23P068-P
Nonlinear bifurcation sate of magnetic islands driven by resonant magneticperturbations
共鳴磁場摂動によって励起する磁気島の非線形分岐状態
Seiya Nishimura1, Shinichiro Toda1, Masatoshi Yagi2,3 and Yoshiro Narushima1
西村征也1, 登田慎一郎1，矢木雅敏2,3，成嶋吉朗1
1National Institute for Fusion Science, 322-6, Oroshicho, Toki, Gifu, 509-5292, Japan
1核融合科学研究所 〒509-5292 岐阜県土岐市下石町322-6
2Japan Atomic Energy Agency, 2-166, Oaza-Obuchi-Azaomotedate, Rokkasho, kamikita, Aomori, 039-3212, Japan
日本原子力研究開発機構 〒039-3212 青森県上北群六ヶ所村大字尾駮字表舘2-166
3Research Institute for Applied Mechanics, Kyushu University, 6-1, Kasuga-koen, Kasuga, Fukuoka, 816-8580, Japan
九州大学応用力学研究所 〒816-8580 福岡県春日市春日公園6-1
Sudden appearance and disappearance of magnetic islands produced by external resonant magnetic
perturbation have been observed in helical plasmas. In this study, nonlinear stability of magnetic islands inthe Large Helical Device is investigated theoretically and numerically. Firstly, we derive a low
dimensional model of magnetic island width, island rotation frequency and poloidal flow velocity. Themodel predicts that magnetic islands shrink below a certain threshold of external magnetic perturbation.
Next, nonlinear numerical simulations are performed. The suppression of magnetic islands is also observed
when neoclassical transport induced poloidal flows are taken into account. In these results, the shrink
mechanism is found to be associated with screening of external magnetic perturbation by poloidal flows.

1. Introduction
In magnetic confinement fusion with toroidal
devices, such as tokamaks and helical systems, it isimportant to control various magnetohydrodynamics(MHD) instability. Recently, external
resonant magnetic perturbation(RMP) by a set of
external current coils attracts considerable attention,
which might provides a control method of MHD
activity[1]. RMP drives reconnection of magnetic
field lines, produces magnetic island structure andmodifies MHD stability and plasma confinement
property.
In helical plasmas, such as the Large HelicalDevice(LHD) and TJ-II, sudden appearance anddisappearance of magnetic islands by RMP havebeen observed, when global plasma parameters areslowly changed[2]. Such fast event is not simply
understood by the conventional model based onthree-dimensional MHD equilibrium. In the LHD, it
is also observed that, radial profile of plasma flowchanges when magnetic islands appear or disappear.
These factors motivate us to study effects of plasma
flows on magnetic island stability.
In this paper, we report results of theoreticalanalyses and numerical fluid simulations ofmagnetic islands in the LHD.
2. Reduced MHD modelFirstly, we introduce a conventional reduced setof MHD equations of the electrostatic potential, thevector potential parallel to magnetic field lines, theelectron pressure and the parallel ion velocity.
Detailed explanation of similar model is given inRef.[3]. In the present model, we take into accounttwo representative effects of rippled magnetic fieldof helical plasmas: the poloidal neoclassical dragforce and the average normal magnetic field line
curvature, where the former produces the poloidal
flows and the latter drives the perturbed
Pfirsch-Schluter(PS) current. RMP is introduced by
the finite edge boundary condition of the perturbed
magnetic flux. In helical plasmas, RMP produces
magnetic islands even in the absence of plasmas,
this is because the vacuum field has magnetic shear.
Magnetic island width in the vacuum limit is calledvacuum island width in the following. For theanalyses, representative parameters of the LHD are
considered.
3. Low dimensional model
To understand the basic mechanism of thedisappearance of magnetic islands, we derive a low
dimensional nonlinear model of rotating magnetic
islands with RMP and poloidal flows. Following
the conventional asymptotic matching method, weobtain zero-dimensional evolution equations ofmagnetic island width and magnetic island rotation
frequency, where the island rotation frequency ismainly determined by the poloidal flow. To close
these equations, we introduce one-dimensionalradial profile of the poloidal flow. The model in thelimit of zero magnetic field line curvature is shownin Ref.[4].
Firstly, we numerically solve the low
dimensional model. The initial condition is given
by large magnetic island state, which corresponds
to the saturation state in the absence of the poloidal
flow. Figure 1 shows the vacuum island width ( wv )dependence of saturated magnetic island width ( w ),where a is the minor radius, δVR is the linear
layer width and D is the interchange modestability parameter proportional to€ the normal€
magnetic field line curvature. In our parameters,the€ perturbed PS current €driven mode is unstable€ . It is found that magnetic islands
for D > 0.04
shrink in the low wv regime for all cases. The sizeof the damped islands close to δVR is outside of thescope of the model, except for D=0.06. On the other€hand, large magnetic islands are maintained in thelarge w€v regime. It is confirmed that the stabilityof magnetic islands €are linked to the poloidal flow
profile, and the shrink mechanism is understood bya screening effect of RMP by poloidal flows. The€ detailed calculation shows that the threshold of theshrink is given by

wv = wv0 −21/ 4w ps4(1)where wv0 indicates the threshold value for D=0
and w ps ( sgn(w ps ) = sgn(D) ) represents the€effect of the perturbed PS current.

€€

assume the limit of zero perturbed PS current(similar to D=0 in Sec.3). In the initial state, thefinite RMP is finite at the edge, but perturbation at
the rational surface is small.
Figure 1 shows contour plots of magnetic
surfaces in the poloidal cross section. We examine
the cases (a) with and (b) without poloidal flows,
where the magnitude of RMP is the same value inboth cases. Magnetic islands are not observed in
Fig.2(a). On the other hand, magnetic islands areformed in Fig.2(b). In Fig.2(b), the magnetic island
width grows to almost the same width as that of thevacuum islands. This result clearly shows thatpoloidal flows have the screening effect of thepenetration of RMP and is consistent with the low
dimensional model.
Results of parameter surveys will be shown in
the presentation.

€Fig.2 Magnetic surfaces (a) with and (b) without thepoloidla flow. (Results of numerical fluid simulations)

4. Summary
The low dimensional model and the numericalsimulations of the reduced magnetohydrodynamics
equations show that magnetic islands by RMP
shrink in the presence of fast poloidal flows. These
results might explain the sudden disappearance
mechanism of magnetic islands in the Large HelicalDevice.
Acknowledgments
This work is partially supported by Grant-in-Aidfor JSPS Fellows. We also acknowledge acollaboration program of Research Institute forApplied Mechanics.

Fig.1 Vacuum island width dependence of nonlinearlysaturated magnetic island width (Results of a low
dimensional model).

4. Numerical simulation
Next, we perform direct nonlinear simulations of
the reduced MHD model and examine effects ofpoloidal flows on magnetic islands by RMP. To
focus on the stability of magnetic islands, weReferences[1] T. E. Evans et al.: Phys. Rev. Lett. 92 (2004)
235003.
[2] Y. Narushima et al.: Nucl. Fusion 51 (2011) 083030.
[3] S. Nishimura, and M. Yagi: Plasma Fusion. Res. 6(2011) 2403119.
[4] S. Nishimura et al.: Plasma Fusion. Res. 5 (2011)040.