Transcript Document

Max-Planck-Institut für Plasmaphysik
Comparison of 2D Models for the Plasma Edge with
Experimental Measurements and Assessment of
Deficiencies
A.V.Chankin and D.P.Coster
Acknowledgements:
L.K.Aho-Mantila, N.Asakura, X.Bonnin, G.D.Conway, G.Corrigan, R.Dux,
S.K.Erents, A.Herrmann, Ch.Fuchs, W.Fundamenski, G.Haas, J.Horacek,
L.D.Horton, A.Kallenbach, M.Kaufmann, Ch.Konz, V.Kotov, A.S.Kukushkin,
T.Kurki-Suonio, B.Kurzan, K.Lackner, C.Maggi, H.W.Müller, J.Neuhauser,
R.A.Pitts, R.Pugno, M.Reich, D.Reiter, V.Rohde, W.Schneider, S.K.Sipilä,
P.C.Stangeby, M.Wischmeier, E.Wolfrum
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Outline
Introduction: 2D edge fluid codes
Measurements and simulations of:
- parallel ion flow in SOL
- divertor and target parameters
- Er in SOL
Possible causes of discrepancies between modelling and experiment
Summary
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Main 2D edge fluid codes for SOL and divertor modelling
SOLPS: B2-Eirene (AUG), EDGE2D-Nimbus,Eirene (JET), UEDGE-DEGAS (DIII-D)
- Plasma description: collisional parallel transport model,
with kinetic limiters for transp. coeff.;
anomalous perp. coefficients, drifts included
- Neutrals description: kinetic Monte-Carlo codes,
inside and outside of computational grid
Computational grid
and vessel structures
separatrix
Physical and chemical sputtering from surfaces
Multiple impurity charged states
input
power
Consensus (prior to 2000): 2D edge fluid codes
reproduce existing experiments within a factor of 2
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Parallel ion SOL flow in JET – comparison with EDGE2D
reciprocating
probe
[S.K.Erents et al., PPCF 2000 & 2004]
56723 Normal Field q95 = 2.93
59737 Reverse Field q95 =3.00
56723 Normal Field q95 = 2.75
56737 Reverse Field q95 = 2.84
59723 Normal Field q95 =2.54
56737 Reverse Field q95 = 2.67
Average
reciprocating
probe
Normal Bt
ballooning
JG
04
.6
1-
30
c
Average
Reversed Bt
Distance from Separatrix (Mid-plane mm)
Parallel flow: ballooning + drift
Bt-independent
(Average flow)
Bt-dependent
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Parallel ion SOL flow in JET – comparison with EDGE2D
EDGE2D: Mach No.
0.1
Mach number
0.1
0.05
0
Normal Bt
Ohmic case,
-3
ns=7.3e18 m
-0.05
recipr.
probe
EDGE2D: Mach No.
0.05
0
Normal Bt
Ohmic case,
-0.1
-3
ns=5.3e18 m
-0.05
-0.1
Reversed Bt
-0.2
-0.25
0.02
0.03
0.04
Distance from separatrix [m]
56723 Normal Field q95 = 2.93
59737 Reverse Field q95 =3.00
56723 Normal Field q95 = 2.75
0
0.01
0.02
0.03
0.04
Distance from separatrix [m]
56737 Reverse Field q95 = 2.84
59723 Normal Field q95 =2.54
56737 Reverse Field q95 = 2.67
Average
30
c
0.01
-0.2
-0.25
04
.6
1-
0
Reversed Bt
-0.15
JG
-0.15
reciprocating
probe
Normal Bt
Average
EDGE2D underestimates effect of Bt reversal
by factor ~ 3
UEDGE underestimates effect of Bt reversal in
JT-60U by factor 2 [N.Asakura et al., 2004]
Reversed Bt
Distance from Separatrix (Mid-plane mm)
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Parallel flows in JT- 60U and TCV: effect of Bt reversal
JT-60U: measured ion flow at outer midplane
agrees with Pfirsch-Schlüter ion flow formula:
Same conclusion for TCV
[R.A.Pitts et al., EPS-2007]
[N.Asakura, et al., PRL 2000]
V||PS   sinθ
2 q  dpi

