1 mhd simulation on pellet plasmoid in lhd r. ishizaki and n. nakajima 6 th japan-korea workshop on...
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MHD simulation on pellet plasmoid in LMHD simulation on pellet plasmoid in LHDHD
R. Ishizaki and N. Nakajima
6th Japan-Korea Workshop on Theory and Simulation of Magnetic Fusion Plasmas
NIFS, Toki, JAPANJuly 28 – 29, 2011
National Institute for Fusion Science
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1.1. It is observed in tokamak experiments that the ablation cloud drifts to the lower field side. It is observed in tokamak experiments that the ablation cloud drifts to the lower field side.
2.2. The ablation cloud dose not approach the core plasma in LHD even if the pellet is injected The ablation cloud dose not approach the core plasma in LHD even if the pellet is injected from the high field side. from the high field side.
Introduction.Introduction.
Baylor, Phys. Plasmas 7, 1878 (2000)
Sakamoto, 29th EPS conference on Plasma Phys. and Contr. 26B, P-1.074 (2002)
High field Low field
Plasmoid
Pellet
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Topics : Drift motionTopics : Drift motion1. P.B.Parks and L.R.Baylor, Phys. Rev. Lett. 94, 125002 (2005).1. P.B.Parks and L.R.Baylor, Phys. Rev. Lett. 94, 125002 (2005). Theory, no resistivity, constant B-fieldTheory, no resistivity, constant B-field2. R.Samtaney et al., Comput. Phys. Commun. 164, 220 (2004).2. R.Samtaney et al., Comput. Phys. Commun. 164, 220 (2004). Ideal MHD simulation, pellet is point source with ablation modelIdeal MHD simulation, pellet is point source with ablation model3. V.Rozhansky et al., Plasma Phys. Control. Fusion 46, 575 (2004).3. V.Rozhansky et al., Plasma Phys. Control. Fusion 46, 575 (2004). No resistivity, constant B-field, pellet is point source, mass and moment eqNo resistivity, constant B-field, pellet is point source, mass and moment eq
uationsuations4. H.R.Strauss and W.Park, Phys. Plasmas 7, 250 (2000).4. H.R.Strauss and W.Park, Phys. Plasmas 7, 250 (2000). Ideal MHD simulation, pellet is plasmoid, no heatingIdeal MHD simulation, pellet is plasmoid, no heating
The other works on motion of the ablation cloud.The other works on motion of the ablation cloud.
1. In order to clarify the drift motion in LHD plasmas, MHD simulation has been carried out.
2. The plasmoid motions are evaluated in various configurations (LHD, tokamak, RFP and vacuum field) in order to obtain the universal understanding.
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1.1. Code, geometry and basic equations.Code, geometry and basic equations.
2.2. Simulation results on drift motions of plasmoiSimulation results on drift motions of plasmoidsds
①① TokamakTokamak②② LHDLHD③③ RFPRFP④④ Vacuum fieldVacuum field
3.3. Consideration about simulation results.Consideration about simulation results.
OUTLINE.OUTLINE.
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CAP code and numerical scheme.CAP code and numerical scheme.
1.1. We are developing the CAP code in order to investigate the dynaWe are developing the CAP code in order to investigate the dynamics of the pellet ablation. (Multi-phase code)mics of the pellet ablation. (Multi-phase code)
R. Ishizaki et al, Phys. Plasmas, 11 4064 (2004).R. Ishizaki et al, Phys. Plasmas, 11 4064 (2004).
2.2. MHD version of the code has been developed in order to investigMHD version of the code has been developed in order to investigate the plasmoid motion in torus plasmas.ate the plasmoid motion in torus plasmas.
R. Ishizaki and N. Nakajima, J. Plasma and Fusion Res. SERIES 8, 995 (2009).R. Ishizaki and N. Nakajima, J. Plasma and Fusion Res. SERIES 8, 995 (2009).
3.3. A plasmoid induced by pellet ablation has locally and extremely lA plasmoid induced by pellet ablation has locally and extremely large perturbation, namely nonlinear one, in which the plasma bearge perturbation, namely nonlinear one, in which the plasma beta is > 1. Therefore, Cubic-interpolated pseudoparticle (CIP) metta is > 1. Therefore, Cubic-interpolated pseudoparticle (CIP) method is used in the code in order to solve such a large perturbation hod is used in the code in order to solve such a large perturbation stably.stably.
T. Yabe and P.Y. Wang, J. Phys. Soc. Jpn 60, 2105 (1991).T. Yabe and P.Y. Wang, J. Phys. Soc. Jpn 60, 2105 (1991).
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u
JBut
B
HJuupdt
dp
uBBpdt
du
udt
d
222
2
0
3
41
3
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Geometry and basic equations.Geometry and basic equations.
Z
R
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Poloidal cross sections in LHD.Poloidal cross sections in LHD.
Horizontally elongated cross section
Saddle point
Coil
Direction of lower field side
Vertically elongated cross section
Saddle point
R
Lowest field Highest field
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1.1. Code, geometry and basic equations.Code, geometry and basic equations.
2.2. Simulation results on drift motions of plasmoiSimulation results on drift motions of plasmoidsds
①① TokamakTokamak②② LHDLHD③③ RFPRFP④④ Vacuum fieldVacuum field
3.3. Consideration about simulation results.Consideration about simulation results.
OUTLINE.OUTLINE.
