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. Technological impacts of the study of edge turbulence.

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Simulations of the core/SOL transition of a tokamak plasma

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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.


The limiter at the center of the study

The limiter: at the center of the study

limiter

Mach=1

Mach=-1


Simulations of the core sol transition of a tokamak plasma

  • 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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