X.Q. Xu1, R.H. Cohen1, W.M. Nevins1, T.D. Rognlien1,

D.D. Ryutov1, M.V. Umansky1, L.D. Pearlstein1, R.H. Bulmer1,

D.A. Russell2, J.R. Myra2, D.A. D'Ippolito2,

M. Greenwald3, P.B. Snyder4, M.A. Mahdavi4

1) Lawrence Livermore National Laboratory, Livermore, CA 94551 USA2) Lodestar Research Corporation, Boulder, CO 80301 USA3) MIT Plasma Science & Fusion Center, Cambridge, MA 02139 USA4) General Atomics, San Diego, CA 92186 USA

Density Effects on Tokamak Edge Turbulence and Transport with Magnetic

X-Points*

Presented at the

IAEA Fusion Energy Conference

Vilamoura, Portugal

Nov. 1-5, 2004

* Work performed under the auspices of U.S. DOE by the Univ. of Calif. Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48 and is partially supported as LLNL LDRD project 03-ERD-09.

IAEA 11/3/04 2

Lodestar MIT GA

Goal: understand role of edge-plasmas on limiting high-density operation

• High density can increase fusion power (Pfus):

Pfus n2 <v>

• Tokamaks usually disrupt when the Greenwald limit is exceeded

– 1- current profile shrinkage 2 MHD instability

3 disruption

– Greenwald empirical scaling

nG = Ip/a2

– higher density with central peaking implies an edge limit

IAEA 11/3/04 3

Lodestar MIT GA

Goal: understand role of edge-plasmas on limiting high-density operation

• High density can increase fusion power (Pfus):

Pfus n2 <v>

• Tokamaks usually disrupt when the Greenwald limit is exceeded

– 1- current profile shrinkage 2 MHD instability

3 disruption

– Greenwald empirical scaling

nG = Ip/a2

– higher density with central peaking implies an edge limit

Our turbulence/transport simulations provide details of an edge-plasma collapse ==> current profile shrinkage

IAEA 11/3/04 4

Lodestar MIT GA

We have progressively improved edge turbulence and transport models together with basic understanding

1. Turbulence behavior with density

– turbulence for fixed densities

– short-time profile evolution

– plasma “blob” formation and dynamics

2. Long-time transport effects

– coupling BOUT to 2D UEDGE for wall recycled neutrals

– role of impurity radiation

3. X-point & divertor leg effects

– X-point shear decorrelation

– a new beta-dependent divertor instability

Turbulence model is 3D BOUT code• Braginskii --- collisional, two-fluids• full X-point geo. with separatrix

• electromagnetic with A||

IAEA 11/3/04 5

Lodestar MIT GA

Saturated fluctuations for 3 densities: high collisionality drives turbulent transport up& parallel correlation down

b) 0.58xNG

c) 1.12xNG

a) 0.28xNG

• Base-case (a): radial ni and Te,i profiles from DIII-D expt. tanh fit

• Two other cases (b,c) with 2x and 4x density together with 0.5x and 0.25x temperatures

IAEA 11/3/04 6

Lodestar MIT GA

Large perpendicular turbulence transport can exceed parallel transport at high density

D as n , D exhibits a nonlinear increase with n strong-transport boundary crossed• Large turbulence reduces Er shear layer allowing large transport to extend inwards

IAEA 11/3/04 7

Lodestar MIT GA

Numerous simulations varying density, Ip, and Bt show strong turbulence consistent with experimental limits

• P0 = n0T0 held fixed while n0 changes

• q held fixed while Ip changes

• No change w/ Bt while Ip is fixed

• Transport coefficients measured at separatrix

Greenwald Limit: nG=Ip/a2

IAEA 11/3/04 8

Lodestar MIT GA

Profile-evolving simulation shows generation and convection of plasma “blobs” as density increases

• Ion density evolved for ~1 ms from ionization of neutral source

• Neutral density has spatial form

nn= n0 exp(x/xw);

xw = (icx)1/2;

mimics wall recycling

• Turbulence develops stronger ballooning character with blobs

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

6

8

2

0

4

Po

loid

al d

ista

nce

(c

m)

-2 0 2x (cm)

ni [x,y,t] (1019 m-3)

-0.6 0.0 0.6 1.2 1.8 2.4 3.0

DIII-D

Separatrix

IAEA 11/3/04 9

Lodestar MIT GA

Profile-evolving simulation shows generation and convection of plasma “blobs” as density increases

ni [x,y,t] - ni[t=0] (1019 m-3)

DIII-D

Po

loid

al d

ista

nce

(c

m)

-2 0 2 x (cm)

8

0

4

0.

