Parametric Decay Instability (PDI) in Tokamaks · (PDI) in Tokamaks Guangye Chen, Frederick Jaeger,...

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ParametricDecayInstability(PDI)inTokamaks

GuangyeChen,FrederickJaeger,LeeBerry,JimMyra(Lodestar)

TheodoreBiewer,PhillipRyan,JohnWilgenFusionEnergyDivisionseminar

11/23/2009

G.ChenFusionEnergyDivisionseminar11/23/2009 1

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WhatisPDI?•  InaheaOngexperiment,linearwavescanbeexcitedbyexternalsources.

•  Ahighamplitudewave(pumpwave@f0)cannon‐linearlyexciteotherwaves(daughterwaves@f1,f2).–  ParOcleswithoscillatoryvelocityu(f0).–  FluctuaOngdensityn(f2).–  TheabovetwoquanOOesproduceacurrentnu,whichcandriveaplasmawaveatf1(=f2‐f0).

–  Theplasmawave(f1)andtheoscillatoryvelocityatpumpfrequency(f0)producesaponderomoOveforcethatdrivesthelowfrequencyperturbaOon.


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PDIandEdgeIonHeaOnginIBWandICRFExperiments

G.ChenFusionEnergyDivisionseminar11/23/2009

Rost2002,CMODPinsker1993,DIII‐D

Wilgen2006,NSTXBiewer2005,NSTX

antenna freq.

Probe NPAERDReflectometer

a b

c d

3

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MoOvaOon•  PDIhasbeenwidelyobservedintokamakICRFandIBWheaOngexperiments(NSTX,AlcatorC‐MOD,DIII‐D,TST‐2,HT‐7,etc.).

•  PDIinthescrape‐off‐layer(SOL)canleadtosignificantpowerloss,degradingtherfheaOngefficiencyinthebulkplasma(eg.directIBW).

•  OnNSTX,edgePDIlossaccountsfor30%oftotalrfpower(alowerboundesOmate).

•  WeneedamorequanOtaOveunderstandingofPDI.


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Outline

•  KineOctheoryandmodelequaOons•  Numericalmethods

•  AORSA1DsimulaOonsandPDIdispersioncalculaOons– AlcatorC‐MOD– NSTX

•  Summary

•  Futurework


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•  MaxwellianplasmainaoscillaOngframe,,

•  VlasovequaOonintheoscillaOngframe:

•  ,•  SoluOons,with

•  ElectrostaOctheory:chargedensity+Poisson’sequaOonNonlinearCoupling

OscillaOngFrame,KineOcTheory


dipolepump

6

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PDIModelEquaOons

•  Pumpwaveissolvedindependently,andassumedconstantintheSOL

•  Daughterwavesaresolvedby

•  SlecOonrules:


€

−c 2

ω02 ∇ ×∇ ×E0( ) + K0 ⋅E0 = −

iε0ω0

Jantenna

€

−c 2

ω12 ∇ ×∇ ×E1( ) + K1 ⋅E1 = C1(E0,E1,E2) −

iε0ω1

Jnoise,1

€

−c 2

ω22 ∇ ×∇ ×E2( ) + K2 ⋅E2 = C2(E0,E1,E2) −

iε0ω2

Jnoise,2

€

ω0 =ω1 +ω2

k0 = k1 + k2

Nonlinearcouplingterms

7

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SuccessiveApproximaOonsDivergeforLargeCoupling


FastwaveIBW+Quasi‐Mode

Weakcoupling

Strongercoupling

IteraOvemethodagreeswithdirect

method

IteraOvemethoddiverges

8

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PDISimulaOonsforAlcatorC‐MOD


f2 53.4 MHz f3 26.6 MHz Te 15 eV Ti 3 eV ne 1 x 1019 m-3 B0 5.3 T rt 0.9 m ky 2000 m-1

40

ExponenOalgrowthofthedaughterfield

€

nφ

Pumpfield(a.u.)

E(IBW)(a.u.)

9

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Whichwavestosimulate?

•  PDIdaughterwavessaOsfytheselecOonrules.

•  Oneofthedaughterwavesisalinearplasmawave.


€

ω0 =ω1 +ω2

k0 = k1 + k2

10

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TwoBranchesofIBW’s

•  •  Damping(lel)<<damping(right)•  Slow convergence for large


€

ω2 /Ωc = 2

Ar3ficialdampingapplied Ioncyclotrondamping

€

k⊥€

k⊥ (left) << k⊥ (right)

11

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IBWDispersionRelaOon&DecayChannels


FASTWAVE

QM IBW

IBW QM

QM IBW

CMODMinorityhea3ngregime

12

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PDIDispersionRelaOon


€

E⊥ = 9kV /m

€

E⊥ = 45kV /m


MOST UNSTABLE MODE

13

Growth rate

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Diamond‐shape‐waveExcitaOon


amplificaOon

damping

WKBapproximaOon

14

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PDIThresholdConsistentwithExperiment


 Linear3DAORSAsimulaOonspredicttypicalfastwaveedgeamplitude=(5,12)kV/[email protected]. ScalingtrendsforthePDIthresholdbehaviorwithdensity,temperatureareconsistentwithRef.[Rost2002].

ExponenOalgrowth

FastwaveIBW+QM

noise


15

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PDISimulaOonsforNSTX


•  DaughterIBWamplitudesvs.frequencyatafixedpointintheedge.

•  BothweakandstrongPDIaresimulated.

•  Peaksareseparatedbythecyclotronfrequencyattheprobe().

•  SimulaOonparameters:–  Te=Ti=50eV,–  ne=2x1018m‐3,

–  =0.45T–  ky=7000m‐1,=15

€

nφ

Antennafrequency

Logscale

probemeasurements[Diem,APS04]

€

Ωi

€

Ωi

€

Bφ

16

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PDIDispersionRelaOon


Growthrate

MOST UNSTABLE MODE

17

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PDIDependenceConsistentwithEdgeIonHeaOngMeasurements


€

kφ

RelaOveAmplitu

deofP

DI

Gen

erated

IBW

PRF=1.2‐1.3MW

€

Bφ = 0.5 T

  Predicted power threshold is consistent with previous reflectometer measurements (100 to 300kW), (Wilgen 2005).

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Summary•  Fastwave‐>IBW+QMissuccessfullyexcitedusingtheextendedAORSAcode.

•  Themostunstablemodesarefoundtobethewavesexcitedjustabovethecyclotronharmonic.

•  PDIsimulaOonsareconsistentwiththethresholdreportedinminorityheaOngexperimentsonAlcator

C‐MOD.•  PDIsimulaOonsshowthethresholddecreaseswith,consistentwiththeedgeionheaOngmeasurements.

•  PredictedPDIthresholdinNSTXisabout100KW,consistentwithpreviousreflectometermeasurements.


€

kφ

19

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FutureWorkCorehea?ngvs.edgeionhea?nginNSTX


Bphi=0.45T Bphi=0.55T

??

J.Hosea,etal.Phys.Plasmas15,056104(2008)

a b

c d

20

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FutureWorkCorehea?ngvs.edgeionhea?nginNSTX


Bphi=0.45T Bphi=0.55T

c d

e f

Alerrfison

Beforerfison

262728 212223

21

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AnotherExample


222324

G.Taylor,APS‐DPP2009

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Parametric Decay Instability (PDI) in Tokamaks · (PDI) in Tokamaks Guangye Chen, Frederick Jaeger,...

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