Issues in Zonal Flows and Drift
Wave Turbulence
P.H. Diamond
CMTFO and CASS, UCSD; USA
WCI Center for Fusion Theory, NFRI; Korea
ISSI Workshop, 4-9 March, 2012
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Preamble I
planets
Tokamaks
Zonal Flows:
m=n=0
finite kr
potential fluctuations
4
Preamble II
→ Re:Plasma?
→ 2 Simple Models
a.) Hasegawa-Wakatani (collisional drift inst.)
b.) Hasegawa-Mima (DW)
c
a.) V = ẑ × ∇φ + Vpol
B
→ ms
L > λD → ∇ · J = 0 → ∇⊥ · J⊥ = −∇� J�
J⊥ =
(i)
n|e|Vpol
J� : ηJ� = −(1/c)∂t A� − ∇� φ + ∇� pe
b.)
dne /dt = 0
→
e.s.
n.b.
MHD: ∂t A� v.s. ∇� φ
DW:
∇� pe v.s. ∇� φ
∇� J �
dne
+
=0
dt
−n0 |e|
5
So H-W
ρ2s
d 2
∇ φ̂ = −D� ∇2� (φ̂ − n̂/n0 ) + ν∇2 ∇2 φ̂
dt
D� k�2 /ω
d
n − D0 ∇2 n̂ = −D� ∇2� (φ̂ − n̂/n0 )
dt
n.b.
PV = n −
ρ2s ∇2 φ
total density
2
D
k
b.)
� � /ω � 1 → n̂/n0 ∼ eφ̂/Te
d
(φ − ρ2s ∇2 φ) + v∗ ∂y φ = 0
dt
n.b.
n.b.
is key parameter
d
(PV) = 0
dt
(m, n �= 0)
→ H-M
PV = φ − ρ2s ∇2 φ + ln n0 (x)
Zonal Flows:
ρ2s
d 2
∇ φ = −µ∇2 φ + ν∇2 ∇2 φ
dt
6
An infinity of models follow:
- MHD: ideal ballooning
resistive → RBM
- HW + A�: drift - Alfven
- HW + curv. : drift - RBM
- HM + curv. + Ti: Fluid ITG
- gyro-fluids
- GK
N.B.: Most Key advances
appeared in consideration
of simplest possible models
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Heuristics of Zonal Flows a):
Simplest Possible Example: Zonally Averaged Mid-Latitude
Circulation
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Some similarity to spinodal decomposition phenomena
→ both `negative diffusion’ phenomena
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What is the H-mode?
What is a transport barrier?
40
shows an example close to the power or density threshold
where the discharge dithers between the L and I phases—
illustrated by the divertor tile shunt current (/ SOL flow).
Experimental motivation
[Conway ‘11 PRL]
shot
[Schmitz, TTF ‘11]
FIG. 2 (color online). (a) Tim
-3) expanded reflectometer sp
!  L-H threshold Power in low density region (typically lower than 3x1019m(b)
FIG. 1 (color online). (a) GAM existence plot in terms of Pnet
for higher intensity, with (c)
! vs I-phase
a transient
between
high confinement,
transition.
centralasline
averagephase
density.
(b) low
Edgeand
radial
electric fieldi.e.
Er L!I!H
fluctuation
level SD , and (d)
for oscillation
L (PECH in
¼prior
0:35 to
MW)
and I in
phase
(1.1 MW)
rates ‘10
andPoP],
turbulence
! profiles
Limit cycle
the transition
TJ-II[Estrada
‘10 EPL],shearing
NSTX[Zweben
¼ 0:8EAST[Xu
MA, q95
4:5, n! e ¼ 3 '
shot
24 811,
BT ¼ !2:3 T,‘11IpPRL],
L to I phase. BT ¼ !2:3 T, Ip
ASDEX
Upgrade[Conway
‘11#PRL]
19 m!3 , T # 3 keV, P
1019 m!3 , Teo # 2:4 keV, and favorable lower X point.
10
eo
ECH
!  Radial structure of mean flow shear in the I-phase limit-cycle oscillation
!  Dual shear layer in DIII-D [Schmitz, TTF ‘11]
065001-2
!  Poloidal rotation involving in the transition process in JT-60U [Kamiya
‘10 PRL]
41
42
43
44
→ EAST Results (G.S. Xu, et.al., ’11)
→ hardened, reciprocating probes
→ quasi-periodic Er oscillation (f < 4 kHz), with associated turbulence modulation
→ Er and �ṽr ṽθ �E exhibits correlated spikes prior to transition
→ support key role of zonal flow in L→H transition
Power spectra peaks at f < 4kHz
spike in Er and �ṽr ṽθ �E
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Slow Power Ramp Indicates L!I!H Evolution.
L-mode
Intermediate phase
Limit Cycle Oscillations
H-mode
a) turbulence
b) ZF
c) log(MF)
7
r/a
time
48
Cycle is propagating nonlinear wave in edge layer
ZF
Period of cycle increases approaching transition.
Turbulence intensity
Mean flow shear
•  Turbulence intensity peaks just prior to
transition.
•  Mean shear (i.e. profiles) also oscillates
in I-phase.
49
Mean shear location comparisons indicate
inward propagation.
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If you build it, they will came...
Basic experiment:
- large, rotating, ∼ QG (tilted caps) liquid metal or
equivalent with Rm ∼ 100
- extend domain of PPPL experiment of H. Ji, et.al.
- aims:
- MHD dynamics of zonal flows, jets
- zonal fields, QG dynamo (L-Smith, Tobias)
- aspects of MHD momentum transport
(i.e. solar tachocline physics)
52
‘Confinement’ experiments:
(EAST?)
- high power, low τext ITB
- multi-channel DBS imaging study of qmin region, on meso-scale
-multi-channel CHS to eliminate mean flows (including poloidal)
- high space-time resolution profile evolution, i.e. corrugations?
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