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Numerical Simulation of Profile Evolution
during SMBI at HL-2A with BOUT++
Z H Wang1,2, X Q Xu2, T Y Xia3, P W Xi4, L H Yao1
1Southwestern Institute of Physics, Chengdu, China
2Lawrence Livermore National Laboratory, Livermore, CA 94550, USA 3Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, China
4School of Physics, Peking University, Beijing, China
Presented at
54th Annual Meeting of APS Division of Plasma Physics
Providence, Rhode Island, Oct 29-Nov 2, 2012
This work was performed under the auspices of Southwestern Institute of Physics, Chengdu, China and the U.S. Department of Energy by Lawrence Livermore National Security, LLC, Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. LLNL-PRES-598432.
Outline
• Motivation
• Physical Model
• Numerical Results
Transport During SMBI
SMBI at Low and High Plasmas
Comparisons Between SMBI and GP
Comparisons Between Simulation and Experiment
• Conclusions and Future Plans
2
SMBI Fuelling for Fusion
Laval
• SMBI (Supersonic molecular beam injection) is a simple and efficient fuelling source
by comparing with GP (gas puffing) and Pellet injection fueling methods.
– Results in a high density, directed particle source, with fuelling efficiencies often
in excess of 30%.
• SMBI is an useful tool for density control to
– maintain plasmas within stable operational boundaries
– actively manage deleterious ELMs
• SMBI is also an useful tool for:
– Confinement improvement, such as L-H transition
– Perturbative transport study, i.e., nonlocal transport
3
BOUT++ has been originally developed for modeling tokamak edge
turbulence* and is extending to include neutrals for 3Dplasma transport
BOUT++ is an unique code to simulate boundary
plasma turbulence in a complex geometry
− Proximity of open+closed flux surface
− Presence of X-point
BOUT++ is being to include neutrals for 3D plasma
transport in a new trans-neut module
− B2, SOLPS and UEDGE are 2D plasma transport
codes
− Added BOUT++ capabilities can handle the
localized 3D sources for neutrals, and late on for
impurities.
• X.Q. Xu and R.H. Cohen, Contrib. Plasma Phys. 38, 158 (1998), Xu, Umansky, Dudson & Snyder, CiCP, V. 4, 949-979 (2008);
