EDGE TURBULENCE AND TRANSPORT AS A POSSIBLE CAUSE …g/papers/eu-ttf-02.pdfShaping: B/qR vs I/a2...
Transcript of EDGE TURBULENCE AND TRANSPORT AS A POSSIBLE CAUSE …g/papers/eu-ttf-02.pdfShaping: B/qR vs I/a2...
EDGE TURBULENCE AND TRANSPORT AS A POSSIBLE CAUSE OF THE TOKAMAK DENSITY LIMIT
MARTIN GREENWALD
MIT - PLASMA SCIENCE & FUSION CENTER
Presented at 9th EU-US Transport Task Force Workshop
Cordoba, Spain September, 2002
DENSITY LIMITS - AN IMPORTANT ISSUE FOR MAGNETIC FUSION
2
DTR n vσ∝ •
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Plasma pressure limited by MHD
stability
At fixed pressure, there is an
optimum temperature ⇒ optimum
density
No guarantee that this density is achievable in any given device
Critical issue for conventional tokamak reactor
DENSITY LIMIT OFTEN CHARACTERIZED BY EMPIRICAL SCALING
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First motivated by
observation that impure
plasmas disrupted at
lower densities
Murakami limit ~1976
0/T OhmicB R j P∝ ≈
Hugill plot ~ 1978
Leading dependence is
with plasma current density (Axon 1980)
2P
LIMB InqR a
∝ ≈ (Note absence of significant power scaling)
SCALING REFINED BY INCLUSION OF DATA FROM SHAPED TOKAMAKS
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Greenwald limit: 2P
GInaπ
=
(with n: 1020/m3, IP: MA, a: m)
Identical to Hugill for circular
plasmas
Differs significantly for shaped
plasmas
Recent data from new
machines roughly consistent
(for flat density profiles)
GLOBAL SCALING BY ITSELF IS AN INSUFFICIENT FOUNDATION FOR PREDICTING THE PERFORMANCE OF FUTURE MACHINES
Scaling does an OK job •
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- (Does empirical equation tell us anything about the physics?)
but
Scaling variables are only proxies for the real physics dependences
Covariance in data, may confuse dependences (IP and PIN for example)
Misses important local physics - density profiles
Need verified, first principles model
Big questions
Where does the catastrophe come from – how do we unroll cause and effect?
How do we compute the density limit?
DENSITY LIMITS - THE PHYSICS PROBLEM
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Density or collisionality dependent transport ⇒ edge cooling
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What physics can limit the density?
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◆
◆
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Ideal MHD only cares about pressure (and current) not density
Temperature profile influences current profile
Resistive MHD can be important at low temperatures
Radiation cooling ( )2RAD e Z eP n f R T∝
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−
Neutral shielding: fueling limits
No widely accepted first principles theory available
Not even agreement on critical physics
BASIC PHENOMENOLOGY OF DENSITY LIMIT
Range of Normalized Densities (n/nLIMIT)
MARFEs 0.4-1
Divertor detachment 0.3-1
Drop in H-mode confinement 0.3-1
Change in ELM character ?
H/L transition 0.8-1
Poloidal detachment 0.7-1 (for clean plasmas)
MHD and Disruptions ~1
The density limit in tokamaks is apparently an edge limit
FURTHER EVIDENCE FOR AN EDGE DENSITY LIMIT
EXCEEDING THE EMPIRICAL LIMIT - PEAKED DENSITY PROFILES
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Particles in core apparently don’t drive density limit
2
1
01.5
05
Input
Line Average Density
0
1400 160 0e (ms)
2200 2400 2600 2800
×1020
Greenwald “Limit”
Radiative Power (MW)
τ EITER
93–H
τ E
w, p Not Subtractedcore
rad
•
w, p Subtractedcore
rad
• H93 = 1
(Maingi, Mahdavi 1997)
Density profiles not stiff
Peaked by core fueling,
edge pumping, transport
modification
Power (MW)
0 1800 200Tim
•
h
h
• h
RADIATION POWER BALANCE - EDGE OR SCRAPE-OFF LAYER (SOL)
Motivation − Very dirty plasmas don't reach high density
− ( )2RAD e Z eP n f R T∝ - edge cooling
Choose physical phenomenon to model
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−
Global thermal collapse
Radiation condensation
Poloidal detachment
Divertor detachment
Radiation dominated transport ⇒ MHD unstable pressure profiles
Solve coupled equations for energy, momentum, particle balance
(+ Ad hoc assumptions; transport, nedge/ncore)
ARE RADIATION MODELS SUFFICIENT?
