ThePlasmaMicroturbulenceProject http://fusion.gat.com/theory/pmp/ - - PowerPoint PPT Presentation

8/03/01 PlasmaMicroturbulenceProject 1

ThePlasmaMicroturbulenceProject

http://fusion.gat.com/theory/pmp/

DirectNumericalSimulationofPlasmaMicroturbulence

PresentedatPPPL,August3-4,2001by G.W.Hammett(&B.I.Cohen)forW.M.Nevins,P.I.

*ThisworkwassupportedundertheauspicesoftheU.S.DepartmentofEnergyattheUniv.ofCalifornia LawrenceLivermoreNationalLaboratoryunderContractNo.W-7405-ENG48.

8/03/01 PlasmaMicroturbulenceProject 2

ComputerSimulations—ATestbed for UnderstandingTurbulentTransport

Turbulentplasmatransportis:

Animportantproblem:

Sizeofanignitionexperimentdeterminedby fusion self-heating ⇔ turbulenttransportlosses

Achallengingproblem:

Turbulenceistheoutstandingunsolvedproblem

• fclassicalphysics

Aterascale problem

Teraflop computersmakehighresolutionsimulation

• fthefullsetoffundamentalequationspossible

8/03/01 PlasmaMicroturbulenceProject 3

ComputationalCenterfortheStudyof PlasmaMicroturbulence

• Developmentandapplicationsofadvancedgyrokinetic

simulations,andcomparisonstotheoryandexperiment

• Developmentanddeploymentofsharedsoftwaretools,

includinginterfaces,diagnostics,andanalysistools

• EstablishmentofaSummerFrontierCenterforPlasma

Microturbulence

• Multi-institutionalteam:GA,LLNL,PPPL,UMD,CU,

UCLA.(P.I.=BillNevins)

• ProjectbuildsonexperienceandinvestmentinNum.

Tok.Turb.ProjectandleveragesoffOFESTheorybase program.

8/03/01 PlasmaMicroturbulenceProject 4

WhyisSimulationofPlasmaTurbulenceImportant?

• EnergyconfinementiskeyprobleminMFE

– Confinementqualitymeasuredby nτET – Currentexperimentshaveachieved nτET~1021keV-s/m3 – Burningplasmaexperimentrequires nτET~1022keV-s/m3 – Facilitycostscales(roughly)withnτET

• Dominantenergylossmechanisminmagneticconfinement

devicesisturbulenttransport Understandingturbulenttransportwouldallowustogetmore nτETforthesamedollars

• Directnumericalsimulation ofturbulenceisacost-effectiveand

easilydiagnosedproxyforveryexpensiveexperiments. Simulationsfacilitateunderstandingandarenecessarytodevelop apredictivemodelingcapability.

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ThePlasmaMicroturbulenceProject HasProducedResults

• Numerousinvitedtalksat‘00&‘01APS-DPP,‘00IAEA,‘01TTF,and‘01

Sherwood:Dimits,etal.,IAEA‘00;Dorland,IAEA‘00;Linetal.,IAEA ‘00;Y.Chen,APS-DPP‘00;Nevins,APS-DPP‘00;Cohen,APS-DPP‘01; Waltz,APS-DPP‘01;Jenko,Sherwood‘01;Leboeuf,Sherwood‘01;Candy andWaltz,EPS‘01;Jenko,EPS‘01;Hallatschek TTF‘01;etc.

• Numerouspublicationsinrefereedjournals:Dorland,etal.,PRL85 (‘00);

Rogers,Dorland,etal.,PRL85 (‘00);Y.ChenandParker,PoP 8,441& 2095(‘01);Dimits,etal.,Nuc.Fusion41,(‘01);Kim&Parker,J.Comp.Phys. 16 (‘00);Leboeuf,etal.,PoP 7 (‘00);LinandChen,PoP 8 (‘01);Rettig, Leboeuf,etal.,PoP 8,(‘01);Snyder&Hammett,PoP 8(‘01);etc.

