studying nonlinear turbulence and zonal flow … · august 2007 g.r. tynan, 2007 int'l summer...
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August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
Studying Nonlinear Turbulence and Zonal Flow
Dynamics in Magnetically Confined Plasmas
G.R. Tynan
2007 Asian Summer School
This talk is made possible by the many discussions and contribution of materials and results from
collaborators and colleagues:
J. Boedo, M. Burin, P.H. Diamond, R. Fonck, A. Fujisawa, O. Gurcan, C. Holland, K. Itoh, S. Itoh, G. McKee, R. Moyer, J. Yu, S. Zweben
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
Questions of Interest
• What Drives the Turbulence (I.e. Free Energy
Source & Underlying Instability)?
• What are Spatio-temporal Scales of
Turbulence?
• How Do Nonlinear Interactions Lead to
Observed Spatio-temporal Scales?
• What does resulting flux v gradient curve look
like ?
Background and Motivation
•Turbulence in MFE Plasmas
•Why Is Turbulence of Interest in Fusion?
•What are Zonal Flows?
•Why Care About the Nonlinear Interactions
Between Turbulence and Zonal Flows?
Images of Turbulence in Tokamaks
GYRO
DIII-D
J. Yu C-III Emission (UCSD)
Background and Motivation
•Turbulence in MFE Plasmas
•Why Is Turbulence of Interest in Fusion?
•What are Zonal Flows?
•Why Care About the Nonlinear Interactions
Between Turbulence and Zonal Flows?
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
Zonal Flows are Common & Effect Transport in Many Systems
CASSINI Imaging Team, NASA
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
2D Dynamics in Magnetized Plasmas & Rotating Fluids
t+ v • v + 2 v =
1p +
2v
Navier-Stokes Eqn for Rotating Fluid:
I.e. momentum conservation same form for rotating fluid
And magnetized plasma > DYNAMICS ARE SAME !
vvBvv21
+=+•+ pt
Momentum Eqn for Magnetized Plasma:
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
Result: Strong Similarity Between Planetary Flows
& Magnetized Plasma Flows
1. Turbulence driven2. No linear instability3. No direct radial transport
ZFs are "mode", but:
ITER
ExB flows
Zonal flow on JupiterFrom GYRO
m=n=0, kr = finite
Ref: K. Itoh, APS 2005 Invited Talk, PoP May 2006
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
Origin of Zonal Flow Lies in 2D Dynamics
t+ v • v + 2 v =
1p +
2v
Navier-Stokes Eqn for Rotating Fluid:
For
v = 0I.e. no velocity gradient along direction of axis of rotation
v << v = 0 = 0
Flow Generation from Turbulence: the Vortex Merging Picture
3-D 2-D
0z
vz
z
==> Vortex Stretching
…Generate Flows on
Smaller Scales
= 0z
vz Vortex Merging
z
z
z
+
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
krZ= kr
Z r̂ u = uZ
Consider a Zonal Flow to Have:21
, kkk <<Z
r
corrZZ
rZtuk >>/1~
F.T., Write as KE, and Average Energy Eqn over Z-flow scales:
where
NL Energy
Transfer
PkZturb
= Re uZ
* kZ( ) u k1( )i( )u k2( )k1k2kZ =k1 +k2
1
2
uZ
2 kZ( )
tPkZturb = μ u
Z
2 kZ( )
u
t+
uru
r= dampu
Usual Reynolds Stress Term in Simplified Momentum Eqn
(ala Diamond et al. PRL 1994 and others)
“Radial Transport of
Angular Momentum”
Flow Generation from Turbulence: Fourier Space
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
k i~1k0 Ln~0.1
Inertial
Range
Unstable
Region
Large
Scale
Damped
Flow
FLR
Dissipation
Power
Spectrum,
| k|2
Power
Transferred,
Pk
μ=<kk
;0
( ) 0,21>kkT
k
( ) 0,21<kkT
k
0>k
( )21
,, kkTkk
kZ a>1
Flow Generation from Turbulence: Fourier Space
• Free Energy Source
Releases Energy On One
Scale
• Nonlinear Energy
Transfer Moves Energy to
Dissipation Region
• Shear Flows Develop Via
Transfer of Energy to
LARGE SCALES (small
k)
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
Outline
• Basic Physics of Drift Instabilities & Zonal
Flows
• Intro to Statistical Tools for Turbulence/Zonal
Flow Studies
• Laboratory Plasma Studies
• Confinement Experiment Studies of
Turbulence and Zonal Flows
• Conclusions & Open Issues
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
