23P073-P
MHD simulation of pellet injection in LHD
LHDにおけるペレット入射のMHDシミュレーション
Ryuichi Ishizaki, Noriyoshi Nakajima
石崎 龍一, 中島 徳嘉
National Institute for Fusion Science322-6 Oroshi-cho, Toki 509-5292, Japan
核融合科学研究所 〒509-5292 土岐市下石町322-6
In order to clarify the difference on the motion of a plasmoid induced by a pellet injection between
tokamak and helical plasmas, MHD simulations have been carried out in a tokamak and Large Helical
Device (LHD) configurations. It is found that the plasmoid motion depends on the initial location of theplasmoid in the LHD, whereas the plasmoids drift in the direction opposite to that of the curvature vector ina tokamak. It is also verified that there are two main forces acting on the plasmoid, and the connection
length determines the dominant force.

1. Introduction
It is well known that an ablation cloud; a highdensity and low temperature plasmoid, drifts tothe lower field side in tokamak plasmas, whichleads to a good performance on fueling intokamak [1]. Such a good performance, however,has not been obtained yet in Large Helical Device(LHD) experiments [2]. In order to clarify thedifference on the plasmoid motions between
tokamak and LHD, the tree-dimensional (3D)MHD code of ablation processes (CAP) [3] hasbeen developed to investigate plasmoid motions.
2. Plasmoid motion in the LHD
An initial plasmoid is located inside the torus on
the horizontally elongated cross section in the LHD
as shown in Fig. 1. A circle is an initial plasmoid
whose peak values of density and temperature of
the plasmoid are 1000 times the density and 1/1000
times the temperature of the bulk plasma,respectively. The plasmoid, whose half width is0.03, encounters electrons with a fixed temperatureof 1.0 keV and density of 0.8 x 1020 m-3 [4]. The
helical plasma has a saddle point of the magnetic
pressure on the poloidal cross section. Then, theplasmoid is located at the lower field side than thesaddle point and the curvature vector is positive inthe major radius direction. The simulation result isshown in Fig. 2. It is found that the plasmoid drifts
slightly back and forth in the direction of the major
radius. This result is different from one in thetokamak because the plasmoid drifts to the lowerfield side in the tokamak. The dominant force
acting on the plasmoid is expressed by thefollowing equation [5]:Bϕ 0 Bϕ 1(1)∂B+ B0 R1
FR = −∂lR
where the cylindrical coordinate (R, φ, Z) is used.

B0 is the equilibrium magnetic field and B1 is theperturbation of the field induced by the plasmoid.
The first term represents 1/R force due to thetoroidal field. The second term is the force inducedby the dipole field around the plasmoid. Figure 3(a)shows ∂B / ∂l and B 2 along the toroidal
R10angle, where brackets show the average on thepoloidal cross section within the plasmoid. It isfound that ∂B / ∂l and B 2 have similar
R10behaviors. Figure 3(b) shows those values in aconventional tokamak. The connection length
in the LHD is shorter than one in the tokamak
because the LHD has ten toroidal pitches.
∂B / ∂l and B 2 have similar behaviors
R10also in the tokamak. Therefore, thecharacteristic length of ∂B / ∂l can beR1

regarded as the connection length. The second
term in Eq. (1) can be approximately expressed by
B0BR1/Lc. Lc is the connection length which depends
on the magnetic configuration.

Fig.1. Horizontally elongated poloidal cross section.
Colors and contours show the magnetic and plasmapressures. Circle represents initial plasmoid.

Since Lc is long in the tokamak, the first term
becomes dominant in FR. On the other hand, since
Lc is short in the LHD, the second term becomes

(a)

B02

∂BR1 / ∂l

B02∂B R 1 / ∂l

(b)

B02
∂B R 1 / ∂lB02∂BR1 / ∂ldominant. Then, the plasmoid motions between in
the tokamak and LHD are different.
The temporal evolution of the magnetic field
perturbation is shown in Fig. 5. The dipole fields
appear as shown in Fig. 5(a) at first, andsubsequently the deformation of the fields isinduced and the plasmoid drifts across the flux
surface. However, the poloidal field prevents theplasmoid from drifting. Thus, the poloidal
component of the magnetic field perturbation isinduced inside the plasmoid in Fig. 5(b). The
poloidal component becomes small in Fig. 5(c) andsubsequently it is induced outside the plasmoid inFig. 5(d). They are corresponding to the motion thatthe plasmoid drifts slightly back and forth in thedirection of the major radius.

Plasmoid

Fig.3. Horizontally elongated poloidal cross section.
Colors and contours show the plasma and magneticpressures. Circles represent initial plasmoids.

(a)

(b)

(c)

(d)

Fig.2. Density profiles at t = 0 (red), 1 (green), 2 (blue)and 3 (pink) as a function of the major radius, R.

3. Summary
It is verified by simulations using the CAP codethat the motions of the plasmoids with a highpressure induced by heat flux are different between
a tokamak and the LHD. Although the plasmoids
drift in the direction opposite to the magnetic
curvature vector in a tokamak, vacuum toroidal
field, RFP-like configurations, the plasmoid slightly
drifts back and forth in the major radius direction
when it is initially located inside the torus on thehorizontally elongated poloidal cross section in theLHD. The plasmoid motion is determined mainly
by 1/R force due to the toroidal field and the force
due to the dipole field induced by the diamagnetic
effect. The former forces imply drifts in thedirection opposite to the curvature vector which aredominant in the tokamak. Since the latter forces aredominant when the plasmoids are located inside thetorus in the LHD, the plasmoid motions in the LHD
differ from those in a tokamak. It is verified that theconnection length determines the force that
dominates the plasmoid motion. This may explain
the difference in the behavior of the plasmoid
motion between in a tokamak and the LHD.

Fig.4. Plasmoids (red) and magnetic field perturbations(blue) at (a) t = 0.16, (b) 1.5, (c) 2.3 and (d) 2.6.
References[1] L. R. Baylor et al., Phys. Plasmas, 7 (2000) 1878.
[2] R. Sakamoto et al., in proceedings of 29th EPS
conference on Plasma Phys. and Contr. Fusion, 26B,P-1.074 (2002).
[3] R. Ishizaki et al., Phys. Plasmas, 11, (2004) 4064.
[4] R. Sakamoto et al., Nucl. Fusion, 46, (2006) 884.
[5] R. Ishizaki and N. Nakajima, Plasma Phys. Control.
Fusion, 53 (2011) 054009.