationbyMGIhasbeensimulatedpreviouslyfor ITER[2] usingtheTOKEScode[3] whichhasbeendevelopedover thepastdecadeatFZK-KIT forintegrated2Dsimulations of tran-sient events in tokamaks The simulations include interaction of the plasma with the injected high Z impurities, with the diver-torandwiththefirst wallarmorin divertedmagnetic configura-tions Eachexcitation level ofeach ionspeciesin plasmatreated

in TOKES asseparate fluid Dynamics of the level populations is calculated and radiation intensity is calculated according to this dynamics Comprehensive description of the code has been per-formed in [3] The code has been benchmarked against MGI ex-perimentsinJETandinDIII-D[4–7] RecentlytheTOKEScodehas beenupdatedtoaccountfor3Deffectsinradiationheatloads dur-ingMGI.MGIintheDIII-Dtokamakhasalsobeensimulatedusing the NIMROD code withemphasis given to estimation of toroidal peakingfactoroftheradiationheatload,see[8–10] andthe refer-encesthere.OneshouldalsonotefirstattemptofMGIsimulations forJETusingJOREKcodereportedin[11]

The simulations reported hereinclude the ITERfirst wall ge-ometryandtheset-upoftheITERDMSandmodeltheflowfrom theinjector into thevacuumvessel, seeFig 1 Heatload mitiga-tionhasbeenoptimizedinthesimulations toavoidmeltingfrom theradiationflashwhilstkeepingaradiationlevelhighenoughto http://dx.doi.org/10.1016/j.nme.2016.12.007

2352-1791/© 2016 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/ )

Please citethisarticleas:S.Pestchanyietal.,TOKES studiesofthethermalquenchheatloadreductioninmitigated ITERdisruptions,

2 S Pestchanyi et al / Nuclear Materials and Energy 0 0 0 (2016) 1–8

Fig 1 Arrangement of the injectors of the ITER disruption mitigation system The positions of the three upper injectors and the midplane injector are shown in the left

panel Examples of Ne flow from the midplane injector and from the upper injector are shown in the middle and right panels The logarithmic gray scale gives the Ne density Time dependences for the gas flux from the midplane injector (P 0 /32 particles in the injector plenum) is shown in lower left panel and corresponding flux from the upper injector (P 0 ) – in lower right panel

ensuresufficientmitigationofheatloadsthroughconduction.The

injectionquantity,thenumberofinjectors,andtheirlocationhave

beenvaried

2 TOKES technique to account for 3D effects of wall radiation

2.1 Sketch of 2D TOKES simulation principles

The 2D TOKES code uses fluid plasma dynamics for plasma

propagationalongmagneticfieldaswellasfordiffusionand

ther-moconductivities across the magnetic field in tokamak magnetic

configurationswithdiverted magneticfield (Braginskii [12]

equa-tions for multi-species plasma with ionization-, recombination-,

excitation-dynamicsandwithphotonicradiationcooling)

Turbu-lentenergyandparticlestransportduringthedisruptionis

simu-latedbyenhancingthecross-fieldtransportcoefficients.Noblegas

propagationintheinjectoranditsguidingtubeismodeledin1D

approximation.Due to the 2D nature ofthe TOKES code,the

in-jectorissimulatedasatoroidallysymmetricslit,injectingNG

uni-formlyalongthetoroidaldirection.Inside theITERvacuumvessel

(VV)thegasstreamisassumedtopropagateinaprescribedcone

withthe conicalanglecorresponding tothe Machnumberofthe

gas stream The simulation of MGI in the 2D TOKES code starts

from NG propagation in the injector and in the VV Then, after reachingtheseparatrix,theNGisionizedinthepedestal,whichis cooleddownbyNGionizationandbyphotonicradiationfromthe

