Direct observation of current in type I ELM filaments on Asdex Upgrade

0.99 MB·English

by  N. Vianello

Directobservation ofcurrent intype I ELMfilaments onASDEX Upgrade
N. Vianello,1 V. Naulin,2 R. Schrittwieser,3 H.W. Mu¨ller,4 M.Zuin,1 C. Ionita,3 J.J. Rasmussen,2
F. Mehlmann,3 V. Rohde,4 R. Cavazzana,1 M. Maraschek,4 and the ASDEX Upgradeteam4
1Consorzio RFX, Associazione Euratom-ENEA sulla Fusione, Padova, Italy
2Association EURATOM-RisøDTU, OPL-128 Risø, DK-4000 Roskilde, Denmark
3AssociationEURATOM/O¨AW,InstituteforIonPhysicsandAppliedPhysics,UniversityofInnsbruck,Austria
4Max-Planck-Institut fu¨r Plasmaphysik, EURATOMAssociation, Garching, Germany
(Dated:January17,2011)
1
Magnetically confined plasmas are often subject to relaxation oscillations accompanied by large transport
1
events.Thisisparticularlythecaseforthehighconfinementregimeoftokamakswheretheseeventsaretermed
0
2 edgelocalizedmodes(ELMs).Theyresultinthetemporarybreakdownofthehighconfinementandleadtohigh
powerloadsonplasmafacingcomponents. PresenttheoriesofELMgenerationrelyonacombinedeffectof
n edgecurrentandtheedgepressuregradientswhichresultinintermediatemodenumber(n=10 15)structures
a ∼ −
(filaments)localizedintheperpendicularplaneandextendedalongthefieldline. Itisshownherebydetailed
J
localizedmeasurementsofthemagneticfieldperturbationassociatedtoanindividualtypeIELMfilamentthat
4 thesefilamentscarryasubstantialcurrent.
1

PACSnumbers: 52.35.PY52.55.Fa52.55.RK52.70.Ds
]
h
p
Edge localised modes (ELMs) are short (ms) breakdowns DOP
-
m of the high confinement regime (H-mode), which is envis- 0.4 0.6 0.7 0.8 0.9
50
s aged to be used in power producing tokamaks. Due to the 40
a highpowerfluxesassociated,thepresenceofELMsposesde- z] 30 1.0
pl mands on the design of plasma facing components, that are f [kH 20 ce 0.8 EInltmer Elm
. hard to meet. Thus understanding, with the aim of control- 10 n 0.6
s e
sic lriensge,arEcLh.MMeovreenotvseri,saopnaertofrfotmhethfeorienmteoressttpfroirofruitsieiosninorfieunsitoedn 0.4 coher 00..24
hy pcilnasamtinags,atnhaeliongtieerseswtiitnhEsLpoMrapdhicyseixcpsliosseivnehaenvceendtsbayssoobmseerfvaesd- I [A]sat 00..23 0.0 5 10 15 20 25 30
p 0.1 f [kHz]
forexampleinsolarflares[1]orinmagneticsubstorms[2]. 0.0
[
4.184.204.224.244.26
ELMsareatpresentthoughttooriginatefroma combina- t [s]
4
tionofcurrentandpressuregradientdrivenMHDmodes[3],
v
2 and are known to result in a medium number (n 10 15) FIG. 1. Top: Degree of Polarization (DOP) analysis as a function
≈ −
6 of structures [4–7], localised in the perpendicular plane and oftimeandfrequency. Bottom: Ionsaturationcurrent(Isat). Right:
3 extended along the magnetic field. These filaments travel CoherencebetweenIsatandbpcomputedintheELMandinter-ELM
2 throughtheScrapeOffLayer(SOL)andhavebeenmeasured phases. Thetimeintervalsareshowninthebottompanelwithcol-
0. usingLangmuirprobesonvariousmachines,seee.g.[8],and oredboxes.
