Y. Kishimoto Naka Fusion Research Establishment, Japan Atomic Energy Research Institute US-Japan...
27
Y. Kishimoto Naka Fusion Research Establishment, Japan Atomic Energy Research Institute US-Japan JIFT workshop, December 15-17, Kyoto University, Kyoto, Japan Local and non-local gyro-fluid simulation of ITG and ETG turbulence and statistical properties In collaboration with J. Q. Li, N. Miyato, T. Matsumoto, and Y. Idomura Li et al., the 13 th Toki conf. Miyato et al., 13 th Toki conf. Matsumoto et al., 13 th Toki conf. Idomura et al., 13 Toki
Y. Kishimoto Naka Fusion Research Establishment, Japan Atomic Energy Research Institute US-Japan JIFT workshop, December 15-17, Kyoto University, Kyoto,
Y. Kishimoto Naka Fusion Research Establishment, Japan Atomic
Energy Research Institute US-Japan JIFT workshop, December 15-17,
Kyoto University, Kyoto, Japan Local and non-local gyro-fluid
simulation of ITG and ETG turbulence and statistical properties In
collaboration with J. Q. Li, N. Miyato, T. Matsumoto, and Y.
Idomura Li et al., the 13 th Toki conf. Miyato et al., 13 th Toki
conf. Matsumoto et al., 13 th Toki conf. Idomura et al., 13 th Toki
conf.
Slide 2
Contents Background and motivation Fluctuation dynamics of
micro-scale ETG turbulence Summary Fluctuation = turbulent part +
laminar-like flow part Control the fluctuation by changing the
partition Hierarchical interaction among different scale
fluctuation Enhanced ETG-driven zonal flow dynamics based
gyro-fluid model (cf. Hamaguchi-Horton equation + electromagnetic
effect) Statistical properties of fluctuation such as fractal
dimension and PDF Fluctuation dynamics of meso-scale ITG turbulence
Nonlinear Global gyro-Landau fluid simulation Toroidal and
electromagnetic effect on zonal flow
Slide 3
[Idomura et al., 00] [Matsumoto, Naitoh, PoP, 03] Nonlinear
fluctuation dynamics Local inverse/normal cascade Mixed
turbulent/zonal fluctuation system Internal kink event MHD-driven
Er-field Zonal- [Idomura, PoP, 00] ETG streamers found near
threshold are essentially linear structures whose nonlinear
interaction is weak. [Dorland, et al., IAEA, 02] MHD ion electron
skin size [Jenko-Kendel,PoP, 02] Wendelsteien 7AS simulation
[Kendel, PoP, 03] Nonlinearly generated convective cell mode
Slide 4
Nonlinear turbulent-convective cell system with complex
activator and suppressor roles Nonlinear free energy source
Maternal fluctuation Transport Low m/n drive Flow driven tertiary
nonlinear instability GAM : Stringer-Winsor : Kelvin-Helmholtz mode
GKH mode collisonal damping p-profile q-profile streamer
Neo-classical mean shear flow [Kim-Diamond, PoP, 03]
Slide 5
Trigger of barrier formation Global 2-fluid nonlinear EM
simulation [Thyagaraja, PPCF,00] profile-turbulence interaction
Long wavelength EM modes induce corrugations, modifying the
evolution of electric field and bootstrap current Reduced MHD
equation [Ichiguchi, et al., IAEA,02] Resistive interchange modes
induce a staircase structure, leading to a linearly unstable high-
profike
Slide 6
Turbulent de-correlation by flow and transport dynamics
[Hahm-Burrel, PoP, 02, Hahm, et al., PoP, 99] Time varying Random
shearing Scattering to high-k [Hahm, et al.,PoP, 99 ] Heat flux PDF
: almost Gaussian process
Slide 7
Nonlinear free energy source MHD ion electron skin size Various
Zonal modes are exited through modulational instability Flow :Field
: Pressure : [Holland-Diamond, PoP, 02, Jenco et al., IAEA, 02,
Miyato, et al., PPCF, 02] Reynolds stress Maxwell stress
Collisional damping Pressure anisotropy (Stringer-Winsor term)
[Lin, et al., PRL, 99, Kim, et al., PRL, 03] [Hallatshek-Biskamp
PRL, 01] Small scale pressure corrugations are hardly controllable
SOC dynamics Large scale component may change the q-profile
Slide 8
ITG transport modulation due to small scale flow [Li-Kishimoto,
