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. ChiavassaM2P2, Marseille

Technological impacts of the study of edge turbulence

1. Determination of profiles: density, temperatureOptimization of plasma performance

2. Determination heat fluxes on plasma-facing componentsEstablishment of constraints on plasma operations with appropriate thermal load on plasma facing components

« 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.

The limiter: at the center of the study

Mach=1 Mach=-1

limiter

Core plasmaClosed magnetic surfaces in the coreDouble periodicity:•poloidal angle•toroidal angle

Field lines intersect limiter on inboard and outboard side

Scrape-off layerField lines intersect both sides of limiter

•Poloidal periodicity lost,•Only toroidal periodicity preserved.

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=1 Mach=-1

Kelvin-Helmholtz instability

• Driven by shear in parallel momentum• Stabilized by density gradient

• Instability criterion (WKB analysis)

0ln 22

drnd

drdM eqeq

Model equations

nDnvn Et2*

2*22

Dvncn Est

Particle conservation (n paticle density)

Momentum conservation (Γ parallel momentum)

2

0/lnB

nnBvE

Additional equation – electric drift

Model equations – elementary mechanisms

nDnvn Et2*

2*22

Dvncn Est

Particle conservation

Momentum conservation

Acoustic waves: finite parallel wavenumberDrift waves : finite perpendicular wavenumber

Dynamics only accessible through 3D simulations

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

Axisymmetric equilibriaSystematic convergence of axisymmetric computation towards steady state.

Show:Natural radial stratification in density,Large Mach number flows limited to scrape-off layer.

Large gradients at the transition

core SOL

core

SOL

•Maximum gradient increases when background turbulence decreases.•Kelvin-Helmholtz instability: stabilizing and destabilizing factors maximum at the same location. Overall effect ?

Radial profiles of the instability parameter

core SOL •Stabilization by density stratification globally dominant,

•Global stability for lowest values of transport

•Unstable region just inside the transition for largest value of transport.

Linear instability growth

Simulation parametersD*=3x10-2

q=3

Resolution 100x64x32

Linear instability of mode with toroidal wavenumber n=1.

Most unstable mode (n=1)

Localized on corner of limiter

Toroidal mode n=3

•Mode driven close to the limiter•Larger poloidal extent than n=1

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.

Perspectives

• Systematic study of linear growth of non-axisymmetric perturbations

• Nonlinear phase

• Extension of model to take into account interchange instability.