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공학석사 학위논문
Al t er at i on ofLow Dens i t y Ope r at i on RangebyRes onant Ma gnet i cPer t ur bat i on i n KSTAR
KSTAR 의 자기공명섭동에 의한 저밀도 운전영역의 변화에 관한 연구
2 0 1 6
년2
월서울대학교 대학원
에너지시스템공학부
손 정 훈
Al t er at i on ofLow Dens i t y Ope r at i on RangebyRes onant Ma gnet i cPer t ur bat i on i n KSTAR
지도교수 나 용 수
이 논문을 공학석사 학위논문으로 제출함
2 0 1 6
년2
월서울대학교 대학원
에너지시스템공학부
손 정 훈
손정훈의 석사 학위논문을 인준함
2 0 1 6
년2
월위 원 장 황 용 석 (인) 부위원장 나 용 수 (인) 위 원 인 용 균 (인)
Abst r act
Al t er at i on ofLow Dens i t y Ope r at i on RangebyRes onant Ma gnet i cPer t ur bat i on i n KSTAR
Son,Jeong-hoon DepartmentofEnergySystem Engineering TheGraduateSchool SeoulNationalUniversity
Knowing the operation range of tokamak is important since the operation parameters determine the fusion outputpowerand plasma operationscenarios.InthisthesistheoperationrangeofKSTAR was revealed via Hugilldiagram and Greenwald density fraction diagram.
In total 1740 experimental shots were selected carefully for this analysis which were performed from 2011 to 2014 in KSTAR.By comparing the operation range ofKSTAR with thatofDIII-D via Hugill diagram,it was found that KSTAR can reach far lower density,insisting thatKSTAR hasextremely low intrinsicerrorfield.
The range of the achievable Greenwald fraction of KSTAR was showntobe6% to60% inthepresentdatabase.
the achievable low density operation range were investigated.The condition forthegeneration oftherunaway electron in KSTAR was found via Dreicer condition with dedicated runaway electron generation experiments. Although these experiments satisfy the condition forgenerating runaway electrons,allofthese shots could be sustained without significant interruptions. Based on this observation the runaway electrons are notthoughtto be the main factortosetthelow density operationlimitinKSTAR.Ontheother hand,plasma shots with the increased error field by applying the resonant magnetic perturbation(RMP) often showed the plasma lockingphenomenonsothataccesstothelow densityoperationrange wassignificantly constrained.The plasma locking threshold is found to be differed by the position ofthe applied RMP coiland the
value.The RMP coilcurrentmagnitude needed for plasma locking from themiddlecoilisabouthalfofthatfrom thetoporthebottom coil.And the lower value showed the lower density operation range, with ≈ in cases and ≈ in
cases.The influence ofRMP to the low density range is investigated in terms of the L-mode to H-mode transition power which shows thataccess to the optimaldensity range ofthe L-H transition can belimitedby applying RMP.Therefore,itissuggested to take this effectinto accountin designing operation scenarios for tokamaks employing RMP to suppress edge localized modes in H– modeplasmasinparticular.
keywords:KSTAR,Density limit,Hugilldiagram,Greenwald density fraction,Resonantmagneticperturbation, Runaway electron,tokamakoperation
StudentNumber:2013-23182
Cont ent s
Abstract ···ⅰ Contents ···ⅳ ListofFigures ···ⅵ
Chapter1 Introduction···1
1. 1Mot i vat i on · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·1
1. 2Pr ecedi ng r esear ches· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·2
1.2.1Operationlimit···2
1.2.2Physicsbackgroundofthelow densitylimit···3
1. 3Pur poseoft hi sst udy· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·4
Chapter2 Operation rangeofKSTAR ···7
2. 1Dat aacqui si t i on· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·7
2. 2Oper at i on r angeofKSTAR· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 11
Chapter3 Alteration oflow density operation range···14
3. 1Ef f ectofr unaway el ect r ons· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 14
3. 2Ef f ectofr esonantmagnet i cper t ur bat i on( RMP)· · · 16
3.2.1RMP applicationinKSTAR···16
