Density Effects on Tokamak Edge Turbulence and Transport with Magnetic XPoints

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Density Effects on Tokamak Edge Turbulence and
Transport with Magnetic X-Points
X.Q. Xu Lawrence Livermore National Laboratory,
Livermore, CA 94551 USA In collaboration with
R.H. Cohen, W.M. Nevins, T.D. Rognlien, D.D.
Ryutov, M.V. Umansky, L.D. Pearlstein, R.H.
Bulmer, D.A. Russell, J.R. Myra, D.A. D'Ippolito,
M. Greenwald, P.B. Snyder, M.A. Mahdavi
Presented at the PRC-US fusion workshop Dalian,
P.R.China May. 18-19, 2006
Work performed under the auspices of U.S. DOE
by the Univ. of Calif. Lawrence Livermore
National Laboratory under contract No.
W-7405-Eng-48 and is partially supported as LLNL
LDRD project 03-ERD-09.
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Density Limit Studies

• Achieving high energy confinement at high density
  is important
• fusion power Pfus ? n2 lt?vgt
• Density limits have been observed on Tokamaks,
  and other toroidal devices
• In tokamaks, the limit ultimately leads to
  disruptions
• Greenwald empirical scaling law works well
• nG Ip/?a2
• Tokamak scenario
• current profile shrinkage-?MHD
  instability?disruption
• what leads to the collapse of current profile?
• Over 40 years, many theoretical models have been
  developed, nothing is conclusive yet.
• Most work, to date, has concentrated on impurity
  radiation as the principal drive.

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A Density Limit Scenario from BOUT-UEDGE modeling

• After mode transition, either limiter or divertor
  configuration could lead to the density limit.
• Rapid edge cooling due to large radial transport
  is a key for the physics of the tokamak density
  limit.

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BOUT is 3D EM Boundary Plasma Turbulence Code

• Braginskii --- collisional, two-fluids
  electromagnetic equations
• Realistic X-point geometry
• openclosed flux surfaces
• BOUT is being applied to DIII-D, C-mod, NSTX,
  ITER (for Snowmass), ...
• LOTS of edge fluctuation data!
• BES, GPI, PCI, Probe, and Reflectometer
• Provide excellent opportunity for validating BOUT
  against experiments.
• BOUT benchmarked with UEDGE for 2D transport
  without neutrals

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A suite of the codes work together to make BOUT
simulation results similar to real experiments
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Density Limit High collisionality drives
fluctuationlevel/transport up parallel
correlation length down
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At high density, perpendicular turbulence
transport exceeds parallel transport, destroying
the edge shear layer

• D ? as n ? , D exhibits a discontinuous behavior?
  catastropic boundary crossed
• Destruction edge shear layer ? the region of
  large transport extends inward
• The same mechanism may operate in other
  configurations

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Large transport boundary vs current and
densityis consistent with expt. operational
limits

• q is held fix while Ip changes
• Transport coefficient at LCFS
• Large transport leads to a collapse of edge
  plasma

• P is held fix while n changes
• No change w/ Bt while Ip is fixed
• Greenwald Limit NGIp/?a2
• (with n 1020 /m3, Ip MA, am)

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Large perpendicular transport leads to an X-point
MARFE

• Use convective velocity Vr increasing from 0 to
  300 m/s between sep. and wall
• Vr peaked around outer midplane of SOL
• Large perpendicular transport yields peaked
  density and radiation near the X-point due to
  neutral penetration

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A simple analytical neutral mode added
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Profile-evolving simulation shows generation and
convection of plasma blobs as density increases
ni x,y,t - nit0 (1019 m-3)
Poloidal distance (cm)
1.06 ms
0.86 ms
DIII-D
0.69 ms
-2 0 2 x (cm)
Analytic neutral model provides source for
density buildup over 1 ms Rapid convective
transport to wall at higher densities
Density (1019 m-3)
1.22 ms
1.17 ms
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Blob vorticity at maximum density (0) and
vorticity dipole extrema()
Poloidal y
Time (?s)
Blobs are born near the separatrix with net
vorticity or rotation (0). The dipole ()
blossoms with detachment and persists after the
overall rotation has subsided. For
sheath-connected blobs, the rotation subsides on
the timescale of the electron temperature
relaxation since it is caused by the radial
gradient in the Bohm sheath potential Te(r).
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Blob Dynamics
Parallel Loss to X-points -
Curvature-Induced Charge Separation
The curvature drift separates charge within the
blob, generating a poloidal (dipole) electric
field and radial ExB velocity Ux.

• The velocity is found to be a simple function of
  blob size (a) for
• Sheath-Connected blobs, where J// ? and Ux
  a-2, and
• Disconnected blobs, where J// ?????a2 and Ux
  a-1/3 ,
• assuming, e.g., that the current loop is
  short-circuited by the ion polarization current
  near the X-points. This estimate is consistent
  with the simulation results ltUxgt a0.

Ryutov Cohen, Contrib. Plasma Phys. 44 168
(2004).
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Plot of spatial distribution of RMS fluctuations
amplitude shows that fluctuations grow in regions
of unfavorable curvature
In BOUT simulations turbulence is found in
divertor leg region
Cross-correlation plot shows that divertor
turbulence is not correlated with upstream
turbulence
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Results show that strong spatial dependence of
transport must be included
Results consistent with expt.
a) Typical previous model
b) Our new coupled results
Open - DIII-D Filled - C-Mod

• Poloidal variation understood from curvature
  instability

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Summary

• BOUT-UEDGE simulations show
• turbulence fluctuation levels and transport
  increase with collisionality
• Near density limit
• Mode transition resistive X-point resistive
  ballooning
• Er-well is destroyed
• ?r gtgt ? gives rapid edge cooling
• In divertor geometry, X-pt MARFE
• The rapid edge cooling mechanism due to large
  radial transport may work for other
  configurations
• BOUT simulations demonstrate
• Blob detachment from separatrix
• Monopole vorticity ?rotation, Dipole vorticity
  ?translation
• Turbulence zone near the separatrix, blob zone in
  the SOL
• Decorrelation of turbulence between the midplane
  and the divertor leg due to strong X-point
  magnetic shear

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A kinetic edge code is required to model both
todays tokamaks and ITER

• Fluid approximation requires
• Not satisfied on DIII-D todayWont be satisfied
  on ITER
• Need to move beyond fluid codes

DIII-D Edge Barrier
or
? Describe each species with akinetic
distribution function, F(a)(y, ?, ?, E0, ?,)
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Tempest is a 5D Continuum Edge Gyrokinetic Plasma
Code

• Gyrokinetic equations
• Valid for edge ordering
• Nonlinear Fokker-Planck collision
• Finite banana orbit
• Realistic X-point geometry
• openclosed flux surfaces
• Edge Simulation Laboratory
• Partners LLNL, GA, LBNL,UCSD
• Collaborators PPPL,LANL,MIT,LRC

Simulate neoclassical transport, turbulence and
plasma-Surface interactions
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Tempest exhibits collisionless damping of GAMs
and zonal Flow
f(t)/f(t0)
Rosenbluth-Hinton Residual zonal flow
Collisionless damping of zonal flow and GAM
wGAMsim/wGAMth1.06
Time(vti/R0)
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GAMs simulations converge with nv, nq, and KEmax
ny30, nq50, nE30, nm15
ny30, nq50, nE60, nm30
ny30, nq50, nE100, nm50
ny30, nq100, nE60, nvy30
ny30, nq50, nE30, nm15, KEmax10
KEmax15 rtol10-7, atol10-12 r/R0.02 q2.23
Rosenbluth-Hinton Residual zonal flow