 enE r 

enB  dr

 Measured flows
are consistent with
P-S formula, when
pi, Er … are taken
from experiment
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Parallel flow in SOLPS: simulating AUG Ohmic shots
0.25
Mach number M
of ||parallel ion flow
0.2
SOLPS - direct
Parallel flow
at outer midpl.
0.15
..
SOLPS - Pfirsch-Schluter
0.1
0.05
V||PS   sinθ
0
1.3
2 q  dpi

 enE r 

enB  dr

0.8
19 -3
Separatrix density (10 m )
0.5
 Simulated flows are consistent with P-S formula (pi, Er … - from code)
But: simulated flows are below measured in AUG by factor 3 (as in JET)
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Simulated vs. measured parallel ion flows
Both in the codes and experiments, flows are broadly consistent with
Pfirsch-Schlüter formula (at outer midplane position)
But absolute values in codes < experimental by factors 2-3
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SOLPS simulations of AUG divertor conditions
Fitting experimental outer midplane profiles by choice of D,e, i
H-mode #17151
D: #17151
Ohmic #18737
Ohmic #21320
SOLPS: #12096
5
Edge Thomson
scattering
4
Lithium beam
3
SOLPS
2
1
0
800
700
600
500
400
300
200
100 Electron
temperature
0
core
101
10 0
SOL
[L.D.Horton
et al., 2005]
-1
i neoclassical
-0.02
e = i
D perp.
e
i
10
Ion temperature
0
 


0.02
Distance from separatrix [m]
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SOLPS simulation of AUG divertor conditions - results
 For matching upstream profiles and boundary conditions, in medium to
high density plasmas, SOLPS predicts colder and denser plasma in divertor
than in experiment
At very low plasma ne,
SOLPS predicts AUG
target profiles reasonably
well [M.Wischmeier et al., 2007]
Conclusion confirmed by available evidence:
- target Langmuir probe data
- divertor spectroscopy: Ha, CIII emissions
- sub-divertor neutral flux
- carbon content at plasma edge
H-mode #17151: Ha,code > Ha,exp
3
x 10
20
Ohmic #18737: Te,code < Te,exp , ne,code > n e,exp
Ha,CIII emission at outer target
4
3
separatrix
2.5
Ha SOLPS
2
2
1
0
1.05
Ha exp.
1.5
CIII exp. x 2
1
CIII SOLPS x 2
0.5
0
1.05
1.1
x 10
1.15
1.2
1.25
s(m) target (m)
distance along
1.3
25
20
15
10
5
0
1.05
19
Plasma density at outer target
sep.
ne Langmuir probes
ne SOLPS
1.1
1.15
1.2
1.25
1.3
Plasma temperatures at outer target
Te Langmuir probes
Te SOLPS
1.1
1.15
1.2
1.25
1.3
s(m)
distance along target (m)
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SOLPS simulation of AUG divertor conditions - results
 SOLPS fails to simulate large asymmetry between the targets, and detachment
at inner target [M.Wischmeier, et al., 2007]
 Talk by M.Wischmeier,
next session, O-25
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SOL flow and divertor discrepancies
target Te
(ne, recycling)
- SOLPS vs. AUG
-EDGE2D vs. JET
-SOLPS vs. AUG
-UEDGE vs. JT-60U
- SOLPS vs. AUG
- EDGE2D vs. JET
Debye
sheath
Radial electric field:
eEr  3 r Te,target
V||PS  2 cos
parallel ion SOL flows
SOL Er
a B  Er pi 



