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1 Role of Non-resonant Modes in Zonal Flows and Intrinsic Rotation Generation Joint US-EU Transport Taskforce Workshop TTF 2011 April 6-9, 2011 San Diego, California Sumin Yi, J.M. Kwon, T. Rhee, P.H. Diamond [1] , and J.Y. Kim WCI Center for Fusion Theory, NFRI, Korea [1] CMTFO and CASS, UCSD, USA

11 Role of Non-resonant Modes in Zonal Flows and Intrinsic Rotation Generation Role of Non-resonant Modes in Zonal Flows and Intrinsic Rotation Generation

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Page 1: 11 Role of Non-resonant Modes in Zonal Flows and Intrinsic Rotation Generation Role of Non-resonant Modes in Zonal Flows and Intrinsic Rotation Generation

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Role of Non-resonant Modes in Zonal Flows and Intrinsic

Rotation Generation

Role of Non-resonant Modes in Zonal Flows and Intrinsic

Rotation Generation

Joint US-EU Transport Taskforce Workshop TTF 2011April 6-9, 2011

San Diego, California

Sumin Yi, J.M. Kwon, T. Rhee, P.H. Diamond[1], and J.Y. Kim

WCI Center for Fusion Theory, NFRI, Korea[1] CMTFO and CASS, UCSD, USA

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Introduction and MotivationIntroduction and Motivation

• In gyrofluid and gyrokinetic simulations, qualitatively different trans-

port phenomena were observed for different non-resonant mode config-

urations of the fluctuation spectrum.

• A transport barrier is found to develop in the gap region if non-resonant

modes are artificially suppressed in the simulation (Garbat et al PoP 2001,

Kim et al NF submitted, Sarazin et al J. Phys.: Conf. Ser. 2010).

• Finite non-resonant modes were observed in numerical studies of the re-

versed shear plasmas (Idomura 2002 and Candy 2004).

• We study role of non-resonant modes in the self regulating dynamics of

turbulence and zonal flows.

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Central ThemeCentral Theme

Radial propagation of turbulence by nonlinear mode coupling affects

〈 kr 〉 of Turbulence Spectrum & Reynolds Stress

Zonal Flows

Turbulence Level

Temperature Profile

〈 kθ 〉 of Turbulence Spectrum

Parallel Asymmetry &

Toroidal Flow

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gKPSP : global gyrokinetic δf PIC codegKPSP : global gyrokinetic δf PIC code

• Simulation code: gKPSP [Kwon IAEA2010] Global δf PIC gyrokinetic simulation code δf Coulomb collision operator (W.X. Wang et al

PPCF’99) No external heat source → turbulence intensity

front by profile relaxation General equilibrium from EFIT data

• Quasi-ballooning representation of fluctuating potential

N

Nnn in )],((exp[),(

)2,(,,

iinNijnijn e

qdB

B~),(

0

,,1

( , ) ( ) ( )n n ij i ji j N

Q Q

Qi(ψ) and Qj(θ) : quadratic spline centered at ψi and θj

for periodicity in θ

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Quasi-ballooning representation of fluctuating potentialQuasi-ballooning representation of fluctuating potential

N

Nnn in )],((exp[),(

modes with m/n = q

include modes with m/n ≠ q

m

n

mod

es w

ith m

/n =

q

modes with m/n ≠ q

modes with m/n ≠ q

• Proper resolution of “amplitude” part ϕn(ψ,θ) is important for modes with m/n ≠ q, so called non-resonant modes

• Usually, enough number of grid points in poloidal direction is used Nθ ≥ 32

• In this work, this feature is utilized to study the role of non-resonant modes i.e. we compare Nθ = 32 and Nθ = 6 cases

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Suppression of Non-resonant ModesSuppression of Non-resonant Modes

• By artificially restricting the poloidal extent Nθ, non-resonant modes are suppressed→ Scattering in spectral space through mode-mode interaction is reduced

• Monotonic q-profile (Cyclone case) q = 0.8 - 3.0 (s = 0.84 at r/a=0.5)

W/O non-resonant modes With non-resonant modes

Non-resonant mode contribution

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Zonal Flow Evolution

• When non-resonant modes are included, zonal flow (ZF) becomes stronger and continues to grow in radially outward.