3.2.2Typesofplasmalocking···17
3.2.3Severalfeaturesoflockedplasmas···19
3.2.4Low densitylimitchangebyRMP···22
3.2.5ImpacttoL-H powerthresholdbyRMP···24
References···28 국문 초록 ···31
Li stofFi gur es
Fi gur e1. 1Hugi l ldi agr am [ 3 ]· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 2 Fi gur e1. 2L-H t r ans i t i onpowe rt hr e s hol di nKSTAR wi t ht he e xper i me nt si n2010and2011[ 2]· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 5
Fi gur e 2. 1 Exa mpl e ofs e l e c t i ng 5 t i me poi nt s ( gr e e n)i n t he pl as maf l a t t op( r e d)( # 9 1 9 7 )· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 8 Fi gur e2. 2Exc l ude ds hotduet odat as hor t a geofmi norr adi us , ma j orr a di usande l onga t i o n.Theda t al ac k a r e ai si ndi c at e d by gr e e nboxe s( # 5 8 9 9 )· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 9 Fi gur e 2. 3 Exc l ude d s hot due t o c ont i nuous de ns i t y r i s i ng ( gr e e nar e a)c a us e dbyf r i ngej umpe r r or( # 8 0 3 5 )· · · · · · · · · · · · · · · · · · · · ·1 0 Fi gur e 2. 4 ( a ) The ope r at i on r ange of KSTAR vi a Hugi l l di agr am,( b)Compa r i s onoft heope r at i onr angeo fKSTAR wi t h DI I I -D [ 9 ]· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·1 2 Fi gur e2. 5Theope r at i onr angeofKSTAR vi aGr e e nwa l d de ns i t yl i mi tandt heGr e e nwal dde ns i t yf r ac t i on· · · · · · · · · · · · · · · · · · · · · · ·1 3
Fi gur e3. 1 Ove r vi e w o ft hede di c at e dr unawa y e l e c t r on pl as ma
( # 7 5 9 8 )· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·1 4
Fi gur e3. 2Thepos i t i onoft hede di c a t e dr una waye l e c t r on
s hot sonHugi l ldi a gr am· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·1 5
Fi gur e 3. 3 ( a )Conf i gur at i on oft he KSTAR I n-Ve s s e lc ont r ol
c oi l s ,( b)Sc he mat i cdi a gr a m oft heI n-Ve s s e lc o nt r olc oi l sand
f i e l de r r orc or r e c t i onc o i l s[ 1 3 ]· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·1 6
Fi gur e3. 4Pos s i bl ec onf i gur at i onso ft heRMP phas e[ 1 4]· · ·1 7
Fi gur e 3. 5 Two c a s e s o f pl a s ma l oc ki ng:( a ) Loc ki ng wi t h
H-L bac k-t r ans i t i on and s ubs e que nt di s r upt i on whe n RMP
appl i e d i n H-mode pl as ma s ( # 9 0 6 3 )whi c h i s c ompa r e d wi t h a
no RMP c as e ( # 9 0 6 4 ) ,( b) Loc ki ng ove r t hr e s hol d RMP c oi l
c ur r e nti nL-modepl as mas( # 8 8 5 6 )· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·1 8
Fi gur e3. 6Ove r vi e w of# 8 9 7 3wi t hpl a s mal o c ki ngpo i nt· · · · · ·1 9
Fi gur e3. 7MHD s pe c t r ogr a m of# 8 9 7 3· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·2 0
Fi gur e3. 8Evol ut i on oft het e mpe r at ur epr of i l ei nt i me ;t= 2 . 4
s( bl ac k) ,t= 2 . 7s( r e d) ,t= 3s( bl ue )t= 3 . 3s ( gr e e n)a nd
t=3 . 6s( mage nt a )· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·2 1
Fi gur e3. 9Pl otoft hel oc ki ng poi nt si nGr e e nwal df r a c t i onand
RMP c oi lc ur r e ntwi ndo w · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·2 2
Fi gur e3. 10Pl otoft hepl a s mal oc ki ng poi nt ss ho wn i n Fi gur e
3 . 9wi t hHugi l ldi agr a m a ndGr e e nwa l df r ac t i ondi agr am · · · · ·2 3
Fi gur e 3. 11 Di a gr am of pl as ma l oc ki ng r a nge ove r L-H
t hr e s hol d powe rve r s usGr e e nwal d de ns i t y f r a c t i on f or ( gr e e n)
and ( vi o l e t ) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·2 5
Chapt er1 I nt r oduct i on
1.1Motivation
In nuclear fusion research for developing fusion power plants, finding outtheoperation rangeofa tokamak device,especially with respectto the plasma density is importantfor tokamak operations since the operation range can influence the fusion performance ofa tokamak.