PRL, 02, PoP, 03] GF-ITG simulation with micro-scale ETG driven
flows Upper state Lower state high-k low-k Non-local mode coupling
and associated energy transfer channel to high kx damped region No
flow Micro-scale flow intermittently quenches ITG turbulence
[Li-Kishimoto, PRL, 02, Idomura, et al., NF, 02 ]
Slide 9
[ Smolyakov, et al., PoP, 00, Malkov, et al., PoP, 01,
Li-Kishimoto, PoP,02] Modulational instability and zonal flow ITG
case (adiabatic electron except k || =0) ETG case (adiabatic ion)
(b) Large grow rate for Streamer-like anisotropic pump wave :
Parameter to change the ratio of turbulence part and zonal part
(a)
Slide 10
ETG-driven zonal flow spectrum Modulational instability
analysis : 3 and 5 fields H-M model Slow or marginal process
Instability increases in small kx regime cf. saturation at low
level by spectrum change : Slab ETG-mode : x k weak s broader
narrower x Zonal flow instability in weak magnetic shear regime
pump wave :
Slide 11
(A) S=0.2 (B) S=0.1 Self-organization to flow dominated
fluctuations disappearance of anomaly in high pressure state Weak
magnetic shear increases linear instability sources, but
nonlinearly transfers energy to zonal components [Kishimoto,Li, et
al., IAEA 02] [Kendel, Scott, et al., PoP, 03] Zonal flow energy
Drift-Alfven turbulence in edge plasma total energy turbulent
energy
Slide 12
[Koshyk-Hamilton, JAS, 01] [courtesy of Earth simulator center]
turbulent energy zonal flow energy Energy partition change due to
zonal flow excitation sun Earth environment sun Earth environment
??? Change of fluctuation characteristics in high pressure
state
Slide 13
Condensation of turbulent energy in flow dominated plasma 0.8
0.6 0.4 0.2 1.0 Isotropic spectra at short wavelength, but energy
condensation to narrow k y region : with zonal flow 1.0 0.8 0.6 0.4
0.2 w/o zonal flow Isotropic spectra in short and long wavelength
region
Slide 14
KH mode weakly unstable in an enhanced zonal flow Weakly
unstable KH Marginally unstable KH Linear analysis intoroducing
ETG-driven zonal flow pattern Zonal flow instability and KH mode
instability DW ZF KH Near marginal and quasi-linear process
[Kim-Diamond, PoP 02]
Slide 15
Turbulent structure in an enhanced zonal flow Spatial
correlation function: 10 20 0 -10 -20 0 -101020 With zonal flowW/O
zonal flow 0 -20-101020 10 20 0 -10 -20 Coherent in y-direction
Incoherent in x-direction
Slide 16
Size distribution of heat pulse from GK simulation [Nevince,00,
Holland, et al., IAEA,02] TEXTOR: Signal from Langmuir probes
[Budaeev, et al., PPCF, 93] d= 12-16 (attached) d=6-7 (detached)
d=30 (from 15) (induced H-mode) CHS : Electron density fluctuation
[Komori, et al., PRL, 94] d~ 6.1 (RF heating) d~6.2 (NBI heating)
d~8.4 (RF+NBI) 1. 1.Fractal dimension 2. Probability Distribution
PDF of density fluctuation of PISCES-A linear device and SoL of the
Tore Supra [Antar,et al.,PRL,01] Statistical nature of turbulence
Noise forcing by coherent structure Non-Gaussian PDF for the
Reynolds stress and hest flux [Kim, et al., IAEA,02] Probabilistic
view of L-H transition
Slide 17
Statistical nature of turbulence-zonal fluctuation system
Fractal dimension and PFD rate strong flow case Shrinking
dimensionality due to coherent structure [Matsumoto, et al.,
Toki-conf, 03] Heat flux No flow case rate
Slide 18
Electromagnetic effect on turbulent transport Finite
b-stabilization consistent to with Okawa-scaling [Labit-Ottaviani,
PoP, 03, Okawa, Phys. Lett., 78] Reduction of zonal flows due to
the cancellation of the Reynolds stress by the Maxwell stress
[Li-Kishimoto, PoP, submitted] Cancellation between Reynolds stress
and Maxwell stress =0 =1.5% =3.0% =7.5%
Slide 19
Zonal flow in toroidal geometry B. D. Scott, 2003, Edge
turbulence simulation by DALF3 Geodesic curvature effect, i.e.