Controlled Shear De-Correlation Experiment (CSDX)
CSDX parameter Typical value
Gas pressure 0.5 - few mTorr
Te
~ 3 eV
Ti
~ 0.7 eV
ne
1-10 x 1012 cm-3
Source (Helicon 13.56 MHz) 1500W (typically)
Magnetic Field Up to ~ 1000 G
Multi-tip Langmuir probe was inserted in this port
m=0 Helicon Plasma Source
RF
source
Exit
Pump
Ar gas injection
~1m
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
Evolution of Energy Spectrum w/ Magnetic Field
Low-k Region
Fills In
Spectral
Index Region
Develops
2
2
2
+=
eB
kk
k
Tk
ek
n
nE
Burin et al, May 2005 PoP
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
Real and Imaginary Frequencies of Linear
Eigenmodes
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
Free Energy Sources Are Known Can Find Linearly Unstable Region
• Include grad-P,
Vshear Free Energy
Sources
• Include Neutral Flow
Drag (Effective at high
k), FLR Damping
• Find Stable &
Unstable Regions
Implies Energy MUST Be Transferred Into
Low-k Region Via Nonlinear Processes
Local Wavenumber
Tynan et al Nov 2004 PoP
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
Conclusions from Laboratory Plasma
Experiment
• Drift Waves Develop if Grad-P is High Enough andDamping Small Enough
• Coherent Waves Obey Linear Dispersion Relation
• Weakly Dispersive Waves Allow NONLINEAR 3-Wave Coupling to Begin
• Nonlinear Energy Transfer Re-arranges Spectrum
• Broad Spectrum Emerges & Shows Indicates ofINVERSE ENERGY TRANSFER…
• PART II… EMERGENCE OF ORDERED FLOWSOUT OF TURBULENCE, CONFINEMENT DEVICERESULTS, BIFURCATIONS,…
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
EVIDENCE FOR EXISTENCE OF
SHEAR LAYER SUSTAINED BY
TURBULENT REYNOLDS
STRESS
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
Mach Probe Measures V , Vz Profiles
0
0.5
1
1.5
2
0 50 100 150 200 250 300 350
RM
= I
sat
(up)/I
sat
(down)
(degrees)
RM
= exp[K sin / (Mpar
cos + Mperp
sin )]
Shikama et al., Phys. Plasmas (2005),Van Goubergen et al., PPCF 41 L17 (1999),Gunn et al., Phys. Plasmas (2001)
B
Rotate
about
probe axis
to find M||,
Mperp
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
Observe Fluctuation Propagation Speed w/ Multipoint Probe Array or
Fast Imaging
+
r y
B
-0.2
0
0.2
0.4
0.6
0.8
1
-100 -50 0 50 100
y = 0.37 cm
y = 0.74 cm
y = 1.10 cm
y = 1.46 cm
y = 1.83 cm
Ry
(μs)
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
We Can Also Infer Flowfield from Motion of
Density Perturbations
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
Independent Measurements of Shear Layer
Sound speedcs = (Te/Mi)1/2
= 2.8x105 cm/s
0
2 104
4 104
6 104
8 104
0 1 2 3 4 5 6 7
r (cm)
V (cm/s)
Mach probe
Probe TDEvelocityMovie TDE
velocity
100 kHz framerate, from G.Antar
Azi
mut
hal V
eloc
ity,
V,
(104
cm/s
ec)
2
0
4
6
8
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
( ) μ iiiiiorVVvvr
rr
22
2
~~1+=
Mea
sure
d R
eyno
lds
stre
ss
Use Measured Reynolds Stress in AzimuthalMomentum Balance & Solve for V Profile
Tynan et al April 2006 PPCF Holland et al, in press, PRL
Estimate Dissipation from Measurements
Tidla
a
= 0.7eV
Tgasdla
a
= 0.4eV
Measure:
Assume:Ti(0) > Ti(a)
Tgas(a) = Twall
μii =310 i
2ii
Pgas = ngasTgas = const
μ ii 4 104cm2 /sec
μii(0) > μii(a)
i0 ~ 6 103 sec 1
Tynan et al, April 2006 PPCF,Holland et al, in press, PRL
μii niTi1/2
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
Measured Velocity Profile Consistent with Turbulent Momentum Balance
Tynan et al, April 2006 PPCF, , Holland et al, PRL 2006
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
No Turbulent Particle Transport AcrossShear Layer
Tynan et al, April 2006 PPCF, Holland et al, In press, PRL
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
Shear Layer Formation
in Collisional Drift
Turbulence Simulations
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
• (2D) Hasegawa-Wakatani model in cylindrical geometry.– Includes ion-neutral flow damping effect , neglects nonlocal (finite s / Ln)
terms, fixed parallel wavenumber.
