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X.Q. Xu1, R.H. Cohen1, W.M. Nevins1, T.D. Rognlien1,
D.D. Ryutov1, M.V. Umansky1, L.D. Pearlstein1, R.H. Bulmer1,
D.A. Russell2, J.R. Myra2, D.A. D'Ippolito2,
M. Greenwald3, P.B. Snyder4, M.A. Mahdavi4
1) Lawrence Livermore National Laboratory, Livermore, CA 94551 USA2) Lodestar Research Corporation, Boulder, CO 80301 USA3) MIT Plasma Science & Fusion Center, Cambridge, MA 02139 USA4) General Atomics, San Diego, CA 92186 USA
Density Effects on Tokamak Edge Turbulence and Transport with Magnetic
X-Points*
Presented at the
IAEA Fusion Energy Conference
Vilamoura, Portugal
Nov. 1-5, 2004
* 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.
IAEA 11/3/04 2
Lodestar MIT GA
Goal: understand role of edge-plasmas on limiting high-density operation
• High density can increase fusion power (Pfus):
Pfus n2 <v>
• Tokamaks usually disrupt when the Greenwald limit is exceeded
– 1- current profile shrinkage 2 MHD instability
3 disruption
– Greenwald empirical scaling
nG = Ip/a2
– higher density with central peaking implies an edge limit
IAEA 11/3/04 3
Lodestar MIT GA
Goal: understand role of edge-plasmas on limiting high-density operation
• High density can increase fusion power (Pfus):
Pfus n2 <v>
• Tokamaks usually disrupt when the Greenwald limit is exceeded
– 1- current profile shrinkage 2 MHD instability
3 disruption
– Greenwald empirical scaling
nG = Ip/a2
– higher density with central peaking implies an edge limit
Our turbulence/transport simulations provide details of an edge-plasma collapse ==> current profile shrinkage
IAEA 11/3/04 4
Lodestar MIT GA
We have progressively improved edge turbulence and transport models together with basic understanding
1. Turbulence behavior with density
– turbulence for fixed densities
– short-time profile evolution
– plasma “blob” formation and dynamics
2. Long-time transport effects
– coupling BOUT to 2D UEDGE for wall recycled neutrals
– role of impurity radiation
3. X-point & divertor leg effects
– X-point shear decorrelation
– a new beta-dependent divertor instability
Turbulence model is 3D BOUT code• Braginskii --- collisional, two-fluids• full X-point geo. with separatrix
• electromagnetic with A||
IAEA 11/3/04 5
Lodestar MIT GA
Saturated fluctuations for 3 densities: high collisionality drives turbulent transport up& parallel correlation down
b) 0.58xNG
c) 1.12xNG
a) 0.28xNG
• Base-case (a): radial ni and Te,i profiles from DIII-D expt. tanh fit
• Two other cases (b,c) with 2x and 4x density together with 0.5x and 0.25x temperatures
IAEA 11/3/04 6
Lodestar MIT GA
Large perpendicular turbulence transport can exceed parallel transport at high density
D as n , D exhibits a nonlinear increase with n strong-transport boundary crossed• Large turbulence reduces Er shear layer allowing large transport to extend inwards
IAEA 11/3/04 7
Lodestar MIT GA
Numerous simulations varying density, Ip, and Bt show strong turbulence consistent with experimental limits
• P0 = n0T0 held fixed while n0 changes
• q held fixed while Ip changes
• No change w/ Bt while Ip is fixed
• Transport coefficients measured at separatrix
Greenwald Limit: nG=Ip/a2
IAEA 11/3/04 8
Lodestar MIT GA
Profile-evolving simulation shows generation and convection of plasma “blobs” as density increases
• Ion density evolved for ~1 ms from ionization of neutral source
• Neutral density has spatial form
nn= n0 exp(x/xw);
xw = (icx)1/2;
mimics wall recycling
• Turbulence develops stronger ballooning character with blobs
QuickTime™ and aYUV420 codec decompressor
are needed to see this picture.
6
8
2
0
4
Po
loid
al d
ista
nce
(c
m)
-2 0 2x (cm)
ni [x,y,t] (1019 m-3)
-0.6 0.0 0.6 1.2 1.8 2.4 3.0
DIII-D
Separatrix
IAEA 11/3/04 9
Lodestar MIT GA
Profile-evolving simulation shows generation and convection of plasma “blobs” as density increases
ni [x,y,t] - ni[t=0] (1019 m-3)
DIII-D
Po
loid
al d
ista
nce
(c
m)
-2 0 2 x (cm)
8
0
4
0.