The so-called density limit can be subdivided into the upper density limit and the low density limit.The upper density limit affects the fusion power output,since the fusion reaction rate is known to be proportionalto[1].Therefore,many studies about operation rangehavebeen focused on upperdensity limits,sincethe outputfusion powerisdirectly related to maximum density.Butthe low density limitcan also affectthefusion performancein termsof the L-mode to H-mode (L-H)transition powerthreshold.In many devices, optimal density exists where the L-H transition power exhibitsthelowestvalue.Ifthisdensity can notbeaccessed dueto thelow density limit,moreheating powerwillbeneeded to achieve H-modessothatthefusion powermultiplication factor(Q)could be reduced and more power will be needed for a fusion reactor. Therefore,in this thesis,the operation range willbe investigated, mostlyinview ofthislow densitylimit.
Figure1.1Hugilldiagram [3]
1.2Preceding researches
1. 2. 1Oper at i on l i mi t
TheoperationalrangecanbecharacterizedbyHugilldiagram[3],as shown in Figure 1.1.The Hugill diagram was originally set by collecting experimentaldatafrom severaltokamaks.Eachboundary of the diagram represents its own condition for density limit. The left-hand side is the low density limit,usually set by runaway electrons.The upperside is limited by the plasma currentlimitat low safety factor.The righthand side is setby the powerbalance betweentheinputpowerandtheplasmaradiation.Thelowerpartis the plasma confinement limit between the plasma density and the
plasma current,represented as Hugilllimit[4][5].The Hugilllimitis later replaced by the Greenwald density limit, expressed as
.The Greenwald density limitindicates the maximum achievable density in each tokamak.Butlaterthe condition forthe density limitisknown torelated with theedgeplasmadensity only, so one can exceed the Greenwald density limitby plasma shaping, centralfuelling,edgepumping,andothers.
1. 2. 2Physi csbackgr ound oft hel ow densi t y l i mi t
Thelow density limitcanbesetby severalreasons.Oneisbythe runawayelectrons,asmentionedinHugilldiagram.Earlyexperiments oftokamak showed thedisruptionsin low density operation because of massive impurities generated by runaway electron[6][7]. The condition for generating runaway electron is determined by the Dreicer’s model[8]. In this model, the runaway electron can be generated over the critical electric field, ,, where
and
ln
≅ with assuming
ln ≈ .So itis expected thatthe numberofrunaway electrons willincreaseasthedensitygoesdown.
Anotherreason forthelow density limitistheplasmalocking due to errorfields.Weconsidertwo types oferrorfields in this thesis. The first one is the intrinsic error field.Every tokamak has the intrinsicerrorfield becauseoftheimperfection ofthecoilsymmetry.
Thelow density limitsetby theintrinsicerrorfield wasstudied in DIII-D[9].In this study,the large intrinsic error field in DIII-D inducedplasmalocking,henceresulting inincreaseofthelow density limit. This phenomenon was mitigated by applying additional magneticfieldstocompensatetheerrorfield,theso-callederrorfield correction.The otheris the resonantmagnetic perturbation (RMP). The RMP can affect the plasma rotation, density, and so on.
Especially,large magnitude of RMP is known to induce plasma lockinganddisruptions.
1.3Purposeofthisstudy
The Korea Superconducting Tokamak Advanced Researches (KSTAR)device was constructed and achieved the firstplasma in 2008.Itaims atachieving long-pulse high performance steady-state plasmaoperations.
A varietyofresearcheshavebeenmadetoinvestigatethetokamak operation rangewith thedensity limitsin severaltokamak machines, however KSTAR has not addressed this yet.In this thesis,the operation rangeofKSTAR willbeinvestigated.Particularfocuswill beupontheexplanationofthelow densitylimitidentifiedinKSTAR.
The intrinsic error field of KSTAR was investigated recently, insisting thatthe KSTAR hasan extremely low intrinsicerrorfield comparedtoothertokamakdevices[10].Inthispointofview,KSTAR isexpected to havelittleinfluenceoferrorfield to determination of thelow densitylimit.
On the other hand,the effectofthe runaway electrons and the errorfieldbyRMP isnotclearly revealedyet.Furthermore,theRMP isgenerallyusedtosuppressedgelocalizedmodeinH-modeplasmas and to study the neoclassicaltoroidalviscosity.Many experiments usingRMP havebeenperformedinKSTAR andlotsofplasmashots showedplasmalocking andsometimesdisruptionswhen RMP applied duringexperiments.