1 observedthroughhighspeedcameras[7]orGasPuffImaging
9
diagnostic[9]. Inthisletterwepresentresultsofdirectmea-
0 outatASDEXUpgrade(AUG)tokamakbymeansofanewly
surementsof all three componentsof the magneticfield per-
: constructed probe head described in detail elsewhere [12].
v
turbationsassociated to ELM filamentstructures in the SOL
i Theprobeheadconsistsofacylindricalgraphitecase((cid:31)=60
X togetherwithanestimateofthecurrentcarriedbyfilaments.
mm)whichholdssixgraphitepins. Oneofthetipsmeasured
r Magnetic fluctuations associated with ELMs are usually theionsaturationcurrent,onetipwasswept, whereasallthe
a
believed to originate from MHD activity. Measurements of othershadbeenkeptfloating. Insidethecase,20mmbehind
the magnetic activity have previously been performed using the front side, a magnetic sensor measuring the time deriva-
magnetic pickup coils close to the vessel wall [7, 10] or on tiveofthethreecomponentsofthemagneticfieldismounted.
insertable probes [11]. These measurements generally take The sensor has a measured bandwidth of 1 MHz. A similar
placefarfromthefilamentsincomparisontotheirradialex- probe with combined electrostatic and magnetic signals has
tent. This makes it difficult to observe the magnetic pertur- already been used in AUG [11], but with a wider magnetic
bation goingalong with individualfilamentsand to examine coil and a larger radial separation between electrostatic and
the magnetic fine structure of the ELMs. Both would result magneticsensors.Theprobehead,mountedonthefastrecip-
in important information such as the excursion of magnetic rocatingmidplanemanipulator,isinsertedfromthelowfield
fieldlinesfromtheirequilibriumpositionandiftheELMsare side of the torus for 100 ms 12 mm inside the limiter posi-
associatedwithreconnectionevents[1]. tion.Thedatahavebeenobtainedintype-IELMyplasmadis-
Here we report on measurements of type I ELMs carried charges(# 23158,23159,23160,23161,23163)with a toroidal
TypesetbyREVTEX
2
A] 0.4 (a) (a) (b) 5.1
I [0sat.0001..020 0.010 T] 1.7
(c) m
0.005 br bp (b) 0.005 [bλ2−1.7
[T] 0.000 b [T]p 0.000 −5.1
−6.3 −2.1 2.1 6.3
−0.005 −0.005 bλ1 [mT]
−0.010 −0.010
4.234 4.236 4.238 4.240 −0.0100−0.00330.0033 0.0100 FIG.3. (a)TrajectoryofELMfilamentassociatedmagneticfieldex-
t [s] b [T]
r cursions in all three spatial directions. The direction of minimum
varianceisshown(blackline)togetherwiththedirectionoftheequi-
libriumfield(blueline). (b)Hodogramofthemagneticperturbation
FIG.2. (a)Ionsaturationcurrent(b)Poloidalandradialcomponent
associatedwithELMcurrentfilamentreconstructedinthemaximum
ofthemagneticfield. Theredboxhighlightsthetimeintervalwhen
varianceplane.Theredlineshowstheellipticalfit.
the two components change their phase relation. (c) Hodogram of
theradial/poloidalmagneticfieldcomponent.Theclosedloopinred
referstothetimeintervalshighlightedinpanel(a,b).
tudeincreases,theradialandpoloidalcomponents(b andb
r p
)changetheirphaserelationashighlightedbythecolorbox.
magneticfieldof-2.5T,0.8MAofplasmacurrent,6.5 1019 Wenowconsiderthehodogramoftheperpendicularmagnetic
m 3centralelectrondensityandaq valueof5.2. × perturbation(Fig. 2 (c)), i.e. the magneticfield perturbation
− 95
trajectoryintheb b plane,duringthepassingoftheELM.
During the analysis we have used the ion saturation cur- r− p
Hereoneclosedorbitcorrespondstothetimeintervalmarked
renttoinferthepassingofatype-IELMfilamentstructurein
in Figure 2 b. Closed loops are compatiblewith the passing
frontoftheprobe,asdoneforexamplein[13]. Inanalyzing
of currentfilamentsin frontof the probe. Outside the ELM,
the ELM events we employ the idea that the magnetic sig-
the magnetic field perturbation exhibits an almost linear po-
nalduringtheELMcanbeseparatedintodifferentfrequency
larizationintheperpendicularplane. Thisshowsclearlythat
components.Higherfrequencies,abovefewhundredkHz,we
magneticactivityinbetweenELMs(wavelike)differsqualita-
presumeto be generatedmostly by Alfve´nicactivity or high
tivelyfromthemagneticperturbationduringanELM,which
frequencyturbulence.Thesearenotconsideredinthepresent
seemstobeduetothemotionofcurrentfilaments.