• Experimentalcontributions: Budny(JET),McKee(DIII-D),Murakami(DIII-

D)IAEA’00,Kinsey(DIII-D)PRL’01.Ernst(TFTR)PoP’00,manyothers.

• ThePMPhashadthesinglelargestallocationatNERSCforafew years.

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ThePhysicsModel

MagneticCoordinates: B=∇ ∇ ∇ ∇α×∇ ∇ ∇ ∇ψ Perturbed5-Ddistributionfunction: hs=hs(ψ,α,θ,ε,µ) Gyrokineticequation: where: ReducedMaxwell’sEquations Electrostaticpotential: δB⊥: δB||:

t F q i h i v t

T d

∂ ∂ ∂ε ∂ ω ω Φ − Φ =

• +

∇ ⋅ + ∇ ⋅ Φ ×∇ ⋅ + ∂ ∂

* ||ˆ

ˆ b b Φ = J0

k⊥v ⊥ Ω

( ) φ − v||

c A

||

• +

J1

k⊥v⊥ Ω

( )

k⊥v⊥ Ω

mv⊥

2

q δB

||

B ∇⊥

2φ = 4π

q d

2v qφ ∂F

∂ε + J0

k⊥v ⊥ Ω

( )

h

• s
• ∇⊥

2 A || = − 4π

c d

2v qv||J0 k ⊥v⊥ Ω

( )

h

• s
• δB

||

B = − 4π B

2

d

2v mv⊥ 2 J1 k ⊥v ⊥ Ω

( )

k ⊥v ⊥ Ω

h

• s

8/03/01 PlasmaMicroturbulenceProject 7

PlasmaTurbulenceSimulation CodesAlreadyDeveloped

• BuildsonNTTPeffort
• RealisticGeometry&

efficientgridsaligned withB() :

– Flux-tubecodes – Globalcodes

• EfficientAlgorithms

Gyrokinetic—Continuum Gyrokinetic—PIC

• Demonstratedscalingto

100’sofprocessors

⊥

<< k k||

8/03/01 PlasmaMicroturbulenceProject 8

PlasmaMicroturbulenceProject ReliesonaSmallSuiteofCodes

• PMPcodesuite:2x2matrixofglobalandflux-tubecodesusing

gyrokineticVlasov continuumandparticlemethods.Buildingshared backendsfordiagnosticsandvisualization,sharedfrontendfor experimentaldatainterfaces.

• Bothglobalandflux-tubecodesareneeded.Flux-tubeismore

efficientforparameterstudies,doesnot tripoverproblemsofplasma particleandenergysourcesorprofilerelaxation,andmorereadily includesphysicsatscaleslessthantheionLarmor radius(e.g.,ETG). Global(nonlocal)accommodatesequilibriumprofilevariationsand scalingwrtLarmorradiusoverminorradiusnonperturbatively.

• Vlasov continuumandparticleapproacheshavedifferent

computationaladvantages/disadvantages.Havingtwoapproacheshas beenvitalforcross-checkingresultsanderrorcorrection,andhas providedopportunitiesforinnovationandcreativity.

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ExistingCodes(I) GyrokineticParticleCodes

• IntegratesGKEalong

characteristics

Manyparticlesin5-D phasespace Interactionsthrough selfconsistentelectric &magneticfields

Particlesadvanced inparallel

Cray-J90 Cray-C90 Origin2000 T3E 107 106 105 104 1 10 100 1000 NumberofProcessors NumberofParticles-Timestep/Second

8/03/01 PlasmaMicroturbulenceProject 10

ExistingCodes(II): 5-DContinuumCodes

• SolvesGKEonagridin5-D

phasespace(multipledomain decompositionused)

• Eliminatesdiscreteparticle

noise

• Linearphysicsishandled

implicitlyinGS2

Kineticelectrons& electromagnetismhaveless impactontimestep

• GlobalcodeGYROis

explicit,usesadvancedCFD methods.

