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Model prediction of impurity retention in ergodic layer and comparison with edge carbon emission in LHD
(Impurity retention in the ergodic layer of LHD)
M. Kobayashi, Y. Fenga, S. Morita, M.B. Chowdhuri, M. Goto, K. Sato, S. Masuzaki, I. Yamada, K. Narihara, H. Funabaa, N. Tamura, Y. Nakamura, T. Morisaki, N. Ohyabu, H. Yamada, A. Komori, O.
Motojima and the LHD experimental group
National Institute for Fusion Science,322-6 Oroshi-cho, Toki 509-5292, Japana Max-Planck-Institute fuer Plasmaphysik, Wendelsteinstrasse 1, D-17491 Greifswald,
Germany
18th PSI 26-30 May 2008, Toledo, Spain
2
Implication of impurity screening at high density operation
Even at very high density operation with more than
1021 m-3 & peaked density profile,
no significant impurity accumulation Zeff < 2
Implication of a possible mechanism of impurity retention (screening) in the edge region.
Neo classical transport model in core region can not interpret it.
3
1D impurity transport model along B field lines
iii
iii
TT
VTn
//5.2
0
//2/5~
>1 impurity retention
Introduction : Condition for impurity retention in 1D model
iz
siiz TZm
CVV //2
////
Condition for impurity retention
forcethermal
forcefriction score SOL
LCFS
targ
et
Ti
dTi/ds
ViII
Recycling
friction ion thermal force
dominant terms
....6.271.01 22
//
s
TZ
s
TZZeE
VVm
s
nT
nt
Vm ie
s
ziz
zi
z
zz
In force balance, impurity velocity becomes,
iz
sii TZ
mCV //
2//
Impurity retention : dense and cold plasma, flow acceleration, suppress //-grad T.
Z-independent
Outline of the talk
1. Introduction : IDB plasma with Zeff < 2
2. 3D impurity transport modelling in LHD
Geometrical effect on impurity transport
3. Comparison with experiments
Density dependence of carbon emission
4. Summary
5
Basic field structure: island overlapping stochastic
poloidal
radial
10/8
10/710/6
10/2
10/3
10/4
10/5
Low-order islands m/n
ConfinementRegion*
StochasticRegion*
Edge surfaceLayers*
*Terminology: N. Ohyabu et al., Nucl. Fusion, Vol. 34, No.3 (1994)
Connection length / m
radial
poloidal
6
3D modelling of LHD edge region (EMC3-EIRENE)
Boundary conditionsBohm condition at divertor platesPower entering the SOLDensity on LCMSSputtering coefficient
SOLPSOL
Core plasma
LCMS
wall
targ
et
EMC3
Div
erto
rle
gs
C0
H,H2
Computational mesh, configuration and installations Core, CX-neutral transport, particle source SOL, EMC3 simulation domainVacuum of plasma*
Cross-field transport coefficients e=i=3D roughly holdsspatially constant (global transport) determined experimentally
Example of LHD helical divertor
Physics modelStandard fluid equations of mass, momentum, ion and electron energyTrace impurity fluid model (Carbon)Kinetic model for neutral gas (Eirene)
7
From thermal-force to friction-dominated impurity transport
Plasma ion flow nvII
Thermal force dominant inward flow
friction dominant outward flow
Carbon density distribution
Impurity flow
Impurity flow
nLCMS=2×1019 m-3
3×1019
4×1019
(1018 m-3)1.0
0.1
0.01
Incr
ease
ne
1010
1011
1012
1013
1014
60 65 70
rad_P08_D0.5_SHI1.5_C3_NUP4
reff (cm)
stochastic
edge surface
0.0
0.2
0.4
0.6
0.8
0
2
4
6
60 65 70
rad_P08_D0.5_SHI1.5_C3_NUP4
reff (cm)
0
1
2
3
4
0
100
200
60 65 70
rad_P08_D0.5_SHI1.5_C3_NUP4
reff (cm)
Edge surface layers : effective retentionStochastic region : flat profile (suppression of thermal force)
Edge surface
Stochastic
0.1
1
10
60 65 70r
eff (cm)
stochastic edge surface
2e19 m-3
3e19 m-3
4e19 m-3
Carbon density
thermal
friction
9
poloidal
radi
al
Te/eV
0
190
Island structure affects plasma transport
m/n=10/3
10/5
10/7
R / cm
Te
/ e
V
* Thomson (t=1.24,1.27,1.3)EMC3/EIRENE*
EMC3-EIRENE
10
Reduction of II-conductive heat flux by -transport
i252 q
dr
dTT
dr
dTn i
iii
i/
1D radial energy transport for ions:
i
i
iT
n
2
25
/
If << 1 (long connection length),-heat conduction makes significant contributions.
