Magneti Coil System for the TCABR Tokamak
E.A. Saettone, A. Vannui, F.T. Degasperi, R.M.O. Galv~ao,
Y. Kuznetsov, E.K. Sanada, and I.C.Nasimento
Laboratoriode Fsiade Plasmas,
InstitutodeFsia,Universidade deS~aoPaulo,
S~aoPaulo,CEP05315-970, SP,Brazil
Reeivedon3July,2001
Inthiswork,wedisussthepreliminaryanalysisofsomedisruptiveplasmadishargesintheTCABR
tokamak,operatinginthehighdensitylimit. TheFourieranalysisoftheMHDativitywasgreatly
failitatedbeausethemagnetioilsinsidetheTCABRwereinstalledastotakeintoonsideration
thetoroidalgeometryofthesystem,inastraightforwardmanner. Whatwehaveobservedisthat
them=3;4and7MHDomponentsdominateduringalmostthewholedishargeduration,whereas
the m= 2MHD mode inreased substantially justbefore the ourrene ofa major disruption.
Also,weouldestimatetheangularveloityofthemagnetiislands,whihwasobservedtoinrease
uptothreetimesjustbeforethemajordisruption.
I Introdution
Ithasbeenexperimentallyprovedthattheuseof
mag-netioilsareessentialfordeterminingtheMHD
om-ponents, responsible for triggeringthedisruptive
phe-nomenon in tokamaks. The disruption instability
im-posessevererestritionsontheplasmaurrentand
par-tile density [1℄, ausing a sudden expansion of the
plasma olumn, whih is followed by alarge negative
spikeintheV
loop
signal,inspiteoftheapparentnormal
evolutionoftheplasmadisharge[2℄. Itisusually
pre-ededbyintenseMHD ativity(Mirnovosillations).
Theoretially,thebasisonwhihthisinstability
o-ursintokamaksisnottotallywellknown,yet.Usually,
the high density disruptions are understood as being
triggered by an interation between magneti islands
[3℄. Experimentally,in mosttokamaks it hasbeen
ob-served that the m= 2MHD omponent
(orrespond-ing to themagneti islands loatedwithin the surfae
q=2)growexponentially,triggeringthedisruption.
II Experimental set-up
The TCABR tokamak is a middle size tokamak with
themainparametersshowedin Table1. Themagneti
oilsystemisomposedof22magnetiprobes,installed
aroundoneretangularrosssetioninsidethevauum
vessel of the tokamak [4℄, as shown in Fig. 1. Eah
probe has two windings, perpendiular to eah other,
retion.
TABLE1. MainparametersoftheTCABRtokamak.
ToroidalMagnetiField BT 1:07 T
MajorRadius Ro 0:61 m
MinorRadius a 0:18 m
PlasmaCurrent Ip 100k A
DishargeDuration d 150ms
EletroniCentralDensity n
e 310
19
m 3
EletroniCentralTemperature T
e
400eV
Figure1. UpperviewoftheTCABRtokamak,showingthe
Thepositioning ofthemagnetiprobeswashosen
as to takeinto aount automatially the toroidal
ef-fetsofthesystemduethetoroidalgeometryofthe
to-kamak (Fig. 2). Thisorretionwasintroduedby
fol-lowingtheangulardistributiongivenbytheMerezhkin
orretion,[5℄
=+sin (1)
where is thepoloidalangle onsidering(in the
ylin-drialapproximation)anequalangulardistributionfor
theoils,andisgivenbythefollowingexpression[5℄:
= r mn R mn h p (r mn )+ 1 2 ` i (r mn )+1
i
(2)
where
p
is thebeta poloidal and l
i
istheinternal
in-dutane oftheonnedplasma.
Figure 2. Retangular ross setion of thetokamak
show-ing thepositionofeahmagnetiprobe,distributedinthe
poloidal diretion, taking into aount the toroidal eet
duetothetoroidalgeometry.
Theeetive area(sensibility)of eahoil was
ex-perimentallydeterminedbyreatinganosillating
mag-neti eld using a Helmholtz oil, with amplitude of
1:810 5
T. The frequeny range of the osillating
magnetieldwashosenbetween5kHz and40kHz.
During the experiments, all the 44 probe signals
were bandpass ltered, between 1kHz and 100kHz,
and amplied eletronially. Afterwards,these signals
weredigitalizedandsavedusingtheTCAqs(aquisition
data systemof the TCABR tokamak), with 250 kHz
ofaquisitionsamplingrate. Aomputerprogramwas
onstruted to Fourier analyse the experimental data
andto alulatethedominantMHD modespresenton
thedisruptiveTCABRdishargesanalyzed.
