1. 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, M. Greenwald 3, P.B. Snyder 4, M.A. Mahdavi 4 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 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.

2. 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 (P fus ): P fus  n 2 Tokamaks usually disrupt when the Greenwald limit is exceeded –1- current profile shrinkage 2  MHD instability 3  disruption –Greenwald empirical scaling n G = I p /  a 2 –higher density with central peaking implies an edge limit

3. 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 (P fus ): P fus  n 2 Tokamaks usually disrupt when the Greenwald limit is exceeded –1- current profile shrinkage 2  MHD instability 3  disruption –Greenwald empirical scaling n G = I p /  a 2 –higher density with central peaking implies an edge limit Our turbulence/transport simulations provide details of an edge-plasma collapse ==> current profile shrinkage

4. 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 ||

5. IAEA 11/3/04 5 Lodestar MIT GA Saturated fluctuations for 3 densities: high collisionality drives turbulent transport up  & parallel correlation down b) 0.58xN G c) 1.12xN G a) 0.28xN G Base-case (a): radial n i and T e,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

6. 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 E r shear layer allowing large transport to extend inwards

7. IAEA 11/3/04 7 Lodestar MIT GA Numerous simulations varying density, I p, and B t show strong turbulence consistent with experimental limits P 0 = n 0 T 0 held fixed while n 0 changes q held fixed while I p changes No change w/ B t while I p is fixed Transport coefficients measured at separatrix Greenwald Limit: n G =I p /  a 2            

8. 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 n n = n 0 exp(x/x w ); x w = ( i  cx ) 1/2 ; mimics wall recycling Turbulence develops stronger ballooning character with blobs 6 8 2 0 4 Poloidal distance (cm) -2 0 2 x (cm) n i [x,y,t] (10 19 m -3 ) -0.6 0.0 0.6 1.2 1.8 2.4 3.0 DIII-D Separatrix

9. IAEA 11/3/04 9 Lodestar MIT GA Profile-evolving simulation shows generation and convection of plasma “blobs” as density increases n i [x,y,t] - n i [t=0] (10 19 m -3 ) DIII-D Poloidal distance (cm) -2 0 2 x (cm) 8 0 4 0. -0.5 1.0 3.0 2.0 Density (10 19 m -3 ) 1.22 ms 1.17 ms 1.06 ms0.86 ms 0.69 ms Analytic neutral model provides source for density build=up over ~1 ms Rapid convective transport to wall at higher densities

10. 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) Vorticity (MHz) 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) Poloidial y (cm) Vorticity as density blob (contours) passes 1 0 10 20

11. 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: V r ~ a -2 – X-point J  : V r ~ a -1/3 – And others, … Curvature charge separation Parallel charge transport Perpend. charge transport; X-point shear + + + + + - - - - - E ExB/B 2 Ion  B Electron  B

12. 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 m TurbulenceTransport BOUT UEDGE profiles fluxes

13. 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

14. 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

15. 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

16. IAEA 11/3/04 16 Lodestar MIT GA  T e  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  > v A /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 ~ ~

17. 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” n GW –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 E r for long-time turbulence/transport evolution Include self-consistent impurities Enhance expt. comparisons Simulate divertor-leg instability Develop a 5D kinetic edge code