23D13
Studies of energetic-ion-driven MHD instabilities in low magnetic shear helicalplasmas
低磁気シアヘリカルプラズマにおける高速イオン励起MHD不安定性研究	 
Satoshi Yamamoto1), Shinji Kobayashi1), Shinsuke Ohshima2), Masashige Suwa3),
Keisuke Yasuda3) et al.,
山本 聡1), 小林進二1)，大島慎介2)，諏訪勝重3), 安田圭佑3), Enrique Ascasíbar4),
Ruben Jiménez-Goméz4), 永岡賢一5), Donald Spong6), Boyd Blackwell7),
David Pretty7), 長崎百伸1), 水内 亨1), 岡田浩之1), 南 貴司1), 中村祐司3), 花谷 清1),
木島 滋1), 向井清史3), 李 炫庸3), 佐野史道1)
1) Institute of Advanced Energy, Kyoto University, Uji, Kyoto, 611-0011, Japan
2) Pioneering Research Unit for Next Generation, Kyoto University, Uji, Kyoto, 611-0011, Japan
3) Graduate School of Energy Science, Kyoto University, Uji, Kyoto, 611-0011, Japan
4) National Laboratory for Magnetic Fusion, CIEMAT, Madrid, Spain
5) National Institute for Fusion Science, Toki, Gifu, 509-5292, Japan
6) Oak Ridge National Laboratory, Oak Ridge, Tennessee, 37831-6169, U.S.A.
7) Plasma Research Laboratory, The Australian National University, Canberra, ACT, 0200, Australia
1) 京都大学 エネルギー理工学研究所 〒611-0011 京都府宇治市五ヶ庄2) 京都大学 次世代開拓研究ユニット 〒611-0011 京都府宇治市五ヶ庄3) 京都大学 エネルギー科学研究科 〒611-0011 京都府宇治市五ヶ庄
4) CIEMAT マドリッド スペイン
5) 核融合科学研究所 〒509-5292 岐阜県土岐市下石町322-6
6) オークリッジ国立研究所 オークリッジ アメリカ合衆国
7) オーストラリア国立大学 キャンベラ オーストラリア
Energetic-ion-driven MHD instabilities such as Alfvén eigenmode (AE) have been studied in thethree-dimensional magnetic configurations with low magnetic shear and low toroidal field period that are
the features of advanced helical devices. Comparison of experimental results obtained from Heliotron J andTJ-II with numerical studies indicates that most unstable AEs are global AE (GAE) in advanced helicaldevices with low rotational transform and helicity-induced AE (HAE) in that with high rotational transform,respectively.

1. Introduction
Most of existing and/or planned advanced
helical devices have a low magnetic shear incombination with a magnetic well, by whichpressure-driven MHD instabilities particularly at
low order rational surface can be avoided orwould be stabilized, and a low toroidal field
period N p to obtain good transport and MHD
stability. To clarify the energetic-ion-driven
MHD instabilities such as Alfvén eigenmode(AE) is important because they would enhance
the anomalous transport of energetic ions and/orexpel them from the plasma before their
thermalization. The existence and stability ofenergetic-ion-driven MHD instabilities arecharacterized by the magnetic configuration
through the shear Alfvén spectra. The effect ofmagnetic configuration upon energetic-ion-driven
MHD instabilities should be investigated in eachmagnetic configuration. Low magnetic shear andthree-dimensional magnetic configuration with
low toroidal field period significantly affect on
the shear Alfvén spectra. They differ not only
from that of tokamaks but also helical devices
with high magnetic shear and high toroidal field
period.
For our study, we have experimentally andnumerically investigated the energetic-ion-driven
MHD instabilities in Heliotron J [1] and TJ-II [2].
Both devices have low magnetic shear and low
toroidal field period N p=4 to obtain high MHD
stability. The rotational transform of Heliotron J
can be varied in the range of ι/2π=0.45~0.65
which is different from that of ι/2π=0.9~2.0 ofTJ-II. We are also able to study the effect ofrotationaltransform
valueontheenergetic-ion-driven MHD instabilities throughthe comparison between Heliotron J and TJ-IIresults.