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UnderPSACIAuspicesthe PMPProposalWasApprovedto:

• Explorenewregimesofplasmamicroturbulence using

existingandnewlydevelopedcodes

• Developadvancedsimulationalgorithmsfor

– Newgenerationsofcomputers,e.g.,IBMSP – Newphysicscapabilities,e.g.,kineticelectronsand electromagneticfluctuations

• Buildadvanced,shareddiagnostics toprovideabridge

betweensimulationeffortandtheory&experimental communities

8/03/01 PlasmaMicroturbulenceProject 12

PMPphysicsfocus:extendto kineticelectrons+electromagnetics

• Pastdecade:majorprogress on“IonTemperatureGradient”(ITG)

plasmaturbulenceintheelectrostaticlimit( , B =const),oftenw/adiabatic/Boltzmann electronsne=exp(-qΦ/T).

• Explainsmaintrendsincoreofmanyexperiments:marginal

stabilityeffects,turbulencesuppression,self-generatedzonalflows. Butnotsufficientlyaccurateforallplasmaregimes,neglected electronheatandparticletransport.

• PlasmaMicroturbulenceProjectmajorgoal:extendtonon-

adiabaticelectronsandfullyelectromagneticfluctuations

– Importantathighβ =(plasmapressure)/(magneticpressure) – Neededforadvancedfusionconcepts – Hard:electronsare60timesfasterthanions,severeCourantcondition – PICnumericalproblemswhenβ>me/mi,recentlysolvedwithsplit-weight /fluid-kinetichybridalgorithm

) , ( t x E Φ −∇ =

8/03/01 PlasmaMicroturbulenceProject 13

PlasmaMicroturbulenceProject AddressesScientificIssues

• Secondaryinstabilities,streamerandzonalflow

dynamics

• Kineticelectronsandelectromagneticfluctuations
• Formationanddynamicsofinternaltransport

barriers

• Theroleofmeso-scalesinturbulenttransport

Tractablemodelsofturbulenttransport

8/03/01 PlasmaMicroturbulenceProject 14

PlasmaMicroturbulence ProjectDeliverables

Mutuallybenchmarked,welldiagnosed,electromagnetic, microturbulence codes(‘01-’02) Advanceddataanalysisandvisualizationcapability(‘01-’02) Prototypenationaldatabaseforstoringcodeoutput(workingwith fusioncollaboratory,tobedetermined) Betterunderstandingofplasmamicroturbulence,detailed experimentalcomparisons(continuing) SUMMITsharedelectromagnetic+kineticelectroncode(Fall‘01) GYROaddselectromagneticcapability(Fall‘01) Paceofcodedevelopmentisslowedcomparedtoproposal becauseofreducedfunding.

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Studiesofimportanceof“zonal flows”,secondaryinstabilities…

CL

Zonalflows(onsmallscale, drivenbysecondaryinstabilities, limitstheprimaryinstabilities). Whydon’tzonalflowsalways growtokillturbulence? Primaryinstabilities,carry heatfromcentertoedge

(enlargedviewofsmallscaleturbulencenottoscale)

8/03/01 PlasmaMicroturbulenceProject 16

PhysicsProgressI: SecondaryInstabilities

• Parasiticinstabilitieson

zonalflows

Limitszonalflowamplitude IncreaseinITGturbulence andplasmatransport Mechanismfor‘Dimits shift’

• TalkbyW.DorlandIAEA2000,Rogers

PRL2000

• AlsoseenbyDimitsinPG3EQ(Nevins,

TTF‘01)

8/03/01 PlasmaMicroturbulenceProject 17

PhysicsProgressII:GS2Simulationsof ElectromagneticITGTurbulence

• Asβ approachesidealballooninglimit,characterofITGchanges.
• Energytransportdominatedbynonlinearmagneticfluttertransport.

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PhysicsProgressIII: PICStudiesofITGTurbulence

• Dependenceofχi onT'',Φ''

Importanceofionradialforce balanceininitialstate

• Dependenceofχi on

– magneticshear – E×Bshear – Toroidal flowshear Significantdepartures fromWaltz-Dewar-Garbet transportreductionmodel

• A.Dimits atIAEA2000andTTF‘01,

PG3EQflux-tubesimulations

8/03/01 PlasmaMicroturbulenceProject 19

PhysicsProgressIV: SOC&HeatPulseAnalysis

• InanalogytoNewman’s

workonSOC& transport:

– Decomposeheatfluxinto sumof‘heatpulses’ – ProbabilityDist.Function: pulseratevs.pulsesize PDFyieldspowerlaw

ExplanationofBohm transportscaling?

