Transcript Sustained Spheromak Physics eXperiment

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.
Density Limit Studies
•
Achieving high energy confinement at high density is important:
– fusion power: Pfus  n2 <v>
•
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
– open+closed flux surfaces
• BOUT is being applied to DIII-D, Cmod, 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 fluctuation
level/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 density
is 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: NG=Ip/a2
(with n: 1020 /m3, Ip : MA, a:m)
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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
Poloidal distance (cm)
ni [x,y,t] - ni[t=0] (1019 m-3)
8
4
0
0.69 ms
DIII-D
-2
0
0.86 ms
1.06 ms
2 x (cm)
3.0
Analytic neutral
model provides
source for density
build=up over ~1 ms
Rapid convective
transport to wall at
higher densities
Density
(1019 m-3)
2.0
1.0
1.17 ms
0.
1.22 ms
-0.5
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Blob vorticity at maximum density (0) and vorticity dipole
extrema(±)
wz
(MHz)
(+)
(0)
Poloidal y
(0) (+)
Time (s)
(-)
(-)
x(c
m)
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
d 2
Ni    || J || - 2 y Ni
dt
++++++ B X
Ux
Ey
---------
= 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
i)
Sheath-Connected blobs, where J// ~  and Ux ~ a-2, and
ii) 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 <Ux> ~ a0.
*Ryutov & Cohen, Contrib. Plasma Phys. 44 168 (2004).
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In BOUT simulations turbulence is found in
divertor leg region
Plot of spatial distribution of RMS
fluctuations amplitude shows that
fluctuations grow in regions of
unfavorable curvature
Cross-correlation plot shows
that divertor turbulence is not
correlated with upstream
turbulence
ref =38
upper
x-point
lower
x-point
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Results show that strong spatial dependence of
transport must be included
a) Typical previous model b) Our new coupled results
Results consistent with expt.
Experiment (DIII-D, C-Mod)
0.1
•
Open - DIII-D
Filled - C-Mod
0
2
4
Radial distance (cm)
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 >> || 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
today’s tokamaks and ITER
•
Fluid approximation requires:
mfp
T2


n
c
~ 2R
orbit
or width  plasma scale length

DIII-D Edge Barrier
mfp
 c
Orbit width
•
Not satisfied on DIII-D today
Won’t be satisfied on ITER
•
Need to move beyond fluid codes
 Describe each species with a
kinetic 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
– open+closed 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
(t)/(t0)
Rosenbluth-Hinton
Residual zonal flow
Collisionless damping
of zonal flow and GAM
 (t  )
1

 (t  0) 1 + 1.6 q 2

 0.02, q  2.23,   0.02
wGAMsim/wGAMth=1.06
Time(vti/R0)
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GAMs simulations converge with nv, n, and KEmax
ny=30, n=50, nE=30, n=15
ny=30, n=50, nE=60, n=30
ny=30, n=50, nE=100, n=50
ny=30, n=100, nE=60, nvy=30
ny=30, n=50, nE=30, n=15, KEmax=10
Rosenbluth-Hinton
Residual zonal flow
KEmax=15
rtol=10-7,
atol=10-12
r/R=0.02
q=2.23
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