Studies of Mode Lok Instability
in the HL-1M Tokamak
QingweiYang, Longwen Yan, and Jun Qian
Southwestern Instituteof Physis,Chengdu,Sihuan610041, China
Reeivedon26June,2001
LokedmodeinstabilityintheHL-1Mtokamakhasbeeninvestigatedinthispaper. IntheHL-1M
tokamak the mode lok instability often appears in with low density disharges (n
e
<110 19
m 3
). Thepreursorperturbationsonbothsoft-XraysandMirnovsignalssimultaneouslyinrease
beforemodeloking.Theirfrequeniesarethesameandgraduallydeease,whihindiatethatthe
perturbationis global. Theirexistene time-saleis about10ms. Theplasma will suddenlystop
rotating whentheutuation amplitude or frequenyreahes a threshold. Modelok instability
anoftenausemajordisruptions. Therotationfrequenyisdereasedtoabout3kHzbeforemode
lokingintheHL-1Mtokamak,whihisonsistentwiththetheoretialmodel.
I Introdution
Major disruptions in plasmas are dangerous not only
for present tokamaks but also for future reators. It
isimportantto study themehanismofmajor
disrup-tion, and try to avoid it. A few kinds of major
dis-ruption, suh as the displaement disruption, density
limited disruption, low q
a
disruption and limit
dis-ruption have been observed in tokamak experiments.
TheyalwaysareonnetedwiththeMHDinstabilities.
Inthispaper,themajordisruptionausedbythemode
lokinstabilityhasbeenstudied. Thefrequeniesofthe
moderotationgraduallyslowdownwhiletheMHD
in-stabilities growup,andthen mode lokappearswhen
therotationstops suddenly. Themodelokinstability
anbeobservedaturrentrampup,plateauandramp
down phases. In partiularly, it is easy to appear in
low-densitydisharges.
The experimental results on JET tokamak [1℄
showedthatmajordisruptionsausedbythemodelok
instability often appeared when the eletron density
waslowerthanathreshold. Thethresholdisdependent
ontheplasmaparameters. For example,thethreshold
willdereasein theexperimentswithneutralbeam
in-jetion. The error eld instability is the main reason
of mode lok instability. A small asymmetrial
mag-netieldanleaduptothedevelopmentoferroreld
instability. In D III - D tokamak [2℄, the mode lok
instability was observed with preursor perturbations
beforethelowdensityorthedensitylimitdisruptions.
Thelokedmodemayappearatoneorseveraltoroidal
plaes. Themodelokinstabilityouldbeenhanedor
suppressedbyanadditionaln=1magnetield. The
varietyofthestable operationregiondependswhether
the error eld is inreased or dereased. The
experi-ments ofJT-60U tokamak [3℄indiated that the error
eld instabilitywasobservedwiththelargeelongation
ratio (k = b=a > 1:5). In the neutral beaminjetion
(NBI) experiment, the error eld instability was
sup-pressed. TheexperimentsofCOMPASS-Ctokamak[4℄
indiatedthattheerroreldinstabilityisnotaserious
problemin smallsizetokamaks.
II Theoretial model
Tousethenonlineartearingmodetheoryandonsider
theinterationbetweenrotatedplasmaandstati
reso-nantmagnetiperturbation,Fitzpatrikgavethe
equa-tionabouttheritialamplitudeofradialmagneti
per-turbationasfollow[5℄:
B
r;mn
B
t
r=a
6:7[g 2
℄ "
r
s
a
2 m
q 2
r
s
m 4
R
0
1=3
0
0 r
s
S
B
1=3 #
[(f
A )
4=3
where m and n are the mode numbers at the
ratio-nal surfae r
s (q(r
s
)= m=n):The fator g in the rst
parenthesisisweaklydependentonvisosity. Theterm
in the seond parenthesis is the funtion of urrent
prole and the MHD mode. Here 0
0 r
s
is the
non-dimensionalparameteroftearingmode,andS
B = r d dq dr
is the fator of magneti shear. The parameters f
and
A
in the third parenthesis are the frequeny of
plasmarotationandtheAlfventime,respetively. T
ak-ing A R 0 ( 0 nm i ) 1=2 =B t ,m i
beingthemassofion,
weanobtainthefollowingequationforonsideringthe
2/1mode: B r21 B t r=a fR B t 4=3 n 2=3 (2)
FortheCOMPASS-CandDIII-Dtokamaks,the
alu-latedvaluesfromformula(2)areonsistentwiththe
ex-perimentalresults. Toinreasethefrequenyofplasma
rotation,weanobtainthehigherthresholdvalueofthe
magnetiperturbation.