The L-H transition power threshold is investigated using the database collected from experiments performed in 2010 and 2011 of theKSTAR campaign,andtheresultisshowninFigure1.2[2].From thisresult,onecan seethereisan optimaldensity forefficientL-H transition with the lowest auxiliary heating power in KSTAR.
Assuming thatthisphenomenon can beprojected toafusion reactor ifthedensitycannotreachthisregionbyseveralreasons,theheating power forL-H threshold mustbe increased,and itcan affectthe fusionamplificationfactor.
In conclusion,the operation range and the effectofthe runaway electron and the RMP to the low density limitin KSTAR willbe revealed in this thesis.In chapter 2,the preparation process for plotting the Hugilldiagram willbe introduced first,then the overall operationrangeofKSTAR willbeintroducedviaHugilldiagram and the Greenwald density fraction.The effectofrunaway electron and the RMP to low density limit will be discussed in chapter 3.
Summarization of the results and conclusions will be drawn in chapter4.
Figure 1.2 L-H transition powerthreshold in KSTAR with the experiments in 2010and2011[2]
2.Oper at i on r angeofKSTAR
2.1Dataacquisition
To investigate the operation range ofKSTAR,experimentresults from 2011to2014ofplasmashotswerecollected.Therangeofthe plasma shotsperformed during thisperiod coversfrom shot4469 to shot11726.Five pointswereselected pershotduring theflattop of the plasma.The selection process of the data time points is as follows:
① Smooththeplasmacurrentintime
② Findthebothendsofthecurrentflattop-setas0and1
③ Setthehalfpointofbothend– 0.5
④ Setthehalfpointbetween③ andeachend– 0.25and0.75
⑤ Setthehalfpointbetween③ and④ -0.375and0.675
An exampleoftheselected points is shown in Figure2.1 ofshot 9197.The physics parameters needed to plotHugilldiagram were calculated on these time points by interpolation.Allthese processes wereconducted by using MATLAB codetohandlethelargeamount ofdata.
During these processes,it is found that not allthe shots were suitableforanalysis.Thecasesofunsuitabledatacanbecategorized asfollows.
Figure 2.1 Example ofselecting 5 time points (green)in the plasmaflattop(red)(#9197)
The firstcase is the data shortage ofthe plasma shots.Mostof thiscaseincludesthemissing ofthecriticaldata foranalyses,such as the plasma density orthe plasma current,which are needed to calculate forplotting the Hugilldiagram.Some shots have the data lackin partofthepulse.A typicalexampleofthiscaseisshown in Figure2.2oftheshot5899wherethethreedata,minorradius,major radius,elongation datawerecut-offduring theplasma flattop phase, whichcauseserrorintheinterpolationprocess.
Figure 2.2 Excluded shot due to data shortage of minor radius,major radius and elongation. The data lackareaisindicatedbygreenboxes(#5899)
Thesecondcaseistheimproperdatameasurementsorcalculations. Mostofthis case is caused by density profile.In KSTAR the 280 GHz millimeterwave interferometeris used to measure the electron line average density[11].Since the interferometerhas the possibility ofthefringejump error,theadvanced method[12]isused toreduce thisfringejumperrortogetmoreaccuratedensity.However,someof
Figure 2.3 Excluded shotduetocontinuousdensity rising (green area) caused by fringe jump error (#8035)
the plasma shots showed the continuous density rising.The typical caseisshown in Figure2.3 ofshot8035.Thisphenomenon usually appearedintheH-modephasewiththeELM activity.
Since these unsuitable data can significantly affect the analysis result,shots were carefully selected by excluding these unsuitable shots.
From this data refining process,totally 2593 shots were obtained.
Among them,853 shots showed the disruption during the plasma
flattop, while the remaining 1740 shots were sustained without disruptions.
2.2Operation rangeofKSTAR
The operation range of KSTAR was investigated via Hugill diagram and Greenwald density fraction range,with the 1740 shots which were not disrupted.The three data,the minor radius,the major radius and the elongation, are taken from the real-time equilibrium reconstruction(rt-EFIT).Theminorradiusandthemajor radius are keptthe same value,averaged over the currentflattop phase,atalltheselected timepointsin each shottomislead results duetonon-physicaloscillationsfrequentlyobservedinraw data.
