Prsentation PowerPoint

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3D modelling of edge parallel flow asymmetries
P. Tamainab, Ph. Ghendriha, E. Tsitronea, Y.
Sarazina, X. Garbeta, V. Grandgirarda, J. Gunna,
E. Serrec, G. Ciraoloc, G. Chiavassac aAssociati
on Euratom-CEA, CEA Cadarache, France bEuratom-UKA
EA Fusion Association, Culham Science Centre,
UK cUniversity of Provence/CNRS, France
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Strong poloidal asymmetries in parallel Mach
number measured on all machines
Expected situation symmetrical parallel
flow parallel Mach number at the top M u//
/cs 0
Experimental results asymmetrical flow M0.5
at the top universal phenomenon (X-point and
limiter)
Asakura, JNM (2007)
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Hard to reproduce with transport codes without
any ad-hoc hypothesis

• Modelling attempts with 2D transport codes
  Erents, Pitts et al., 2004

• evidence for influence of drifts (ExB and
  diamagnetic)

• ad-hoc strong ballooning of radial transport
  necessary to recover experimental amplitudes

D?LFS / D?HFS 200
Zagorski et al., 2007
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TOKAM-3D a new numerical tool able to tackle
consistently this kind of issue
3D - full torus
closed open field lines
limiter
simulated region

• 3D fluid drift equations B. Scott, IPP 5/92,
  2001
• density, potential, parallel current and Mach
  number M
• Bohm boundary conditions in the SOL
• flux driven, no scale separation gt Turbulence
  Transport

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3D drift fluid equations
ExB advection
continuity
curvature
parallel dynamics
diffusive transport
charge
vorticity definition
parallel momentum
parallel current
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Neoclassical vs turbulent regime
D?/DBohm ?
1
t
?
?

• high D? neoclassical equilibrium with drifts
  gt only large scale effects

• low D? turbulent regime gt impact of small
  scales

7
Neoclassical regime growth of poloidal
asymmetries even without turbulence

• neoclassical equilibrium with ExB and
  diamagnetic drifts

• non-zero Mach number at the top M0.25

• uniform D? ? not linked to poloidal distribution
  of radial transport

• mechanism combination of global ExB drift and
  curvature

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Is that enough to recover experimental results?

• larger amplitude than that found in previous
  studies but still lower than experiments

• radial extension in the SOL not deep enough

? p/2 (top)
r/a 1.07
The answer seems to be NO there must be
something else
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Edge turbulent transport can generate large
amplitude poloidal asymmetries
Density n

• no limiter gt previous large scale drifts effect
  not included

• low diffusion D? /DBohm0.02
• gt turbulent transport

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90 of the flux at the LFS

• Mach number at the top Mtop0.35

?LFS ?r / ?tot ?r 0.9

• asymmetry due to ballooned transport

HFS
LFS
M
lt?rgt
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How do these two mechanisms overlap in a complete
edge simulation?

• turbulent regime in closed open flux surfaces
• filament-like structures generated in the
  vicinity of the LCFS and propagate in the SOL

12
The superposition of both mechanisms allows a
recovery of experimental features

• experimental large amplitudes Mtop0.5 recovered
  even in far SOL

• good qualitative and quantitative agreement with
  experimental data

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SUMMARY / CONCLUSION

• Parallel flows poloidal asymmetries
• confirmation of the existence of 2 distinct
  mechanisms
• large scale drifts gt coupling between ExB,
  curvature and the limiter
• ballooning of turbulent radial transport gt
  coupling between turbulent scales and curvature
• superposition of both mechanisms leads to good
  agreement with experimental data without
  requiring ad-hoc hypotheses

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The TOKAM-3D Model

• Fluid modeling with no scale separation
• 3D fluid drift equations matter, charge,
  parallel momentum, parallel current (generalized
  Ohms law) Scott, IPP 5/92, 2001
• isothermal closure in current version

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3D drift fluid equations
ExB advection
continuity
curvature
parallel dynamics
diffusive transport
charge
vorticity definition
parallel momentum
parallel current
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Geometrical dependances
Impact of field inversion and of limiter position

• 3 identical cases limiter poloidal shift and B
  reversal (?B drift sign)

LFS
HFS
(Bx?B)ions
M0
Bottom, normal ?B
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Return parallel flow mechanism driven by ExB
and curvature

• step 1 establishment of large poloidal ExB
  drift at LCFS

• step 2 curvature effects trigger symmetric
  inhomogeneities

• step 3 ExB drift advects the density and breaks
  the symmetry

ExB
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Origin of the Mach number asymmetry
ExB drift curvature plays a major role

• step 1 establishment of large poloidal ExB
  drift at LCFS

?r? sign changes gt drift direction does not
change with field direction
LCFS
?
?
?
r
r
r
Bottom, normal ?B
Bottom, reverse ?B
Equatorial, normal ?B
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Origin of the Mach number asymmetry
ExB drift curvature plays a major role

• step 1 establishment of large poloidal ExB
  drift at LCFS
• step 2 curvature effects trigger symmetric
  inhomogeneities

No curvature effect at equatorial plane
LFS
top
N
N
N
?
?
?
Bottom, normal ?B
Bottom, reverse ?B
Equatorial, normal ?B
20
Origin of the Mach number asymmetry
ExB drift curvature plays a major role

• step 1 establishment of large poloidal ExB
  drift at LCFS
• step 2 curvature effects trigger symmetric
  inhomogeneities
• step 3 ExB drift advects the density and breaks
  the symmetry

LFS
top
ExB
ExB
N
N
N
?
?
?
Bottom, normal ?B
Bottom, reverse ?B
Equatorial, normal ?B