h
•
h
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Problem with radiation models
Power and impurity dependence too strong ⇒ ( )/ 1LIM IN EFFn P Z∝ − −
−
−
Threshold mechanisms show up well below density limit
Transport assumptions: ad hoc at best
Evidence for increased transport as cause of edge cooling
Transient transport experiments (Greenwald 1988, Marinak 1993)
Fluctuation measurements (Brower 1991)
Detailed probe measurements in edge: observations of edge turbulence at
high densities (LaBombard 2001)
Edge Simulations (Rogers, Xu, Hallatschek, D’Ippolito)
BACK TO THE BEGINNING IMPURITIES ARE IMPORTANT …. BUT ONLY UP TO A POINT
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1400kW
B around ZEFF ~ 2.5, drops out (Rapp et al, 2000)
1 2 3 4 5 6 7 8 9 10Zeff
0.0
2.0
4.0
6.0Li
ne A
vera
ged
Den
sity
[1019
−
3 ]m
P = 1400kW
600kW, 990kW,
Greenwald limit
Critical densities ofradiative collapse
P =
elow
DENSITY LIMIT IN TOKAMAKS DOES NOT DEPEND STRONGLY ON INPUT POWER
xx
x x
x x
+
12
10
DIVERTORIp = 0.5–1.9 MABT = 0.8–2.1 Ta ∼ 0.63 mb/a ∼ 1.8Pbeam ≤ 7 MW
Ip(MA)0.51.01.51.9
BT(T)2.02.02.02.0
8
6
4
2
00
n e,d
et/I p
(1019
m–3
/MA)
Power dependence in low
confinement mode (L-mode)
varies from P0 - P0.25
Role of neutral beam fueling
and density peaking in power
dependence is uncertain
•
•
+ ++ +1.01.0
1.71.0
2 4Pinput (MW)
6 8 10 12(Petrie 1993)
TURBULENT TRANSPORT IN EDGE INCREASES WITH COLLISIONALITY
h
h
h
Two regimes observed in scrape-off layer (SOL)
Ionization Source-5 0 5 10 15 20
-5 0 5 10 15 20
-5 0 5 10 15 20
-5 0 5 10 15 200.01
0.1
1.0
Density
ρ (mm)
1019
1020
(m-3
)LimiterShadow
Sh
ots
: 10
0060
2017
:899
, 100
0602
021:
597,
100
0517
023:
899
Deff = -Γ⊥/∇n
1022
1023
(m-3
s-1)
(m2 s
-1)
1021
1020
(m-2
s-1) Particle Flux
1.11.6 x1020
m-3ne:2.6
204060 Te
(eV
)
0
−
−
−
−
−
−
Near-SOL: steep gradients
Far-SOL: flat profiles
Particle flux and transport
Near-SOL: cross-field transport low
Far-SOL: cross-field transport high
Fluctuation changes character
Near-SOL: low amplitude, short
correlation times and lengths
Far-SOL: large amplitude, bursty, long correlation times
"bursty" transport in SOL
t = 0
.1.4
68-1
.6 s
ec
ρ=3 mm
-1 0 1 2 31
10
100
Pro
b. D
ist.
Fn.
Light Signal-<Light Signal>time ave
Dio
de 2
Da-
6563
K
aise
r 9
gaussian
skewness=1.0kurtosis=1.1
ρ=9 mm
-1 0 1Light Signal-<Light Signal>time ave
1
10
Pro
b. D
ist.
Fn.
Dio
de 2
Da-
6563
K
aise
r 7
t = 0
.1.4
68-1
.5 s
ec
Probability distribution functions of emission get more skewed toward larger events,as distance into SOL increases
skewness=0.5kurtosis=0.5
FarSOL
250 5 10 15 20
1.0
0.2(102
0 m
-3)
Distance into SOL (mm)
Limiter Shadow
0.0 0.5 1.0 1.5Time (milliseconds)01
2
0.0 0.5 1.0 1.5Time (milliseconds)012
0.0 0.5 1.0 1.5Time (milliseconds)012
I sat
/<I s
at>
0.0 0.5 1.0 1.5Time (milliseconds)012
0.0 0.5 1.0 1.50
12
from
pro
be
Time (ms)
~1.2µs
5.5µs
13µs
10µs
2.2µs
Normalized RMS fluctuation level & auto-correlation time of Isat increase as distance into SOL increases
100
NearSOL
τac
WE CAN VISUALIZE THE FAR-SOL FLUCTUATIONS - BLOBS
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1000
9120
04 f5
810
0091
2004
f38-
63
Fast CCD camera images,
4 µsec framing time
(Zweben, Terry 2001)
D2 gas puff ⇒ localization
Large "blobs" dominate far-
SOL
Blobs move poloidally and
radially
Correlation length, correlation
time, propagation velocity
consistent with probe measurements
2 µ[email protected] s
separatrixprojection ofoutboard limiter
gas puffnozzle
1 cm
( in) radial direction (out )
(
dow
n) v
ertic
al d
irect
ion
(up
)
TURBULENCE DRIVEN CONVECTION CAN COMPETE WITH PARALLEL TRANSPORT
0 5 10 15 20
10
(eV
)
0 5 10 15 20
0.01
0.1
1.0
(MW
)
0 5 10 15 200.01
0.1
1.0(M
W)
⊥ Convection
Sh
ots
: 10
0060
2017
:899
, 100
0517
023:
899
LimiterShadow
Electron Temperature
ρ (mm)
50
(a)
(b)
(c)
nnG
:0.190.43
// Conduction
// Conduction
⊥ Convection
nnG
= 0.19
nnG
= 0.43
0.1
(102
0 m
(d)
Density-3)
1.0In far SOL, cross-field transport
overwhelms parallel transport
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As density is increased, region of large
fluctuations and transport move inward
toward separatrix
Parallel transport ~Te7/2 is stable with
respect to temperature perturbations
Collisionality driven cross-field
transport is unstable
(LaBombard 2000)
AS THE DENSITY LIMIT IS APPROACHED, HIGH TRANSPORT REGIME CROSSES SEPARATRIX AND MOVES INTO MAIN PLASMA
