23P074-P
Evaluation of MHD stability of weak shear configuration in LHD plasma
大型ヘリカル装置LHDにおける弱磁気シア配位でのMHD安定性の評価
Masaaki Okamoto, Kiyomasa Watanabe1, Satoru Sakakibara1, Satoshi Ohdachi1,Yoshiro Narushima1, Mikiro Yoshinuma1, Katsumi Ida1, Yoshihide Shibata2, Noriyasu Ohno2
岡本征晃, 渡邊清政1, 榊原悟1, 大舘暁1, 成嶋吉朗1, 吉沼幹朗1, 居田克巳1,柴田欣秀2, 大野哲靖2
Ishikawa National College Technology, Kitachujo, Tsubata, Kahoku-gun, Ishikawa, 929-0392 JAPAN
石川工業高等専門学校, 〒929-0392 石川県河北郡津幡町北中条タ11
National Institite for Fision Science, Oroshi-cho, Toki, Gihu 509-5292, Japan1
自然科学研究機構 核融合科学研究所, 〒509-5292 岐阜県土岐市下石町322-6
2Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8603, Japan
2名古屋大学工学研究科，〒464-8603 名古屋市千種区不老町

2.  collapse in week shear configuration
In order to form the week shear configuration,

6 (a)
4

Ip/Bt (kA/T)#105387#105390204030(b)2010collapse

0
1.6<dia> (%)

1. Introduction
In toroidal magnetic confinement devices, theincrease of the plasma beta value is one of theimportant issues for the achievement of thenuclear fusion plant. The plasma beta is limitedby the plasma current and/or pressure driven
MHD instabilities. The minor collapse anddisruption are occurred by MHD instabilities intokamak plasmas. In the LHD (one of the typicalhelical device) experiments, the beta collapse
phenomenon has been also observed by MHD
instability in the week shear configuration. This
study's purpose is to clarify the threshold of thebeta limit by the evaluation of the Mercier
parameter DI.
In this study, we have calculated the equilibrium
of LHD plasmas with and without the beta collapse
by using VMEC code [1]. We had alreadycalculated the equilibrium by using the plasmapressure, which is measured by Thomson scatteringsystem, and the rotational transform /2 profile
assumed as uniform, parabolic and hollow current
density profile. However the estimated DI had large
scatter. So, it was found that the current density
profile is important in order to precisely estimate DI.
Therefore, it is used for the calculation of theequilibrium that /2 profile was measured bymotional Stark effect (MSE) diagnostic.

NBI(MW)

In Large Helical Device (LHD) experiments, the beta collapse phenomenon has been occurred bymagneto-hydro dynamics (MHD) instability in the week shear configuration. We have evaluated theMercier parameter about two discharges, which are with and without the beta collapse in the week shear
configuration. The evaluation of the Mercier parameter is used the pressure and rotational transformprofiles measured by Thomson scattering system and motional Stark effect diagnostic, respectively. Wewill clarify the threshold of the beta limit by the evaluation of the Mercier parameter.

1.2(c)

0.8
0.4
0
3.2

3.6

4time(sec)

4.4

4.8

Fig.1. Time evolution of (a) the port through power ofNBI, (b) ratio of plasma current Ip and toroidal magnetic
field Bt, and (c) volume averaged beta <dia> measured
by a diamagnetic loop.

the plasma current is necessary in the LHD
configuration. The plasma current Ip was generated
by unbalanced Neutral Beam (NB) injection. For
example, over 100 kA of plasma current wasobserved by unbalanced NB injection in LHD
device [2]. Figure 1 shows the temporal evolutionof the port through power of NBI, ratio of Ip andtoroidal magnetic field Bt and voluve averaged beta<dia> measured by a diamagnetic loop. Because a1.4
0.8(a) #105387
1.20DI

2

0.4
1
0.8
0.6

MSE(t=3.9sec)
fittng(t=3.9sec)

-0.4
-0.8

1.4(b) #105390

0.8

1.20DI

2

0.4
1
0.8
0.6

MSE(t=4.5sec)
fittng(t=4.5sec)

-0.4

-0.8
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Fig.2. Profiles of rotational transform /2 and Mercier
parameter DI of discharge (a) with collapse and (b)without collapse. Rotational transform profiles aremeasured by MSE diagnostic and calculated by thepolynomial fitting of plasma current profile.

neon gas puff is applied at the discharge of #105387
to increase the ramp-up rate of Ip, the beta collapse
is occurred at about t = 4.17 sec, Ip/Bt = 37.2 kA/T,
and <dia> = 1.29 %. On the other hand, the Ip
ramp-up rate of the discharge of #105390 is smaller
than the rate of discharge with Ne gas puff. So, thedischarge of #105390 cannot be observed the beta
collapse. After t = 4.5 sec, <dia> is decreased withthe electron density because hydrogen gas, which is
the main discharge gas, puff is terminated at t = 4.5sec.

3. Calculation of equilibrium
Figure 2 shows profiles of /2 and DI. In Fig.2(a), opened circles indicate /2 profile measured by
MSE diagnostic, which has time resolution of 0.3sec, at t = 3.9 sec. At t = 3.9 sec, the plasma
parameter is as follows, <dia> = 1.40 % and Ip/Bt =28.2 kA/T. The fitting curve is /2 profile
calculated by the polynomial fitting of plasma
current profile. The curve of DI is evaluated by themeasured pressure profile and fitting curve of /2.
In Fig.2 (b), it shows profiles of /2 and DI at t =4.5 sec. At t = 4.5 sec, the plasma parameter is asfollows, <dia> = 1.34 % and Ip/Bt = 28.8 kA/T.
From the measurement of /2 profile, it is foundthat magnetic shear of #105390 is larger than theshear of #105387 around the resonant surface of
m/n = 1/1 (m and n are the poloidal and toroidal
mode number, respectively). And it is found thatthe DI of #105390 is smaller than DI of #105387
around the m/n = 1/1 surface. These results areindicated that the discharge of #105387 is moreunstable than #105390 and it is consistent with theexperimental result of Fig. 1.
4. Summary
We indicate that DI could be evaluated at LHD
plasma with and without the beta collapse by using
MSE diagnostic. The result is obtained that DI of
the discharge with collapse is larger than DI of thedischarge without collapse. As the future works, wewill evaluate the DI of other discharges and clarify
the threshold of the beta limit by the DI.
References[1] S.P. Hirshman, W.I. Van Rije and P. Merkel, Comput.
Phys. Commun. 43 (1986) 143.
[2] K.Y. Watanabe, et al., Controlled Fusion and Plasma
Physics 24B (2000) 1316.