• Dudson, Umansky, Xu et al., Comp. Phys. Comm. V.180 (2009) 1467; Xu, Dudson, Snyder et al., PRL 105, 175005 (2010).
4
Process of Molecule Reaction
5
2H 02HSupersonic Molecular Beam
SMB Molecules Atoms
Dissociation
Plasmas
eHHe 0
2 2
eH 22
Ionization
Charge Exchange(CX)
eHHe 20
HHHH 00
CXIdissVVV At Edge
plasma
Peter C. Stangeby The Plasma Boundary of Magnetic Fusion Devices, Institute of Physics publishing, 2000
Franck-Condon
scmeVTeVTVV eeethdissethI
3228
,, 1.031.0103ˆˆˆˆ
scmeVeVT
eVeVTV
i
iithCX /
)15(150
)15(5.1109.1107.1 3
3/13/1
3/13/1
88
,
Physical Model (1) - Plasmas
6
p
Ii
c
iiii SND=NV
t
N ˆˆˆˆˆˆ
ˆ2
||||
e
ie
i
ebinddissdissIeIe
c
eee
i
e TT
M
mWWWTTT
N=
t
T
ˆ
ˆˆ2ˆˆˆ3
2ˆ3
2ˆˆˆˆ3
2ˆˆˆ3
2
ˆ
ˆ2
||||||
aiICX
ii
ii
ii
ii
iVV
MN
PV
MN=VV
t
V||||
||
||||
0
||||||||
|| ˆˆˆˆˆˆ
ˆˆˆ
ˆˆ
1
3
4ˆˆˆ
ˆ
e
ie
i
eiIi
c
iiiii
i
iii TT
M
mTTVTT
N=TV
t
T
ˆ
ˆˆ2ˆˆˆˆ3
2ˆˆ3
2ˆˆˆ3
2ˆˆˆ
ˆ2
||||||||||||||
ethIaI VN ,ˆˆˆˆ
ithCXaCX VN ,ˆˆˆˆ
Ie
p
I NS ̂ˆˆ
CXi
p
CX NS ̂ˆˆ 00
25
||ˆ2.3ˆ
eieeie tTMM
00
25
||ˆ9.3ˆ
iiii tT
ethdissmdiss VN ,ˆˆˆˆ
Quasi-neutral ie NN ˆˆ
00,,
0
,||ˆˆ96.0ˆ
iiaiaiai tTN ithVLt ,00
Physical Model (2) - Atoms
diss
p
Ia
c
aaaa SSND=NV
t
N ˆ2ˆˆˆˆˆˆ
ˆ2
||||
a
a
dissai
a
CX
aa
a
aa
aa
aa
aV
N
SVV
MN
PV
MN=VV
t
V||||||
||
||||
0
||||||||
|| ˆˆ
ˆ2)ˆˆ(ˆ
ˆˆ
ˆˆˆ
ˆˆ
1
3
4ˆˆˆ
ˆ
a
CXai
c
a MTD ̂ˆˆˆ
Where, ethIe
a
I VN ,ˆˆˆˆ
ithCXi
a
CX VN ,ˆˆˆˆ
iaa TNP ˆˆˆ
7
dissediss NS ̂ˆˆ
ethdissmdiss VN ,ˆˆˆˆ
ia TT ˆˆ Due to ion CX, assumption:
Strong numerical instability
Flux limited conditions: min
,ˆˆˆ
aath
fl
a LVD
1
ˆ
1
ˆ
1ˆ
c
a
fl
a
e
aDD
D
Physical Model (3) - Molecules
dissmxmxm S=NV
t
N ˆˆˆˆ
ˆ
8
Local Const. Flux Boundary
xm0V̂
0ˆ
mN
][0258.0][300ˆ eVKTm
Flux limited thermal conductivities are also applied:
Constant room temperature
mm
mxxmxxm
xm
MN
P=VV
t
V
ˆˆ
ˆˆˆ
ˆ
ˆ
Where, mmm TNP ˆˆˆ dissediss NS ̂ˆˆ
1
||||
||ˆ
1
ˆ
1ˆ
j
fl
j
e
j
095,||ˆˆˆ LqV jth
fl
j iej ,
GP Model
0ˆxm0 V
Circular HL-2A Geometry w/ X point
9
mR
Z m[ ]
B
00 NNm
smVm /5000
Plasma Radial B.C.
;1.0 02
NNRi eVT
Rie 102
, SMBI
outside mid plane
iiesei MTTcV )(||
seeieeese cTNTq ||||||
seiiiiisi cTNTq ||||||
0|| iN
5.2i 7e
Parallel Sheath B.C.
319
0 /101 mN
1R
2R
0 2
0
ma 42.0mR 65.10
Private flux region B.C.
