MHD simulation on ellet injection in LHD. Ishizaki and N. Nakajima National Institute for Fusion Science 17 th Numerical Exeriment of Tokamak Meeting Tokyo Univ., Kashiwa, JAPAN 15-16 March 212
Introduction 1. It is observed in tokamak exeriments that the ablation cloud drifts to the lower field side. Plasmoid Pellet aylor, Phys. Plasmas 7, 1878 (2) 2. The ablation cloud dose not aroach the core lasma in LHD even if the ellet is injected from the high field side. High field Low field Sakamoto, 29 th EPS conference on Plasma Phys. and Contr. 26, P-1.74 (22) 2
The other works on motion of the ablation cloud. Toics : Drift motion 1. P..Parks and L..aylor, Phys. ev. Lett. 94, 1252 (25). Theory, no resistivity, constant -field 2..Samtaney et al., Comut. Phys. Commun. 164, 22 (24). Ideal MHD simulation, ellet is oint source with ablation model 3. V.ozhansky et al., Plasma Phys. Control. Fusion 46, 575 (24). No resistivity, constant -field, ellet is oint source, mass and moment equations 4. H..Strauss and W.Park, Phys. Plasmas 7, 25 (2). Ideal MHD simulation, ellet is lasmoid, no heating 1. In order to clarify the drift motion in LHD lasmas, MHD simulation has been carried out. 2. The lasmoid motions are evaluated in various configurations (LHD, tokamak, FP and vacuum field) in order to obtain the universal understanding. 3
CAP code and numerical scheme. 1. We are develoing the CAP code in order to investigate the dynamics of the ellet ablation. (Multi-hase code). Ishizaki et al, Phys. Plasmas, 11 464 (24). 2. MHD version of the code has been develoed in order to investigate the lasmoid motion in torus lasmas.. Ishizaki and N. Nakajima, J. Plasma and Fusion es. SEIES 8, 995 (29). 3. A lasmoid induced by ellet ablation has locally and extremely large erturbation, namely nonlinear one, in which the lasma beta is > 1. Therefore, Cubic-interolated seudoarticle (CIP) method is used in the code in order to solve such a large erturbation stably. T. Yabe and P.Y. Wang, J. Phys. Soc. Jn 6, 215 (1991). 4
Geometry and basic equations. Z d u dt du 1 dt d dt u u J t u u 2 1 u 4 3 4 3 2 2 J 2 H 5
Poloidal cross sections in LHD. Direction of lower field side Saddle oint Coil Saddle oint Lowest field Highest field Horizontally elongated cross section 6 Vertically elongated cross section
Configurations and lasmoid locations. LH-i : LHD LH-o : LHD LV-i : LHD Lowest field Direction of lower field side Highest field T-i : Tokamak -i : FP V : Vacuum field 7
Simulation results. LH-i LH-o LV-i ack and forth Outward Direction of lower field side T-i -i V Hardly drift Outward Inward Outward Outward/inward : ositive/negative direction of major radius 8
1 is dominant among forces in all cases. F 2 1 1 1 / 1 1 1 1 1 2 : equilibrium 1 : erturbation LH-i : LHD LH-o : LHD LV-i : LHD T-i : Tokamak -I : FP V : Vacuum field 9
1 ) : Cylinder coordinate,, ( : Perturbation induced by the lasmoid : Equilibrium 1 Z F consists of two forces. e F 1 1 1 1 1 LH-i : LHD LH-o : LHD LV-i : LHD T-i : Tokamak -I : FP V : Vacuum field Second term Second term First term First term First term
The first term in F deends on the connection length. F 1 1 1 1 L 1 1 c L c : Connection length T-i : Tokamak LH-i : LHD t 7 2 t 1 2 1 / Plasmoid 1 / : Average on the oloidal cross section within the lasmoid 11
A leading term in F is determined by the connection length. F L c 1 1 T-i L c : Connection length Tokamak q L c LHD L c M L c F Vacuum field F F 1 1 / Lc / L 1 c 1 1 1/ 1/ force Freidberg, Ideal MHD / LH i, LV - i LH - o LH-i 2L c LV-i FP-like L c a F L 1 1/ c a LH-o 2L c 12
The diole field is created around the lasmoid. F 1 1 What is the first term? LH-i : LHD 1 : Perturbed magnetic field dense 1 1 sarse 1 Perturbed magnetic field becomes Diole field. F 1 13
Initial conditions. 1. LHD lasma axis 3.75 m 3.6% 2. Initial conditions of lasmoids Pellet Case 1: Case 2 : Case 3 : Case 4 : Case 5 : 3.42 m 3.52 m 3.62 m 3.72 m 3.82 m Case A : V. m/s Case : V 3.61 4 m/s 14
Plasmoid densities on the oloidal cross sections. t 6.15 sec. Case 1A : 3.42 m, V. m/s Case 5A : 3.82 m, V. m/s Case 1 : 3.42 m, V 3.61 4 m/s Case 5 : 3.82 m, V 3.61 4 m/s 15
Dislacements of the lasmoids. Case A : V. m/s Case : V 3.61 4 m/s =3.42 m =3.52 m =3.62 m =3.72 m =3.82 m Initial_velocity t 15 ( t 6.15 sec.) 1. The lasmoid drift with the initial velocity in the initial hase. 2. However, the effect of the initial velocity becomes small in the lasmoid motion because of deceleration due to the magnetic field. 3. The dislacement hardly deend on the initial 16 velocity.
The force acting on the lasmoid is determined by the connection length. Case 1A : V. m/s Case 5A : V. m/s Leading force F 1 Lc Diole 1/ 1 Case 1 : V 3.61 4 m/s Case 5 : V 3.61 4 m/s L c 1 : connection length : equilibrium : erturbation (,, Z) : cylinder Case 1 Case 5 The effect of initial velocity becomes small because the lasmoid is decelerated by the force due to diole.
Summary and future work. Summary The drifts of the ellet lasmoid are summarized as follows: 1. It is found that the ellet lasmoid motions in various configurations can be exlained by using the connection length. 2. Esecially, the motions in LHD are different from one in tokamak. This fact qualitatively exlains the difference on the exerimental results between tokamak and LHD. Deendence of an initial velocity: 1. The effect of an initial velocity is small wherever an initial lasmoid is located on the horizontally elongated oloidal cross section. 2. That effect is small even if the initial velocity is 3.6 x 1 4 m/s because of deceleration due to the force by the diole field. Future work 1. The deendence on injection angle (e.g. tangential direction) will be investigated. 2. We will investigate behavior of a lasmoid which a ellet with an initial velocity induces, and clarify suitable condition of ellet injection in the LHD.