1. 1 MHD simulation on pellet plasmoid in LHD R. Ishizaki and N. Nakajima 6 th Japan-Korea Workshop on Theory and Simulation of Magnetic Fusion Plasmas NIFS, Toki, JAPAN July 28 – 29, 2011 National Institute for Fusion Science

2. 2 1. It is observed in tokamak experiments that the ablation cloud drifts to the lower field side. 2. The ablation cloud dose not approach the core plasma in LHD even if the pellet is injected from the high field side. Introduction. Baylor, Phys. Plasmas 7, 1878 (2000) Sakamoto, 29 th EPS conference on Plasma Phys. and Contr. 26B, P-1.074 (2002) High fieldLow field Plasmoid Pellet

3. 3 Topics : Drift motion 1. P.B.Parks and L.R.Baylor, Phys. Rev. Lett. 94, 125002 (2005). Theory, no resistivity, constant B-field Theory, no resistivity, constant B-field 2. R.Samtaney et al., Comput. Phys. Commun. 164, 220 (2004). Ideal MHD simulation, pellet is point source with ablation model Ideal MHD simulation, pellet is point source with ablation model 3. V.Rozhansky et al., Plasma Phys. Control. Fusion 46, 575 (2004). No resistivity, constant B-field, pellet is point source, mass and moment equations No resistivity, constant B-field, pellet is point source, mass and moment equations 4. H.R.Strauss and W.Park, Phys. Plasmas 7, 250 (2000). Ideal MHD simulation, pellet is plasmoid, no heating Ideal MHD simulation, pellet is plasmoid, no heating 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.

4. 4 1. Code, geometry and basic equations. 2. Simulation results on drift motions of plasmoids ① Tokamak ② LHD ③ RFP ④ Vacuum field 3. Consideration about simulation results. OUTLINE.

5. 5 CAP code and numerical scheme. 1. We are developing the CAP code in order to investigate the dynamics 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. MHD version of the code has been developed in order to investigate 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. A plasmoid induced by pellet ablation has locally and extremely large perturbation, namely nonlinear one, in which the plasma beta is > 1. Therefore, Cubic-interpolated pseudoparticle (CIP) method is used in the code in order to solve such a large perturbation 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).

6. 6 Geometry and basic equations. Z R 

7. 7 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 fieldHighest field

8. 8 1. Code, geometry and basic equations. 2. Simulation results on drift motions of plasmoids ① Tokamak ② LHD ③ RFP ④ Vacuum field 3. Consideration about simulation results. OUTLINE.

9. 9 Configurations and plasmoid locations. LH-i : LHDLH-o : LHDLV-i : LHD T-i : TokamakR-i : RFPV : Vacuum field Lowest field Highest field Direction of lower field side

10. 10 A plasmoid is located inside in the horizontal cross section. LH-i : LHD

11. 11 LH-o : LHD A plasmoid is located outside in the horizontal cross section.

12. 12 LV-i : LHD A plasmoid is located inside in the vertical cross section.

13. 13 T-i : Tokamak A plasmoid is located inside in the tokamak.

14. 14  ~ 0.15 q ~ 0.1  ~ 1 B p /B T ~ 1 R-i : RFP A plasmoid is located inside in a RFP-like plasma.

15. 15 A plasmoid is located in a 1/R vacuum field. V : Vacuum field

16. 16 Simulation results. LH-iLH-o LV-i T-iR-iV Back and forthOutward Hardly drift Outward InwardOutward Outward/inward : positive/negative direction of major radius Direction of lower field side

17. 17 1. Code, geometry and basic equations. 2. Simulation results on drift motions of plasmoids ① Tokamak ② LHD ③ RFP ④ Vacuum field 3. Consideration about simulation results. OUTLINE.

18. 18 is dominant among forces in all cases. is dominant among forces in all cases. LH-i : LHDLH-o : LHDLV-i : LHD T-i : TokamakR-I : RFPV : Vacuum field 0 : equilibrium 1 : perturbation

19. 19 F R consists of two forces. LH-i : LHDLH-o : LHDLV-i : LHD T-i : TokamakR-I : RFPV : Vacuum field Second term First term

20. 20 The first term in F R depends on the connection length. LH-i : LHDT-i : Tokamak Plasmoid

21. 21 A leading term in F R is determined by the connection length. Vacuum field Tokamak RFP-like LHD LH-i LH-o T-i LV-i 1/R force Freidberg, Ideal MHD

22. 22 The dipole field is created around the plasmoid. B1B1 B1B1 FRFR Perturbed magnetic field becomes Dipole field. B1B1 B1B1 dense sparse What is the first term? LH-i : LHD

23. 23 A plasmoid is located inside in the horizontal cross section. LH-i : LHD Dipole field B1B1 B1B1 dense sparse

24. 24Summary. ◯ 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 investigated for the first time. ◯ The drifts of the pellet plasmoid are summarized as follows: 1. It is found that the pellet plasmoid motions in various configurations can be explained by using the connection length. 2. Especially, the motions in LHD are different from one in tokamak. This fact qualitatively explains the difference on the experimental results between tokamak and LHD. ◯ Future work: 1. We will obtain the results about drift motion of a plasmoid induced by ablation from a moving pellet.