R1 and same as:
Sheath
12
2,0 21
;260ˆ
ˆ
1
R
iN
14000
ˆ
ˆ
1
,
R
ieT
smc
i
c
e /1ˆˆ 2
smDc
i /1 2
10
rad
mR
rad
mR mR
rad
mR
rad
2D Plasmas Profiles at Steady State Before SMBI
][ 0NNi ][eVTe
][eVTi]/[|| smV i
319
0 /101 mN
separatrix
separatrix
mR 03.2separatrix
separatrix
Neutrals Propagate First Inwards then Outwards due to Competition between Fueling Rate and Ionization/Dissociation Rate during SMBI Plotted at Outside Mid Plane
11
][mR][mR
][ 0NNa][ 0NNm
0.0 4.0 6.0 8.0 0.12.0 0.0 5.0 0.1 5.1 0.2
ms05.0mst 3.2
ms10.0ms15.0ms20.0
ms4.0mst 5.2
ms8.0ms2.1ms6.1][ 0NNa][ 0NNa
]/1[ sa
I ]/1[ sa
I
5.2
0.3
5.3
0.4
319
0 /101 mN
separatrix mR 03.2
separatrix mR 03.2
][mst
Ionization rate peeked inside separatrix Ionization rate peeked outside separatrix
Plasma Profiles Variation During Neutrals Inwards and Outwards Propagation Plotted at Outside Mid Plane
12
][mR ][mR ][mR
ms05.0mst 3.2
ms10.0ms15.0ms20.0
ms4.0mst 5.2
ms8.0ms2.1ms6.1
ms05.0mst 3.2
ms10.0ms15.0ms20.0
ms4.0mst 5.2
ms8.0ms2.1ms6.1
ms05.0mst 3.2
ms10.0ms15.0ms20.0
ms4.0mst 5.2
ms8.0ms2.1ms6.1
][ 0NN i ][eVTe ][eVTi319
0 /101 mN
separatrix mR 03.2
During SMBI, density increases while temperature decreases
separatrix
13
][rad ][rad ][rad
ms05.0mst 3.2
ms10.0ms15.0ms20.0
ms05.0mst 3.2
ms10.0ms15.0ms20.0
][ 0NN i ][eVTe][eVTi
Parallel Plasma Transports Due to Parallel Ion Velocity and Thermal Conductivities Plotted at R=2.04m
ms05.0mst 3.2
ms10.0ms15.0ms20.0
ms05.0mst 3.2
ms10.0ms15.0ms20.0
ms05.0mst 3.2
ms10.0ms15.0ms20.0
ms05.0mst 3.2
ms10.0ms15.0ms20.0
]/[|| smV i]/[ 2
0|| smNe ]/[ 2
0|| smNi
SMBI
319
0 /101 mN
SMBI creates poloidal locality
14
Poloidal Propagation of Plasma Density Ni During SMBI
0 10 20 30 4015 20 2510500.0 5.0 0.1 5.1 0.2
0 20 40 60 8030 40 6020100 5030 40 5020100
mst 35.2 mst 4.2
mst 45.2
mst 3.2
mst 5.2 mst 55.2
][mR ][mR ][mR
][mZ
][mZ
319
0 /101 mN ][ 0NNi ][ 0NNi ][ 0NNi
SMBI creates poloidal density blobs
15
2D Profiles of Plasmas and Neutrals Right after SMBI
rad
mR
rad
mR
rad
mR
rad
mR
rad
mR mR
rad
][eVTi][eVTe
]/[|| smV i
][ 0NNi
Nm[N0 ] Na[N0 ]
319
0 /101 mN
separatrix mR 03.2
separatrix mR 03.2
16
Plasmas Profiles Relaxing after SMBI to Reach Steady States Determined by Boundary Conditions Plotted about 10ms after SMBI
rad
mR
rad
mR mR
rad
][ 0NNi
mR
rad
319
0 /101 mN ][eVTe
][eVTi]/[|| smV i
Ni needs much more time to get steady state
separatrix mR 03.2
separatrix mR 03.2
After SMBI plasma density increases by about 100%
Neutrals Penetration Depths Influenced by Low and High Plasma Density and Temperature Profiles Plotted at Outside Mid Plane
17
][mR
][ 0NNa][ 0NNm
0.0 4.0 6.0 8.0 0.12.0 0.0 5.0 0.1 5.1 0.2
4.3
6.3
8.3
0.4
][mst
2.1
][mR
][mst
Low Ni Low Tei
keVTRie 1
1,
021
NNRi
Low Ni High Tei
High Ni Low Tei
keVTRie 1
1,
041
NNRi
4.3
6.3
8.3
0.4
4.3
6.3
8.3
0.4
][mst keVTRie 5
1,
021
NNRi
keVTRie 1
1,
021
NNRi
keVTRie 1