NGplasma.Theedgecoolingprocessisfastcomparedtostationary transporttimes,oftheorderofmilliseconds,sothattheradial pro-file oftheplasmatemperaturefurther insidethe plasmaremains unaffectedandasharpcoolingfrontbuildsupthatpropagates to-wards the plasma core In TOKES simulations it is assumed that thethermalquench(TQ)startswhenthiscoolingfrontreachesthe

q=2magneticsurface.Atthattime,thecross-fieldtransport coef-ficientsareincreasedandtheplasmathermalenergyislosttothe coreoutskirts where the radiationfrom the NG spreads this en-ergy overthesurrounding firstwall PFCs.Naturally, theradiation heat load inthe simulations is toroidallysymmetric, distributing the heat uniformly over the entiretoroidal circumference of the wall

2.2 TOKES code modifications to account for 3D effect of point-like injection

In ITER the NG will propagate through the injector tubes of

28mmdiameterwithlengthsof6.5mfortheupperinjectorsand

of4.5mforthemidplaneinjector.Thegasisexpectednottocross the separatrix uniformlyin toroidal direction, butrather through

S Pestchanyi et al / Nuclear Materials and Energy 0 0 0 (2016) 1–8 3

Fig 2 TOKES 3D magnetic flux coordinates calculation grid is shown in left panel Various colors indicate sequential layers of cells, each of which are the segments of

one continuous magnetic tube, fully covering one magnetic layer For simulation of plasma dynamics from one ITER injector the torus is ‘tiled’ with N tor identical blocks, consisting of the radiator, the reservoir and the injector each N tor injectors are almost identical to one 2D injector of the 2D TOKES Right panel illustrates Ne gas injection from the midplane injector in y-direction Shown are parts of the radiators, consequently filled by the injected gas Ne plasma propagates from the injection point along the radiators in both directions Shown are three radiators at some radial distance for visibility; in reality the neighboring radiators are touched each other at the injection point Plot of entire radiator from one layer is shown in Fig 3 (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

a spot of 0.5–1m characteristic size toroidally and poloidally in

the vicinity of each injector.The spot size isestimated fromthe

distance D ∼ 0.5÷1m between the injector and the hot plasma

boundary at different stages of the core cooling, accounting the

MachnumberM=3÷1 forthegasflowingoutoftheinjector.The

TOKES code has been upgraded to take this asymmetry into

ac-count.ThisupgradedversionofTOKESisnotafullscale3Dmodel

forplasmadynamicsduringMGI,becauseitdoesnottakeinto

ac-countplasmatransport(diffusionandthermoconductivities)across

magnetic field lines inside the magnetic layers of the tokamak

Cross-field transport during TQ runs in two mutually orthogonal

directions:insidethemagneticlayerandperpendiculartothe

lay-ers– inradialdirection(bothperpendiculartothemagneticfield)