• TalkbyNevins atAPS/DPP2000

Characteristic Event Size

8/03/01 PlasmaMicroturbulenceProject 20

PhysicsProgressV: ComparingGlobalGyrokinetic ParticleSimulationToExperimentalObservations

• Preliminaryworklookslikeapromisingfoundationforfuture

thrustofmicroturbulence effort:DIII-DRadialCorrelationLengths

0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.4 0.5 0.6 0.7 0.8 0.9 1 ∆r(cm) fluxsurfacecoordinatesρ ρs ρθ ,s 5-8 × ρ s

ReflectometryResults

0.5 1 1.5 2 2.5 3 0.4 0.5 0.6 0.7 0.8 0.9 1 ρ ρ ρ ρs ρ ρ ρ ρθ

θ θ θ,s

∆ ∆ ∆ ∆r(cm) r/a

GyrokineticResults(UCAN)

8/03/01 PlasmaMicroturbulenceProject 21

PhysicsProgressVI: ZonalFlows

• ITGturbulence

ZonalFlows

Suppressionof ITG turbulence

• νi dampszonalflows

Burstingbehavior

Averagetransport~νi

• TalkbyZ.LinpresentedatIAEA

2000

collisional damping of zonal flows causes bursts

• f turbulent transport in gyrokinetic simulations

zonal flows

χ

i

12 10 8 6 4 2 1

τ

d

time ( )

A.U.

82 large bursts of fluctuation in TFTR RS plasmas

• bserved period ~ collisional flow damping time

2 . 7 8 2 . 7 9 2 . 8 2 . 8 1 2.

time (second)

RS ERS r/a=0.15

[Mazzucato, et al., PRL, 1996] [Lin, et al., PRL, 1999]

8/03/01 PlasmaMicroturbulenceProject 22

PhysicsProgressVII:Nonlocal Simulation

• fITGTurbulencewithSources
• InclusionofanadaptivesourcetomaintainprofilesinGYROglobal

simulationsofITGcanrestoregyro-Bohmlevelsofthermaltransport.

• Inabsenceofsources,smalldeviationsfromequilibriumprofiles

causedbyn=0perturbationscancause“false”Bohmtransport.

0.5 1 1.5 2 2.5 0.2 0.3 0.4 0.5 0.6 0.7 0.8

χ χ χ χ/[c sρ ρ ρ ρs

2

/a]->

source ρ ρ ρ ρs=0.0025 source ρ ρ ρ ρs=0.0050 nosource nosource a/L T=1.9 a/L n=1.

r/a->

gyroBohm falseBohm 1 2 3 4 5 0.2 0.3 0.4 0.5 0.6 0.7 0.8

• dlnT/dr->

(a/L T) ρ ρ ρ ρs=0.0025 (a/LT) 0 (a/L T) ρ ρ ρ ρs=0.0050 gradT20

a/LT=1.9 a/Ln=1.0

r/a->

• nosource

8/03/01 PlasmaMicroturbulenceProject 23

KineticElectronsand ElectromagneticFluctuations

• Motivation:

– Modelingofparticletransportandelectronthermaltransport – Increasedfidelityinmodelingofρi-scaleturbulence[new sources offree energy,electromagneticcorrections] – Shortwavelengthturbulenceandassociatedelectrontransport [ ρe~(me/mi)1/2ρi throughδe=c/ωpe~(me/βmi)1/2ρi]

• Status:

– Fullyelectromagneticgyrokineticcontinuumcodesexist[benchmarking

• fglobal/fluxtubecontinuumcodesinprogress]

– Electromagnetic,gyrokineticPICcodesbeingdevelopedbasedonthe split-weightalgorithm(Manuilskiy,W.Lee)combinedwithextended hybridalgorithm(Lin,L.Chen,Y.Chen,Parker,Cohen) – SuccessfulworkshopatGA(July24-26)onnewmethodsandphysics

• CriticalIssues:

– Relaxedδe spatialresolutionrequirementsinbothcontinuumandPIC approachesforITGandTEMapplications. – Dominantelectrondissipationintorusislikelyfromtrappedelectrons.