– Parameters used reflect best estimates for averageCSDX values:
• s = 1 cm, Ln = 2 cm, || = 1, = 0.03Cs/Ln,
• Dn = 0.01 s2 Cs/Ln, μ = 0.4 s
2 Cs/Ln
– Advances eqns by combination of 2nd order RK andimplicit treatment of diffusive terms (conserves energy towithin 1%).
( )
( ) μ 42
*
22
||2
2
*
22
||*
+=++
=+++
nvk
Vt
nDnvkn
r
VnV
t
e
BE
n
e
BE
eth
eth
Nonlinear Drift Turbulence Simulation
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
Zonal Flow Forms from Vortex Merging
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
– Simulation uses 64 x 64 pts, results
insensitive to changes in Dn, , μ
– Changing Ln to 10 cm does not
qualitatively affect results
Simulations Show Zonal Flow Formation
Vortex Merging
TimeIso-Potential Contours:
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
Measured Velocity Profile Consistent with Turbulent Momentum Balance
Tynan et al April 2006 PPCF
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
Nagashima, 2007 Private Communication, Kyushu LMD
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
Nagashima, 2007 Private Communication, Kyushu LMD
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
Outline
• Basic Physics of Drift Instabilities & Zonal
Flows
• Intro to Statistical Tools for
Turbulence/Zonal Flow Studies
• Confinement Experiment Studies of
Turbulence and Zonal Flows
• Laboratory Plasma Studies
• Conclusions & Open Issues
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
Pauto( ) =1
Nens
fi ( )2
n=1
Nens
f (t) = f ( )exp(i t)
Pcrs ( ) =1
Nens
fi ( )gi*( )
n=1
Nens
12( ) =Pcrs( )
P1P2, tan ( ) =
Im(Pcrs( ))
Re(Pcrs( ))
Cauto( ) =1
Nens
1
Tfi (t) fi (t + )
T /2
T /2
n=1
Nens
Ccrs ( ) =1
Nens
1
Tfi (t)gi (t + )
T /2
T /2
n=1
Nens
Fourier Transform:
f ( ) =1
2f (t)exp( i t)
tt
Correlation Functions & Power Spectra:
Inter-relation Between Two Signals: coherence and crossphase
Linear Signal Processing Gives Average Spatio-temporal Scales of TIME STATIONARY
Turbulence
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
W n
t= r
Ln+ T n
+ C1 Wn n*( )
W
t= T C2
2 2C3W
W n= nm r,t( )
2
m
W = m r,t( )2
m
T n r, f , f( ) = Re n* r, f( )v r, f f( )1
r
nr, f( )
TZF r, f , f( ) = Re VZF* r, f( )v r, f f( )
1
r
vr r, f( )
Example: Collisional Drift Turbulence Model (Hasegawa-Wakatani 1983)
Internal and Kinetic Energies Defined As
Nonlinear Energy Transfer From Cross-Bispectrum:
Nonlinear Energy Transfer Comes from 3rd Order Spectrum:
Rate and Direction of Energy Transfer Determined by
BiSpectrum
b̂2 1, 2( ) =B 1 + 2( )
X 1( )X 2( )2
X*1 + 2( )
2; 0 < b̂ < 1
B 1, 2( ) = X 1( )X 2( )X*1 + 2( )
1, 2( ) Tan 1Im B 1, 2( )
Re B 1, 2( ); < <
Re B 1, 2( ) = B 1, 2( ) cos 1, 2( )
Energy Transfer Direction and Rate:
BiPhase Determines Phase Delay Between Interacting Waves:
Degree of Phase Coherence Determined by BiCoherence
Bi-spectrum Defined As
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
Outline
• Basic Physics of Drift Instabilities & Zonal
Flows
• Intro to Statistical Tools for Turbulence/Zonal
Flow Studies
• Confinement Experiment Studies of
Turbulence and Zonal Flows
• Laboratory Plasma Studies
• Conclusions & Open Issues
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
Turbulence Measurements in
Tokamak Core Region
Images of Turbulence in Tokamaks
GYRO
DIII-D
J. Yu C-III Emission (UCSD)
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
Existence of Zonal Flows & GAMs
in Confined Plasmas
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
Zonal flows really do exist !