2. Alfvén eigenmode in helical plasmas
In helical plasmas, the magnetic field strength isvaried not only in the poloidal direction but also in
the toroidal direction. This variation of magnetic
field strength on the magnetic surface leads to theformation of frequency gap in the shear Alfvén
continua at the intersection point of two continua
with different parallel wave number k//(m, n) andk//(m+µ, n+νNp) where n and m are the toroidal andpoloidal mode number, and µ and ν are the integer,
respectively [3]. The AEs can be excited in thesefrequency gaps. The frequency gap for
toroidicity-induced AE (TAE), which is often
observed in many tokamaks and helical devices
with high magnetic shear, is formed by thecoupling of poloidal harmonics with mode numberm and m+1 corresponding with the case of µ=1
and ν=0. However, the shear Alfvén continuum ofm cannot intersect with that of m+1 because of low
magnetic shear in advance helical devices. Thismeans that TAE does not exist. Meanwhile, globalAE (GAE) which can exist just below and/or
above the shear Alfvén continua, could bedestabilized by the presence of super-Alfvénicions. Moreover, the variation of magnetic field in
the toroidal direction leads to the toroidal mode
coupling. Both toroidal and poloidal mode
couplings generate the helicity-induced AE (HAE)
gap. Figure 1 shows the calculated shear Alfvén
continua of the mode family Nf=1 for Heliotron J
plasmas. The shear Alfvén spectra with(m+µ, n+νNp) are superposed on and/or coupledwith that of (m, n). There are no low n TAE gapsthat are more dangerous than high n TAE. HAEs
are appeared in the frequency range above 500
kHz under this experimental condition ofHeliotron J. We found the GAE, of which
frequency lying just above the shear Alfvén
spectra of m=2/n=1, as shown Fig.1. Numericalsimulation indicates the most important AEs are
not TAE and HAE but GAE in Heliotron J.
3. Experimental result in iota scan experiments
In NBI heated Heliotron J plasmas, MHD
instabilities are observed. The observed mode isidentified as GAE because the frequency and radial
structure of the mode agree well with the calculated
GAE characteristics. We performed iota scan
experiment where the rotational transform isscanned in the range of ι/2π = 0.47~0.63. Figures
2 (a) and (b) respectively show the GAE
frequency of numerical calculation andexperiment as a function of rotational transform.
We found a few GAE of which frequcny and radial
structure are slightly different from those in theFig.1. Example of shear Alfvén spectra including
continua and eignfunction for Nf=1 of Heliotron J.

(a)(b)

Fig.2. Frequency of GAE obtained from (a) anumerical simulation and (b) the experiment.
numerical simulations. Experimental results show
the GAE frequency increases with an increase of
the rotational transform. This is the same tendency
as that in numerical simulations. No low frequency
GAE (f<50kHz) was observed in experiment
although a GAE with low frequency is found innumerical simulations. This result might beexplained by taking into account the coupling ofsound wave with shear Alfvén wave. On the otherhand, HAEs are mainly observed in the TJ-II iota
scan experiment. It is conculded that most unstable
AEs are GAE in advance helical devices with low
rotational transform and HAE in that with highrotational transform, respectively.
Acknowledgments
This work is supported by NIFS/NINS under the
project of Formation of International Network for
Scientific Collaborations and NIFS collaboration
Research Program (NIFS10KUHL030).
References[1] T. Obiki et al, Nucl. Fusion 41 (2001) 833.
[2] C. Alekaldre, et al, Plasma Phys. Control. Fusion 41(1999) A539.
[3] Ya.I. Kolesnichenko et al., Phys. Plasmas 8 (2001)
491.