23P100-P
Study of toroidal flow generation by the ICRF minority
heating in the Alcator C-Mod plasma
Alcator C-Mod プラズマにおける ICRF 少数イオン加熱時のトロイダル流駆動のシミュレーション研究
S. Murakami, K. Itoh1 , L.J. Zheng2 , J.W. Van Dam2 , P. Bonoli3 , J.E. Rice3 ,C.L. Fiore3 and A. Fukuyama
村上定義，伊藤公孝 1 ，L.J. Zheng2 , J.W. Van Dam2 , P. Bonoli3 , J.E. Rice3 ,C.L. Fiore3 ，福山淳
Department of Nuclear Engineering, Kyoto University, Sakyo, Kyoto 606-8501, JAPAN京都大学工学研究科原子核工学専攻 〒 606-8501 京都市左京区吉田本町
1National Institute for Fusion Science, NINS, Toki 509-5292, JAPAN1
核融合科学研究所，自然科学研究機構，〒 509-5292 土岐市下石町３２２−６2
Institute for Fusion Study, The University of Texas at Austin, Austin, Texas 78712-0262, USA2
テキサス大学オースティン校核融合研究所，オースティン，テキサス 78712-0262, USA
3
Plasma Science & Fusion Center, MIT, Cambridge, Massachusetts 02139, USA
3
プラズマ科学・核融合研究センター，MIT ，ケンブリッジ，マサチューセッツ 02139, USA
The toroidal ﬂow generation by the ICRF minority heating is investigated in the Alcator C-Mod
plasma applying GNET code, in which the drift kinetic equation is solved in 5D phase-space. It isfound that a co-directional toroidal ﬂow is generated outside of the RF wave power absorption region
and that the dominant part of toroidal ﬂow does not depend on the sign of kk . The averaged toroidal
ﬂow velocity reaches about 30% of central ion thermal velocity (PICRF ∼ 1.7MW). When we change
the sign of the toroidal current we obtain a reversal of the toroidal ﬂow velocity, which is consistent
with the experimental observations. We show that the toroidal precession motion of energetic tail ionsaccelerated by the ICRF heating plays an important role in generating the averaged troidal ﬂow. We
also compare with the experimental results about the RF resonance location and plasma parameter
dependencies.

1

Introduction

minority ions is analyzed and the radial proﬁleof the toroidal ﬂow is evaluated. In the simulaImportant role of the plasma ﬂow and its shear in tion we assume a tokamak plasma similar to thethe transport improvement is suggested by many Alcator C-Mod plasma (R = 0.67m, r ∼ 0.21m,
experimental observations, e.g. H-mode transi- Bt ∼ 5.5T).
tion, ITB formation, RWM suppression. In a future reactor the driving of the plasma ﬂow by NBI
2 Simulation Model
heating is not eﬃcient and other driving method isrequired. The spontaneous toroidal ﬂow has been In order to study the ICRF minority heating inobserved during ICRF heating with no direct mo- cluding ﬁnite orbit eﬀect we have developed amentum input in JET[1], Alcator C-Mod[3] and global simulation code, GNET[4, 5], which canetc. Many theoretical studies have been done. solve a linearized drift kinetic equation for enerHowever, further study is necessary to make clear getic minority ions, f , including complicatedminthe generating mechanism of spontaneous toroidal behavior of trapped particles in 5-D phase space
ﬂow during ICRF heating.
∂fmin
In this paper we study the toroidal ﬂow gener+ (vk + vD ) · ∇fmin + a · ∇vfmin(1)∂tation by the ICRF heating using GNET code[5,−C(fmin ) − QICRF (fmin ) − Lparticle = Sparticle
6, 7], which can solve a linearized drift kinetic
equation for energetic ions including complicated where C(fmin ) and QICRF (fmin ) are the linear
behavior of trapped particles in 5-D phase space. Coulomb Collision operator and the ICRF heatThe obtained steady state distribution of energetic ing term. Sparticle is the particle source term by

ionization of neutral particle and the radial proﬁleof the source is evaluated using AURORA code.
4 10The particle sink (loss) term, Lparticle , consists of
3 10
two parts; one is the loss by the charge exchange
2 10
1 10loss assuming the same neutral particle proﬁle as0
the source term calculation and the other is the-1 10
loss by the orbit loss escaping outside of outer-2 10
most ﬂux surface.
-3 10
00.2
0.4
0.6
0.8
1Using GNET code we study the toroidal shear
r/a
ﬂow generation by ICRF minority heating in theAlcator C-Mod Plasma. The resonant magnetic Figure 1: Radial profile of flux averaged toroidal flow.
ﬁeld strength Bres is set to be 5.1T and the location of the resonance in the minor radius, r, is30
80
about r/a = 0.3.
70
Toroidal flow [A.U.]

2121212121212125
203

Simulation Results

151060504030v⊥ \/ vth020
100We perform the simulation using GNET code un5til we obtain a steady state distribution of en0
ergetic minority ions solving Eq. (2). We as-20 -15 -10 -50510 15 20
sume the following plasma parameters; ne0 ∼v\/\/ \/ vth08 × 1019 m−3 , T0 ∼ 3.2keV and B0 =5.4T. The amplitude of RF electric ﬁeld, E0+ , is set to 4.0kV/m. Figure 2: Contour of the flux surface averaged velocity
The parallel wave number, kk , is assumed to be space distribution, ln fmin , of the minority ion at the|kk | = 5m−1 and the perpendicular wave number radial regions; r/a = 0.75 in the broad heating case.
is k⊥ =50m−1 .
We can see a broader proﬁle of the toroidal ﬂux Referencesin Fig. 1. The ﬂux value at the peak position(r/a ∼ 0.7) is similar with that of the local heating[1] L-G. Eriksson, Plasma Phys. Control. Fusion 39(1997) 27.
case[5] and the averaged velocity is about 30% ofion thermal velocity at the plasma center. The[2] M. P. Brown, and K. Austin, Appl. Phys. Lettersheating power is 1.7MW.
85, 2503–2504 (2000).
Figure 2 shows the contour of the ﬂux surface[3] J.E. Rice et al., Nucl. Fusion 45 (2005) 251.
averaged velocity space distribution, ln fmin , ofthe minority ion at the r/a = 0.75. We can see[4] T. Ohkawa, Phys. Plasmas 12 (2005) 094506.
a strong asymmetry in the parallel velocity direc[5] S. Murakami, et al., Proc. 23rd IAEAFusion Ention. This asymmetry enlarges in the radial reergy Conference, THW/P4-03 (2010).
gion r/a ∼ 0.75. Comparing with the local heating case[5] it is found that the asymmetry start[6] S. Murakami, et al., Nucl. Fusion 40 (2000) 693.
rather higher velocity in the broad heating case.
[7] S. Murakami, et al., Nucl. Fusion 46 (2006) S425.
This would be related to the RF power absorption
also occur in the region r/a > 0.5 in the broad
heating case.