• At certain radius, the direction of ZF becomes opposite due to excitation of the non-resonant modes.

W/O non-resonant modes With non-resonant modes

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Turbulence Spectrum in kr and kθTurbulence Spectrum in kr and kθ

• Without non-resonant modes, RS is produced by fluctuations with

• Inclusion of non-resonant modes provides- fluctuations with- and compensates the asymme-

try in spectrum- leads to sign change in RS at

later time

• Why additional positive kr from non-resonant modes ?- from radial propagation/

spreading of turbulence by enhanced non-linear mode coupling

W/O non-resonant modes With non-resonant modes

0kkr

0kkr

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Difference in Reynolds Stress

2~ | |r rv v k k kk

2~ | |rr

V v vk k

t r r

k

k

(Diamond and Kim, Phys. Fluids B1991)

• RS is computed from turbu-lence spectrum

• Difference in RS is consistent with ZF drive and evolution

• By including non-resonant modes:- Reduce shear in RS and ZF- Change ZF drive and direction

Reynolds Stresst=1300-1400 t=1400-1500

Zonal Flow Drivet=1300-1400 t=1400-1500

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Difference in Poloidal Flow Evolution

By including non-resonant modes,

The sign of RS changes

The direction of EB poloidal flow becomes opposite at certain radius

This opposite poloidal flow affects toroidal flow generation

r=0.170

r=0.163-0.180

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Difference in Turbulence Intensity

• Without non-resonant modes

asymmetry in fluctuation spectrum enhanced

RS and ZF drive become stronger

turbulence regulation becomes stronger

Non-resonant mode contribution

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Difference in Temperature Profile

• Without non-resonant modes turbulence regulation becomes stronger

temperature gradient becomes steeper

→ prelude to ITB formation?

consistent trend with previous gyrofluid

(Garbet PoP’01, SS Kim submitted NF)

and gyrokinetic simulations

(Sarazin J.Phys’10)

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Toroidal Rotation and Parallel Wave Number

• Without non-resonant modes, strong toroidal flow is generated and persists after non-linear saturation

• With non-resonant modes, parallel wave number asymmetry becomes weakened and toroidal flow decreases

W/O non-resonant modes With non-resonant modes

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Asymmetry in Parallel Wave Number

• In early phase of non-linear evolution, . It determines parallel wave number asymmetry in fluctuation spectrum in both cases

2mn

0k

W/O non-resonant modes With non-resonant modes

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Asymmetry in Parallel Wave Number (cont’d)

• In later phase of non-linear evolution, by including non-resonant modes, asymmetry in decays due to the excitation of +θ propagating modes (+θ directional ZF in inner radii)

2mn

||k

W/O non-resonant modes With non-resonant modes

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Mode rational surface

• By suppressing non-resonance modes,

the radial scattering/propagation of turbu-

lence is restricted

turbulence spectrum becomes quite station-

ary in the nonlinear saturation phase

so 〈 k|| 〉 and toroidal flow persists

longer into the nonlinear phase

• With non-resonant modes,

→ Enhanced radial scattering of

the + directional modes.

Decay of Parallel Wavenumber Asymmetry

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SummarySummary• By suppressing non-resonant modes,

▶ spurious asymmetry in fluctuation spectrum appears▶ radial scattering/propagation of fluctuation intensity is hindered and turbu-

lence spectrum becomes stationary▶ RS and ZF drives are enhanced▶ turbulence suppression is enhanced▶ asymmetry in fluctuation spectrum persists and leads to stronger toroidal

rotation▶ artificially promotes ITB formation?

• By allowing non-resonant modes,▶ asymmetry in fluctuation spectrum is weakened▶ RS and ZF shears formation are delayed and weakened▶ radial scattering of fluctuation intensity becomes stronger▶ toroidal flow becomes weaker▶ ITB?