GAM?
Z. F.
-0.01 -0.005 0 0.005 0.01
PE (
a.u
.)
/i
-1
-0.5
0
0.5
1
10 11 12 13 14
C (
r 1,r2)
r2 (cm)
r1=12cm
Radial distance
CHS Dual HIBP System
90 degree apart
Er(r,t)
A. Fujisawa,PRL 2004
High correlation on magnetic surface,Slowly evolving in time,Rapidly changing in radius.
Er(r,t)
21
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
Suppression of transport by ZF
Regulation of transport by GAMs
26
Nonlinear Interaction (3)
ZF
HIBP on CHS
Fujisawa, PPCF 2006
HIBP on JFT-2M
Modulation of envelope and transportby GAMs were confirmed.
Ido, submitted to NFTime (ms)
t
GAMs
DW
-1
0
1
40 50 60 70
(V
)
time (ms)
150
100
50
0
f (kH
z)
0
150
f (kH
z) = 1
BE , n
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
GAM-ZF Observed in Edge Region• BES measures localized, long-wavelength (k i < 1) density fluctuations
– Can be radially scanned shot to shot to measure turbulence profiles
– Recent upgrades allow for BES to measure core fluctuations
• Time-delay estimation (TDE) technique uses cross-correlations between two poloidally separatedmeasurements to infer velocity
GAM
˜ n f( )2
V f( )2
DIII-D
McKee PoP 2001
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
Measured V Spectra Exhibit Signatures of Both
ZMF Zonal Flows and GAMs
• Spectra indicate broad, low-frequency structure with zero
measurable poloidal phase shift– Consistent with low-m (m=0?)
– Peaks at/near zero frequency
• GAM also clearly observed near 15 kHz
• ZMF zonal flow has
radial correlation
length comparable
to underlying
density fluctuations
– Necessary for
effective shearing
of turbulence
Gupta et al., PRL 97125002 (2006)
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
GAMs Observed to Peak in Plasma Edge
• GAM velocity oscillationamplitude peaks near r/a ~0.9 - 0.95
– Decays near separatrix
– Decays inboard, stilldetectable to r/a ~ 0.75
– Consistent with HIBPmeasurements on JFT-2M(Ido et al., PPCF 2006)
• ZMF zonal flows notobserved for r/a > ~ 0.9, butdo increase towards core
– Harder to quantify radialdependence because ofbroad spectral characteristics
McKee et al., PPCF 2006
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
Observe Transition from ZMF-Dominated Core
to GAM-Dominated Edge
• Velocity spectra show broad ZF spectrum for r/a < 0.8 ZMF flow
• Superposition of broad spectrum and GAM peak near r/a= 0.85
• GAM dominates for r/a > 0.9
• Consistent with theory/simulation expectations that GAMstrength increases with q
– Increase in GAM strength with q95 also observed (McKee etal., PPCF 2006)
• GAM is highly coherent, with correlation time GAM > 1ms, two orders of magnitude larger than turbulencedecorrelation turb ~ 10 μs
– Indicates GAM is “slow” relative to edge turbulence timescales, andso can effectively interact with turbulence (Hahm et al., PoP ‘99)
McKee IAEA 2006
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
Measuring Nonlinear Effect of Zonal
Flows on Turbulence in a Tokamak
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
BES System Configured to Provide Zonal Flow Measurements Over Large Fraction
of Plasma
• BES measures localized, long-wavelength (k i < 1) density fluctuations
