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Density Effects on Tokamak Edge Turbulence and Transport with Magnetic X-Points *

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Density Effects on Tokamak Edge Turbulence and Transport with Magnetic X-Points*

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 USA

2) Lodestar Research Corporation, Boulder, CO 80301 USA

3) MIT Plasma Science & Fusion Center, Cambridge, MA 02139 USA

4) General Atomics, San Diego, CA 92186 USA

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.

- 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

- 1- current profile shrinkage

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

- 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

- 1- current profile shrinkage 2 MHD instability

Turbulence model is 3D BOUT code

- Braginskii --- collisional, two-fluids
- full X-point geo. with separatrix
- electromagnetic with A||

- Turbulence behavior with density
- turbulence for fixed densities
- short-time profile evolution
- plasma “blob” formation and dynamics

- Long-time transport effects
- coupling BOUT to 2D UEDGE for wall recycled neutrals
- role of impurity radiation

- X-point & divertor leg effects
- X-point shear decorrelation
- a new beta-dependent divertor instability

c) 1.12xNG

b) 0.58xNG

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

- 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

- 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

8

6

Poloidal distance (cm)

4

2

0

-2 0 2

x (cm)

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

- 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

-0.6 0.0 0.6 1.2 1.8 2.4 3.0

Separatrix

DIII-D

8

3.0

4

2.0

1.0

0

0.

-0.5

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

Poloidal distance (cm)

0.86 ms

1.06 ms

DIII-D

0.69 ms

-2 0 2 x (cm)

- Analytic neutral model provides source for density build=up over ~1 ms
- Rapid convective transport to wall at higher densities

Density (1019 m-3)

1.22 ms

1.17 ms

Vorticity as density blob (contours) passes

4

(m)

(+d)

1

(+d)

Poloidial y (cm)

0

Vorticity(MHz)

(-d)

0

20

10

Time (s)

(-d)

-4

0 1 2 3

Radial distance from sep. (cm)

- 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

Spatial history for 1 blob

Convecting blob

Spinning blob

- - - - -

Electron B

E

ExB/B2

Ion B

Perpend. charge transport; X-point shear

Parallel charge transport

Curvature charge separation

+ + + + +

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, …

fluxes

BOUT

UEDGE

Coupling iteration index is m

profiles

Turbulence

Transport

- Density profile converges more rapidly than turbulent fluxes

a) Midplane density profile evolution

b) Midplane diffusion coeff. evolution

a) Constant D model

a) Constant D model

b) Coupled result

b) Coupled result

Effective diffusion coefficient

Neutral density distribution

- Poloidal variation understood from curvature instability

- Wall flux and recycling modifies midplane neutrals

- 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

Poloidal/parallel spatial correlation divertor reference

Poloidal/parallel spatial correlation midplane reference

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

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

Te

~

~

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

- 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