analysis,alsobecauseofthefrequencycut-offbythegraphite
shielding[12]. AdditionalMHDactivitywillstillbe present Themeasurementsofallthreecomponentsofthemagnetic
inthesignalatfrequenciesbelow20kHz,butduringELMfil- perturbationallowstocheckthealignmentofthecurrentfila-
amentsmostofthesignalispresumedtooriginatefromslowly mentsdirectly. InFigure3(a)the trajectoryofthemagnetic
varyingcurrentsconvectedwiththefilaments.Thisisjustified fieldexcursionduringanELMeventinallthreemagneticfield
bythe so-calledDegreeof Polarization(DOP) analysis[14], componentsisshown. Thetimeintervalselectedcorresponds
whichisatestforaplanewaveansatz,quantifyinghowwell totheonehighlightedinFigure2. Aclosedellipticallooply-
the relation k B=0 is satisfied. It is based on the evalu- inginaplaneslightlytiltedwithrespecttothelocalframeof
·
ation and diagonalization of the spectral matrix S= B B , referenceisobserved,asexpectedforfilamentarystructures.
h ∗i ji
calculatedinFourierspace. TheDOPrepresentsameasureto The directionnormalto this plane can be determinedby us-
determinewhetherS representsa purestate quantifyinghow ingtheminimumvarianceanalysis[15]. Themethodisbased
much one single eigenvectorapproximatesthe state. A high onthesolutionoftheeigenvalueproblem(cid:229) 3n =1MµBn nn =l nµ
valueofDOPimpliesthatthefluctuationsconsideredareco- where MµBn = hBµBn i−hBµihBn i is the Magnetic Variance
herentoverseveralwavelengths,andthusthemethodcanbe Matrix,thebracketsindicatingthemeanvaluesaveragedover
usedtodistinguishbetweenpropagatingmodesandcoherent the time the structure spends traveling in front of the probe,
localized fluctuations. Figure 1, panel (a), shows the results µ,n =1,2,3denotingthecartesiancomponentsoftheX,Y and
of DOP analysis as a function of frequency and time. The Z ofthechosensystem,l andnbeingrespectivelytheeigen-
temporal evolution of the ion saturation current is depicted valuesandeigenvectorsofthesystem. Theeigenvectorscor-
in the lower panel. A sudden drop in the DOP is observed respondingtotheeigenvaluesl ,l andl ,representthedi-
1 2 3
in correspondance with a steep increase of I signals: this rectionofmaximum,intermediateandminimumvarianceof
sat
implies that the magnetic field fluctuations during an ELM the magneticfield respectively. Theeigenvectorcorrespond-
canbebetterrepresentedbycoherentstructuresthanbyplane ing to the minimum eigenvalue corresponds to the direction
wavepackets. A coherence analysis between the ion satura- of minimumvarianceand is normalto the plane spannedby
tioncurrentandthepoloidalcomponentofthemagneticfield the magnetic field perturbations. This direction is observed
(Fig. 1(c))revealsanincreaseofcoherencebetweenthetwo tobeparalleltothatoftheequilibriummagneticfield,shown
signals during the ELM activity. A closer look on the be- inthesameplotbyablueline. Thisconfirmsthehypothesis
haviorofmagneticfluctuationsassociatedtoanELMeventis that the ELM filament is aligned with the equilibrium mag-
showninFigure2(b). Whenthemagneticfluctuationampli- netic field. From the sense of the polarization the direction
3
10
B 0.006 (a) 0.006 (b)
8 M 0.004
bλ2 0246 [T] −000...000000022 bλ2(λ1=a)Δ t1 Δ t2 bλ2(λ1=a) 2 1/22 ) [T] + b(bλλ2100..000024 χχ22 MBiopnoolapro =la 3r .=3 81 .×5 11 0×− 110.0−10.