Figure 2.4(a) shows the operation range of KSTAR via Hugill diagram which is compared with thatofDIII-D in GeneralAtomics in the U.S.A.[9]is shown in Figure2.4(b).The shifted position of the diagram is thoughtmainly due to the difference ofthe toroidal magneticfield()asDIII-D isabout1-2T referredto1.5-3.8T of KSTAR. Nonetheless, KSTAR can reach far low density than DIII-D which is thoughtto be resultfrom extremely low intrinsic error field of KSTAR [8].This willbe discussed in more detail below.
Figure 2.5 shows the operation range plotted with Greenwald fraction diagram in ‘ vs’.In thisdiagram thegradientcan be directly expressed in the Greenwald density fraction.The maximum value of the Greenwald fraction showed 80%,but considering the
(a)
(b)
Figure 2.4 (a) The operation range of KSTAR via Hugill diagram,(b)Comparison oftheoperation rangeof KSTAR withDIII-D[7]
Figure 2.5 The operation range of KSTAR via Greenwald densitylimitandtheGreenwalddensityfraction
errorrange ofthe minorradius in EFIT and the data distribution, which is thoughtto be about60%.From the two diagrams with Hugilland Greenwald fraction,itseems thatthe KSTAR has not enough auxiliary power to reach the maximum Greenwald density limit,resulting in the lack ofdata in the high density region.In addition,the pelletinjection which can increase the core density is not available yet in KSTAR.It is noteworthy that the minimum densityisabout6% oftheGreenwaldfraction.
3.Al t er at i onofl ow densi t yoper at i onr ange
3.1Effectofrunaway electrons
The runaway electron is known as the main factor of the low densitylimitinHugilldiagram[3].KSTAR alsoobservestherunaway electrons in low density plasmas,especially in ≥ × condition in view ofthe Dreicer theory[8].To check the effectofrunaway electrontolow densitylimit,theexperimentofthededicatedrunaway electronconductedin2012werestudied.Figure3.1isoneofthetypical
Figure 3.1 Overview of the dedicated runaway electronplasma(#7598)
Figure 3.2 The position ofthe dedicated runaway electron shotsonHugilldiagram
runaway electron experiments,and the position of these shots on Hugilldiagram is indicated in Figure 3.2.The ratio between the applied electric field and the criticalelectric field, ,in these experiments is about6 to 15.This implies thatthese shots would produce the runaway electrons.Nevertheless,these shots could be sustained withoutsignificantinterruptions by the runaway electrons during the plasma current flattop phase. From this result, it is thoughtthatthe generation ofrunaway electron isnotthe essential factortosetthelow densitylimit.
3.2Effectofresonantmagneticperturbation(RMP)
3. 2. 1RMP appl i cat i on i n KSTAR
KSTAR hasin-vesselcontrolcoils(IVCC)forthepurposeoffast plasma position control,field error correction (FEC),and resistive wallmode control[13].By combining the IVCC,the three pairs of FEC coilscan bemadein top,middle,and bottom.Combining these coilscanproduceseveralRMP phases,asshowninFigure3.4.
The RMP is widely used in many KSTAR experiments,such as ELM mitigation and suppression, neoclassical toroidal viscosity studies,and others.However,some shots exhibit plasma locking whentheRMP isapplied.
(a) (b)
Figure 3.3 (a)Configuration oftheKSTAR In-Vesselcontrolcoils (b) Schematic diagram of the In-Vesselcontrolcoils andfielderrorcorrectioncoils[13]
Figure3.4PossibleconfigurationsofRMP phase[14]
3. 2. 2Typesofpl asmal ocki ng
The type of the plasma locking due to RMP can be roughly classified by two cases.One is shown in Figure 3.5(a) which is occurred by the decrease of the toroidal rotation speed and the density when RMP isapplied,resulting theH-L back transition and subsequentdisruption.Thistypeoflocking characteristiccan beseen in H-mode plasmas. Lots of plasma locking phenomena can be classifiedintothistypeinKSTAR ELM controlexperiments.
The othertype ofthe plasma locking is shown in Figure 3.5(b) which indicates thatsufficiently large RMP currentin low density L-modeplasmascan maketheplasma destabilization and disruption.
Mostoftheplasmalockinginthiscasewasoccurredbyn=1RMP.
Itisnoteworthy thattheplasmalocking by n = 2RMP wascaused inonlyafew discharges.
