27pA02
ヘリカル装置における電極バイアスによる閉じ込め改善モード遷移に対する
磁場リップル構造依存性
Configuration Dependence of Improved Mode Transition using a Biased
Electrode in Helical Devices
北島純男、石井啓一、佐藤優、立花丈、小池都司、奥俊博、岡本敦、稲垣 滋1、高山正和2、高橋裕己3、増崎貴3、庄司主3、芦川直子3、時谷政行3、横山雅之3、鈴木康浩3、佐竹真介3、井戸毅3、清水昭博3、長山好夫3、徳沢季彦3、西村清彦3、森崎友宏3、佐野史道4、水内亨4、
長崎百伸4、岡田浩之4、小林進二4、山本聡4
S. Kitajima, K. Ishii, Y. Sato, J. Tachibana, S. Koike, H. Oku, and A. Okamoto et al.
東北大院工、1) 九州大応力研、2) 秋田県立大、3) 核融合研、4) 京大エネ研
Tohoku Univ., RIAM, Akita Prefectural Univ., NIFS, Kyoto Univ.
In neoclassical theories the nonlinearity of theion viscosity plays the important role in thebifurcation phenomena of the L-H transition, whichobserved in tokamaks and stellarators. The effectsof the ion viscosity maxima on the transition to an
improved confinement mode were experimentallyinvestigated by the externally controlled J x B
driving force for a poloidal rotation using the hot
cathode biasing in Tohoku University Heliac(TU-Heliac) [1, 2]. Here, J and B are a biasing
electrode current and a magnetic field. In steadystate the J x B driving force balances with the ion
viscous damping force and the friction to neutral
particles. Then the ion viscosity opposing to thepoloidal rotation can be estimated experimentallyby subtracting the friction term from the driving
force. We observed the transition to an improved
confinement mode from an electrode characteristics,
and the local maximum in ion viscosity (viscositymaxima Πp,n_LM) can be evaluated experimentallyfrom the external driving force at the transition(critical driving force Fc), where the jump of thepoloidal flow velocity (poloidal Mach number Mp)
appeared and the significant increase of the stored
energy and the suppression of the fluctuations inprobe signals were observed. The predictions fromneoclassical theories [3] can explain the estimatedlocal viscosity maxima in different magnetic
configurations.
The importance of the biasing experiment instellarators exists in the ability to understanduniversally the relation between the transition
behavior and the viscosity by taking high ordermagnetic Fourier components into viscosity

evaluation. The achievement of an improved modetransition by the electrode biasing and clarificationof the transition mechanism imply the contribution
to the progress of understanding H-mode physics.
The optimization of helical ripples allows thereduction of viscosity, which is expected to bringgood accessibilities to the improved confinement
modes. The transition conditions will be decided by
the magnetic ripple structure and normalized
collision frequency and will not depend on thedevice size or confinement system. By the survey ofcomparison for a transition condition with many
devices, which have a different magnetic ripple
structure, we can demonstrate the important role ofneoclassical ion viscosity on the transition ofconfinement mode if we can observe theconsistency of experimental results with theories.
Further we can expect the estimation of thresholdcondition for another device from databasesurveyed in many devices. Therefore it is importantto verify whether the transition phenomena
observed in TU-Heliac can appear in the wideplasma parameter range and in the confine systems
that have different magnetic configuration.
We have continued the biasing experiment in ahigh-performance plasma, namely, low collisionalplasma in Large Helical Device (LHD). We
successfully observed the transition and compared
the external driving force J x B required for theimproved mode transition in 3 configurations (Rax =3.53, 3.60 and 3.75) in LHD. Figure 1(a) shows theconfiguration dependence of the critical driving
forces Fc, which were evaluated at the forward andbackward transition point. Figure 1(a) also shows0.3

ForwardExp.

Reverse

Calc.

0.06
0.04

0.1
Bt ~2.7 T
3.5

3.6

3.7

3.8

3.9

0.02
0Rax [m]100040L mode

800

30600

20400EeδVE/(δI /n ) [x1019Exp.

100Calc.
3.5

3.6

3.7

3.8

3.9p(b)δM /δΠp,n3

Ω/m ]5010-1
10-2
10-3
CAL_TU
EXP_TUCAL_HJ
EXP_HJ

10-4
10-5

10-2

10-1

CAL_CHS
EXP_CHSCAL_LHDEXP_LHD

100101

εeff

0.08

0.2

0100

0.1

(a)

Πp,n_LMr

3

Critical J xBt [N/m ]0.4(viscosity maxima) and critical driving force Fc inTU-Heliac, CHS, Heliotron-J and LHD predictedby the neoclassical theory [3], and critical driving
forces Fc. estimated from biasing experiments. The
biasing experiments in many devices, which have adifferent magnetic ripple structure, enable us tocompare the transition condition and to demonstrate
the important role of neoclassical ion viscosity on
the transition in the wide εeff operating range.

Πp,n_LM , FC

the viscosity maximum Πp,n_LM. The viscosity
maximum increases according to the increase in Rax.
The critical driving force Fc and the viscosity
maximum Πp,n_LM have the same tendency. Critical
driving forces Fc at the backward transition weresmaller than that at the forward transition, whichmeans the improved mode can be sustained by thesmaller driving force in the backward transition
phase and is consistent with transition scenariocaused by the local maximum in the ion viscosity.
We also compared the configuration dependence ofradial resistivity in L-mode with the theory. In Fig.
1(b) dMp/dΠp,n was calculated from the viscosity inthe low Mach number Mp region. This value is
proportional to dVE/(dIE/ne) evaluated from theelectrode characteristics. Here, VE and IE are anelectrode voltage and an electrode current. And
these two values represent the radial resistivity.
From Fig. 1(b) it is clear that two parameters in
L-mode decrease with Rax going outward.

2000Rax [m]Fig. 1 Relation between (a) the critical driving force
and the magnetic axis position, (b) the radialresistivity and the magnetic axis position

Further biasing experiments were tried in CHS
and Heliotron-J. Figure 2 shows the operating range
for the effective helical ripple εeff and local maxima
in a neoclassical poloidal ion viscosity Πp,n_LMFig. 2 Operating range for the effective helical ripple εeffand ion viscosity maxima Πp,n_LM and critical driving
force Fc in TU-Heliac, CHS, Heliotron-J and LHD

In this talk we report (1) experimental resultsof the biasing experiment in TU-Heliac, CHS,
Heliotron-J and LHD and observations of the clear
transition phenomena from the electrodecharacteristics in different magnetic configurations
in each device, (2) estimation of critical driving
forces Fc required for the transition and a radialresistivity in each device, (3) the dependency onmagnetic configuration and comparison withtheoretical predictions, (4) measurement of theradial electric field profile under the biasing in
LHD and (5) evaluation of the radial electric field
and the viscosity by the neoclassical transport code
FORTEC-3D [4] for a non-axisymmetric system,and discussion of the electrode voltage required forthe transition from simulation results.

[1]
[2]
[3]
[4]

TAKAHASHI, H. et al., J. of Plasma andFusion Research SERIES 6 (2003) 366.
KITAJIMA, S. et al., Nucl. Fusion 46 (2006)200.
SHAING, K. C. Phys Rev. Lett. 76, 4364
(1996).
SATAKE, S. et al., PPCF, 53, 054018(2011).