3D modelling of edge parallel flow asymmetries

1. 3D modelling of edge parallel flow asymmetries P. Tamainab, Ph. Ghendriha, E. Tsitronea, Y. Sarazina, X. Garbeta, V. Grandgirarda, J. Gunna, E. Serrec, G. Ciraoloc, G. Chiavassac aAssociation Euratom-CEA, CEA Cadarache, France bEuratom-UKAEA Fusion Association, Culham Science Centre, UK cUniversity of Provence/CNRS, France

2. Strong poloidal asymmetries in parallel Mach number measured on all machines M~0 expected M measured M M=+1 M=-1 [courtesy J. Gunn] Expected situation: symmetrical parallel flow parallel Mach number at the top: M = u// /cs ~ 0 Experimental results: asymmetrical flow M~0.5 at the top universal phenomenon (X-point and limiter) [Asakura, JNM (2007)]

3. Hard to reproduce with transport codes without any ad-hoc hypothesis M~0.5 HFS LFS M=+1 M=-1 [Gunn & al., JNM (2007)] • Modelling attempts with 2D transport codes [Erents, Pitts et al., 2004] • evidence for influence of drifts (ExB and diamagnetic) • ad-hoc strong ballooning of radial transport necessary to recover experimental amplitudes: DLFS / DHFS ~ 200 [Zagorski et al., 2007]

4. TOKAM-3D: a new numerical tool able to tackle consistently this kind of issue SOL edge centre • 3D fluid drift equations [B. Scott, IPP 5/92, 2001] • density, potential, parallel current and Mach numberM • Bohmboundary conditions in the SOL • flux driven, no scale separation => Turbulence + Transport 3D - full torus closed + open field lines limiter simulated region

5. 3D drift fluid equations ExB advection continuity curvature parallel dynamics diffusive transport charge vorticity definition parallel momentum parallel current

6. “Neoclassical” vs turbulent regime 8.10-2 D/DBohm ~ * 1 t   • high D: “neoclassical” equilibrium with drifts => only large scale effects • low D: turbulent regime => impact of small scales

7. Neoclassical regime: growth of poloidal asymmetries even without turbulence 1 HFS LFS 0.5 M>0 0 M=0 -0.5 M<0 -1 Parallel Mach number M • 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 • mechanism: combination of global ExB drift and curvature

8. Is that enough to recover experimental results? HFS Top LFS LCFS 1 0.25 0 Parallel Mach number Parallel Mach number 0 -1 40 100 θ 160 Minor radius r/ρL • larger amplitude than that found in previous studies but still lower than experiments • radial extension in the SOL not deep enough θ = π/2 (top) r/a = 1.07 The answer seems to be NO: there must be something else…

9. Edge turbulent transport can generate large amplitude poloidal asymmetries M 1 <rturb>t,, poloidal up/down (m=1,n=0) asymmetry in spite of strongly aligned structures <rdiff>t,, 0 r Density n • no limiter => previous large scale drifts effect not included • low diffusion: D /DBohm=0.02 => turbulent transport

10. 90% of the flux at the LFS LFS HFS 0.4 0 90% of total flux -0.4 • Mach number at the top: Mtop~0.35 LFS r / tot r ~ 0.9 • asymmetry due to ballooned transport: HFS LFS M <r>

11. How do these two mechanisms overlap in a complete edge simulation? HFS LFS HFS LFS N M • turbulent regime in closed + open flux surfaces • filament-like structures generated in the vicinity of the LCFS and propagate in the SOL

12. The superposition of both mechanisms allows a recovery of experimental features • experimental large amplitudes Mtop~0.5 recovered even in far SOL • good qualitative and quantitative agreement with experimental data

13. SUMMARY / CONCLUSION • TOKAM-3D: • new generation of edge codes: 3D transport & turbulence across LCFS success of fully consistent approach • on-going development for model and code improvements • 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

14. The TOKAM-3D Model buffer zone periodic buffer zone 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

15. 3D drift fluid equations ExB advection continuity curvature parallel dynamics diffusive transport charge vorticity definition parallel momentum parallel current

16. Geometrical dependances HFS LFS HFS LFS M=0 (BxB)ions M=0 (BxB)ions Bottom, reverse B Equatorial, normal B Impact of field inversion and of limiter position • 3 identical cases: limiter poloidal shift and B reversal (B drift sign) HFS LFS (BxB)ions M=0 Bottom, normal B

17. ‘Return parallel flow’ mechanism driven by ExB and curvature HFS LFS  LCFS M// r top LFS N top LFS ExB N   • 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

18. Origin of the Mach number asymmetry ExB drift + curvature plays a major role • step 1: establishment of large poloidal ExB drift at LCFS r sign changes => drift direction does not change with field direction LCFS    r r r Bottom, normal B Bottom, reverse B Equatorial, normal B

19. Origin of the Mach number asymmetry ExB drift + curvature plays a major role • step 1: establishment of large poloidal ExB drift at LCFS • step 2: curvature effects trigger symmetric inhomogeneities No curvature effect at equatorial plane LFS top N N N    Bottom, normal B Bottom, reverse B Equatorial, normal B

20. Origin of the Mach number asymmetry ExB drift + curvature plays a major role • 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 LFS top ExB ExB N N N    Bottom, normal B Bottom, reverse B Equatorial, normal B