ForOhmi heated plasmas, the rotationfrequeny
ofmagnetiperturbationisabouttheeletrondrift
fre-quenyf
De :
f f
De / kT e0 eB t a 2 (3)
Here, kis theBoltzmannonstantand T
e0
is the
en-tral eletron temperature. For the COMPASS- C
de-vie, T
e0
600eV, B
t
= 1:1T, R =0.56m, a=0.18m,
thealulatedeletrondriftfrequenyisf
De
15kHz,
and the experimental result is f=13kHz. For the D
III - D tokamak,T
e0
920eV, B
t
=1:3T, R =1.67m,
a=0.67m, f
De
1:7kHz and the experimental result
is f=1.6kHz. Forthe HL-1M tokamak, T
e0
700eV,
B
t
= 2:1T, R =1.02m, a=0.26m, f
De
3:2kHz and
the experimental resultis f =3:1kHz. The theoreti
preditionsare, therefore,veryonsistentwith the
ex-perimentresults.
Supposing that thesafe fatorq
a
and the=a=R
areonstant,thefollowingformulaanbeobtainedby
usingPfeier-Waltzenergyonnementsaling[6℄.
f f
De R 9=5 0 B 1=5 t (4)
Combinedwiththe Murakami salingnB
t =R
0 , the
saling formulaisgivenby:
B r21 B t r=a R 26=15 0 B 14=15 t (5)
The thresholdvalueof m=n=2=1mode perturbation
is approximatelyinverse ofthesquare ofmajor radius
R and toroidaleld B
t
of tokamaks. Thus, themode
lokinstability,aused byerror eld,will beaserious
III Experimental results
HL-1Mtokamak isamiddle sizedevie. Itsmajor
ra-dius is 102m, minor radius is 26m, toroidal eld is
2.8T,plasmaurrentis320kA,anddishargeduration
an reahe up to 4.0 s. Fast vertial and radial eld
feedbak systems are used to ontrol the plasma
dis-plaement. The plasma urrent is ontrolled by
feed-bakaswell. Themodelokinstabilityaresometimes
observed during the HL-1M tokamak disharges, but
thesouresof theerror eld havenotbeenalulated
aurately.
During the HL-1M experiments, the Mirnov oils
andthesoftX-rayarraysareusedtodiagnosethe
mag-netohydrodynamial (MHD) instabilities. 32 Mirnov
oilsareuniformlydistributedinthepoloidaldiretion
atonetoroidalsetion. Theoilloatedathigher
mag-neti eldside isnamed No.01,and atlowereld side
is No.16. 16 of them are used for studying theMHD
perturbationsandare sampledat thesampling rateof
20kbs. Thesignal from the inside oil is MIR01, and
that from the outside one is MIR08. The integrated
signals from SMIR01 to SMIR32, piked up from all
the32oils,aremeasuredatthesamplingrateof2kbs.
3arraysofsoft X-raydetetors areused to detetthe
MHD perturbations at the plasma entral region and
tomaketomographyanalysis.Otherdiagnosti
instru-ments,inluding HCN laser interferometer,bolometer
andLangmuirprobes,areusedto measuretheplasma
density, plasma emission, edge density and
tempera-ture,respetively.