-0.5
1.0
3.0
2.0
Density (1019 m-3)
1.22 ms 1.17 ms
1.06 ms 0.86 ms 0.69 ms
• Analytic neutral model provides source for density build=up over ~1 ms
• Rapid convective transport to wall at higher densities
IAEA 11/3/04 10
Lodestar MIT GA
Characteristics of localized, intermittent “blobs” determined from detailed diagnostics of simulation data
(+d)
(-d)
0 1 2 3
(m)
Vo
rtic
ity
(MH
z)
Radial distance from sep. (cm)
0
4
-4
• 3D turbulence in realistic X-point geometry generates edge blobs
• Higher density results in stronger turbulence giving robust blobs
• Vorticity: = 2
• Example shows blobs spinning with monopole vorticity (m), which decays, allowing convective dipole vorticity (+d,-d) to develop
Spinning blob
Convecting blob
Spatial history for 1 blob
d
(+d)
Time (s)
Po
loid
ial
y (c
m)
Vorticity as density blob (contours) passes
1
0
10 20
IAEA 11/3/04 11
Lodestar MIT GA
Regimes of blob edge-plasma transport understood through analytic analysis
See Poster TH/P6-2, D. A. D’Ippolito, et al., Friday, 16:30
Current continuity eqn: J = 0 becomes • Analysis identifies parallel resistivity & X-point magnetic shear as key in blob velocity vs size, a
– Sheath-connected: Vr ~ a-2
– X-point J: Vr ~ a-1/3
– And others, …
iyi NJdt
dN 2||||
2
Curvature charge separation
Parallel charge transport
Perpend. charge transport; X-point shear
+ + + + +
- - - - -
E ExB/B2Ion BElectron B
IAEA 11/3/04 12
Lodestar MIT GA
For long recycling timescales, we have coupled self-consistent edge turbulence/transport simulations
• Density profile converges more rapidly than turbulent fluxes
a) Midplane density profile evolution b) Midplane diffusion coeff. evolution
Coupling iteration index is mTurbulence Transport
BOUT UEDGE
profiles
fluxes
IAEA 11/3/04 13
Lodestar MIT GA
Results show that strong spatial dependence of transport substantially changes SOL and neutral distribution
a) Constant D model b) Coupled result
• Poloidal variation understood from curvature instability
a) Constant D model b) Coupled result
• Wall flux and recycling modifies midplane neutrals
Effective diffusion coefficient Neutral density distribution
IAEA 11/3/04 14
Lodestar MIT GA
2D transport modeling shows that large radial convection can lead to an X-point MARFE
• Mimic strong BOUT transport in UEDGE by a ballooning convective velocity varying from 0 to 300 m/s btwn. sep. & wall
• Compare no convection and strong convections cases
• Particle recycling and energy loss to radial wall included
• Stronger neutral penetration increases density and impurity radiation loss - higher resistivity
Self-consistent impurity transport still needed
IAEA 11/3/04 15
Lodestar MIT GA
Analysis of simulation shows decorrelation of turbulence between the midplane and divertor leg
Cross-correlations of BOUT data by GKV analysis package shows decorrelation by X-point magnetic shear
Poloidal/parallel spatial correlation midplane reference
Poloidal/parallel spatial correlation divertor reference
IAEA 11/3/04 16
Lodestar MIT GA
Te
New divertor-leg instability driven at “high” plasma-beta (density) by a radial tilt of the divertor plate.
• Unstable mode effectively does not reach X-point if growth rate is large enough, Im > vA/L
• Instability is absent if no plate tilt and increases for larger outward tilt
• Localized mode exists (Im > 1) only if plasma beta high enough
• The mode reduces the divertor heat load without having direct impact on the main SOL
~
~
IAEA 11/3/04 17
Lodestar MIT GA
Summary and ongoing work
• Increasing edge density (or collisionality) in X-point geometry
– drives increasing turbulence that becomes very large “near” nGW
– generates robust blobs – strong radial transport hastens edge
cooling (neutrals, impurities)
• X-point magnetic shear– causes decorrelation between
midplane and divertor leg, large k
– modifies blob dynamics as well as resistive instabilities
• Plate (outward) tilt yields new finite-beta divertor instability
We are working to:
• Couple Er for long-time turbulence/transport evolution
• Include self-consistent impurities
• Enhance expt. comparisons
• Simulate divertor-leg instability
• Develop a 5D kinetic edge code