24D03
Development of resistive wall mode analysis code for rotating plasmas and its
application to JT-60SA
回転プラズマにおける抵抗性壁モード解析コードの開発及びJT-60SAへの応用
Junya Shiraishi1, Nobuyuki Aiba2, Masatoshi Yagi1,3
白石淳也1, 相羽信行2，矢木雅敏1,3
1) Japan Atomic Energy Agency
2-166 Omotedate, Obuchi, Rokkasho, Aomori 039-3212, Japan
日本原子力研究開発機構 〒039-3212 六ヶ所村尾駮表舘2-166
2) Japan Atomic Energy Agency
801-1 Mukoyama, $aka, Ibaraki 311-0193, Japan
日本原子力研究開発機構 〒311-0193 那珂市向山801-1
3) Research Institute for Applied Mechanics, Kyushu University
6-1 Kasugakoen, Kasuga, Fukuoka 816-8580, Japan
九州大学応用力学研究所 〒816-8580 春日市春日公園6-1
A new code is developed to study linear stability of resistive wall modes (RWMs) in tokamak geometry
including plasma rotation. “RWMaC” modules have been developed, which solve electromagneticdynamics in vacuum and the resistive wall. The RWMaC modules have been implemented in theMINERVA code, which solves the linearized ideal magnetohydrodynamic equations in tokamak geometry.
The MINERVA/RWMaC has been benchmarked with the MARS-F code. Numerical results will bereported, which analyze the RWMs in JT-60SA plasmas.

1. Background
Unstable resistive wall modes (RWMs) limit theachievable beta value in high-beta steady-state
tokamaks [1], and hence, they should be stabilized
or controlled for operation of advanced tokamaks
such as JT-60SA [2]. The RWMs originate from theideal external kink modes, which can be stabilized
by effect of vacuum surrounded by a wall. When
the wall is sufficiently close to the plasma surface,it yields eddy currents to cancel the penetration of
the magnetic field. However, the eddy current
decays in the time scale defined by the wall
resistivity, which results in unstable RWMs.
Theoretical [3] and experimental [4] researches
have revealed that the plasma rotation is one of themost promising methods to stabilize RWMs. In
rotating plasmas, there’re many physical processes
that contribute to stabilization: the Alfven or slow
wave continuum damping [5], dissipation [6] suchas resistivity, and the kinetic resonance [7].
A linear ideal magnetohydrodynamics (MHD)
code forms a basis for quantitative analysis of theabove processes. Toward that end, the “RWMaC”
modules have been developed to solve
electromagnetic problems in vacuum regions andthe resistive wall in tokamak geometry [8]. The
RWMaC modules were implemented in theMARG2D code [9], which solves the modified 2D
Newcomb equation, and have been benchmarked
with the NMA code [10]. In this study, a newRWM code is developed by utilizing the RWMaC

modules to study rotation effects on RWMs intokamak geometry.
2. Development of new RWM code
Basic theory of the new code is briefly reviewed.
Figure 1 shows the system under consideration.
Axisymmetric plasma is surrounded by anaxisymmetric resistive wall.

Fig.1. System under consideration.

The vacuum between the plasma surface and thewall is named inner vacuum (IV) and the vacuum
outside the wall outer vacuum (OV). The energybalance in the plasma-vacuum-wall system reads
K + WP + WIV + WOV + DW = 0, where K is the
kinetic energy, WP the potential energy including
rotation, WIV (OV ) the vacuum magnetic energy inIV (OV), and DW the energy dissipation in theresistive wall. The energy functionals related toplasma dynamics, i.e. K and WP , can becomputed by the MINERVA code [11]. MINERVAsolves the Frieman-Rotenberg equation [12](linearized ideal MHD equations with rotation) intokamak geometry by the initial-value approach aswell as the eigenvalue problem. RWMaC modules
compute the remaining energies, i.e. WIV (OV ) andDW by solving Maxwell’s equations in vacuum
regions and the diffusion equation on the resistivewall. By implementing RWMaC modules inMINERVA, it becomes possible to study therotation effects on RWMs. The details on theory
and numerical schemes will be reported in the talk.
3. Benchmark and application to JT-60SA
A benchmark effort with the MARS-F code [13]has been started. The MARS-F code solves theeigenvalue problem associated with the linearized
ideal MHD equations with some additional
dissipation mechanisms. The MARS-F code is now
a widely-used code.
To remove errors arising from numericalcomputation of equilibria, an analytic Solov’ev
equilibrium without rotation has been employed. It
has been confirmed that the marginal wall position
for the external kink modes coincides. Figure 2shows the benchmark results of RWM growth rates
for wide ranges of wall position and wall diffusion
time ( τ w ), which indicates the good agreement
between the MINERVA and MARS-F. It should be
noted that the MINERVA computed the growth rate(and real frequency) by the initial value problem aswell as the eigenvalue problem.

Fig.2. Benchmark results between MINERVA andMARS-F.

Here, τ A is the Alfven transit time and wallposition is defined by wall minor radius/plasma

minor radius. The benchmarking effort including
rotation is under progress.
One of the most critical goals of the JT-60SA
tokamak is to realize the steady-state high-beta
plasmas. These plasmas are prone to unstable
RWMs. To study RWMs in JT-60SA, the RWMaC
modules have been modified to include theJT-60SA wall shape. In the talk, the detailed
numerical results will be reported for high-beta
equilibria obtained in JT-60SA design study,
especially focusing on the rotation effect.
4. Summary
In summary, new modules named “RWMaC”
have been developed to solve the electromagnetic
problems in vacuum regions and the resistive wallin tokamak geometry. The RWMaC modules havebeen implemented in linear ideal MHD code
MINERVA. The new code has been benchmarked
with the MARS-F code, which shows the good
agreement for wide ranges of wall position and wall
diffusion time. The new code is now being applied
to the analysis of JT-60SA plasmas.
Acknowledgments
The authors are grateful to Dr. M. Kikuchi, Dr.
M. Mori, and Dr. T. Ozeki for their support. JSthanks Dr. M.S. Chu, Dr. L.L.Lao, Dr. S. Ide, andDr. M. Takechi for their discussion.
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