III Experimental data treatment
Some proedures have been followed to treat the
ex-aomputerprogram. First,theprogramonsidersthe
eetiveareaoftheoils,obtainedfromthealibration
and,afterwards,italulatesthemagnetield
ompo-sitionmeasuredby thetwooils of eah probe, in the
poloidaldiretion.
Also,theomputerprogramalulates theangular
position of every probe (equation (1)), using from
theequation (2), whih is measuredfrom the vertial
equilibriumeld(B
v
),asgivenbytheequation[6℄:
B v = o I p 4r p ln 8r p a p + 1 2 (3)
whereistheShafranov parameter,denedby
= p + ` i 2 1 (4) where p
is the beta parameter and l
i
is the internal
indutaneof theplasma. Therefore, for theTCABR
tokamak,equation(2)anbewritten as
= a R TCABR p + 3 2 (5) where the TCABR p
orrespondsto thebeta parameter
asmeasuredfromtheMHDequilibrium. Theomputer
program also onsiders that the perturbed magneti
eld, as measured by the Mirnov oils, has a
depen-denewiththedistanegivenby:
_ ~ B m ( k )/ 1 r m+1 k (6) where _ ~ B m ( k
) is the experimental data, as measured
by the probe at the
k
poloidal angle, and r
k is the
ratio a=b
k
, being a the plasma olumn radius and b
k
the distane between the plasma olumn enter and
themagnetioilloatedatangularposition
k (whih
is dierent for eah probe beause of the retangular
rosssetionoftheondutingwalls). Toalulatethe
ontribution of eah MHD mode, in eah plasma
dis-harges,theprogramusesthefollowingexpression[7℄:
_ ~ B m ( k )=A
m
os(m
k )+B
m sin(m
k
) (7)
wheretheFourieronstantsA
m andB
m
arealulated
bythefollowingequations[7℄:
A m = 1 11 22 X k =1 _ ~ B m ( k
)os(m
k ) (8) B m = 1 11 22 X k =1 _ ~ B m ( k
)sin(m
k )
(9)
Finally,theomputerprogramreatesanewsetof
IV Analysis of a disruptive
dis-harge
IntheTCABR tokamak,disruptive disharges are
ob-tainedwheneverthemahineisoperatedatthedensity
limit (n
e
310 19
m 3
). During these plasma
dis-harges, plasma urrents of approximately 80 kA are
obtained for about 50 ms, until the ourrene of a
majordisruption. Typially,the loopvoltageisabout
2V,with nosigniantH
emissionor hardX ray
emission. Theexperimentalmagnetisignalspikedup
bytheMirnovoils,however,showtypial Mirnov
os-illations, with frequenies in the range of 10 kHz to
15kHz.
Fig.3showstheexperimentalsignalsofadisharge
(shotNo2017)inthehighdensitylimit. Itisobserved
amajordisruptionin t=86:8ms, thatannihilatethe
plasma in 20 ms. Note that the Mirnov
osil-lations have a onstant amplitude during almost the
whole disharge, until the disruption takesplae
(be-tween t 50 ms and t 85 ms), whih indiates a
saturation of the magneti islands. The safety fator
forthisdishargewasalulatedtobeq(a)4:4.
20
40
60
80
100
120
Time (ms)
-2
-1
0
1
2
B
4IZ
(a.u.)
-0.2
0
0.2
R-X (a.u.)
0
0.05
0.1
0.15
H
alpha
(a.u.)
0
10
V
loop
(V)
0
20
40
60
I
p
(kA)
TCAqs Shot 002017
TCABR
^
Figure3. ShotNo2017 oftheTCABR tokamakoperating
inthehighdensitylimit. A major disruption ours in
t=86.8ms (arrow atthe bottom). Afterthat, the plasma
urrentdeaystozeroinabout20ms.
aroundthe disruptiontime, areshownin Fig. 4.
Ob-servethat at t =85:2ms, theamplitudeof theMHD
ativitydereasesonsiderably,atthesametimeaspike
isobservedinthehardX-raynon-integratedsignal.
Af-ter that, in t = 86:3 ms, the Mirnov osillations
am-plitude begins to growexponentially, during
approxi-mately 0:5 ms, until the ourrene of the disruption
in t=86:8ms.