R B  B enB 
Ion V||
compensating
ErxB drift
 Lower target Te in codes and flatter Te profiles
 expect lower Er in codes than in experiment:
confirmed – see next
 Er underestimate in codes  SOL flow
underestimate
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SOL Er discrepancy – code results
Vp (plasma potential) and Te profiles across SOL at outer midplane
SOLPS modelling ASDEX Upgrade, EDGE2D modelling JET plasmas [Chankin et al.,NF 2007]
SOLPS: Te and plasma pot.
60
Normal Bt
Reversed Bt
40
Ohmic
EDGE2D: Te and plasma pot.
-3
ns=1.3e19 m
Te
60
Normal Bt
Reversed Bt
0
0
60
0.01
Te
0.02
eVp
40
0.03
Ohmic
0.04
-3
ns=8e18 m
20
0
0
0.01
0.02
0.03Ohmic
0.04
eVp
0
0
0.01
Te
0.02
0.03
Ohmic 0.04
-3
ns=5e18 m
eVp
50
0.05
-3
ns=5.3e18 m
60
20
-3
ns=7.3e18 m
eVp
40
20
Ohmic
40
Te
20
0
0
0
0
100
0.01
0.02
0.04
-3
ns=1.6e19 m
Te
0.02
0.03
Te
150
0.04
0.05
H-mode
-3
ns=1.4e19 m
100
eVp
eVp
50
0
0.03
H-mode
0.01
50
0
0.01
0.02
0.03
0.04
Distance from separatrix [m]
Flat SOL Vp profiles: eEr < |sTe |
0
0
0.01
0.02
0.03
0.04
0.05
Distance from separatrix [m]
 low -eEr/ sTe ratio
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Er from Langmuir probe measurements
Tokamak
ASDEX Upgrade*
JET
-eEr/ srTe
3.1
1.6
comments
standard Ohmic shot
[H-W.Müller, 2007]
average over Ohmic, L-mode,
H-mode shots
[K.Erents et al., 2004]
JT-60U
2.4
TCV
3.3 – 5.0
Alcator C-Mod
1.7 – 1.8
L-mode, middle of density scan
range [N.Asakura 2007]
Ohmic, middle of density scan
range [R.A.Pitts, I.Horacek, 2007]
Ohmic L-mode
[B.LaBombard et al., 2004]
*Similar values - from Doppler reflectometer measurements, when using probe sTe
Experimental -eEr/ srTe ratios in the SOL significantly exceed code
predicted values
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Potential causes of discrepancies
Neutrals
excessive ionisation due to
low perp. mobility in codes
role of fluctuations; problem of
time-averaging (ab  a  b)
[W.Fundamenski 2006, S.I.Krasheninnikov 2007]
7/2
q e||  k(T e,7/2

T
up
e,down )/L ||
Plasma
7/2
q e||  k( Te,7/2

T
up
e,down )/L ||
non-local kinetic effects of
parallel transport
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Non-local kinetic effects in SOL and divertor
(Focus on electrons since e|| >> i||)
Present 2D edge fluid codes (SOLPS/B2, EDGE2D, UEDGE) assume classical
(Spitzer-Härm/Braginskii) heat flow along field lines for ions and electrons
However, real heat conduction starts to deviate from classical collisional formula(s)
beginning with Lm.p.f. /LTe > 0.01 (typically ~ 0.1 in SOLs existing experiments,
and expected in ITER)
The deviation is due to: most of the parallel
heat flux being carried by supra-thermal electrons
with velocities:
v e  3  5 Te / me
Weakly collisional: Lm.p.f.  v e4
Standard corrections for kinetic effects in fluid
codes, introduction of “kinetic flux limiters” –
far insufficient (see later)
Contributions of electrons with different
velocities v to the heat flux qe
Kinetic effects:
- may increase parallel heat flux in divertor, Debye sheath
- affect atomic physics rates (ionisation, excitation)
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Example of existing kinetic codes
ALLA [Batishchev et al., 1996-1999]: Fokker-Planck code for ions and electrons,
with full Coulomb collision operator, kinetic neutrals, “logical sheath” condition
f
f q E|| f
 v||

