11 role of non-resonant modes in zonal flows and intrinsic rotation generation role of non-resonant...
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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?