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 * PowerPoint PPT Presentation


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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*

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

  • 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

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


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


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


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


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


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


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


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


- - - - -

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

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


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

  • 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

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


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

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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