1. 1/1318 th PSI conference – Toledo, May 2008P. Tamain Association EURATOM-CEA 3D modelling of edge parallel flow asymmetries P. Tamain ab, Ph. Ghendrih a, E. Tsitrone a, Y. Sarazin a, X. Garbet a, V. Grandgirard a, J. Gunn a, E. Serre c, G. Ciraolo c, G. Chiavassa c a Association Euratom-CEA, CEA Cadarache, France b Euratom-UKAEA Fusion Association, Culham Science Centre, UK c University of Provence/CNRS, France

2. 2/1318 th PSI conference – Toledo, May 2008P. Tamain Association EURATOM-CEA Strong poloidal asymmetries in parallel Mach number measured on all machines Expected situation: symmetrical parallel flow parallel Mach number at the top: M = u // /c s ~ 0 Experimental results: asymmetrical flow M~0.5 at the top universal phenomenon (X-point and limiter) [Asakura, JNM (2007)] expected Mmeasured M [courtesy J. Gunn] M~0 M=+1M=-1

3. 3/1318 th PSI conference – Toledo, May 2008P. Tamain Association EURATOM-CEA Hard to reproduce with transport codes without any ad-hoc hypothesis [Zagorski et al., 2007] D  LFS / D  HFS ~ 200  Modelling attempts with 2D transport codes [Erents, Pitts et al., 2004] [Gunn & al., JNM (2007)] M=+1M=-1 M~0.5 HFS LFS  ad-hoc strong ballooning of radial transport necessary to recover experimental amplitudes: evidence for influence of drifts (ExB and diamagnetic)

4. 4/1318 th PSI conference – Toledo, May 2008P. Tamain Association EURATOM-CEA TOKAM-3D: a new numerical tool able to tackle consistently this kind of issue centre edge SOL limiter simulated region 3D - full torus closed + open field lines 3D fluid drift equations [B. Scott, IPP 5/92, 2001]  density, potential, parallel current and Mach number M Bohm boundary conditions in the SOL flux driven, no scale separation => Turbulence + Transport

5. 5/1318 th PSI conference – Toledo, May 2008P. Tamain Association EURATOM-CEA 3D drift fluid equations continuity charge parallel momentum parallel current vorticity definition ExB advection curvature parallel dynamics diffusive transport

6. 6/1318 th PSI conference – Toledo, May 2008P. Tamain Association EURATOM-CEA “Neoclassical” vs turbulent regime D  /D Bohm ~ * t 1 8.10 -2    high D  : “neoclassical” equilibrium with drifts => only large scale effects  low D  : turbulent regime => impact of small scales

7. 7/1318 th PSI conference – Toledo, May 2008P. Tamain Association EURATOM-CEA  neoclassical equilibrium with ExB and diamagnetic drifts  non-zero Mach number at the top: M~0.25  uniform D   not linked to poloidal distribution of radial transport LFSHFS Parallel Mach number M M=0 M>0 M<0 0.5 0 -0.5 1 Neoclassical regime: growth of poloidal asymmetries even without turbulence  mechanism: combination of global ExB drift and curvature

8. 8/1318 th PSI conference – Toledo, May 2008P. Tamain Association EURATOM-CEA Parallel Mach number θ 1 0 LFSHFSTop -1 Parallel Mach number 0.25 0 Minor radius r/ρ L 10040160 LCFS Is that enough to recover experimental results?  larger amplitude than that found in previous studies but still lower than experiments  radial extension in the SOL not deep enough The answer seems to be NO: there must be something else… θ = π/2 (top) r/a = 1.07

9. 9/1318 th PSI conference – Toledo, May 2008P. Tamain Association EURATOM-CEA Edge turbulent transport can generate large amplitude poloidal asymmetries  low diffusion: D  /D Bohm =0.02 => turbulent transport poloidal up/down (m=1,n=0) asymmetry in spite of strongly aligned structures M t, ,  r 0 1 Density n  no limiter => previous large scale drifts effect not included