Figure 3.5 Two cases ofplasma locking:(a)Locking with H-L back-transition and subsequent disruption when RMP appliedin H-modeplasmas(#9063)which iscomparedwith a no RMP case (#9064),(b)Locking overthreshold RMP coil currentinL-modeplasmas(#8856)
3. 2. 3Sever alf eat ur esofl ocked pl asmas
ThecharacteristicsoflockedplasmaaboutthecaseofFigure3.5(b) with n = 1RMP applied shotswasinvestigated sincethiscasewas expected to have more effect on the low density limit. Similar investigationwasmadewithn=1andn=2mixedRMP[15].
Figure3.6Oveview of#8973withplasmalockingpoint
Thetypicalshot#8973waschosen and analyzed.Theoverview of the #8973 is shown in Figure 3.6 where the plasma locking time is vertically indicated.In the reference case the locking threshold was defined by the change of the toroidal rotation velocity and the electron temperature.Unfortunately,theexperimentsusedinthiscase did nothave the toroidalrotation velocioty,so thethreshold by the change of electron temperature is thought as the plasma locking point.
When theRMP coilcurrentisincreased and reached thethreshold value,theelectrontemperaturedropsfirst.Andtheplasmais
Figure3.7MHD spectrogram of#8973
Figure3.8 Evolution ofthetemperatureprofilein time;t= 2.4 s(black),t= 2.7 s(red),t= 3s(blue)t= 3.3s (green)andt=3.6s(magenta)
destablized globally,shown in 2.82 second.ThecoilcurrentofRMP was about 2.2 kA, applied by the middle coil. In the MHD spectrogram,ann=1modeisobservedduringtheRMP isapplied.
ThetemperatureprofileevolutionisshowninFigure3.8.Whenthe plasma was destabilized,the edge plasma temperature dropped first. Thistemperaturedrop affected thewholeplasmaregion,resulting in the globalplasma degradation.At3.6 s,the edge temperature drop wasstoppedbutthecoretemperaturewasdecreased.
3. 2. 4Low densi t y l i mi tby RMP
Thelow density limitchangeduetoplasma locking by RMP was investigatedwithrespecttotheGreenwalddensityfractionandHugill diagram.Figure3.9showsthepointsofdisruptedplasmasby plasma locking in theGreenwald fraction and theRMP coilcurrentwindow.
From thisresult,theconditionsfordetermining low density limitby RMP canbecategorizedasfollows.
OneoftheconditionisthepositionoftheapplyingRMP.Inplasma conditionswith a similardensity,thecoilcurrentneeded forplasma lockingbythemiddleRMP isaboutthehalfofthatbythetopor
Figure3.9PlotofthelockingpointsinGreenwaldfractionand RMP coilcurrentwindow
(a)
(b)
Figure3.10 Plotoftheplasmalocking pointsshown in Figure 3.9 with Hugilldiagram and Greenwald fraction diagram
the bottom RMP. This does not appear in Hugill diagram or Greenwald diagram since they do not contain the variable of the RMP coilcurrent.Itisexpected thatifthecoilcurrentisthesame foralltheRMP coils,thelow density limitwillbemuch higherfor themiddleRMP thanthatforthetoporthebottom RMP.
Nextthe value ofthe plasma seemed to influence the density limit.Theplasmashotswith showedthelowerdensitylimit than those with .The plasma parameters for case haveIp= 0.6MA,BT = 2T and elongation(κ)= 1.6,and for
case have the same Ip and BT with elongation(κ) = 1.38.So the plasma with low or low elongation is thought to exhibit low densitylimit.
3. 2. 5I mpactt oL-H powert hr eshol d by RMP
Finally,Greenwald fraction rangeofdisrupted plasma wereapplied to L-H threshold plotto investigate the effectofRMP to the L-H transition threshold power[2].Asthe density limitin this thesis is treated with Greenwald fraction,the L-H threshold plot was also converted from the line average density to the Greenwald density fraction.The density range ofthe disrupted plasma is indicated in Figure3.11forthetwodifferent values.Asnort-EFIT datawas available for the data,since the rt-EFIT was employed from the middle of 2012 campaign in KSTAR.So the direct comparison is limitedhere.Butitisclearlyseenthatthelow densitylimitrange
Figure 3.11 Diagram of plasma locking range over L-H threshold power versus Greenwald density fraction for (green) and
(violet)
setby RMP is in the optimaldensity range for the lowest L-H transitionthresholdpowertoaffectL-H transitionscenarios.
4.Concl usi on
Theoperation rangeofKSTAR is investigated in termsofHugill diagram and the Greenwald density fraction.KSTAR experiments conductedduring 4yearswereanalyzedwhere1740shotswereused carefully selectedbyadatarefining process.ItisfoundthatKSTAR can reach a far low density range with the achievable Greenwald fractionof6%.