Typially,themodelokinstabilityappearsduring
thelowdensity experiments. Inshot 6201, for
exam-ple, the plasma urrent is I
p
= 135kA, the toroidal
eldisB
t
=2.1T,andtheline-averageeletrondensity
isn
e
=0:710 19
m 3
, asshownin Fig. 1. Beforethe
MHDinstabilityisobserved,theedgeeletron
temper-ature drops down from 40eV to a few eletron-volts,
and theedge eletron densityinreases. Therotation
frequenyslowsdowngradually from 5kHz to 3.1kHz,
whiletheamplitudeoftheperturbationgrowsup. The
modelokinstabilityappearsaftertheMHDinstability
hasdeveloped for about 40ms. This MHD instability
hasalso been observedat theentral,hannel soft
X-ray whih indiates that this perturbation is a global
one. Inthisshot,theplasmaurrentwasnotquenhed
by the disruption. This is beause of the low density
and the fast feedbak ontrol of plasma urrent. To
observethemodelokdisruptionin detail,thesignals
from 131ms to 139ms are shown in Fig. 2. After the
modelokinstabilityhasbeentriggered,in2ms,a
Figure 1. Theevolution of the modelok instability that
ourredinshot 6201. Thewaveformsfromtoptobottom
are: intensityofentralhannelsoftX-rays,plasmaurrent,
Mirnovperturbationathighereldside,perturbationofthe
m=2mode,eletrontemperatureand theeletrondensity
atr=a=1.02,respetively.
disruption takes plae at 137ms. The positive spike
indiatesthattheparallelenergyofsuprathermal
ele-trons hanges into perpendiular when the instability
in theveloity-spaeours,and theenergyis rapidly
lost. Then the intensity of the soft X-ray dereases
while theenergyof thermaleletronsis lost. The
dis-ruptionmakestheplasmaurrentdropsdowntoabout
15%. Ontheotherhand,thepoloidalmagnetieldat
lowereldsideinreases,whileitdereasesinthehigher
eld side. A mode is loked at the lower eld side,
whihis the typialphenomenon of themode lok
in-stability. Duringthedisruptionappearane,theplasma
edge eletron temperature and density undergo great
hanges. Theeletrontemperaturerisesrapidly,whih
orresponds to eletronsthat lose their energy within
thetime-saleofabout0.1ms. After0:3ms,theedge
temperature drops down to the original level and the
edge density inreases. This indiates that theenergy
loss ended and the partile loss started. The plasma
storedenergyandpartilesarerapidlylostwithin1ms,
butenergylossisfasterthanthepartileone.
Figure 2. Temporal extensionof modelok onshot 6201.
Thewaveformsfromtoptobottomaretheintensityof
en-tralhannelsoftX-rays,theMirnovperturbationathigher
eldside,theperturbationofm=2mode,thenegative
sig-nalofpoloidaleldathighereldside,thenegativesignal
ofpoloidaleldatlowereldside,theeletrontemperature
andtheeletrondensityatr=a=1.02,respetively.
Anotherdishargewithmodelokinstabilityoflow
density is given in Fig. 3. In this shot, the plasma
urrentisI
p
=135kA,toroidaleldisB
t
=2.1T,andthe
line-average eletron density is n
e
= 0:410 19
m 3
,
respetively. During the existene of MHD ativity
(137ms-143ms), the instability aused two small
pos-itivespikestoappearin theentralhannel softX-ray
signal. Fig. 4givesthedetailofthesewaveformsrelated
tothemodelokinstabilitythattakesplaefrom136ms
to152ms. Asmallpositivespikeisfoundat138ms,and
then them=2modegrowsup. After5ms,themode
lok appears. A big positivespike isobserved on soft
X-raybeforethedisruptionourrene. Theedge
ele-tron temperature rapidly inreased during mode lok
appearane. After several milliseonds, also the edge
eletrondensityinreasessubsequently,whihindiates
that theenergylossis fasterthanthepartileone.