Cross-fieldtransportinsidethelayersisnottakenintoaccount,as

mentionedabove;however,thedisruptiveradial cross-field

trans-portistakenintoaccount

For simulations of the toroidal asymmetry in radiation the

TOKES calculationgrid (which initiallyuses 2D nonlinear

orthog-onalmagneticfluxcoordinates)hasbeendividedintoroidal

direc-tionby Ntor equidistantpoloidalplanes,thusdefininga3D

calcu-lation grid.3D cellsofthisgrid are magneticflux tubes,running

along themagneticfield lines,windingoverthe coreanddivided

in toroidaldirectioninNtor segments asshowninFig 2 The

in-jectiontakesplaceinoneofthesesegments.Themagneticlayeris

thelayerbetweentwoneighboringmagneticsurfaces,limitingthe

cells inradial direction In the TOKES simulations reported here,

eachlayerisfullycoveredwithoneclosedmagnetictube,winding

60–80timestillitclosesinitself

DynamicsofNGplasmainsidethecore,simulatedbyTOKES,is

assumedtoproceedasfollows.Firstofall,atpre-TQstage,theNG

stream from the injector penetrates into the first magnetic layer

(blue layer in Fig 2 ) First portions of NG are fully ionized, but

continuousfeedingofthislayerbyNGatthesamepositionforms coldNGplasmaspot,whichexpandsalongthemagneticfield, be-ingheatedfromhotDTplasmamainlybyelectron thermoconduc-tivityalongthemagneticfieldandcooledbyNGlineradiation Af-ter sufficientcooling oftheplasmaattheinjectionpoint, partof thecontinuouslyinjectedNGcancrossthefirstbluelayerwithout ionization and penetrates further intothe second magnetic layer (grayone in Fig 2 ), causingthesame coldNG plasmacloud for-mation, its expansion along themagnetic field and irradiation of theplasmaenergyfromthislayer.Thisprocessresultsin sequen-tialcooling down ofseveral magnetic layers andpersists till the startofTQ.OneshouldnotethattheneutralNGpropagationis in-fluenced by resonant charge exchange process;the resultsof gas clouddynamicsareillustratedinFig 1

TOKES scenario of MGI assumed that TQ starts after cooling down of predefined magnetic surface (with q=2) TQ simulated

by artificial increase of cross field thermoconductivities (due to startofturbulent plasmaenergytransport) Increasedradial elec-tron thermoconductivity transports plasma thermal energy from corebulk tothe coreedge contaminatedwithNG,wherethe en-ergyirradiatedontosurroundingwalls.InjectionofNG,its ioniza-tionandtheNG plasmaexpansionalong themagnetic field lines proceedsasusualduringTQ,buttheturbulentenergytransportis muchfaster,so wholecoreiscooled down duetoradiationfrom thecontaminatedexternalcorelayers

InTOKES simulations NG plasmaexpands along the magnetic field;diffusionoftheplasmatotheneighboringpartofthe mag-netic tube isneglected Thatmeans the radiation source ineach magnetic layer is spanned along the magnetic tube, in which

NG injected During whole simulation time longitudinal span of expanding NG plasma is assumed to be less than one poloidal turn(which equals to q toroidalturns; q is the safetyfactorand

4 S Pestchanyi et al / Nuclear Materials and Energy 0 0 0 (2016) 1–8

Fig 3 Contaminated plasma dynamics is assumed along one poloidal turn (the radiator) of the magnetic tube in which the NG is injected (bold red arrow in upper left

corner) The radiator is shown from above (left lower panel) and from front (left upper panel) with blue color The rest of the magnetic tube, covering the entire magnetic surface (right panel) is called in TOKES simulations the ‘reservoir’ The reservoir can be moved to a virtual position, schematically shown by a red tube Real positions of the reservoir are shown by red arrows (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

2≤ q <∞closetotheseparatrix)asshownbybluecolorinFig 3

Thisone poloidalturnof thetube iscalled‘radiator’ The restof

themagnetictube withDTplasmawithout NG,called‘reservoir’,

iscooleddown duetothe electronthermoconductivity alongthe

magneticfield.DuringTQthecrossfield turbulentplasmaenergy

transport heats the NGplasma directlyin the contaminated part

ofthe tube,butmainradial heatflux heatsDT plasmainside the

reservoir,whichismuchlargerthanthecontaminatedturn.Then,

thisheat transported to the radiation cloud by electron

thermo-conductivityalong the magnetic field and radiatedonto the first

wallalso

Simulation oftheabove describedscenariohasbeendone

us-ingspecialtrick,whichallowsboiling downof3Dproblemto2D

simulation ofthe plasma dynamics, combinedwith 3D radiation

depositionontothefirstwall

Sinceweassumeabsenceofplasmacross-fieldtransportinside

themagneticlayers,theNGplasmawillbetransportedalongeach

magnetictube independently,without mixingwiththe

neighbor-ingreservoir,coveringthelayer.Radiationfromtheradiatorheats

thewall,so its positionrelative tothe wallis important,butthe

reservoir maybe removedfrom the layer to some ‘virtual’

posi-tionasshowninFig 3 ,becauseits onlyrole inthe processis to

transport energyto the radiator Simulations of the wall heating

withthereservoir inthe layer andwiththe reservoirin the

vir-tualposition are identical.Bearingthisinmind one candefine a

‘block’,whichconsistsofaradiator,connectedwithitsreservoirin

virtualpositionandoftheinjector.Then,onecantiletoroidallyall

thecircumferenceofeachlayerwithNtor blockssidebyside.The

blockswill be joinedwith radiators side by side covering whole

layer, with the reservoirs in virtual positions and with injectors,

approximatingthetoroidalslitinjectorofthe2DTOKESasshown

inFig 2 The plasmadynamicsineachoftheblocksproceeds in-dependentlyonefromanotherandisidentical,sotheplasma dy-namicscan be simulatedwith2D TOKEScode withattachedNtor reservoirsandwith2DNGinjectionincreasedNtortimes