-2 −0.004
−0.006 0.000
-4
4.236800 4.236867 4.236933 4.237000 4.23680 4.23687 4.23695 4.23702
-6 t [s] t [s]
-6 -4 -2 0 2 4 6 8 10 12
bλ1
FIG.5.(a)Timetracesofthetwoperpendicularcomponentsofmag-
FIG.4. Hodogramscalculatedforamonopolar currentdistribution neticfieldduringanELMfilament.(b)Totalperpendicularmagnetic
(M )andbipolarone(B). fieldasafunctionoftime. Superimposedtheresultsofafitforan
expectedmonopolar(red)andbipolar(blue)currentdistributionboth
modulatedbyanexponentialdecay.
ofthecurrentisfoundtobecolinearwiththeplasmacurrent.
The method allows the determinationof the rotation matrix,
sothatthehodogramintheplaneperpendiculartothecurrent betweenthemaximumofbl andthemaximum/minimumof
1
filaments may be reconstructed. This hodogramis shown in bl ,wherebl andbl aretheprojectionsofthemagneticfield
2 1 2
Figure 3 (b) together with a fit to an ellipse. The shape of in the maximum-intermediate variance plane. Thus within
thehodogramcalculatedintherotatedframeofreferencecan theseapproximationsthecurrentmaybeestimatednotingthat
be used to determine the type of current distribution associ- |bl 2(l 1 =a)|= 21µ20pIa0 = 4pDµ0tIv0l 1 Applied to the experimental
atedtoanELM.TheorieshavebothproposedELMfilaments data,thiscomputationisequivalenttocalculatethequantities
tobeassociatedtomonopolar[4,16]andbipolarcurrentdis- depictedinFigure5,whereD t hasbeencalculatedbothatthe
tributions [17]. Up to now no clear evidence of one mecha- maximum and at the minimum of bl . The two values D t1
2
nismpredominantwithrespecttotheotherhasbeenreported. and D t are equal to 38 µs and 42 µs respectively. The esti-
2
Figure4showstheanticipatedshapeofthe hodogramin the mateof thecurrentreliesonthe knowledgeoflocalvelocity
bipolar and monopolar cases. The hodogram in the bipolar in the l direction. This propagation has been reported for
1
case exhibits a cardioid-likeshape with a cusp at the origin, ASDEXUpgrade,e.g. [11,20]. Theexperimentalsetupdoes
which represents a distinct signature and which can not be not allow a reliable local measurements of v or v , neither
r p
recognized in the experimental data (see Fig 3 (b)). To re- can we rely in the presented shots on correlation analysis of
inforce the statement we note that a bipolar-like hodogram wallmountedprobes(whichare 160degreesseparatedfrom
with the presence of a cusp has been previously recognized the manipulator in the toroidal direction). Most likely these
in[18](cfr. fig3(b))whereithasbeenassociatedtoadirect signals are indeed dominated by MHD mode activity in the
measurementof a bipolarcurrentstructures. We emphasize, confinedplasmaratherthancurrentfilamentsintheSOL.As
however, that the filaments observed in [18] are of a com- thebestapproximationwethusassumeasradialpropagation
pletelydifferentoriginasinducedbyDrift-Alfve´nturbulence themostprobablevaluev =1.2km/sas determinedin [20]
r
[19]. A further corroboration of the hypothesis of monopo- andcalculatevl =vr/cos(∠(l 1 r)),where∠(l 1 r)isthe
lar current filaments results from considering the quadrants naglebetweenl 1 andtheradialdi−rectionwhichforth−epresent
1
occupied by the magnetic field trajectory. Indeed while the caseisoftheorderof7 . From[20]wealsoestimateastan-
◦
monopolar current hodogram regularly occupies two of the darddeviationofv ass =700m/s,whichensurethat71%
r vr
quadrants, the bipolar one always spans three of the quad- ofthe eventsare observedwithin(v s ). With these val-
r± vr
rants: thislatterbehaviorisnotobservedintheexperimental uestheaveragedistanceofclosestapproachisapproximately
dataascanbeverifiedbycomparingFigure3(b)andFigure 4cmandusingtheaveragevaluebetweentheminimumand
4. These results make us confidentthat the magnetic fluctu- maximum of bl we obtain an estimate of 1.9 kA. The to-
2
ationsobservedareindeedgeneratedbyamonopolarcurrent
tal perpendicular field b2 +b2 is shown in figure 5 (b).