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Has the potential to explain range
of density limit phenomena
Fluctuations can cool edge,
eliminate edge shear layer
Once perpendicular transport
dominates, stabilizing influence is
lost
Threshold condition? – need to
understand interaction of turbulence
and profiles
(LaBombard 2001)
THIS MODEL IS CONSISTENT WITH H-MODE CONFINEMENT DEGRADATION AND H/L TRANSITION
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CORE EDGEH and T T∇ ∝
Constant edge pressure implies τE
in ent of density
n /n
T
/n
p = c
p ∝ η-0.53
PED
PE
D
e
eG
G
0 0.2 0.4 0.6 0.8 1.00.00
0.04
0.08
0.12
(Osborne 2000)
(Greenwald, Hughes 1997)
Deterioration in edge
confinement can be offset
by internal transport barrier
depend
SOME SUPPORT FROM EDGE TURBULENCE SIMULATIONS
3D gyro-fluid simulations have found regime of extremely high transport •
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2 /Rq d drα β= −
0 0/D s s nc t L Lα ρ=
2
n n
TnL L
λ ∝ →
Region of ultra-high transport
consistent with high density, low
temperature
Similar results from Xu,
Hallatschek (Rogers, Drake 1998)No quantitative predictions yet
Unfortunately models for edge turbulence are incomplete
EXPERIMENTAL SUPPORT FOR TURBULENCE MODEL
α d
α
0 1 2 3 40
1
2
3
Type I ELMsType III ELMs
L-ModeMARFE
H-mode:
ASDEX Upgrade1996 data, divertor IT only
ee
enhancedtransport reduced transport
(Suttrop 1999)
MORE COMPLICATIONS - ROLE OF NEUTRALS IN THE DENSITY LIMIT?
Self shielding - limits gas
fueling
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Energy loss via ionization and
charge exchange
Source + particle transport.
Sets edge gradient length
⇒uns pressure profile
Mom transport.
Flow ng from ion-neutral
collis
Closed lines Open field lines
Relatively small increase in density leads to
large reduction in ionization inside last
closed flux surface
table
entum
dampi
ions.
OTHER DEVICES? - DENSITY LIMITS IN REVERSED FIELD PINCH
0 100
5 101 9
1 102 0
1.5 102 0
2 102 0
0 100 5 105 1 106 1.5 106 2 106
with fast terminationwithout fast termination
ne [
m-3
]
Greenwald limit
Ip/ ( a2) [Am- 2]π
(Bartiromo 2000)RFP operating space
characterized historically
by I/N
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GnIN n
∝
Same scaling !
Limit is quantitatively
identical (!!)
STELLARATORS REACH SIMILAR DENSITIES BUT SHOW DIFFERENT DEPENDENCES
Different scaling with power, size •
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Ptot [MW]
2.01.51.00.50.00
5
10
15
20
n ∝ P0.5 W7–AS
n ∝ P0.25 ASDEX
ne,
max
[10
19 m
-3]
ASDEX: Bt = 2.1 T, 1/qa = 0.34W7-AS: Bt = 1.28 T, ι(a) = 0.33
both with boronized walls
Power dependenceof density limit
(Staebler 1992)Shaping: B/qR vs I/a2 scaling
Scaling with ι = 1/q
Fo es with similar size and fields,
ste will reach about twice the density
of a
tokamak
(Wagner 1997)
r machin
llarator
ISSUES – THE DENSITY LIMIT AND THE NATURE OF EDGE TRANSPORT
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General question: Do we understand the important drives and saturation
mechanisms?
What is the role of open field lines and the separatrix?
Creation and destruction of edge shear layer?
Does model require that complex transport physics boil down to the "correct"
form?
Or is it robust with respect to details?
Where does IP (or BP) dependence come from?
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−
ExB
αMHD
Can we identify a reasonable threshold condition?
ISSUES – NATURE OF BLOBS, BALLISTIC TRANSPORT
Are blobs fundamentally important or just a
side effect?
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o Transition region is likely to be
critical.
o How are blobs shed?
Do the blobs decouple the transport
entirely from boundary conditions?
o Profiles, gradients unimportant?
o Is there an important role for
ionization and fueling?
DISCUSSION - SUMMARY
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None of the proposed models are entirely satisfactory
Radiation models consistent with some data, inconsistent with others
Transport model far from point of making predictions
Need to use self-consistent profiles, transport, power balance etc. for all models
May need combination of turbulent transport and atomic mechanisms
Physics strongly coupled – multiple feedback loops - cause and effects hard to
untangle
Can’t expect analytic form of scaling laws to emerge from theory/simulation
Transport studies need to be extended to other machines