This algorithm has been used for simulation of the first wall radiation heat loadduringMGI in ITERwiththe 2D TOKES code andwithmodified3Dradiationsimulationsubroutine,which cal-culates theheat loadfrom one radiator ofeach layer only Posi-tions oftheseradiatorsare illustratedintherightpanelofFig 2 Thetechniqueexplainedabove allows takinginto accountthe3D nature ofthe radiation heat loads It should be notedthat these heat loads might be overestimated due to the omittance of the cross-fieldtransport.Thus,theresultsreportedheregiveanupper limitoftheheatloads(assumingsymmetryintheradialcross-field transport)whereasthe2Dsimulationsperformedpreviouslygivea lowerlimitduetotheuniformimpuritydistributionintoroidal di-rection

SimulationofMGIfromNinjinjectors,symmetricallydistributed overtoroidalcircumferenceisalsopossible.Theonlydifferencein thiscaseisthereservoirshouldbedecreasedcorrespondingly

3 Simulation results

3.1 2D – 3D simulation results comparison

TheresultsfromthetwoTOKESversions,2Dand3D,havebeen comparedforaninjectionof2kPam3 ofNegasfromeachofthe threeupperinjectorsintoanH-modeITERplasmawith280MJof thermalenergy Inthe 2Dsimulation thetotal Negas amountof

S Pestchanyi et al / Nuclear Materials and Energy 0 0 0 (2016) 1–8 5

Fig 4 Results of 2D (two left panels) and 3D (two middle panels) TOKES simulations of the same MGI Shown are contours for Ne plasma density (two upper panels) and

for the radiation intensity (two lower panels) at the upper part of the poloidal plane at 7 ms On the right panel the radiation intensity from the midplane injector at 5 ms is shown for comparison Color scale for all the plots is shown; maximum value corresponds to red and minimum to blue color Maximum Ne plasma density is 1.2 × 10 22 m −3 for 3D and 2 × 10 21 m −3 for 2D The corresponding maxima in radiation intensity are 73 GW/m 3 and 7 GW/m 3 The maximum in radiation intensity for the midplane injector

is 110 GW/m 3 Injector position is indicated by arrow (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

