25F07
Analysis of the sawtooth-like oscillations observed in the core regionof the LHD using equilibrium by HINT-2
HINT-2による平衡磁場を用いた接線像の逆変換手法による
LHDコア部の鋸歯状振動の解析
S.Ohdachi, Y. Suzuki, T. F. Ming2, K. Y. Watanabe, S. Sakakibara, Y. Narushima, X. Du2,
K. Toi, LHD Experiment Group
大舘暁、鈴木康浩、明廷鳳2、渡邊清政、榊原悟、成嶋吉朗、杜暁第2、
東井和夫、LHD実験グループ
National Instutute for Fusion Science 322-6 Oroshi-cho Toki-shi, 509-5292, JapanThe Graduate University for advanced studies 322-6 Oroshi-cho Toki-shi, 509-5292, Japan核融合科学研究所 〒509-5292 土岐市下石町322-6
総合研究大学院 〒509-5292 土岐市下石町322-6
In the Large Helical Device (LHD), sawtooth-like repetitive relaxation phenomena are observed when thepressure gradient is increased by pellet injection. When the mode is localized in the core, m/n = 3/1 typeprecursors are clearly observed. Reconstruction of the line-integrated soft X-ray image is investigated tostudy the evolution of the pressure driven MHD activities. Using an assumption that radiation is constantalong the magnetic, the tangential viewing lines are projected onto a poloidal cross section based on theestimated magnetic field by HINT-2 code. Reconstruction of the mode structure of the pre-cursor
oscillations is tried.

1. Introduction

mainly discussed.

Since there is no net-current in Heliotron devices,to study the effect on the confinement of thepressure driven modes is important to achieve
high-beta plasmas in the Large Helical Device. The
stability of the pressure driven modes, e.g., theinterchange mode depends on the depth of themagnetic well; the location of the magnetic axis, bywhich the well depth is affected, should be carefullycontrolled.
From the viewpoint of the confinement,
inward-shifted configurations, e.g. magnetic axis
Rax = 3.6m is better for getting good performance.
However, whole plasma are in the magnetic hill inthe vacuum magnetic field and most part of theplasma remains in the hill region with the increaseof the beta. That is to say we are operating the LHD
mainly with an unstable condition of theinterchange mode. Therefore, it is very important tostudy how these unstable modes behave while thebeta increases. So far, we are observing a three kindof phenomena when the amplitude of the MHD
activities evolves. 1) Coherent oscillations, 2)
Saturation of non-rotating mode at rational surfaces.
3) Sawtooth-like repetitive oscillations at rationalsurfaces [1]. q = 2 (m/n = 2/1) type, q = 1 (m/n =1/1) type are commonly observed in LHD. In thisstudy, these kind of sawtooth-like oscillations are

2. Experiment
Fairly high-density plasmas (line averaged
electron density ne > 1020 m-3 ) are produced by thesequentially injected hydrogen ice pellets.
Sawtooth-like oscillations are observed in this typeof discharges when the magnetic axis is inward
shifted (Rax = 3.55m, 3.6m and 3.65m). While theelectron density decreases the profile shape
becomes gradually peaked. Together with thepeaking of the electron temperature, the pressure
gradient increases and is 2 ~ 3 times larger than thegradient found in normal operation with gas
fueling.
As the pressure gradient increases, sawtooth-likeevents begin at several rational surfaces, e.g, 1/q =
1/1, 1/2 and 1/3. Note that, q profile in LHD is adecreasing function where q ~ 3 is located in thecore and q ~ 3/2 in the edge region. Here, we
discussed the q = 3 (m/n = 3/1) type sawtooth (corelocalized) since the clear pre-cursor like oscillations
are observed; it is a good example for studying thenon-linear evolution of the pressure driven mode.
Fig.1 shows the fluctuating components of theline-integrated image from the tangential viewing
soft x-ray camera at the time of the maximum
fluctuation amplitude. First, an m=3 mode evolves

within 100 ms and deforms the magnetic surface(Fig. 1 (B2) bright area). This m=3 triangularstructure expands and reaches the region around=0.4, an enhanced heat flux from the core to theedge is observed, thereby causing a flattening of thepressure profile.

the magnetic field line using HINT-2 equilibrium [5, 6].
Since the magnetic field can calculated in the regulargrid location, we can trace the magnetic field line evennear the magnetic axis. The reconstruction of the mode
structure based on this technique and the characteristicsof the relaxation phenomena in LHD will be given in thepresentations.

3. Reconstruction of the line-integrated image
Though line-integrated images give a roughimageofthephenomena,
tomographic
reconstruction might be useful to study the exact
structure pre-cursor and the nature of the collapse
events.
Reconstruction assuming the constant emission
along the magnetic field lines has been tried [2]. In
this method, tangential viewing lines are projected
on a poloidal plane as curved lines (see, Fig. 2) and2D reconstruction method is performed. In theprojection process, tracing of the magnetic fieldlines is required. Magnetic field was estimatedusing a VMEC [3] based equilibrium. However, thedensity of the flux surfaces in the VMEC
coordinate in the core region is not enough. It is notpossible for the reconstruction of the core-localized
modes, such as m/n =3/1 sawteeth.

Fig.2 A sample of the projection of the magnetic fieldlines on a poloidal plane. (Fig.2 of Ref [4])Acknowledgments
This study is supported by NIFS budget codeULHH508, ULHH509, ULPP021 and is also
partially supported by the Ministry of Education,
Science, Sports and Culture, Grant-in-Aid for
Scientific Research (B), 17360446, 23340184, andby the “SPS-CAS Core-University Program” in thefield of “Plasma and Nuclear Fusion”.
References[1] S. Ohdachi, et. al, ‘2D structure of MHD instabilities
and their evolution in the Large’ in Proc 21st IAEA
Fusion Energy Conference, Chendu, China, October
2006, EX/P8-15 (2006)[2] S. Ohdachi et. al., Plasma Science and Technology, 8,45, (2006)[3] S. P. Hirshman and P. van RIJ, Computer Physics
Communications 43, 143j (1986)[4] T. F. Ming, S. Ohdachi, et. al., Plasma and Fusion
Research 6, 2406120 (2011)[5] Y. Suzuki et al., Nucl. Fusion 46, L19 (2006).
[6] Y. Suzuki et al., Contrib. Plasma 50, 576 (2010).

Fig.1. Line integrated tangential image of asawtooth-like crash. Fluctuation components are shownin (B2) and (B3)
We have developed [4] new method for the estimation of