distribution. Under this basic assumptionthe currentcarried q l 1 l 2
The magnetic field variation can be fitted with a function of
bythisfilamentmaybeestimated. Intherotatedframeofref-
einretnhceel f1odriraecctiirocnu,lathremtwonooppeorlpaernsdyimcumlaertrmicagfinlaemticenfitelddricfotimng- the form f =(cid:18)√(t−at0)2+b −g (cid:19)e−(t−t0)/t e, t0 being the time
ponents may be written as bl 1 = −l r210+Ba02a and bl 2 =−rl021B+0al 21 iunlsatranfitelcdorarnesdptoendthineget-ofothldeinmgatxiimmeu,manodftahsesutmotianlgpethrpeemndaigc--
whereB = µ0I0 anda isthedistancebetweenthetrajectory netic field is the response from a passing monopolarcurrent
0 2p r0
ofthecenterofthefilamentsandtheprobe,representingalso filament. Thegoodqualityofthefitprovidesadditionalsup-
the distance of closest approach, r is the radius of the fila- portforthemonopolarnatureofthefilament,alsocomparing
0
mentsandI itscurrent. Thedistanceacanbeapproximated, withthefitexpectedfromabipolarcurrentdistributionshown
0
assuming the filament to propagate with a constant velocity in blue line which exhibitsan higherc 2. The average decay
alongthe l 1 direction: a=D tvl whereD t is thetime delay time is determined as t e 200 µs. In order to increase the
1 ≈
4
PdF thatthesamecurrentdensitywasestimatedin[11]assuming
Min Max 14 themagneticperturbationtobe inducedby arotatinghelical
25 (a) 12 (b) structurewithabi-directionalcurrentcloseto,butstillinside,
20 10
mT] 15 # 8 the separatrix. The value foundis higher than the measured
b[δλ2105 246 kjsAat/mcu2)r.reCnotndcelnusdiitnygtointthheisiolentt-ebriawseedhativpe(parpopvriodxeidmeavtiedlyen5c0e
0
thatELMfilamentscarryconsiderablecurrentsforwhichwe
10 20 30 40 50 0 20 40 60 80 100
dt [μs] ∠(λ−r) [degree] havefoundareasonableestimate. Themagneticsignalsdur-
1
10 ing ELM filamentsdiffer substantially from wave activity in
SOL (c)
8
kA] 6 between ELMs. We have shown that the current in the fila-
[M 4 mentsis co-alignedto theplasma currentand approximately
IEL 2 of a magnitude as expected for the edge. The current flows
0 along the unperturbed magnetic field lines and has a unidi-
−2 0 2 4 6 8
r−r [cm] rectionalnature. This poses the question where the filament
sep
currents close in the SOL and why such high current densi-
FIG.6. (a)JointPDFofD t andbl (l 1=a)(b))Histogramofthe tiesaresustainedintheELMfilaments. We hopethatfuture
anglebetweenl 1 andtheradialdire2ction. (c)Filamentscurrentes- experimentswillcontributetoanswerthesequestions,which
timatevsdistancefromtheseparatrixestimatedwithvr=1.2km/s. willthrownewlightontheinstabilitymechanismsforELMs.
Errorbarsresultsfromthepropagationofvelocityuncertaintyinthe
This work, supported by the European Communities under
estimateofaandI.
thecontractofAssociationsbetweenEURATOMandENEA,
Risø/DTU, O¨AW Innsbruck, and IPP Garching, was carried
statisticreliabilityofthepreviousestimatewehaveanalyzed out within the framework of the European Fusion Develop-
eventsfrom5differentshotswithsimilarconditions. There- ment Agreement. This work was also supported by project
sults are shown in Figure 6. In the panel (a) the joint PDF P19901oftheAustrianScienceFund(FWF).
of the independent experimental values D t and bl used for
2
thecurrentevaluationisshown,highlightinghowthebulkof
the filaments have values of approximately25 µs and 5 mT.