6kPam3hasbeeninjectedthroughatoroidallysymmetricslit.The

simulations show thatthecontaminated plasmacloudconsistsof

morethan90%ofNeionsandlessthanon10%ofD-Tmixtureat

the position of maximum density.The Neplasma densityof the

2D simulation and the corresponding projection of the Ne

den-sity onto the poloidal plane for the 3D simulation are shownin

Fig 4 at7ms,whichcorresponds roughlyto themaximumin

ra-diated power.Note that all timesinthis paperare givenrelative

totheopeningtimeoftheinjectorvalve.The spatialdistributions

of the neonions are qualitatively similar for both cases, asseen

in Fig 4 However, the peak Ne densityis 6 times larger in the

3D version compared to2D:1.2× 1022m−3 and2×1021m−3

cor-respondingly The photonic radiation source intensities are given

forthesametimeinthelowerpanel ofFig 4 Theintensity

max-ima approximately correlate with the peaks in Ne plasma

den-sity, but the maximum value in the 3D simulation is more than

10timeslargerthanfor2D:73GW/m3 and7GW/m3,

correspond-ingly.Thesedifferencesarequiteexpectable,becausein3Dthe

in-jectedNeplasmaconcentrated toroidallyclosetoinjectorsandin

2D simulationit isevenly distributedalongthe toroidalangle.In

both cases the Ne plasma expandsalong the magneticfield, but

the expansion dynamics are not identical.The plasmaenergy in

each magnetic layeris transportedalong the magneticfield lines

tothelocationofhighNeiondensitywhereitisradiatedand

de-posited tothe surrounding walls The energytransport is mainly

duetoelectronthermoconductivity,butinthe2D casethe

trans-port is over half poloidal turn from both sides of the Ne cloud

whereas in the 3D case the transport is over a distancea factor

(Ntor/Ninj− 1)>>1larger

Note,thatthe Neplasmaofnoticeabledensityspansover less

than 1/3 of poloidal circumference at 7ms, see upper panel in

Fig 4 This confirms the assumption, stated in Section 2.2 The

sameisvalidfortheradiationintensity,lowerpanelinFig 4 The radiation intensity spans over less than one poloidal turn up to

∼20ms,whenalmostalltheplasmaenergyisirradiated

The cross-fieldtransport coefficients duringtheTQ have been adjustedtoensureacharacteristicrisetimefortheradiatedpower

P rad of 1–2ms, see Fig 5 The 3D simulations show a slow de-cayP rad (t),which canbe explained bythe equipartition time be-tweenelectronsandions.Thethermalenergyoftheionsis dissi-patedthroughtheheattransfertotheelectrons, furthertransport

byelectronthermoconductivitytotheradiatorandthenirradiation fromNeplasmacloud.P rad (t)decreaseswithin5–10msasseenin theleftpanelofFig 5 Theresultingwallheatloadsandthe corre-spondingwalltemperaturesareshowninFigs 5 and6 The maxi-mumwalltemperatureislowerinthe2Dsimulationcomparedto 3D dueto the more uniformspread ofthe radiation source The corresponding maximumwall heatflux is by a factor 2–3lower Theduration ofheatflux depositiononthe firstwallis longerin the 3D case, which can be expected because of the longer dis-tances over which the plasma thermal energy is transported to theNeplasmacloud Thepoloidalpositionof theheatflux max-imaissimilar inboth cases,2D and3D Butin3D casethe heat fluxconcentratedintoroidaldirectionclosetothethreeinjectors, whereas it is constant in toroidal direction in the 2D case The toroidalpeakingfactor(TPF)oftheheatfluxonthewallhasbeen calculatedinthe3Dcasetobeintherangeof2–3atthepoloidal positionwheretheheatfluxmaximafromtheupperinjectorsare situated(seeFig 7 ).Forthepoloidalpositionwherethemaximum appearsforthemidplaneinjector,theTPFisabout10.Itis impor-tanttonotethattheheatfluxpeaksatdifferenttimesforthe up-perinjectorsandforthemid-planeinjector.Thetimedifferenceis about2msforthisspecificsimulation.Thepoloidalpeakingfactors (PPFs)arealsooftheorderof10forthesections,runningthrough

6 S Pestchanyi et al / Nuclear Materials and Energy 0 0 0 (2016) 1–8

Fig 5 Comparison of the temporal evolution of the total radiated power from the plasma core (left panel), of the peak wall heat flux (middle panel) and of the peak wall

temperature (right panel) The results of 3D simulation are shown with red color and for 2D with blue The maximum wall temperature in the 2D simulation is smaller than

in 3D due to the uniform spread of the radiation source along the toroidal angle (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig 6 Wall heat flux distribution over the ITER first wall at 7 ms simulated with

the 3D TOKES code (upper panel) and with 2D TOKES (lower panel) The maximum

in the color scale (red) corresponds to Q max = 0.44 GW/m 2 (For interpretation of the

references to color in this figure legend, the reader is referred to the web version

of this article.)

thepeaks andseveraltimeslower fortoroidal positionsbetween theinjectors

3.2 Wall heat load optimization

The Negas ineach injector is storedina plenumof 200cm3 volume with a pressure of up to 10MPa The maximum Ne gas amount in each injector is therefore P0=2kPam3 This quantity canbereducedbyreducingthepressureintheplenum