Thisaccessibility to thelow density range is investigated by two main factors known to set the low density limits,the runaway electron andtheplasmalocking by theerrorfield.Itisrevealedthat the runaway electron does not impact the sustainment of plasma discharges at low density even though significant fraction of the runaway electrons is suspected to present.Instead,increased error field by auxiliary applied RMP can significantly interrupted the plasma dischargesresulting in plasmalocking and disruption so that access to the low density range was signficantly restricted.The condition forplasmalocking by RMP can bedifferedby theposition ofRMP andthe valueoftheplasma.Thehigher plasmawith middle-applied-RMP is expected to have a higher value of low densitylimitfraction.TheimpactoftheerrorfieldincreasedbyRMP is studied forL-H transition.The Greenwald fraction range ofthe plasmalocking seemstocovertheoptimaldensity rangeoftheL-H transition pointin KSTAR,so caution is needed to design operation scenarios with RMP to suppress edge localized mode in H-mode
plasmas.
Thisstudy ismainly donetoanalyzen = 1RMP from themiddle coilbutcanbeextendedton=2RMP andupper/bottom coilswhich need detailed calculation ofthe penetrated errorfield.Comparison of the RMP effect on n = 1 and n = 2 would be interesting and important to prepare ITER where employing RMP is being considered.
Ref er ences
[1]Martin Greenwald,“Density limitsin toroidalplasmas”,Plasma PhysicsandControlledFusion44,R27(2002)
[2]J.-W.Ahn,H.-S.Kim,Y.S.Park,L.Terzolo,W.H.Ko,J. -K.Park,A.C.England,S.W.Yoon,Y.M.Jeon,S.A.
Sabbagh,Y.S.Bae,J.G.Bak,S.H.Hahn,D.L.Hillis,J.Kim, W.C.Kim,J.G.Kwak,K.D.Lee,Y.S.Na,Y.U.Nam,Y.K.
Oh and S.I.Park,“Confinementand ELM characteristics of H-modeplasmasinKSTAR”,NuclearFusion52,114001(2012) [3]M.Greenwald,J.L.Terry,S.M.Wolfe,S.Ejima,M.G.Bell,
S.M.Kaye,G.H.Neilson,“A new look atdensity limits in tokamaks”,NuclearFusion28,2199(1988)
[4]M.Murakami,J.D.Callen,L.A.Berry,“Someobservationson maximum densities in tokamak experiments”,Nuclear Fusion 16,347(1976)
[5] S.J. Fielding, J. Hugill, G.M. McCracken, J.W.M. Paul, R.
Prenticeand P.E.Stott,“High-density dischargeswith gettered toruswallsinDITE”,NuclearFusion17,1382(1977)
[6] V.S. Vlasenkov, V.M. Leonov, V.G. Merezhkin and V.S.
Mukhovatov,“The runaway electron discharge regime in the Tokamak-6device”,NuclearFusion13,509(1973)
[7]V.V.Alikaev,K.A.Razumova and Yu.A.Sololov,“Runaway- electron instability in the TM-3 Tokamak ”,Sovietjournalof plasmaphysics1,546(1975)
[8]R.S.Granetz,B.Esposito,J.H.Kim,R.Koslowski,M.Lehnen, J.R.Martin-Solis,C.Paz-Soldan,T.Rhee,J.C.Wesley,L.
Zeng and ITPA MHD Group,“An ITPA joint experimentto study runaway electron generation and suppression”,Physicsof Plasmas21,072506(2014)
[9]J.T.Scoville,R.J.LaHaye,A.G.Kellman,T.H.Osborne,R.
D.Stambaugh,E.J.Strait,T.S.Taylor,“Locked modes in DIII-D and a method forprevention ofthelow density mode”, NuclearFusion31,875(1991)
[10]Y.In,J.K.Park,J.M.Jeon,J.Kim and M.Okabayashi,
“Extremely low intrinsic non-axisymmetric field in KSTAR anditsimplications”,NuclearFusion55,043004(2015)
[11]Y.U.Nam,K.D.Lee,“A 280GHzsingle-channelmillimeter- wave interferometersystem forKSTAR”,Review ofscientific instruments79,10E705(2008)
[12]Y.U.Nam,“Multi-fringecountingtechniqueofmillimeter- waveinterferometersystem forKSTAR”,Transactionsoffusion scienceandtechnology55,180(2009)
[13]H.K.Kim,H.L.Yang,G.H.Kim,Jin-Yong Kim,Hogun Jhang,J.S.Bak,G.S.Lee,“Design features ofthe KSTAR in-vesselcontrolcoils”,Fusion Engineering and Design84, 1029(2009)
[14]Y.M.Jeon,S.W.Yoon,J.H.Kim,S.H.Hahn,W.C.Kim, Y.K.Oh,Jong-GuKwak,W.H.Ko,S.G.Lee,J.G.Bak,K.
