First-PrincipleSimulationofParticleTransportintheinversed-density-gradient

profile

1)KMiki,1)NMiyato,2)B.Scott,and1)M.Yagi1)QST,Japan2)IPP,Germany

6/5/2017 APTWGA-OV1NagoyaUniv.,Japan

1

Contents

• Introduction• BasicFrameworkofdFEFI• Benchmarkofcyclone-base-caseparameter• Resultsontheinversed-density-gradientcaseparameter

• Summary

2

Inversed-density-gradient appearsinfuelingoperations.

Temperature

density

• Hollowdensityprofileduepelletorgas-puffinjection

⇒inverseddensitygradientappearsintheedgeregion.

r

• Relevantto・Whatmechanismoftheparticleflux(pinch?)

Wehereundergothefirst-principlesimulationontheparticletransportintheinversed-densitygradientregion.

3

• FuelingphysicscontributesITER/DEMOdevelopment.

• Worksonvalidationofparticletransportphysics.[Angioni‘09][Wan‘10][Tangered ‘16]

(Note:inthiswork,profilerelaxationisoutofourtarget,duetolocalapproach.)

dFEFI:delta-f gyrokineticsolverforionsandelectrons.[B.Scott,PoP(2010)]

• delta-fElectromagneticGKequation

Polarizationequation:

Inductionequation:

4

• Field-alignedcoordinate• Shiftedmetric• Fixedboundaryon

radius• Localcode,butremains

globality ontheboundaryconditions.

(x:radial,y:binormal,s:magneticfieldline)

Benchmarkoncyclone-basecase(CBC)parametercoreplasma:a/R =0.184,L^/R=0.145,min(kyrs)=0.025.Ti/Te=1,qR/L^=9.67,be(qR/L^)2=1e-3,rq’/q=1.14,L^/Ln=0.321,L^/Lte=L^/LTi=1.0Ly/Lx=4.0,(nx,ny,ns,nz,nw)=(128,128,32,48,16)

-0.2

-0.18

-0.16

-0.14

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

00 0.1 0.2 0.3 0.4 0.5

w(L^/cs)

dFEFIGS2

0

0.01

0.02

0.03

0.04

0.05

0.06

0 0.2 0.4 0.6

GS2 dFEFI

g(L^/cs)

kyrs

kyrsLineargrowthrate frequency

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R/LTi=6.9R/LTe=6.9R/Ln=2.2

Linearcalculationexhibitstwomodeswithionandelectrondirectionrotation

Edgeplasmaparameters:R0=165cm,ne=2.0x1013 cm-3,Te=100eV,Ln=-7cm,LTi=LTe=3.5cm,B=2.5T,Ti/Te=1,a/R=0.303,L^/R=0.0212,q=3.5,Normalizedbeta=6.44x10-5,ni(L^/cs)=000956,ne=(L^/cs)=0.823(nx,ny,ns,nz,nw)=(32,128,32,32,16),Lx/Ly=1.0,Dt=0.005

WeobserveITG-likeandTEM-likemodesgrowing.

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0 0.2 0.4 0.6 0.8 1 1.2

Iondirection:=ITG-likemode

electrondirection:=TEM-likemode

w(L^/cs)

kyri

Powerspectrainlinearphase

kyri0.01 0.1 1 10

neTiTef

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TimeevolutionofParticleFlux⇒ Inward,withphase-shifted

t(cs/L^)

Heatflux

ParticleFlux

0.1|ef/Ti|2

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Inversedgradientcase

Phaseshiftfornormalgradient (Ln=7cm)

Phaseshiftforinversedgradient(Ln=-7cm)

Fortheinversed-density-gradientcase,weexpectlargerphaseshiftsinthedensity-potentials.

Spectralanalysesonelectrostaticpotentialandparticleflux.

SpectrumoffHighwavenumber(TEM-like)modesdisappearint=400.

• Inthenonlinearphase,thelowerwavenumbermodesurvives.

• Bothpeakscontributestoinwardparticlefluxes.Inthenonlinearphase,modeswith0.1<kyrs <0.8contributestheinwardflux.

