Proceedings of ITC/ISHW2007

Configuration Dependence of Pressure Driven Modes in HeliotronPlasmas
S. Sakakibara, K.Y. Watanabe, H. Yamada, S. Ohdachi, Y. Suzuki, H. Funaba, Y. Narushima,
F. Watanabe, K. Toi, K. Ida, I. Yamada, K. Narihara, K. Tanaka, T. Tokuzawa
and LHD Experimental Group
National Institute for Fusion Science,322-6 Oroshi-cho, Toki 509-5292, Japan
This article describes experimental results on finding the onset parameters of the low-m MHD modes and theparameter dependence of the amplitude in the Large Helical Device. The control of peripheral pressure gradientswith the gas-puff modulation technique was done in the plasmas with different magnetic Reynolds number S. The
m/n = 1/1 mode excited in the periphery appeared when the pressure gradient on the resonance exceeded the criticalvalue. The critical pressure gradient for the mode-onset is almost the same even in different S plasmas. Also it was
found that the mode was enhanced clearly with the decrease in S under the condition with the same pressure
gradient and magnetic configurations. These results contribute to verify the validity of the linear MHD stability.
Keywords: Large Helical Device, Heliotron Configuration, MHD Instability, Interchange Mode,
Magnetic Reynolds Number

1. Introduction
An understanding of characteristics of pressure
driven modes is one of the major issues for high-beta
plasma production in magnetic confinement systems.
Experimental characterization of ideal/resistive interchange
instability has been required for clarifying the validity oftheoretical prediction on linear stability boundary, which
contributes the extension of free degree of configuration
optimization in stellarators and heliotrons. In Large
Helical Device (LHD), experimental studies on ideal andresistive instabilities by making a use of wide free degreeof magnetic configurations are possible, and we haveinvestigated them focusing on the effect of MHD activity
on the plasma profile and confinement [1-4]. The
experimental results suggest that MHD activities near ideal
stability boundary affect the plasma profile and sometimes
lead to the minor collapse, whereas they never grow aslarge as that causing the disruption in tokamaks [5]. It has
been predicted that the resistive modes are unstable even in
the low-beta plasmas and enhanced with beta value, while
the growth of the mode is stopped immediately and theeffect on the confinements seems to be weak in the beta
range of 5 % [6].
The findings of the onset and saturation level of themode are suitable for characterization of the instability. We
have proceeded to construct the database on the above
parameters of magnetic fluctuations observed in several
machines in order to find the common understanding of
MHD activity in stellarators and heliotrons [7]. Regarding
the saturation level of the mode, the amplitude has clear
author’s e-mail: sakakibara.satoru@lhd.nifs.ac.jp

dependence of the magnetic Reynolds number S, and thedependence is close to that of the linear growth rate of theresistive interchange mode [5]. This tendency can be seenin different machines with different S plasmas [1]. On theother hand, we made the experiments for controlling edgepressure gradient using movable limiter in order to find theonset of the mode [8]. The peripheral modes disappeared
one after another when the limiter was inserted, and we
found the S and DR at the onset of each mode, where DR isthe index of the stability boundary of the resistiveinterchange mode. The results were consistent within afactor of two with theoretical prediction [8].
Here we report the experimental results of pressure
gradient control using the gas-puff modulation technique inorder to clarify the effects of pressure gradient and S on theonset of MHD mode. The active control of the pressure
gradient is useful to find the onset-parameters because theperipheral MHD modes appear in the beginning ofdischarge, which means difficulty in identifying themode-onset in the quasi-steady-state plasmas. The edgepressure (and the pressure gradient) was changed by theincrease and decrease in gas-fueling in the different S
plasmas. Here we focus on the behavior of the m/n = 1/1
mode which is excited in the periphery with magnetic hill.
2. Experimental Condition
The LHD is the heliotron device with a pair ofcontinuous helical coils and three pairs of poloidal coils
and all of coils are superconductive. The magnetic axis
position Rax can be changed from 3.4 to 4.1 m bycontrolling poloidal coil currents, whereas plasma aspect