The first wall temperatures during MGI of 2kPam3 Ne from each ofthethree upperinjectorsandfromthemidplaneinjector are shown inFig 7 Forthis case, the melt threshold is reached

at 4.6ms The melted surface area then grows and reaches of

S max=9.1m2 at5.8ms.The meltisfullyre-solidifiedat8ms.The maximumwalltemperaturereachedinthiscaseisclosetothe va-porization temperature, T max=2700K (T vap=2744K) The melting

ismainlydrivenbytheradiationheatloadfromthemidplane in-jector because of the small distance between the separatrix and thewallatthislocationandthefastertimescales.Themeltedarea

isindicatedbyablacklineintheleftpanelofFig 7 Thefirstwall doesnot melt infront of the upperinjectors It is interesting to comparetheseresultstoacaseforwhichtheinjectiontakesplace throughtheupperinjectorsonly.Theresultingtemperatureforan injectionof2kPam3 Nefromeachupperinjectorisshowninthe rightpanelofFig 7 The maximumwalltemperatureinthiscase

isT max=1280K,noticeablysmallerthanT melt=1560K

Aseriesofsimulations withsequentialtwofolddecreaseof in-jectedgasamounthasbeenperformedwiththeaimtoreducethe first wall heatfluxes fromtheradiation flash andto identifythe minimumquantity required tokeep radiation levels highenough

to ensure sufficient thermal quench mitigation in ITER In accor-dancewithourexpectations,thereduction ofthegaspressurein the plena has led to reduction of the maximum radiated power andtostretching theheatingpulsein time,asseeninFig 8 For thecasesinvestigated,thepeak walltemperatureafterirradiation

oftheentireplasmathermalenergyisconsequentlyreduceduntil

31Pam3ofNeisreachedintheplenum.Forthisquantitythe ther-malenergyisnotfullyradiatedandapproximately18%ofthe ini-tialthermalenergyremainsinthecore.Simulationresultsforthe caseof3+1injector with62Pam3 ofNe, forwhichthe plasma energyisstillfullyradiated,showadecreaseofthemaximumwall temperaturebelowT melt,toT max=1490K,whereasforatwotimes largerinjection(125Pam3)thewallstillmeltsat8msfor∼1.6ms withameltedareaofS max=1.4m2

S Pestchanyi et al / Nuclear Materials and Energy 0 0 0 (2016) 1–8 7

Fig 7 The simulated wall temperature distribution for MGI of 2 kPa m 3 Ne from each of the three upper injectors and the midplane injector into an ITER plasma with thermal energy of 280 MJ is shown in the left and middle panels for two time moments: 6 ms, when most of the heat flux is caused by the midplane injector (left panel,

T max = 2340 K) and 8 ms, when the heating of the wall is dominated by the upper injectors (middle panel, T max = 1540 K) The right panel shows the wall temperature pattern for the case without midplane injector, T max = 1280 K The black line in the left panel outlines the melted area Positions and estimations for poloidal (PPF) and toroidal (TPF) peaking factors for the heat flux on the first wall are shown

Fig 8 Simulated total radiated power for different gas amounts in each of the four

injectors (P 0 = 2 kPa m 3 ) Ne gas has been injected into ITER plasma with thermal

energy of 280 MJ

DisruptionmitigationbyMGIinITERhasbeensimulatedusing

anupgradedversionoftheTOKEScodetotakeintoaccount3D ef-fectsofthepenetrationoftheinjected noblegasintotheplasma andofthe radiationheat loads on theITERfirst wall The simu-lationsincludetheITERfirst wallgeometryandthe set-upofthe injectorsofITERDMS.Thelatterconsistsof3+1injectors:3 up-perandone midplane,containingup to2kPam3 ofNegas each ThesimulationshavebeenperformedforanH-modeITERplasma with280MJofplasmathermalenergy.Theefficiencyofheatload mitigationhasbeenassessedinthesimulationswithrespectto in-jectionquantity,tothenumberofinjectorsandtheirlocation Thesimulations have shownthat first wall meltingcausedby the radiation flash during the mitigated thermal quench can be avoidedbyeitherreducingthequantityofinjectedneonorby us-ing theupper port injectorsonly Injection fromthe upperports with the maximum amount of Ne – 2kPam3 from each of the threeinjectorsresultedinatemperatureriseup toT max=1280K, wellbelowthemeltlimit.Addingthemidplaneinjectorresultedin

adrasticincrease inthepeak wall temperature,almost upto the vaporization temperature The wall hasbeen melted in thiscase overan area of S max=9.1m2 andre-solidifiedafter slightlymore than2ms