– Can be radially scanned shot to shot to measure turbulence profiles
– Recent upgrades allow for BES to measure core fluctuations
• Time-delay estimation (TDE) technique uses cross-correlations between two poloidally separatedmeasurements to infer velocity
GAM
˜ n f( )2
V f( )2
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
Measuring Nonlinear Energy Transfer in Tokamaks
• TnY(f’,f) measures the transfer of energy between density
fluctuations at f and poloidal density gradient fluctuations at f’ ata specific spatial location due to poloidal convection– A positive value of Tn
Y indicates that n(f) is gaining energy from n/ y(f’)
– A negative value indicates that n(f) is losing energy to n/ y(f’)
• Have all the quantities needed to experimentally calculate theportion of Tn
Y(f’,f) associated with GAM convection (with I n)1. n(r,t) = (n1 + n2)/2
2. n/ y(r,t) = (n1 - n2)/ y
3. Vy(r,t) from TDE algorithm
TnY
f , f( ) = Re n* f( )Vy f f ( )n
y f ( )
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
GAMs Drive Clear Forward Transfer of Internal Energy in
Frequency Space
• TnY(f ,f) clearly shows that
fluctuations at f = f + fGAM gainenergy, while those at f = f - fGAM
lose energy
• Density fluctuations gain energy fromlower frequency gradient fluctuations,and lose energy to higher frequencygradient fluctuations
• Simple picture: energy movesbetween n, n/ y to high f in “steps” offGAM
Net transfer of energy to high f!
• Demonstrates that the convection ofdensity fluctuations by the GAM leadsto a cascade of internal energy tohigh f
TnY
f , f( ) = Re ˜ n * f( )Vy f f ( )˜ n
y f ( )
Den
sity
fluc
tuat
ions
f (k
Hz)
Holland PoP 2007
Gradient fluctuations f (kHz)
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
Clear Similarity Between Zonal Flow Driven Energy
Transfer in Experiment and Simulation
• Effects of zonal flow convection of density fluctuations
can be directly quantified by
– Measures rate at which zonal flow transfers energy into a density
fluctuation with frequencies f from one with frequency f’
• Calculation of TnY(f’, f) indicates the zonal flows transfer
internal fluctuation energy to higher frequencies in both
experiment and simulation
– Red curves to right indicate zonal flows remove energy from
density fluctuation spectrum (black curves) at low
frequencies, add energy to higher frequencies
• Results represent strongest direct experimental
validation of the impact of zonal flows on turbulence to
date (establish “directionality” as well as bicoherence)
TnY
f , f( ) = Re ˜ n * f( )VyZF f f ( )
˜ n
y f ( )
Density Spectrum | n(f)|2
Net energy transfer df’ TnY(f’, f)
frequency (kHz)
frequency (Cs/a)
GY
RO
DII
I-D
BE
S
Review Results Against Basic Theoretical
Expectations
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
Schematic of NONLINEAR drift turbulence-zonal Flow interactions
GenerationBy vortex tilting
Damping by collisions Tertiary instability
Suppression of DWby shearing
Drift waveturbulence
Zonal flows
Shearing
Collisional flow damping
SUPPRESS
Nonlinear flow damping
energyreturn
DRIVE
<vx vy>~~
T, n...
