Simulations of the core/SOL transition of a tokamak plasma

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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

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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

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 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.

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The limiter at the center of the study
limiter
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• 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
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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 ?

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Kelvin-Helmholtz instability

• Driven by shear in parallel momentum
• Stabilized by density gradient
• Instability criterion (WKB analysis)

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Model equations
Particle conservation (n paticle density)
Momentum conservation (G parallel momentum)
Additional equation electric drift
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Model equations elementary mechanisms
Particle conservation
Momentum conservation
Acoustic waves finite parallel wavenumber Drift
waves finite perpendicular
wavenumber Dynamics only accessible through 3D
simulations
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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

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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.
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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 ?

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Radial profiles of the instability parameter

• 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
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Linear instability growth
Simulation parameters D3x10-2 q3 Resolution
100x64x32
Linear instability of mode with toroidal
wavenumber n1.
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Most unstable mode (n1)
Localized on corner of limiter
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Toroidal mode n3

• Mode driven close to the limiter
• Larger poloidal extent than n1

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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.

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Perspectives

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