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Configurations and plasmoid locations.Configurations and plasmoid locations.
LH-i : LHD LH-o : LHD LV-i : LHD
T-i : Tokamak R-i : RFP V : Vacuum field
Lowest field
Highest field
Direction of lower field side
1010
A plasmoid is located inside in the horizontal cross section. A plasmoid is located inside in the horizontal cross section.
LH-i : LHD
1111
LH-o : LHD
A plasmoid is located outside in the horizontal cross section.A plasmoid is located outside in the horizontal cross section.
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LV-i : LHD
A plasmoid is located inside in the vertical cross section.A plasmoid is located inside in the vertical cross section.
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T-i : Tokamak
A plasmoid is located inside in the tokamak.A plasmoid is located inside in the tokamak.
0.0
2.0
4.0
6.0
8.0
10.0qprof.9.dat
0.0 0.2 0.4 0.6 0.8 1.0
r/a
1414
~ 0.15q ~ 0.1
~ 1Bp/BT ~ 1
R-i : RFP
A plasmoid is located inside in a RFP-like plasma.A plasmoid is located inside in a RFP-like plasma.
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A plasmoid is located in a 1/R vacuum field.A plasmoid is located in a 1/R vacuum field.
V : Vacuum field
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Simulation results.Simulation results.
LH-i LH-o LV-i
T-i R-i V
Back and forth Outward
Hardly drift
Outward Inward Outward
Outward/inward : positive/negative direction of major radiusOutward/inward : positive/negative direction of major radius
Direction of lower field side
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1.1. Code, geometry and basic equations.Code, geometry and basic equations.
2.2. Simulation results on drift motions of plasmoiSimulation results on drift motions of plasmoidsds
①① TokamakTokamak②② LHDLHD③③ RFPRFP④④ Vacuum fieldVacuum field
3.3. Consideration about simulation results.Consideration about simulation results.
OUTLINE.OUTLINE.
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is dominant among forces in all cases.is dominant among forces in all cases.10 BB
110110211011 2/ BBBBBBBBBpF
LH-i : LHD LH-o : LHD LV-i : LHD
T-i : Tokamak R-I : RFP V : Vacuum field
0 : equilibrium1 : perturbation
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coordinateCylinder :),,(
plasmoid the by induced onPerturbati:
mEquilibriu:
1
0
ZR
B
B
FFRR consists of two forces. consists of two forces.
R
BBBB
R
BBBBBBeF R
RRR101
010
1010
LH-i : LHD LH-o : LHD LV-i : LHD
T-i : Tokamak R-I : RFP V : Vacuum field
Second term Second term
First term First term
First term
2020
The first term inThe first term in F FRR depends on the connection length. depends on the connection length.
LH-i : LHDT-i : Tokamak
plasmoid the within section cross poloidal the on Average:
R
BBBB
R
BBBBF R
RR101
010
10
2 0B
/1
RB
/1RB
20B10t
2 0B
20B
Plasmoid
/1RB
/1
RB
7t
length Connection:cL
R
BB
L
BB
c
R 1010
2121
A leading term in A leading term in FFRR is determined by the connection length. is determined by the connection length.
R
BB
L
BBF
c
RR
1010
cL
M
RLc
aRLc
RqRLc
0/110 RR
BBFR
aL
BBF
c
RR /110
o-LH//
i-LV i,LH/
1010
10
RBBLBB
LBBF
cR
cRR
Vacuum field
Tokamak
RFP-like
LHD
010 R
BBFR
length Connection:cL
cL2
cL2
LH-i
LH-o
T-i
LV-i
1/R forceFreidberg, Ideal MH
D
2222
The dipole field is created around the plasmoid.The dipole field is created around the plasmoid.
0B
R
B1
B1
FR
0B
R
Perturbed magnetic field becomes Dipole field.
B1
B1
dense
sparse
What is the first term?R
BBBBF R
R101
0
field magnetic Perturbed:1RBLH-i : LHD
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A plasmoid is located inside in the horizontal cross section.A plasmoid is located inside in the horizontal cross section.
LH-i : LHD
0B
R
Dipole field
B1
B1
dense
sparse
R
BBBBF R
R101
0
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Summary.Summary.
◯ ◯ For systematic understanding of the drift of pellet plasmoid, For systematic understanding of the drift of pellet plasmoid, An MHD version of CAP code has been developed with CIP scheme. An MHD version of CAP code has been developed with CIP scheme. Various configurations; LHD, Tokamak, RFP-like and vacuum field, are invVarious configurations; LHD, Tokamak, RFP-like and vacuum field, are inv
estigated for the first time. estigated for the first time.
◯ ◯ The drifts of the pellet plasmoid are summarized as follows: The drifts of the pellet plasmoid are summarized as follows: 1.1. It is found that the pellet plasmoid motions in various configurations can be It is found that the pellet plasmoid motions in various configurations can be
explained by using the connection length. explained by using the connection length.
2.2. Especially, the motions in LHD are different from one in tokamak. This fact Especially, the motions in LHD are different from one in tokamak. This fact qualitatively explains the difference on the experimental results between tokqualitatively explains the difference on the experimental results between tokamak and LHD.amak and LHD.
◯ ◯ Future work: Future work: 1.1. We will obtain the results about drift motion of a plasmoid induced by ablatiWe will obtain the results about drift motion of a plasmoid induced by ablati
on from a moving pellet.on from a moving pellet.