24pE07PJT-60U トロイダル回転プラズマにおけるタングステン輸送の解析
Analysis of Tungsten Transport in JT-60U Toroidally Rotating Plasmas
清水 友介 1, 藤田 隆明 1, 岡本敦 1, 有本 英樹 1, 星野 一生 2, 林 伸彦 2, 仲野 友英 2, 本多充 2
Y.Shimizu1, T.Fujita1, A.Okamoto1, H.Arimoto1, K.Hoshino2, N.Hayashi2 etal.
1

名大工 2 原子力機構
Nagoya Univ. 2JAEA

1

2. PHZ Pinch for Rotating System
It is considered that bulk plasma and tungsten ions rotate
at the similar velocity. Considering in a system rotatingwith bulk plasma (rotating system), tungsten ions areconcentrated on low field side on magnetic surface due tothe centrifugal force. Thereby the fraction of the trapped
particle increases. In this study, radial electric field is notconsidered as a first step.
In rotating system, the sum of potential energy derived bycentrifugal force and kinetic energy is conserved.
1𝑚 (𝑣 2 − 𝑅2 𝛺∗2 )2 𝑍
1/2𝑍𝑚𝑖 𝑇𝑒Ω∗ = Ω [1 −]𝑚𝑍 (𝑇𝑖 + 𝑇𝑒 )
ℇ=(1)
(2)

Here, the velocity of tungsten ion is thermal speed (𝑣 =𝑣𝑡ℎ,𝑤 ).

The charge state Z, the position r and poloidal angle 𝜃are given by𝑑𝑍 𝜕𝜈 𝜕𝑇𝜕𝜈(𝑟 − 𝑟0 ) +(𝑍 − 𝑍0 )=𝑑𝑡 𝜕𝑇 𝜕𝑟𝜕𝑍𝑑r= 𝑣𝑟 = −𝑣𝑑 sin 𝜃𝑑𝑡𝑑θ𝑣∥=𝑑𝑡 𝑞𝑅0(3)(4)(5)

where 𝜈 is reaction frequency (𝜈 = 𝑛𝑒 (〈𝜎𝑣〉𝑖 − 〈𝜎𝑣〉𝑟 )and 𝑣∥ is the velocity parallel to the magnetic field. PHZpinch velocity in pitch angle 𝜉 (𝜉 = 𝑣∥0 ⁄𝑣) is given by
𝑉𝑃𝐻𝑍 = 〈𝑣𝑟 〉 =∫ 𝑣𝑟 𝑑𝑡
𝑇(6)3. Result
We numerically calculate the 𝑉𝑃𝐻𝑍 for all pitch angles.
The plasma parameters were as follows: major radius =3.35 m, magnetic field = 3.5 T, plasma current = 1.6 MA,
neutral beam (NB) heating power = 15 MW. 𝑇𝑒 , 𝑇𝑖 ,𝑛𝑒 and q are taken from experimental data. Figure 1 shows
𝑉𝑃𝐻𝑍 at 𝑟0 =0.8 m and the particle orbit (𝜉 = 0.7). 𝑉𝑃𝐻𝑍
becomes larger with increase in the rotating velocity until
𝑉𝑡 = 0.5 × 104 m/s. Passing particles have becometrapped particles by the effect of centrifugal force. Whenthe fraction of trapped particle is large enough for 𝑉𝑡 >0.5 × 104 m/s, 𝑉𝑃𝐻𝑍 almost vanishes. However, thesimple average PHZ velocity for all pitch angle 〈𝑉𝑃𝐻𝑍 〉does not change very much with increase in the rotating
velocity until 𝑉𝑡 = 0.5 × 104 m/s.
0.005

ξ =0.70VPHZ (m/s)

1. Introduction
In JT-60U, it was observed that tungsten accumulation isenhanced with increase in the toroidal rotation in theopposite direction (CTR-rotation) to the plasma current in
H-mode plasmas [1]. From theoretical considerations,
Hoshino et al. have proposed PHZ pinch and Er pinchmodel related to toroidal rotation and radial electric field[2]. We have introduced these models in TOTAL code andstudied dependence of the tungsten accumulation on thetoroidal rotation [3]. We investigated the effect of the PHZ
pinch only because the Er pinch model equation was not
valid in the experimental conditions. By introducing thePHZ pinch, the larger accumulation observedexperimentally at higher toroidal rotation was reproducedin the simulation. However, the dependence on toroidal
rotation was weaker in the simulations than in theexperiments.
In the experiment, tungsten ions and bulk plasma seem torotate with the similar speed. In the original PHZ pinchmodel, however, orbits of tungsten ions are analyzed
neglecting the effect of bulk plasma rotation. The plasma
rotation causes centrifugal force, which makes poloidal
asymmetry in heavy impurity ion density. In fact, it wasobserved that tungsten ions were concentrated on low fieldside in JET [4]. In this study, we numerically analyze thePHZ pinch when the centrifugal force is taken into account.

-0.005-0.015-0.02-1

Vt=0Vt=0.3e5
Vt=0.5e5
Vt=1.0e5

Vt=0
Vt=0.1e5
Vt=0.3e5
Vt=0.5e5
Vt=1.0e5-0.01-0.50ξ

0.5

1R(m)Fig.1 𝑉𝑃𝐻𝑍 for all pitch angles at 𝑟0 =0.8 m when the 𝑉𝑡changes and the particle orbit at the each 𝑉𝑡 (𝜉 = 0.7)
[1] T. Nakano, J. Nucl. Mater. 415, S327-S333 (2011)[2] K. Hoshino, et al., Nucl. Fusion 51, 083027 (2011)[3] Y. Shimizu, et al., Plasma and Fusion Res. 10, 3403062 (2015)[4] C. Angioni, et al., Nucl. Fusion 54, 083028 (2014)