10. 10/1318 th PSI conference – Toledo, May 2008P. Tamain Association EURATOM-CEA 0 0.4 -0.4 HFS LFS 90% of the flux at the LFS  Mach number at the top: M top ~0.35  LFS  r /  tot  r ~ 0.9 M <r><r> HFSLFS  asymmetry due to ballooned transport: 90% of total flux

11. 11/1318 th PSI conference – Toledo, May 2008P. Tamain Association EURATOM-CEA  turbulent regime in closed + open flux surfaces  filament-like structures generated in the vicinity of the LCFS and propagate in the SOL How do these two mechanisms overlap in a complete edge simulation? N HFSLFS M HFSLFS

12. 12/1318 th PSI conference – Toledo, May 2008P. Tamain Association EURATOM-CEA  experimental large amplitudes M top ~0.5 recovered even in far SOL The superposition of both mechanisms allows a recovery of experimental features  good qualitative and quantitative agreement with experimental data

13. 13/1318 th PSI conference – Toledo, May 2008P. Tamain Association EURATOM-CEA SUMMARY / CONCLUSION  Parallel flows poloidal asymmetries: confirmation of the existence of 2 distinct mechanisms: -large scale drifts => coupling between ExB, curvature and the limiter -ballooning of turbulent radial transport => coupling between turbulent scales and curvature superposition of both mechanisms leads to good agreement with experimental data without requiring ad-hoc hypotheses  TOKAM-3D: new generation of edge codes: 3D transport & turbulence across LCFSsuccess of fully consistent approach on-going development for model and code improvements

14. 14/1318 th PSI conference – Toledo, May 2008P. Tamain Association EURATOM-CEA The TOKAM-3D Model Fluid modeling with no scale separation  3D fluid drift equations : matter, charge, parallel momentum, parallel current (generalized Ohm’s law) [Scott, IPP 5/92, 2001]  isothermal closure in current version periodic buffer zone

15. 15/1318 th PSI conference – Toledo, May 2008P. Tamain Association EURATOM-CEA 3D drift fluid equations continuity charge parallel momentum parallel current vorticity definition ExB advection curvature parallel dynamics diffusive transport

16. 16/1318 th PSI conference – Toledo, May 2008P. Tamain Association EURATOM-CEA Geometrical dependances  3 identical cases: limiter poloidal shift and B reversal (  B drift sign) Impact of field inversion and of limiter position Bottom, normal  B LFSHFS M=0 (Bx  B) ions Equatorial, normal  B LFSHFS M=0 (Bx  B) ions Bottom, reverse  B LFSHFS M=0 (Bx  B) ions

17. 17/1318 th PSI conference – Toledo, May 2008P. Tamain Association EURATOM-CEA ‘Return parallel flow’ mechanism driven by ExB and curvature r  LCFS  step 1: establishment of large poloidal ExB drift at LCFS LFSHFS  step 2: curvature effects trigger symmetric inhomogeneities  step 3: ExB drift advects the density and breaks the symmetry M // ExB N topLFS  N ExB LFStop 

18. 18/1318 th PSI conference – Toledo, May 2008P. Tamain Association EURATOM-CEA Origin of the Mach number asymmetry ExB drift + curvature plays a major role  step 1: establishment of large poloidal ExB drift at LCFS Bottom, normal  B Bottom, reverse  B Equatorial, normal  B rrr  LCFS  r  sign changes => drift direction does not change with field direction

19. 19/1318 th PSI conference – Toledo, May 2008P. Tamain Association EURATOM-CEA Origin of the Mach number asymmetry ExB drift + curvature plays a major role Bottom, normal  B Bottom, reverse  B Equatorial, normal  B NNN   top LFS  step 1: establishment of large poloidal ExB drift at LCFS  step 2: curvature effects trigger symmetric inhomogeneities No curvature effect at equatorial plane

20. 20/1318 th PSI conference – Toledo, May 2008P. Tamain Association EURATOM-CEA Origin of the Mach number asymmetry ExB drift + curvature plays a major role Bottom, normal  B Bottom, reverse  B Equatorial, normal  B NNN   top LFS  step 1: establishment of large poloidal ExB drift at LCFS  step 2: curvature effects trigger symmetric inhomogeneities  step 3: ExB drift advects the density and breaks the symmetry ExB