 C (collisions & sources)
t
l||
m  v||
..
1D in physical space,
adaptive mesh
symmetry
plane
α  e, i
..
neutrals
heat flux
divertor
plate
0
L||
plasma core
400
300
2D in velocity space
(energies E||, E),
adaptive mesh
E|
T
Cells
0.08
v
E|
T
200
0
0
Axis
E|| / T
0.08
100
2
0
-300
-200
-100
0
100
E|| / T
th
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300
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Kinetic code results on parallel e
In upstream SOL plasma, depletion of supra-thermal electron population 
use of flux limiters for heat fluxes in fluid codes is justified.
Their values depend on plasma conditions and geometry of experiment
(variation 0.03 – 0.8 reported)
In divertor, parallel heat flux may exceeds classical 
instead of flux limiters, flux enhancements
e > e,Braginskii/Spitzer-Härm
[K.Lackner, et al., 1984]*
[R.Chodura, 1988]
[A.S.Kukushkin, A.M.Runov, 1994]
[K.Kupfer et al., 1996]
[O.V.Batishchev et al., 1997]
[W.Fundamenski, 2005] (review)
*Used a fit to kinetic results
by Luciani et al., 1983
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Kinetic code results on parallel e (cont.)
Consensus view reflected in:
Progress in the ITER Physics Basis [Nucl. Fusion 47 (2007) S1-S413]
Chapter 4: Power and particle control
Section 2: Experimental basis
Parallel energy transport is determined by classical conduction and
convection, with kinetic corrections to heat diffusivities χ ||i,e at low

(separatrix) collisionalities ν i, e
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Kinetic simulations for SOL of ASDEX Upgrade H-mode
Helsinki University of Technology & IPP Garching
ASCOT code, adapted for kinetic electron
transport in SOL of AUG H-mode shot #17151
[L.Aho-Mantila et al., 2008]
Test electrons are launched at outer midplane
with local Maxwellian distribution consistent
with Te of the background generated by SOLPS.
Electrons collide with the background plasma
and traced down to targets.
Test electron energy distributions at the targets
are recorded and compared with the target Te
of the background (SOLPS) plasma.
Fraction of total target electron heat flux carried
by supra-thermal electrons:  70 % near outer
strike point
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Are kinetic effects in SOL of AUG relevant for ITER ?
Yes: Ohmic plasmas in AUG at low-medium densities have similar separatrix
electron collisionality as that expected in ITER
AUG standard Ohmic #18737:
ITER H-mode scenario:
ne,sep = 1.3x1019m-3
ne,sep = 4x1019m-3
Te,sep = 47 eV
q95 = 4
R=1.7 m
Te,sep = 150 eV
q95 = 3
R=6.3 m
nee = 13.8
nee = 11.6
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Summary
 Discrepancies between 2D fluid edge codes and experiments:
- parallel ion SOL flow
- divertor parameters, target asymmetries
- Er in the SOL
 Outer target, Er and ion SOL flow discrepancies are related to each other and
caused by the codes tendency to underestimate divertor Te and overestimate ne
 Cause of the discrepancies is unknown, presently under investigation:
- neutrals treatment by kinetic Monte-Carlo codes
- role of fluctuations, present in experiments but missing in codes
- non-local kinetic effects of parallel electron transport
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Spares
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SOLPS simulation of AUG divertor conditions (cont.)
Satisfy experimental boundary conditions:
H-mode #17151
- Input power into the grid
D: #17151
- Particle balance: Gas puff, NBI source,
cryo-pump efficiency
- Power to target:  determine separatrix
position, density
SOLPS: #12096
5
Edge Thomson
scattering
4
Lithium beam
3
SOLPS
2
1
0
Input
power
Gas puff,
NBI source
800
700
600
500
400
300
200
100 Electron
temperature
0
core
101
10 0
Pumping
SOL
[L.D.Horton
et al., 2005]
i neoclassical
-0.02
e = i
D perp.
e
i
10-1
Ion temperature
0
0.02
Distance from separatrix [m]
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Some results (Batishchev et al. 1996-1999)
Parallel electron heat flux density, for case Te/Te = 10 (upstream to target Te ratio)
Lm.p.f. /L = 0.1, typical for the SOL of ASDEX Upgrade:
At hot end, depletion
of energetic electrons
At cold end, large surplus
of energetic electrons 
flux enhancement needed
(rather than flux limit)
1
v|| v2 f
0.8
0.6
0.4
hot
0.2
0
-0.2
-0.4
Braginskii
-0.6
4
8
2
6
0
E/T
cold
10
12
14
e >
e,Spitzer-Harm
 Solution for IPP: develop kinetic module for SOLPS(B2)
for parallel electron heat flux (later – also for ions)
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