In the panel (b) the histogram of the angle between l and
1 [1] W.Fundamenskietal.,PlasmaPhys.Control.Fusion49,R43
the radial direction is shown, showing that the l direction
1 (2007).
isacomplexcombinationofradialandpoloidalpropagation.
[2] A.Lui,IeeeTrans.PlasmaSci.28,1854(2000).
Finally in the panel (c) the current estimated accordingly to [3] P.B.Snyder,H.R.Wilson, andX.Q.Xu,Phys.Plasmas12,
the aforementioned formula is plotted vs the position of the 056115(2005).
filaments with respect to the separatrix, taking into account [4] A.Kirketal.,PlasmaPhys.Control.Fusion48,B433(2006).
thepositionofthemanipulatorandthedistanceofclosestap- [5] M.Fenstermacheretal.,Nucl.Fusion45,1493(2005).
[6] A.Herrmannetal.,J.Nucl.Mat.363-365,528(2007).
proach estimated. The errors shown represent the influence
[7] A.Kirketal.,Phys.Rev.Lett.96,185001(2006).
of the velocity uncertainty on the estimate of a and conse-
[8] A.W.Leonardetal.,PlasmaPhys.Control.Fusion48,A149
quently on I. The bulk of the distribution of these filaments
(2006).
are thus observed in the SOL, even taking into account the [9] RMaquedaandRMaingiandNSTXteam,Phys.Plasmas16,
uncertainty on v : the median of the distribution of the fila- 056117(2009).
r
mentsdetectedintheSOLwithintheerrorintheirpositionis [10] H.Takahashi,E.D.Fredrickson, andM.J.Schaffer,Phys.Rev.
1.4 kA, correspondingto a j 4.5MA/m2 for 1 cm radius Lett.100,205001(2008).
filaments. Thesevaluesareckon≈sistentwithmeasurementsof [11] A.Herrmannetal.,ininProceedingsofthe22ndEnergyFu-
sionConference,Geneva,IAEA-CN-165/EX/P6-1(2008).
edgecurrentasseenforexamplein[21]. Ithasalreadybeen
[12] C.Ionitaetal.,J.PlasmaFusionRes.Series8,413(2009).
supposed in [22] that, in case ELM breakdown is driven by
[13] M.Endleretal.,PlasmaPhys.Control.Fusion47,219(2005).
peeling instabilities, this will lead to a flattening of the cur- [14] J.SamsonandJ.Olson,GeophysicalJournalInternational61,
rent density profile over the separatrix and a subsequent in- 115(1980);O.Santol´ık,RadioSci.38,13(2003).
crease of currentsflowing into the SOL. These currentswill [15] D.R.Weimer,J.Geophys.Res.108,12(2003).
benearlyforce-freeandwillbeaccompaniedbypoloidalhalo [16] J.R.Myra,Phys.Plasmas14,102314(2007).
[17] V. Rozhansky and A. Kirk, Plasma Phys. Control. Fusion 50,
currentsclosingthroughthedivertortiles. Actuallythesecur-
025008(2008).
rentshavebeenmeasured[12,23]withvaluesuptofewtens
[18] M.Spolaoreetal.,Phys.Rev.Lett.102,165001(2009).
of kA, supportingthe presenceof rapid flow of toroidalcur-
[19] N.Vianelloetal.,Nucl.Fusion50,042002(2010).
rents from the plasma into the SOL The resulting histogram [20] A.Kirketal.,tobepublished onPlasmaPhys.Contr.Fusion
may also be compared with the estimate for ELM filaments (2010).
in JET given in [24]: in this case the most probable current [21] D.Thomasetal.,Phys.Plasmas12,056123(2005).
has been found of the order of 450 A, but with a lower ra- [22] E.Wolfrumetal.,inProceedingsofthe22ndIAEAEnergyFu-
sionConference,Geneva(IAEA,2008)pp.EX/P3–7.
dial velocity postulated. For completeness it must be noted
5
[23] P.McCarthyetal.,inInproceedings30thEPSConferenceon PlasmaPhysics,St.Petersburg,Vol.27A(2003)pp.P–1.064.
[24] PMigliucciandVNaulin,Phys.Plasmas17,072507(2010).