D.Lee,Y.U.Nam,J.Y.Kim,H.L.Yang,H.K.Kim and KSTAR team,“AspectsandApplicationsofNon-Axisymmetric Coils on KSTAR”, 16th workshop on MHD Stability Control(USA,2011)
[15]J.Kim,Y.In,G.Kim,J.Y.Kim,J.G.Bak,Y.Park,G.Yun, J.Seol,S.A.Sabbagh and the KSTAR team,“Disruption threshold of error-field-induced locked mode under n=1 and n=2 mixed non-axisymmetric fields”, 25th IAEA Fusion EnergyConference(Russia,2014)EX/P8-4(2014)
국문초록
토카막의 운전조건은 핵융합 출력과 플라즈마 운전 시나리오에 영향을 주기 때문에,각 토카막의 운전영역을 아는 것은 중요한 연구주제이다.이 논문에서는 한국형 토카막 장치( KSTAR) 에서의 운전영역을 Hugi l l도표와 Gr e e nwa l d 밀도 비율 도표를 바탕으로 분석해 보았다.이 분석을 위해 2 0 1 1 년부터 2 0 1 4 년까지 KSTAR에 서 수행된 실험가운데 1 7 4 0 개의 샷들을 골라내었다.Hugi l l도표를 통해 KSTAR의 운전영역을 DI I I -D의 운전영역과 비교해 봄으로 서,KSTAR는 상당히 낮은 밀도까지 도달할 수 있음을 발견하였 으며,이를 통해 KSTAR가 상당히 낮은 자체 오차장을 가지고 있 음을 주장할 수 있다.현재의 데이터베이스를 바탕으로 했을 때 KSTAR의 도달 가능한 Gr e e nwal d 비율의 범위는 6 %에서 6 0 %로 나타나는 것으로 보였다.
저밀도 운전 영역을 변화시킬 수 있는 두 가지 요인인 이탈 전
자와 오차 장에 대한 효과를 조사하였다.KSTAR에서의 의도된
이탈전자 발생 실험을 바탕으로 이탈전자의 발생에 대한 조건이
Dr e i c e r조건을 바탕으로 조사되었다.비록 이 실험들이 이탈전자
를 발생시키기에 충분한 조건을 가졌지만,이 샷들은 중대한 방해
가 없이 지속될 수 있었다.이 관찰을 통해 이탈 전자는 KSTAR
에서의 저밀도 운전 제한에 영향을 주는 주 요인이 아닌 것으로
보인다.반면에,자기공명섭동( RMP) 이 들어감으로 인해 오차장이
증가한 플라즈마 샷들은 종종 플라즈마 잠김 현상을 나타내었고
저밀도 운전영역의 접근이 심각하게 제한되었다.플라즈마 잠김
임계점은 인가된 RMP코일과
값에 의해 변화되는 것으로 발견
되었다.중간 코일에서 플라즈마 잠김을 일으키기 위한 RMP 코일
전류의 크기는 상부나 하부의 코일에서 인가되는 것에 비해 절반
정도의 크기로 나타났다.그리고 낮은
의 값을 가질수록 낮은 밀도에서의 운전이 가능함을 보였으며,
에서는 ≈ 로 나타났고
에서는 ≈ 로 나타났다.저밀도 영역에서의 RMP의 영향이 L-mode에서 H-mode 로의 전이에 필요한 외부 인가 출력의 관점에서 조사되었으며,L-H의 효과적인 운전 영역으로의 접근이 RMP 인가에 의해 제한될 수 있음을 보였다.
따라서,토카막에서 H-mode 에서 RMP를 활용할 때에 이 효과를 고려해서 운전 시나리오를 구성해야 할 것을 제안하는 바이다.
주요어 :KSTAR,밀도 제한,Hugill도표,Greenwald밀도 비율, 자기공명섭동,이탈 전자,토카막 운전
