1. Simulations of the core/SOL transition of a tokamak plasma Frederic Schwander,Ph. Ghendrih, Y. Sarazin IRFM/CEA Cadarache G. Ciraolo, E. Serre, L. Isoardi, G. Chiavassa M2P2, Marseille

2. Technological impacts of the study of edge turbulence 1.Determination of profiles: density, temperature Optimization of plasma performance 2.Determination heat fluxes on plasma-facing components Establishment of constraints on plasma operations with appropriate thermal load on plasma facing components

3. « Academic » impacts of the study of edge turbulence Core-SOL transition intrinsically sheared Active role on turbulence ? Propagation of turbulence between core and SOL ? Impact of three-dimensional effects on edge turbulence.

4. The limiter: at the center of the study Mach=1Mach=-1 limiter

5. Core plasma Closed magnetic surfaces in the core Double periodicity: poloidal angle toroidal angle Field lines intersect limiter on inboard and outboard side Scrape-off layer Field lines intersect both sides of limiter Poloidal periodicity lost, Only toroidal periodicity preserved.

6. Core/SOL transition: an intrisically sheared region Core – Parallel flows essentially at rest – Relatively large density Scrape-off layer – High velocity parallel flows – Low density Shear in momentum and density at the transition: Triggering of instabilities ? Mach=1Mach=-1

7. Kelvin-Helmholtz instability Driven by shear in parallel momentum Stabilized by density gradient Instability criterion (WKB analysis)

8. Model equations Particle conservation (n paticle density) Momentum conservation (Γ parallel momentum) Additional equation – electric drift

9. Model equations – elementary mechanisms Particle conservation Momentum conservation Acoustic waves: finite parallel wavenumber Drift waves : finite perpendicular wavenumber Dynamics only accessible through 3D simulations

10. Numerics Cylindrical domain (no curvature at this stage) Non-periodic coordinates (radial, poloidal) – Second-order finite differences Periodic direction (toroidal) – Fourier modes Parallel dynamics: Lax-Wendroff TVD scheme Advection by drift motion: Arakawa scheme Background turbulent transport: treated implicitly

11. Axisymmetric equilibria Systematic convergence of axisymmetric computation towards steady state. Show: Natural radial stratification in density, Large Mach number flows limited to scrape-off layer.

12. Large gradients at the transition coreSOL core SOL Maximum gradient increases when background turbulence decreases. Kelvin-Helmholtz instability: stabilizing and destabilizing factors maximum at the same location. Overall effect ?

13. Radial profiles of the instability parameter coreSOL Stabilization by density stratification globally dominant, Global stability for lowest values of transport Unstable region just inside the transition for largest value of transport.

14. Linear instability growth Simulation parameters D*=3x10 -2 q=3 Resolution 100x64x32 Linear instability of mode with toroidal wavenumber n=1.

15. Most unstable mode (n=1) Localized on corner of limiter

16. Toroidal mode n=3 Mode driven close to the limiter Larger poloidal extent than n=1

17. Conclusions Possible excitation of Kelvin-Helmholtz modes in reduced model of core/SOL dynamics, Instability favoured for large values of background turbulence, Mode not driven at core/SOL transition, but on top of limiter.

18. Perspectives Systematic study of linear growth of non- axisymmetric perturbations Nonlinear phase Extension of model to take into account interchange instability.