Simulations of the core/SOL transition of a tokamak plasma

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 • Determination of profiles: density, temperatureOptimization of plasma performance • Determinationheat fluxes on plasma-facing componentsEstablishment of constraints on plasma operationswithappropriate thermal load on plasma facing components

3. « Academic » impacts of the study of edge turbulence • Core-SOL transition intrinsicallysheared • Active role on turbulence ? • Propagation of turbulence betweencore and SOL ? • Impact of three-dimensionaleffects on edge turbulence.

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

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

6. Core/SOL transition: an intrisicallyshearedregion Core • Parallelflowsessentiallyatrest • Relatively large density Scrape-off layer • High velocityparallelflows • Lowdensity Shear in momentum and densityat the transition: Triggering of instabilities ? Mach=1 Mach=-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 – elementarymechanisms Particle conservation Momentum conservation Acoustic waves: finite parallel wavenumber Drift waves : finite perpendicular wavenumber Dynamics only accessible through 3D simulations

10. Numerics • Cylindricaldomain(no curvatureatthis stage) • Non-periodiccoordinates(radial, poloidal) • Second-orderfinitedifferences • Periodic direction (toroidal) • Fourier modes • Paralleldynamics: Lax-Wendroff TVD scheme • Advection by drift motion: Arakawa scheme • Background turbulent transport:treatedimplicitly

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 SOL core SOL core • 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 instabilityparameter • Stabilization by density stratification globally dominant, • Global stability for lowest values of transport • Unstable region just inside the transition for largest value of transport. core SOL

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.