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∝ •

•

•

•

•

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

•

•

•

•

•

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

•

•

•

•

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 •

•

•

•

•

•

•

- (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

•

Density or collisionality dependent transport ⇒ edge cooling

•

•

What physics can limit the density?

−

◆

◆

−

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∝

−

−

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

•

•

•

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

−

−

−

−

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

•

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 µsecsnapshot@0.92 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

•

•

•

•

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?

−

−

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