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. Xu 1 , R.H. Cohen 1 , W.M. Nevins 1 , T.D. Rognlien 1 , D.D. Ryutov 1 , M.V. Umansky 1 , L.D. Pearlstein 1 , R.H. Bulmer 1 , D.A. Russell 2 , J.R. Myra 2 , D.A. D'Ippolito 2 ,

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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

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.


Goal understand role of edge plasmas on limiting high density operation

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


Goal understand role of edge plasmas on limiting high density operation1

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

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


Density effects on tokamak edge turbulence and transport with magnetic x points

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

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


Density effects on tokamak edge turbulence and transport with magnetic x points

c) 1.12xNG

b) 0.58xNG

a) 0.28xNG

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

  • 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


Large perpendicular turbulence transport can exceed parallel transport at high density

Largeperpendicular 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


Density effects on tokamak edge turbulence and transport with magnetic x points

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


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

8

6

Poloidal distance (cm)

4

2

0

-2 0 2

x (cm)

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

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 = (icx)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


Profile evolving simulation shows generation and convection of plasma blobs as density increases1

8

3.0

4

2.0

1.0

0

0.

-0.5

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

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


Density effects on tokamak edge turbulence and transport with magnetic x points

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)

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

  • 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


Density effects on tokamak edge turbulence and transport with magnetic x points

- - - - -

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, …


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

fluxes

BOUT

UEDGE

Coupling iteration index is m

profiles

Turbulence

Transport

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


Density effects on tokamak edge turbulence and transport with magnetic x points

a) Constant D model

a) Constant D model

b) Coupled result

b) Coupled result

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

Effective diffusion coefficient

Neutral density distribution

  • Poloidal variation understood from curvature instability

  • Wall flux and recycling modifies midplane neutrals


2d transport modeling shows that large radial convection can lead to an x point marfe

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


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

Poloidal/parallel spatial correlation divertor reference

Poloidal/parallel spatial correlation midplane reference

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


Density effects on tokamak edge turbulence and transport with magnetic x points

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

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

~

~


Summary and ongoing work

Summary and ongoing work

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


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