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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. Technological impacts of the study of edge turbulence.

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simulations of the core sol transition of a tokamak plasma

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

technological impacts of the study of edge turbulence
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
academic impacts of the study of edge turbulence
« 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.
slide5

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

core sol transition an intrisically sheared region
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

kelvin helmholtz instability
Kelvin-Helmholtz instability
  • Driven by shear in parallel momentum
  • Stabilized by density gradient
  • Instability criterion (WKB analysis)
model equations
Model equations

Particle conservation (n paticle density)

Momentum conservation (Γ parallel momentum)

Additional equation – electric drift

model equations elementary mechanisms
Model equations – elementarymechanisms

Particle conservation

Momentum conservation

Acoustic waves: finite parallel wavenumber

Drift waves : finite perpendicular wavenumber

Dynamics only accessible through 3D simulations

numerics
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
axisymmetric equilibria
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.

large gradients at the transition
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 ?
radial profiles of the instability parameter
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

linear instability growth
Linear instability growth

Simulation parameters

D*=3x10-2

q=3

Resolution 100x64x32

Linear instability of mode with toroidal wavenumber n=1.

most unstable mode n 1
Most unstable mode (n=1)

Localized on corner of limiter

toroidal mode n 3
Toroidal mode n=3
  • Mode driven close to the limiter
  • Larger poloidal extent than n=1
conclusions
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
Perspectives
  • Systematic study of linear growth of non-axisymmetric perturbations
  • Nonlinear phase
  • Extension of model to take into account interchange instability.
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