84
84.5
85
85.5
86
86.5
87
87.5
Time (ms)
-0.5
0
0.5
B
4IZ
(a.u.)
-0.2
0
0.2
R-X (a.u.)
0
0.03
0.06
0.09
H
alpha
(a.u.)
-20
-10
0
10
V
loop
(V)
56
58
60
62
64
I
p
(kA)
TCAqs Shot 002017
TCABR
^
^
^
1
2
3
Figure4. ShotNo2017 oftheTCABRtokamakexpanded
intimearoundtheourreneofthedisruption. Int=85.2
ms(arrowNo1),MHDativitydereases onsiderably. In
t=86.3ms(arrowNo2),theMirnovosillationamplitude
growsexponentiallyuntildisruptionours,int=86.8ms
(arrowNo3).
Experimentally, theexponentialgrowthrateof the
MHD ativity, just before the disruption, was
alu-latedtobe
exp
=8:910 3
s 1
. Comparingthisvalue
tothetheoretialresistivegrowthrate,alulatedtobe
res
=3:110 4
s 1
, (thetheoretialvalueoftheideal
growthratewasalulatedtobe
ideal
=1:310 6
s 1
)
thedisruptiveeventinthisdishargeouldbeexplained
in terms of an interation between magneti islands.
Thefrequenyofthepreursorosillationswasalso
ob-servedto inreasefrom10kHz to 13kHz,in
approx-imately0:2msbeforethedisruptiontakesplae. This
probably meansthat the angular veloity ofmagneti
pe-As to ompare the evolution of theMHD poloidal
modesexistinginthisplasmadisharge,weFourier
an-alyzedtheexperimentalsignalsbetweent=75msand
t = 76 ms, when there was no evidene yet of any
preursorto thedisruptiveinstability. Itwasthen
ob-servedthattheMHDmodesm=3;4and7were
domi-nant(Fig. 5),andtheangularveloityofthemagneti
islands, between these two instants of time, was
esti-matedtobe!
rot
=1:610 3
rad=s.
Figure 5. Polardiagrams(left) and MHDspetra(right),
alulated at(a)t=75msand(b)t=76ms,fortheshot
No2017 oftheTCABRtokamak.
Figure 6. Polardiagrams(left) and MHDspetra(right),
alulated at(a)t=86.3msand (b)t=86.75ms,ofthe
shotNo2017 oftheTCABRtokamak.
Thesamealulationswerealsoarriedoutjust
be-foredisruption,forthesameplasmadisharge. As
ob-servedin Fig. 6-b, the MHD modesorrespondingto
m=2andm=7arelearlydominant,justbeforethe
magnetiislandsjust beforedisruption, wasestimated
tobe!
rot
=5:010 3
rad=s. New oilsare being
po-sitionedinside thevaum vessel, in dierent toroidal
position,toverify thennumberforthesemodes.
V Conlusions
Some disruptive disharges, that ourred when the
TCABRisoperatedatthedensitylimit,wereanalized
inthisartile. ItwasobservedthattheMirnov
osilla-tions,alongthedisharge,haveafrequenyof10kHz.
Itwasalso determinedthat the m=3;4and 7MHD
modesdominates during thewhole disharge,with an
angularveloityoftheorrespondingmagneti islands
estimatedtobe1:610 3
rad=s.
However, just before disruption (approximately
0:2 ms before the ourrene of the disruption), it
wasobservedthattheMirnovosillationsfrequeny
in-reases up to 13 kHz. At this time, a larger
ontri-butionof them=2MHD omponent wasalulated,
whih probably wasthe responsible for triggeringthe
disruption. Theangularveloityfortheorresponding
magnetiislandswasestimated to be5:010 3
rad=s,
threetimesmorethanduringtherestofthedisharge.
Finally, theexponentialgrowthrate ofthe Mirnov
osillationswasomparedtothetheoretialvalues,
re-latedtotheresistiveandidealgrowthrates,fromwhih
weinferredthat theourreneofthedisruptionould
beexplainedintermsofamagnetiislandsinteration.
Aknowledgments
ThisworkhasbeenpartiallysupportedbyFAPESP
andbytheMinistryofSieneandTehnologythrough
the PRONEX program. Also we want to thanks Mr.
NelsonM.Cuevas,Mr. AblioPiresdosReisandJuan
I.Elizondoforthetehnialsupport.
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