coupling between pressure an-isotropy and vorticity, plays an
important role for the zonal flow generation
Slide 20
Electromagnetic Landau fluid global simulation [N. Miyato, et
al, Toki-conf., 03] Density equation Vorticity equation Ion
parallel velocity equation Ohms law [c.f. Electrostatic toroidal
simulation by Garcia, Leboeuf, et al, IAEA, 00 ]
Slide 21
Electromagnetic Landau fluid global simulation Ion temperature
equation With R/a=4, i /a=0.0125, Te=Ti, D 10 -7 m 4, =410 - With
definition : [cf. Snyder, et al., PoP, 02] r/a N 0 / N c T 0 / T c
q
Slide 22
Nonlinear EM toroidal simulation [Rewoldt, 87, Zonca, 01,
Falchetto, 02] Onset of KBM above a critical beta: [cf. Nonlinear
GK simulation, Snyder, et al., PoP, 02, Candy, et al. PoP, 02]
Growth rate time
Slide 23
Zonal flow: Heat flux: Zonal flow: Heat flux: Nonlinear EM
toroidal simulation Nearly stationary zonal flow in inner low-q
region Oscillatory zonal flow dominated in outer high-q region :
[Hallatschek-Biskamp 01, Schoch 02, Ramisch et. al. 03, McKee et.
al. 03] time
Slide 24
Reynolds 17.1 Maxwell -0.182 GAM -14.7 Reynolds 6.84 Maxwell
-0.433 GAM -5.53 Nonlinear EM toroidal simulation time
Slide 25
Energy loop of DW-ZF system GAM term is a sink [B Scott 2003
(4-field drift-Alfvn)] or a source [K Hallatschek and D Biskamp
2001(Electrostatic Braginskii)] for zonal flow ? Our results shows
that GAM term is a sink. Drift wave turbulence Zonal flow Pressure
asymmetry p 10 Reynolds stress [, 2 ] [,p] Toroidal coupling
Slide 26
Unified MHD-ITG turbulence simulation MH D io n electro n ski n
siz e Potential q KBM(n=20,=1.5%) Positive magnetic shear Potential
Toroidal ITG(n=20) Positive magnetic shear q Vector potential q
Double tearing mode negative magnetic shear Zonal field and
associated flattening of q-profile emerge at an lower rational
surface, c.f. q=1.5
Slide 27
Unified MHD-ITG turbulence simulation Rich activities in
macro-scale MHD and micro mesoscale fluctuation Physical challenges
Anomalous transport MHD/Microturbulence solved Slow evolution
Transport equation solved Plasma shaping Realistic geometry High
temperature Large Reynolds numbers Collisionality Resistive MHD
Strong magnetic field Highly anisotropic transport Resistive wall
Non-ideal boundary conditions Computational challenges Wide
spatial-temporal scales non-adiabatic ion/electron fluid response;
internal boundary layers; small dissipation; mesoscale Extreme
anisotropy Special direction determined by strong magnetic
field