-0.5

1.0

3.0

2.0

Density (1019 m-3)

1.22 ms 1.17 ms

1.06 ms 0.86 ms 0.69 ms

• Analytic neutral model provides source for density build=up over ~1 ms

• Rapid convective transport to wall at higher densities

IAEA 11/3/04 10

Lodestar MIT GA

Characteristics of localized, intermittent “blobs” determined from detailed diagnostics of simulation data

(+d)

(-d)

0 1 2 3

(m)

Vo

rtic

ity

(MH

z)

Radial distance from sep. (cm)

0

4

-4

• 3D turbulence in realistic X-point geometry generates edge blobs

• Higher density results in stronger turbulence giving robust blobs

• Vorticity: = 2

• Example shows blobs spinning with monopole vorticity (m), which decays, allowing convective dipole vorticity (+d,-d) to develop

Spinning blob

Convecting blob

Spatial history for 1 blob

d

(+d)

Time (s)

Po

loid

ial

y (c

m)

Vorticity as density blob (contours) passes

1

0

10 20

IAEA 11/3/04 11

Lodestar MIT GA

Regimes of blob edge-plasma transport understood through analytic analysis

See Poster TH/P6-2, D. A. D’Ippolito, et al., Friday, 16:30

Current continuity eqn: J = 0 becomes • Analysis identifies parallel resistivity & X-point magnetic shear as key in blob velocity vs size, a

– Sheath-connected: Vr ~ a-2

– X-point J: Vr ~ a-1/3

– And others, …

iyi NJdt

dN 2||||

2

Curvature charge separation

Parallel charge transport

Perpend. charge transport; X-point shear

+ + + + +

- - - - -

E ExB/B2Ion BElectron B

IAEA 11/3/04 12

Lodestar MIT GA

For long recycling timescales, we have coupled self-consistent edge turbulence/transport simulations

• Density profile converges more rapidly than turbulent fluxes

a) Midplane density profile evolution b) Midplane diffusion coeff. evolution

Coupling iteration index is mTurbulence Transport

BOUT UEDGE

profiles

fluxes

IAEA 11/3/04 13

Lodestar MIT GA

Results show that strong spatial dependence of transport substantially changes SOL and neutral distribution

a) Constant D model b) Coupled result

• Poloidal variation understood from curvature instability

a) Constant D model b) Coupled result

• Wall flux and recycling modifies midplane neutrals

Effective diffusion coefficient Neutral density distribution

IAEA 11/3/04 14

Lodestar MIT GA

2D transport modeling shows that large radial convection can lead to an X-point MARFE

• Mimic strong BOUT transport in UEDGE by a ballooning convective velocity varying from 0 to 300 m/s btwn. sep. & wall

• Compare no convection and strong convections cases

• Particle recycling and energy loss to radial wall included

• Stronger neutral penetration increases density and impurity radiation loss - higher resistivity

Self-consistent impurity transport still needed

IAEA 11/3/04 15

Lodestar MIT GA

Analysis of simulation shows decorrelation of turbulence between the midplane and divertor leg

Cross-correlations of BOUT data by GKV analysis package shows decorrelation by X-point magnetic shear

Poloidal/parallel spatial correlation midplane reference

Poloidal/parallel spatial correlation divertor reference

IAEA 11/3/04 16

Lodestar MIT GA

Te

New divertor-leg instability driven at “high” plasma-beta (density) by a radial tilt of the divertor plate.

• Unstable mode effectively does not reach X-point if growth rate is large enough, Im > vA/L

• Instability is absent if no plate tilt and increases for larger outward tilt

• Localized mode exists (Im > 1) only if plasma beta high enough

• The mode reduces the divertor heat load without having direct impact on the main SOL

~

~

IAEA 11/3/04 17

Lodestar MIT GA

Summary and ongoing work

• Increasing edge density (or collisionality) in X-point geometry

– drives increasing turbulence that becomes very large “near” nGW

– generates robust blobs – strong radial transport hastens edge

cooling (neutrals, impurities)

• X-point magnetic shear– causes decorrelation between

midplane and divertor leg, large k

– modifies blob dynamics as well as resistive instabilities

• Plate (outward) tilt yields new finite-beta divertor instability

We are working to:

• Couple Er for long-time turbulence/transport evolution

• Include self-consistent impurities

• Enhance expt. comparisons

• Simulate divertor-leg instability

• Develop a 5D kinetic edge code