<vx p>~~
Transport
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
7
GAM
New feature: geodesic acoustic coupling (GAC) B D Scott 2003
= cs/R
VV
ZF = 0
n ~ 0
Large Scale Sheared Flows Can Develop
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
13a
Impact of ZFs on Turbulence
Random stretchingof DW eddies
Note: Conservation energy between ZF and DW
Energy for ZFs excitation is extracted from DWs
time
k r
2 Dk t
of DW packet k r
2
Wk = k NkDW energy
k =k Vd
1 + k 2s2
Dk k2 VZF
2c
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
Generation Mechanism
A
A'
B
B'
C
C'
(2) Modulational Instability
ZF
d
d
ZF d2
ZF –
k – = k x – qr
+
k + = k x + qr
9
(1)Tilt of convection cell by a sheared flow
r
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
2 External shear flow External shear flow breaks streamersbreaks streamers
RBM [Beyer et al, 00]
Potential
Pressure
Flux
Increasing velocity shear VE'
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
Implication: Plasma Predicted to Sit At/Near Marginal Stability
Lackner DEISY Symposium 2005
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
Experiments Confirm Essential Elements of
Nonlinear Turbulence-Zonal Flow Interactions
• Inverse Energy Transfer Exists in Drift Turbulence
• Zonal Flow Can Be Self-consistent w/ Turbulent R/S
• Particle Transport Across Shear Layer Inhibited
• Fluid-based Turbulence Simulations are Consistent w/ CSDX
Experiments
• Kyushu LMD Experiments Show Inverse Kinetic Energy
Transfer
• Zonal Flows (ZMF and GAMs) Exist in Confinement Devices
• They Regulate Spatial Scale of Turbulence
• They Regulate Cross Field Particle Flux
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
Open Questions
• Can We Measure the NL Kinetic Energy Transfer?
• Can We Show Self-consistent Picture of LinearInstability, NL Energy Transfer, and SaturatedSpectra?
• Is the ZF Driven by Turbulence in Hot Fusion-gradePlasmas?
• Do Reynolds-stress Driven Flows Trigger TransportBarrier Formation?
• Is the NL Turbulence-ZF Interaction Consistent withMarginal Stability?
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
References: Drift Turbulence-Zonal Flows
• Theory:
• Itoh, K., Itoh, S.I., Diamond, P.H., Hahm, T.S., Fujisawa, A., Tynan, G.R., Yagi, M., Nagashima, Y., Physics
of Zonal Flows, invited talk, Physics of Plasmas, 13 055502 (2006).
• Diamond, Itoh, Itoh, and Hahm, PPCF 2005 – Overview of the Theory of Zonal Flows in Magnetized
Plasmas
• A. Hasegawa and M. Wakatani Phys. Rev. Lett. 59, 1581 (1987)
• Experiments:
• Gupta DK, Fonck RJ, McKee GR, et al. Phys. Rev. Lett. 97 (12): Art. No. 125002
• McKee GR, Fonck RJ, Jakubowski M, et al Phys. Plasmas 10 (5): 1712-1719 Part 2 MAY 2003
• A. Fujisawa et al, Phys. Rev. Lett. 93 (16) 165002 (2004)
• M.J. Burin, G.R. Tynan, G.Y. Antar, C. Holland,On the Transition to Turbulence in a Magnetized Plasma
Column, Physics of Plasmas, 12 052320 (2005).
• Tynan, G.R., Holland, C., Yu, J.H. et al, Observation of Turbulent-driven Shear Flow in a Cylindrical
Laboratory Plasma Device, Plasma Physics and Controlled Fusion, 48, S51 (2006)1.
• Holland, C., Tynan, G.R., Yu, J.H. et al, Observation of Turbulent-driven Shear Flow in a Cylindrical
Laboratory Plasma Device, Phys. Rev. Lett. 96 195002 (2006).
• All the papers in the April 2006 special issue of Plasma Physics and Controlled Fusion.
Homework Question
Suppose the mean pressure gradient driving
turbulence is constant, and the turbulence is
coupled to a zonal flow such as discussed in
this talk. How does the turbulence amplitude
respond to an increase or decrease in the
damping rate of the zonal flow?
August 2007 G.R. Tynan, 2007 Int'l SummerSchool, Chengdu
13b
Hint for HW Problem: Self-regulation -Predator-prey model, Malkov 2001
DW amplitude is strongly influenced by ZF damping.
If no ZF damping
VZF
steadystate forZF
s.s. forDW
DWamplitude
time
time
DW
ZF
ZF
DW
DW
ZF
t E d = L E d – 2 E d2 – VZF
2E d
t VZF2 = – damp VZF
2 + VZF2
E d