11

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

22

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

33

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.

44

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.

55

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).

66

u

JBut

B

HJuupdt

dp

uBBpdt

du

udt

d

222

2

0

3

41

3

41

Geometry and basic equations.Geometry and basic equations.

Z

R

77

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

88

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.

99

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.

1212

LV-i : LHD

A plasmoid is located inside in the vertical cross section.A plasmoid is located inside in the vertical cross section.

1313

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.

1515

A plasmoid is located in a 1/R vacuum field.A plasmoid is located in a 1/R vacuum field.

V : Vacuum field

1616

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

1717

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.

1818

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

1919

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

2323

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

2424

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.