8/03/01 PlasmaMicroturbulenceProject 24

ProgressonKineticElectronsI:HybridPIC Split-WeightSchemesin2-1/2DSlab

• Algorithmdemonstrated

in“2-1/2”Dtestproblem

– Simplifiedgeometry – Reduceddimensionality

• Accuratelinearphysics

required:

∆t resolution: Resolutionofelectronlayer [ xe~(me/mi)1/2Ls/Ln ρi ]

• SeeCohenetal.,APS/DPP

2000and2001,Sherwood‘01

k||ve∆t ≤ O(1)

CollisionlessDriftWave

O δf

*hybrid

8/03/01 PlasmaMicroturbulenceProject 25

ProgressonKineticElectronsII: Split-WeightsinFieldLineCoordinates

• 3-Delectromagnetic

gyrokineticPIC (Y.Chen-Parker)

• Fulldriftkineticelectrons

(i.e.,ignoresfiniteρe)

• Accuratephysics
• n

ρi gridfor

– β

• 0.5%

– k||vte∆t

• O(1)
• TalkbyY.Chenat

APS/DPP2000andPoP

WithDIII-DH-modeparameters,χ is muchhigherwithkineticelectrons.

i

8/03/01 PlasmaMicroturbulenceProject 26

What’sNextwithKineticElectrons andElectromagneticEffects

• GS2flux-tubecontinuumcodehaskineticelectronsand

electromagnetics;increasephysicsthroughput, benchmarks,andexpanduserbase

• LLNL/CU/UCLAmergingPG3EQandTUBEwithδB

andkineticelectronsinasharedcode(SUMMIT)

• KineticelectronsworkinginGYROglobalcontinuum

code,andelectromagneticimminently

• InclusioninGTC(aglobalGK-PICcode)

– Kineticelectrons+electrostaticswork.Electromagneticnext. – CollaborationwithL.Chen,UCIrvine

8/03/01 PlasmaMicroturbulenceProject 27

Diagnostics&VisualizationI: InteractiveDataAnalysiswithGKV

• Anobject-oriented data

analysissystemwith:

– Correlationfunctions,cross correlation,bicoherence,etc. – Spectraldensity,cross spectra,bi-spectra,etc. – x-space⇔ k-space transformations – Heatpulseanalysis – Animations – …(moretocome)

• GKVinterfaceswith:

– Pg3eq(LLNLGK-PICcode) – GTC(PPPLGK-PICcode) – GS2(U.ofMd GK-Ccode) – UCLAGK-PICcode – BOUT(LLNLedgecode) – …(moretocome) – NevinspresentationsatAPS- DPP‘00andTTF‘01

8/03/01 PlasmaMicroturbulenceProject 28

DataAnalysis:TheBridgebetween

SimulationandtheTheory/ExpCommunities

• InteractiveDataAnalysiswithGKV

– Productivedataexploration “Granularity”

• Significantresults

froma fewcommands

• Flexibility

– Standardanalysisroutines

• Spectraldensity
• Correlationfunctions

– CustomAnalysis

• ParticleTrapping
• HeatPulseAnalysis

QuantifyingtheImportance Ofparticletrapping

8/03/01 PlasmaMicroturbulenceProject 29

Cδφ(∆y)

GTC pg3eq GTC envelope

pg3eq

(adiabatic electyrons)

Tube

(kinetic electrons)

Hilbert envelope

CorrelationFunctionsCalculatedwithGKV: Allowsdetailedcrosscomparisonsofcodes(and eventuallywithexpt.fluctuationmeasurements)

8/03/01 PlasmaMicroturbulenceProject 30

τc DeterminedbyEffective E×B Shear

• EffectiveE×BShearingRate:

– Contributions from andzonal flows – Removehigh-ω,high-kx componentsofzonalflow

• L-Modesimulationdatashows

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 0.01 0.02 0.03 0.04 0.05

τcγeff τcγeff = π

V'external

γ eff = ∆R ∆y ′ V

external 2

+ ′ V

zonal 2 ωτc<1

kr∆R<1

τc ≈ π γ eff ′ V

external

GKV

eff cγ

τ

8/03/01 PlasmaMicroturbulenceProject 31

DataAnalysisandVisualizationII: OtherVisualizationTools

• GYROVisualization

tools

• SeeinvitedtalkbyWaltz

atAPS/DPP2001

usingacontinuousstreamof animationstoillustratethe drift-ballooningmodesand zonalflowsinlinearandfully developedstatesofITG turbulence

8/03/01 PlasmaMicroturbulenceProject 32

DataArchiving

• Amajorissueincomparingresultsbetweencodes

isaccesstodata

• BillDorlandisworkingwithGreenwald/Yuh(MIT)

and Schissel (GA)onprototypesystem

– BasedonMDSPlus(dataarchivingsystemwidelyusedby experimentalists) – DesigningMDSPlustree:

• Input(gridparams,physicsparams,transp run,…)
• Output(recordofwhatinformationwassaved)
• Rawdata
• Dataarchivingeffortwillbeexpanded(insupportof

PMPandotherPSACIprojects)

8/03/01 PlasmaMicroturbulenceProject 33

GS2UserCommunity

• C.Bourdelle, PPPL:NSTX
• E.Belli,PPPL:stellarator,NCSX
• R.Budny,PPPL:JET,transportbar.
• S.Cowley,ImperialCollege:tailof

Goldreich-Sridharcascade

• A.Dimits,LLNL:GKbenchmarks
• W.Dorland,UMD:Collisional

TEM,EMITG/ETG,codesupport

• D.Ernst,PPPL:shearstab.models
• P.Goswami,UMD:dipoles,LDX
• M.Greenwald,MIT:MDS+

interface,C-Modstability

• K.Hallatschek,IPP-Garch:particle

transportandpinchanalysis

• G.Hammett,PPPL:Advancedalg.

development,benchmarking

• F.Jenko,IPP-Garch:ETG&TEM
• M.Kotschenreuther,IFS:Advanced

alg.development,novelconfigs.

• D.Mikkelsen,PPPL:Experimental
• bserv.ofDimitsshift,C-Mod
• B.Osborne,UMD:Javainterface
• S.ParkerandY.Chen,CU:

collisionlessTEMbenchmarks

• E.Quataert,UCBerkeley:

Astrophysics(β~1),blackhole accretiondisks

• M.Redi,PPPL:ITBformationinC-

Mod

• B.Rogers,Dartmouth:EMturb.&

reconnection

• D.Ross,FRC:Expt.Comparisons,

DIII-DandC-Mod

• A.Vinas,NASA-Godd.:Solarwind
• H.Yuh,MIT:Stab.&Turb inC-Mod

EDAmodes

8/03/01 PlasmaMicroturbulenceProject 34

8/03/01 PlasmaMicroturbulenceProject 35

What’sNextforthe PlasmaMicroturbulenceProject?

• Continueandexpandcurrenteffortsin:

– Increasinginteractionswithexperiments:collaborationswith experimentalistsandcomparisonstodataatDIII-D,C-MOD,JET, NSTX,LDXdipole,andstellarators – Developanddeploysinglefrontandbackendforflux-tube/globaland continuum/PICcodes – DeployPMPcodesthroughtheFusionCollaboratoryProject – Improveddataanalysisandvisualization

ExploitGKVandotherPMP-shareddiagnosticstocomparesimulationsto

• neanotherandexperiments-> moreusers

– Codedevelopmentandmorephysicsinmodels – Morephysicsresultsfromexistingcodes

• Thepaceoftheseactivitiesisslowedrelativetotheproposal’smilestone

schedulebecauseofreducedfunding.Moremoney->fasterpaceand conveneSummerFrontierCenterforalongerperiod.