1,
041
NNRi
keVTRie 5
1,
021
NNRi
319
0 /101 mN
separatrix mR 03.2separatrix SMBI penetrates deeper in colder plasmas
Plasma Profiles Evolution during SMBI at Different Low and High Initial Plasma Density and Temperature Plotted at Outside Mid Plane
18 ][mR
][eVTe][ 0NN i
][mst
][mst
Low Ni Low Tei
Low Ni High Tei
High Ni Low Tei
4.3
6.3
8.3
0.4
4.3
6.3
8.3
0.4
200 40 8060 100 2000 400 800600 1000
200 40 8060 2000 400 800600
1000 2000 40003000 5000
1000
319
0 /101 mN
separatrix separatrix ][mR
5 10 2015
][mst
0
4.3
6.3
8.3
0.4
30 025
19
Neutrals Penetrate Deeper Using SMBI than GP
][mR][mR
][ 0NNa][ 0NNm
0.0 4.0 6.0 8.0 0.12.0 0.0 5.0 0.1 5.1 0.2
5.2
0.3
5.3
0.4
5.2
0.3
5.3
0.4
][mst
][mst SMBI SMBI
GP GP
edge localized
319
0 /101 mN
separatrix separatrix
Plasma Density Increases and Temperature Decreases More during SMBI than GP Plotted at Outside Mid Plane
20
][mR ][mR ][mR
ms05.0mst 3.2
ms10.0ms15.0ms20.0
ms05.0mst 3.2
ms10.0ms15.0ms20.0
ms05.0mst 3.2
ms10.0ms15.0ms20.0
][ 0NN i ][eVTe ][eVTi
ms05.0mst 3.2
ms10.0ms15.0ms20.0
ms05.0mst 3.2
ms10.0ms15.0ms20.0
ms05.0mst 3.2
ms10.0ms15.0ms20.0
SMBI
GP
319
0 /101 mN
separatrix mR 03.2
separatrix
SMBI provides more efficient fueling source
21
Total Injected Particles within 2ms SMBI in Simulation is about the Same Order as that in Experiment
319
0 /101 mNm smVm /5000
SMBI
ma 42.0
mstinjc 2
19
00
1008.2
injcinjcmmtotal tSNVN
208.22 mRwSinjc
0mT
0mN0mV
dwRmR 07.2
Yu DL et al NF 2012 52 082001
mw 16.0
Experiment Simulation
22
Line Averaged Plasmas Density and Temperatures Qualitatively Consist with Experiments
Yu DL et al NF 2012, 52 082001 Yao L H et al NF,2001, 41 817
][eVTe
][mst
cmR 195 cmZ 5.3
]1.0[ 0NNi
][mst
319
0 /101 mN
][mst0 10 15 205
0
2
46
][eVTi
][eVTe
][ 0NNi
400
500
600
400
500
600][eVTi
][eVTe
][ 0NNi
0 10 15 20502468
10
300
400
200
300
400
SMBI fueling efficiency ~ 30%
Simulation Simulation
Experiment Experiment
Conclusions and Future Plans • A eight-field physical model of fueling has been developed to study 3D
neutrals and plasmas transport and during SMBI (or GP);
• A new BOUT++ module trans_neut code has also been developed and the
simulations of SMBI in a real HL-2A geometry with X point has been done;
• In colder plasmas, the neutrals penetrate into the separatrix during SMBI
while neutrals are difficult to penetrate into the separatrix during GP;
• However, in hotter plasmas, neutral penetration depth decreases during SMBI
due to the increase of dissociation and ionization rates;
• Line averaged plasma density increases and temperatures decrease have been
observed during SMBI which are consistent with the experiments;
• Easily turn on the toroidal direction simulation in trans_neut code to study 3D
neutrals and plasmas transport;
• More Physics of SMBI fueling will be studied, such as fueling efficiency,
penetration depth, ELM mitigation etc.
23