23P118-P
Nonlinear MHD simulation on the formation of helical structure in RFP
逆磁場ピンチにおける３次元構造の形成に関する	 
非線形ＭＨＤシミュレーション	 MIZUGUCHI Naoki1,2, SANPEI Akio3, FUJITA Shin-ichi3, OKI Kensuke3,HIMURA Haruhiko3, MASAMUNE Sadao3 and ICHIGUCHI Katsuji1,2
水口直紀1,2, 三瓶明希夫3, 藤田慎一3, 大木健輔3, 比村治彦3, 政宗貞男3, 市口勝治1,2
1

2

National Institute for Fusion Science, The Graduate University for Advanced Studies
322-6 Oroshi-cho Toki, Gifu 509-5292, Japan12核融合科学研究所, 総合研究大学院大学 〒509-5292	  土岐市下石町322-6
3Kyoto Institute of TechnologyMatsugasaki, Sakyo-ku, Kyoto 606-8585, Japan3
京都工芸繊維大学 〒606-8585	  京都市左京区松ヶ崎橋上町

Nonlinear three-dimensional magnetohydrodynamic(MHD) simulations have been applied to the reversed-field pinch(RFP) plasma to reveal the physical mechanism of the formation processes of helicalstructures, such as so-called the quasi-single helicity (QSH) state. The simulations are executed by using
the MIPS code in a realistic experimental geometry of the RELAX device with reconstructed initial
equilibria calculated by the RELAXFit code. Long term evolutions have shown remarkable formation of
n=4 structures as a result of dominant growth of the m/n=1/4 resistive mode. The quasi relaxed helical state
consists of a bean-shaped and hollow pressure profile in the poloidal cross section. The simulation results
are compared with the experimental observations in RELAX.

1. Introduction
The reversed-field pinch (RFP) is an elaborate
toroidal confinement concept, in which the plasma is sustained by making use of its formative
nature with a simple and compact magnetic system. The configurations can contain high-beta
plasma with intrinsic large toroidal current, which
simultaneously provides effective Ohmic heating
for a potential reactor. On the other hand, thesystem tends to be destabilized for the tearing
mode instabilities in the core region because of
the large current and the adjacent rational magnetic surfaces. The existence of such multiple
rational surfaces can cause interactions between
the modes and chaotizing of the field lines. To
avoid such a way of degradation of confinement,a passive control method is examined experimentally. Namely, by concentrating most of themode activity into a single mode, a large magnetic island, in which the confinement property isimproved, is formed in the core region. Several
types of such a small number of helicity state
have been observed experimentally[1,2], i. e., thequasi single helicity (QSH), in which almost all
activities converge into a single mode, or the single helical axis (SHAx) state, in which the secondary arising zero point forms anotherthree-dimensional magnetic axis. In the REversed
field pinch of Law-Aspect ratio eXperiment"RELAX", the rotation of the helical structure areobserved[2].
In this study, we apply the nonlinear
three-dimensional magnetohydrodynamic (MHD)
simulation which has been developed for more thanten years at the National Institute for Fusion Science (NIFS) for modeling of the tokamak or helicalplasmas[3] to the RFP system. The simulation results are immediately compared with the experimental data of RELAX. By collaborating the numerical simulation with the experiment, we aim atrevealing the unknown dynamics on the formationof helical structures in RFP.
2. Simulation Model
We solve the standard set of the nonlinear, resistive, compressive MHD equations explicitly withthe 4th-order finite difference and Runge-Kutta
scheme by using the MHD Infrastructure for Plasma Simulation (MIPS) code [4]. The numerical gridis a cylindrical full-toroidal geometry with a rectangular mesh in the poloidal plane. The grid size is(112,112) for the poloidal plane, and 128 for toroidal direction. The initial condition is reconstructed
experimental equilibria obtained by the RELAXFit
code[5].
As a nature of RFP, the toroidal magnetic field
passes through zero near the peripheral region. In
other words, the safety factor, q, goes to zero whichallows all the toroidal modes to be destabilized forthe m=0 mode, where m is the poloidal mode num-

ber. By setting the adhering conductor wall in theplasma boundary, such m=0 modes can be effectively suppressed.
3. Simulation Result
Perturbations applied in the initial equilibrium
can spontaneously grow with the dominant n=4mode, where n indicates the toroidal mode number.
The growth rate strongly depends on the resistivity.
The poloidal component is almost single m=1 mode.
Although the initial equilibrium contains slightly
the q=1/4 surface in the central region, the displacement of the growing m/n=1/4 mode extends
globally, as shown in Fig.1(a). Figure 2 shows thetime development of the total kinetic energy. As
shown here, the system experiences two peaks ofenergy and quasi relaxed state at t=305τA, where τA
is the Alfven transit time.

Fig.3. Formation of helical structure in RFP obtainedby the nonlinear MHD simulation. A contour map and an
iso-pressure surface is plotted.

After t=305τA, the system are rapidly rearranged,maybe because of some magnetic reconnections in
the core region. The system becomes highly disordered state with multiple mode number components.
4. Summary
Nonlinear MHD simulations have reproduced theformation of quasi relaxed helical structure in RFP.
The results are comparable to the observations in
RELAX. It is found that non-resonant resistive instability forms a bean-shaped hollow profiles with
an n=4 deformation.

Fig.1. (a)Fluctuation component for the n=4 mode.
(b)Poloidal pressure profile at t=305τA.

Fig.2. Time development of total kinetic energy

At t=305τA, the system ceases by keeping then=4 deformation, as shown in Fig. 3. The plasma
flows concerning the helical deformation and thepoloidal equilibration along the magnetic surfaces
make the shape of the plasma poloidal cross section
into a bean shape. Moreover, the poloidal flows
formed mainly in the off-axis region causes thepoloidal profile hollow, as shown in Fig.1(b).

Acknowledgments
This work is supported in part by the Japanese
Ministry of Education, Culture, Sports, Science,and Technology, Grant No. 20760583 and in partby the NIFS Collaborative Research Programs,Grant
Nos.
NIFS11KNTT011,andNIFS11KNST024. The MIPS code has been developed by Dr. Y. Todo.
References[1] Lorenzini R., et al., Nature Phys. 5 (2009) 570.
[2] Oki K., et al., J. Phys. Soc. Jpn. 77 (2008) 075005.
[3] Mizuguchi N., et al., Nucl. Fusion 49(2009) 095023.
[4] Y. Todo et al.: Plasma Fusion Res. 5 (2010) S2062.
[5] Sanpei A., et al., J. Phys. Soc. Jpn. 78(2009) 013501.