Condition for significant reductionof parallel ion heat conduction:
(Y .Feng, Nucl. Fusion 46 2006)
IIdl
dr
rcore SOL
LCMS
targ
et
Ti w
w/o
qII
q II
upstream
downstream
q
~10-4 (LHD)
11
109
1010
1011
1012
0.60 0.65 0.70
rad_imp_P08_NUP4.0
reff (m)
C+1
C+2
C+3
C+4
C+5
C+6
C(all)
109
1010
1011
1012
0.60 0.65 0.70
rad_imp_P08_NUP2.0
reff (m)
C+1
C+2
C+3
C+4
C+5
C+6C(all)
4Z 3Z
nup=4e19 m-3nup=2e19 m-3
edge surface layer
accumulation retention
Clear separation of profile between C+1~C+3 & C+4~C+6
Impurity retention : C+1,C+2,C+3 C+4,C+5,C+6
Impurity density profiles of different charge states
Ionization potential :CIII (C+2) : 48 eVCIV (C+3) : 65 eVCV (C+4) : 392 eVCVI (C+5) : 490 eV
big gap
Spectroscopy
Density dependence of carbon emission : indication of impurity retention
CIII: 977Å, 1S22S2-1S22S2P (VUV monochromators)CIV: 1548Å, 1S22S-1S22P (VUV monochromators)CV: 40.27Å, 1S2-1S2P (EUV spectrometer)
Absolutely calibrated100
101
0 2 4 6 8
CIII/neCIV/neCV/ne
lin. avg. ne (e19 m-3)
Exp.
(a)
101
102
0 2 4 6 8
CIII/neCIV/neCV/neCIII/ne w/o frictionCIV/ne w/o frictionCV/ne w/o friction
ne (1019 m-3)
Model
(b)
CV/ne
CIII/ne
CIV/neCIII/ne w/o fric.
CIV/ne w/o fric.
CV/ne w/o fric.
Other works : Impurity transport analysis of ergodic layer
D.Kh. Morozov et al., POP 2 (1995) 1540.
Importance of friction of background plasma to exhaust impurity.M.Z. Tokar, POP 6 (1999) 2808
Core carbon content (C6+) reduction with decreasing edge Te in Tore Supra.Y. Corre et al., NF 47 (2007) 119
Y. Feng et al. NF 46 (2006) 807 (W7-AS)M. Kobayashi et al. CPP 48 (2008) 255 (LHD)
Prediction of impurity retention @ high density with 3D modelling
Viscosity terms related to thermal flux.
14
Summary
The impurity transport in the ergodic layer of LHD is analyzed, using the edge transport code (EMC3-EIRENE) in comparison with edge carbon emission.
Magnetic field structure of the ergodic layer in LHD : Edge surface layer : short and long flux tubes coexist.Stochastic region : remnant islands with Lc > ~ 100 m.
Plasma transport, particle and energy, follows the island structure as confirmed by the 3D modelling as well as experiments.3D code predicts impurity retention in the ergodic layer :
Flow acceleration in edge surface layersCross-field transport prevents large // T drop suppress thermal
force.Good agreement in carbon emission btw 3D modelling & exp. :
Indication of impurity retention in ergodic layer by friction force.The retention model could apply also for high Z impurity :
Balance btw friction & thermal force is Z-independentHigh Z impurity has shorter neutral penetration length than low Z impurity.