ParticleFluxSpectrawithrespecttokyrs

Candidate?Ion-Mixing-Mode[Coppi ‘78PRL]• SlabfluidModel• Modedispersion

• Non-trivialmode:

Electronadiabaticity isaffectedbytheelectronthermalforce.

ParticleFlux：

!nen=e !φTe1+ (1+αT )

iωχ

(ω −ω*e +32ηeω*e )

⎡

⎣⎢⎢

⎤

⎦⎥⎥ ωχ ≡ χ̂ek||

2Te / (meνe )

Γ= !n !vEx = −(2c / B)Im( ky !φk !nk )k∑

However,Isthisassumptioncorrect？

ω ~ω*e <ωχ

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Estimatefromsimulationresults~-0.73

1+ iA+ k||2 Temi

ωTi

ω 3 −ω*e

ω= 0 A = 3

2ηeω*e

ωχ

(1+αT )

ITG-likemodeω = −[(k||

2Te /mi )ωTi / (1+ A2 )]1/3(1− iA)1/3

Assumption: Diagonaleffects(prop.togradn)arecancelled,remainingoff-diagonal(prop.togradTe)term.

k||2vth,i2 /ν i <ω ≤ k||

2vth,e2 /νe

6.7x10-3 0.05 0.12ne>k||vthe,w

0.823 0.26 0.05

ValidationofIon-Mixing-Mode

ω*e =kycTeeB

d lnndr

~ −0.05(cs / L⊥ )

ω(ky = 0.1) ~ −0.063(cs / L⊥ )

!nen=e !φTe1+ (1+αT )

iωχ

(ω −ω*e +32ηeω*e )

⎡

⎣⎢⎢

⎤

⎦⎥⎥

Measuresdegreeofthecancellation.

dTe/dr dependency

ωχ = χ̂ek||2Te /meνe ~ 0.7(cs / L⊥ )>ω*e

A = 32ηeω*e

ωχ

(1+αT ) ~ 0.2 >me

mi

Thismodeisenoughlargecomparedwithcollisionaleffects.

ω ~ω*e <ωχ Iscorrect?

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0.1

0.73

ParameterScan(1)nscan

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G(n0cs)

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0.8 0.85 0.9 0.95 1

g

(𝛁n)/(𝛁n)ref• 𝛁n scanonsaturatedparticlefluxisalmostsimilarwithinfluctuations.• Diffusivepartisnotsignificant

• Higher𝛁n gives(slightly)highergrowthrate.

x1.0

x0.9 x0.8

IntheIMMtheory,adiffusivepartonparticlefluxisnotsignificant,sincew~w*e issatisfied.

Growthrate

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

00.8 0.85 0.9 0.95 1

d(=<nv>/f^2)

Parameterscan(2)GradTi Scan

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GradTiscan(x1.0,x0.9,x0.8)

• Higher𝛁Ti giveshighersaturatedinwardparticleflux.

• Higher𝛁Ti giveshighergrowthrates,relatedtoITGmode.

• Highter 𝛁Ti givesdrasticallyhigherphaseshift(d=G/<f2>).

00.0050.010.0150.020.0250.030.0350.040.0450.05

0.8 0.85 0.9 0.95 1

g

(𝛁Ti)/(𝛁 Ti)ref(𝛁Ti)/(𝛁 Ti)ref

Higher𝛁Ti =>higherInwardflux,originatedfromphaseshift,aswellasincreaseofgrowthrates

G(n0cs)

Phaseshift

Growthrate

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

00.8 0.85 0.9 0.95 1

d(=<nv>/f^2)

summary• Wehavesimulatedtheturbulenceincasethatdensitygradientinversed.Inlinearphase,twomodesappear;oneisITG-like,andtheotherisTEM-likemodes.

• TheTEM-likemodesdisappearsinthenonlinearphase.• TheITG-likemodemaybeidentifiedastheion-mixing-mode.NotethattheIMMisuniquetotheinversed-density-gradientcase.

• Infuturework,toroidalIMMmodelshouldbederivedforfurtherunderstandingofthesimulationresults.

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Implications:• Furtherphysicsshouldenterinhollowdensityprofile.• Electrontemperatureisakeyforthecase,inthatelectronthermalfluctuationcanmodulatethephaseshift.