Simulations withreduced injectionquantities have revealeda steadydecreaseoftheradiationinducedwalltemperature.Forthe injectionwithallinjectors,meltingwaspreventedbyreducingthe

8 S Pestchanyi et al / Nuclear Materials and Energy 0 0 0 (2016) 1–8

injectedNeamountsto62Pam3fromeachinjector.Themaximum

walltemperaturereachedwasT max=1490K.Furtherreductionto

31Pam3ofNeledtoinsufficientradiationandpartofthethermal

energywasremainingintheplasmaformorethan40ms

Furtherinvestigationsofthefirstwallheatloadmitigation

dur-ing MGI in ITER are still needed One can propose further wall

damagemitigationadjustingtime delaysbetweeninjectors.These

investigationsareplannedandtheresultswillbereportedinnext

papers.Itisalsoimportanttonotethatthesimulationspresented

heretakeintoaccountasymmetriesinradiationcausedbythe

in-jectiongeometry,butapossibleimpactoftheMHDeventsdriving

thethermalquenchonpoloidalandtoroidalradiationdistribution

havenotbeenconsideredsofar.TheeffectoflargescaleMHDon

theradiationdistributionhasbeenfoundin[10] tobeequally

sig-nificantwiththeNeplasmaspotdynamics

Acknowledgments

ThisworkwassupportedbyFusionforEnergyandbytheITER

Organizationandcarriedoutwithintheframeworkofthecontract

F4E-OPE-584.Theviewsandopinionsexpressedhereindonot

nec-essarilyreflectthoseofIOandF4E.ITERisaNuclear Facility

INB-174

References

[1] M Lehnen , et al , Nucl Fusion 51 (2011) 123010 [2] I Landman , et al , Fusion Eng Des 88 (2013) 1682–1685 [3] I.S Landman , Tokamak Code TOKES Models and Implementation, Report of Forschungszentrum Karlsruhe, 2009 FZKA-7496

[4] I.S Landman , S.E Pestchanyi , Y Igitkhanov , R Pitts , Two-dimensional modeling

of disruption mitigation by gas injection, Fus Eng Des 86 (2011) 1616 [5] S Pestchanyi , M Lehnen , A Huber , I Landman , Verification of TOKES sim- ulations against the MGI experiments in JET, Fusion Eng Des 87 (2012) 1195–1200

[6] S Pestchanyi , M Lehnen , A Huber , S Gerasimov , Yu Igitkhanov , I Landman ,

et al , Analysis of energy cross-transport during MGI: JET experiments and TOKES simulations, Fusion Eng Des 88 (2013) 1127–1131

[7] S Pestchanyi , A Boboc , A Bazylev , I Landman , Optimization of MGI in JET using the TOKES code and mitigation of RE damage for the first wall, Fusion Eng Des 89 (2014) 2159–2163

[8] V.A Izzo , Impurity mixing and radiation asymmetry in massive gas injection simulations of DIII_D, Phys Plasmas 20 (2013) 056107

[9] D Shiraki , N Commaux , L.R Baylor , N.W Eidietis , E.M Hollmann , V.A Izzo , Characterization of MHD activity and its influence on radiation asymmetries during massive gas injection in DIII-D, Nucl Fusion 55 (7) (2015) 073029 [10] V.A Izzo , et al , The role of MHD in 3D aspects of massive gas injection, Nucl Fusion 55 (2015) 073032

[11] A Fil , et al , Three-dimensional non-linear magnetohydrodynamic modeling of massive gas injection triggered disruptions in JET, Phys Plasmas 22 (2015)

062509 [12] S.I Braginskii , in: M.A Leontovich (Ed.), Reviews of Plasma Physics, vol I, Con- sultants Bureau, New York, 1965, p 205