For omparing the mode lok instability with the
normalMHDinstabilities,typialdiagnostiwaveforms
orresponding to high density disharges are given in
thetoroidaleldisB
t
=2.0Tandtheline-average
ele-tron density is n
e
=7:010 19
m 3
, respetively. The
edgetemperatureontinuouslydropsandtheedge
den-sitygraduallyinreaseswiththeriseoftheeletron
den-sity. Thepreursorosillationappearsatabout270ms.
Majordisruptiontakesplae afterafewminor
disrup-tions. Finally,thedishargeis suddenlystopped. The
positivespikesonsoftX-raysandlokedmodehavenot
beenobservedduringhighdensitydisruption,whih
re-veals that the suprathermal eletrons are very low at
high density disharges. Forthe dishargeswith high
density, the MHD mode annot be loked before the
minor disruptions,as shown in Fig. 6. Afterthe last
minor disruptions,theedgetemperaturerises. It
indi-atesthatmuhofthestoredenergyislostthroughthe
plasmaedge. Itisdierenefromthatinmodeloking
disharges.
Figure3.Theevolutionofthemodelokinstabilitythat
o-urredinshot6211. Thewaveformsfromtoptobottomare
the intensityofentralhannelsoftX-ray,plasmaurrent,
line-average eletron density, the Mirnov perturbation at
highereldside,perturbationofm=2mode,eletron
tem-Figure4. Temporalextensionof modelok onshot 6211.
Thewaveformsfromtoptobottomaretheintensityof
en-tralhannelsoftX-rays,theMirnovperturbationathigher
eld side, the perturbation of m = 2 mode, the eletron
temperatureandtheeletrondensityatr=a=0:98;
respe-tively.
IV Conlusion
ModelokinstabilityontheHL-1Mtokamakhasbeen
investigatedinthispaper. Thepreursorperturbations
betweenmodelokinstabilityandhigh-density
disrup-tionare ompared. Loked mode instabilityoften
ap-pearsinverylowdensitydisharges(n
e
<1 10 19
m 3
).
Magnetiperturbationsonbothsoft-XraysandMirnov
signals simultaneously inrease before mode loking.
Theirfrequeniesarethesameandgraduallyderease,
indiatingthat the perturbation is aglobal one. The
orrespondingtime-saleisabout10ms.
Therotationfrequenyisdereasedto about3kHz
before mode loking in the HL-1M tokamak, whih is
onsistentwiththeprediationoftheoretimodel.
Ma-jor disruption takes plae after loked mode appears,
within a few milliseonds. Plasma stored energy and
partilesarerapidlylostwithin1ms,butenergylossis
servedwithinthetime-saleof0.2msduringmajor
dis-ruption, whih shows that the suprathermal eletrons
are lost faster than the thermal ones. The poloidal
magneti eld at inside drops, while it inreases
out-side,whihrepresentsthattheMHDinstabilityappears
mainlyat lowersideofthemagnetield.
Thebestwaytosuppressthemodeloking
instabil-ityisto dereasetheinhereneerroreld in tokamaks
andtoinreasetheplasmadensity.
Figure 5. A typialdisruption withhigh density for shot
6079. Thewaveformsfromtoptobottomaretheintensity
ofentralhannelsoftX-rays,theplasmaurrent,the
line-averageeletrondensity,theMirnovperturbationathigher
eld side, the perturbation of m = 2 mode, the eletron
temperatureandtheeletrondensityatr=a=0.98,
respe-tively.
Figure6. Temporalextensionofhigh-densitydisruptionfor
shot6079. Thewaveformsfromtoptobottomarethe
inten-sityofentralhannelsoftX-rays,theMirnovperturbation
at higher eldside, the perturbation of m =2 mode,the
eletrontemperatureandtheeletrondensityatr=a=0.98,
respetively.
Aknowledgement
ThisresearhispartiallysupportedbyNational
Si-eneFoundationofChinaundergrantofNo. 19889504.
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