Proceedings of ITC/ISHW2007

Fig.1 Rotational transform and V” profiles at theconfiguration with Rax = 3.6 m and Ap = 5.8.
ratio Ap can be selected from 5.8 to 8.3. The configuration
with Rax of 3.6 m and Ap = 5.8 was applied for thisexperiments, which is the standard configuration in LHD.
The toroidal magnetic field Bt was set at 1, 1.5 and 2 T
for changing S.
Figure 1 shows the typical profiles of rotationaltransform and V” in the plasmas with <β> = 0 and 1 %,respectively, where V denotes the volume encircled bythe magnetic surface. The positive and negative V”
regimes correspond to the magnetic hill and well,respectively. These profiles are calculated by 3D MHD
equilibrium code VMEC under the currentless condition.
The pressure profile was assumed as P0(1-ρ2)(1- ρ8),
which is close to an actual profile in the low-beta plasma.
The rotational transform profile slightly changes due tofinite-beta effects, while the location of the ι/2π = 1
resonant surface at which m/n = 1/1 mode is excitedalmost remains at around ρ of 0.9. The V” decreases withthe beta value due to the outward shift of the magnetic
axis, whereas there is still magnetic hill, especially, in theperiphery. The DR at the ι/2π = 1 resonance increases
with the beta value and the pressure gradient, andapproaches 0.1 when the <β> is around 1 %. Ideal
interchange mode in the periphery is stable in thisexperiment.
Electron density is controlled by Hydrogengas-puff. Electron temperature and density profiles weremeasured with Thomson scattering system and FIRinterferometer,respectively.
For
identifying
characteristics of MHD modes, 22 magnetic probes wereapplied mainly.
3. Gas Puff Modulation Experiments
Figure 2 shows the example discharge withmodulating H2 gas-fueling in the configuration with Bt =1.5 T. The co- and counter neutral beams (NB) wereapplied here and the each input power is 1.3 and 2.5 MW,
respectively. The NB’s were injected from 0.3 s, andco-NB was turned off at 2.02 s. The gas-puff was applied
from 0.7 s and started to decrease at 0.9 s, and thenline-averaged electron density n̄e and the volume averaged
beta value <βdia> started to increase and oscillated between
0.8 % and 1 %. The central electron temperature Te0 isabout 2 keV at 0.9 s and decreased stepwise when the n̄eincreased. The magnetic fluctuation with up to 50 kHz wasenhanced with the increase in n̄e. The several MHD modes
such as m/n = 1/1, 2/3, 3/4, 4/5 and 4/6 were observed asshown in the bottom figure, where m and n are poloidal
and toroidal mode numbers, respectively. These modes
nominally rotated in the electron-diamagnetic direction andare expected to be located in the periphery as predictedfrom Fig.1, if they are resonant modes. While the m/n = 1/1
mode appeared when the n̄e and <βdia> were increased, it
disappeared with the decreases in the n̄e and <βdia>. The
frequencies of other modes were oscillated with n̄e and Te,
which is predicted to be due to the change of the rotation of
the bulk plasma with gas-puff modulation. The modes
except for m/n = 1/1 one were continuously observed. The
plasma current Ip decreasing the rotational transform
gradually increases with time and reached about 15 kA at
the end of the discharge. The current is mainly driven by
NB because of unbalanced injection of NB. The central
rotational transform is decreased to 0.03 when the Ip isFig.2 MHD activities in the Discharge with modulating
gas-fueling in the configuration with Rax = 3.6 m and Bt= 1.5 T.

Proceedings of ITC/ISHW2007
15kA and has the parabolic profile, which hardly affects
the stability property in the periphery.
The gas puff modulation experiments were done in
the different Bt configuration in order to change the S.
Figure 3 shows the temporal changes of S, the beta
gradient dβ/dr at the ι/2π = 1 resonance and the m/n = 1/1
mode in the configurations with 2, 1.5 and 1 T. The
perturbations of the S and dβ/dr due to the gas modulationin the Bt = 2 T case is relatively smaller than the othercases because the modulation speed is relatively highcompared with the fig.3 (b) and (c) cases. The <βdia> wasset to 0.8 ~ 1.3 % at any configurations. The dβ/dr wasincreased and decreased with the increase and decrease ingas-fueling. The m/n = 1/1 mode appeared at around when
the dβ/dr exceeded 3~ 4 %/m at Bt = 2 and 1.5 T cases,
whereas the mode was continuously observed appear
above the critical value of the dβ/dr as shown in Fig.3 (c).
The onset seems to strongly depend on the dβ/dr rather
than S. On the other hand, the mode was enhanced with thedecrease in S rather than the increase and the decrease ofdβ/dr. The changes of the amplitude of the mode weresummarized in Fig.4. The data in the steady state plasmas

Fig.4 The amplitude of the m/n = 1/1 mode in the S anddβ/dr diagram. The open circle denotes no observation of
the m/n = 1/1 mode, and the closed circle corresponds to
the root mean square of the amplitude of the mode during
10 ms. The change of the color of the closed circle fromgray to black corresponds to bθ/Bt = 1 × 10-6 to 3 × 10-5.
of 12 discharges was applied here. The amplitude of themode was increased with the decrease in S at the constantdβ/dr. This tendency is consistent with the previous study
on high-beta plasma [5].

Fig.3 Temporal changes of magnetic Reynolds number,beta gradient at the ι/2π = 1 magnetic surface and m/n =1/1 mode in the configuration with (a) 2 T, (b) 1.5 T and(c) 1 T.

4. Discussion and Summary
The relationship between the mode property and theparameters related with the resistive interchange mode, thebeta gradient and magnetic Reynolds number, has been
investigated in the low-beta plasmas through theexperiments with gas puff modulation. The plasmas weresituated in ideal-stable and resistive-unstable regimes.
According to the linear theory on the resistive interchangemode, the growth rate increases with DR with the beta
gradient as the driving term, and with the reduction of themagnetic Reynolds number [9]. Therefore, we speculatethat the stability boundary which corresponds to‘mode-onset’ has the same dependence. Regarding theamplitude of the mode, it strongly depends on the magnetic
Reynolds number, and the mode was stabilized in thehigh-S region even under the condition that the beta
gradient is constant as shown in Fig.4. The mode onset
seems to depend on the beta gradient rather than magnetic
Reynolds number, however, the analyses in the wider rangeof the beta gradient are required for clarifying the relation
with their dependences For example, the regime with lower
beta gradient and lower magnetic Reynolds number should
be investigated.
The significance of the linear stability boundary,Proceedings of ITC/ISHW2007
especially, of the resistive interchange mode, should beclarified experimentally because the mode is predicted to
be unstable even in the low-beta plasma of the heliotron
configuration despite several low-order resonances arelocated in the most unstable region. It has been foundexperimentally that their modes have the weak effect on
the profile and the global confinement in the present beta
range with up to 5%. However, there is the possibility thatthe island overlap due to their modes affect the property ofthe plasma confinement and the magnetic topology in thehigher beta range. Therefore, the experiments for theidentification of the mode-onset are important to verify thevalidity of the stability prediction.
Acknowledgements
This work is supported by NIFS under contract
No.NIFS05ULHH517.
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