Proceedings of ITC/ISHW2007

Studies of Configuration Control Effects
on Dynamic Behavior of Heliotron J Plasmas
Tohru Mizuuchi, Shinji Kobayashi, Satoshi Yamamotoa, Hiroyuki Okada, Kazunobu Nagasaki,
Gen Motojimab, Shinya Watanabeb, Hajime Arimotob, Kensuke Muraib, Fumiyori Hamagamib,
Daisuke Katayamab, Hironori Matsuokab, Akino Nakajimab, Hiroshi Takahashib, Hiroyuki Yasudab,
Kiyofumi Mukaib, Akiyuki Matsuyamab, Yusuke Kowadab, Katsuyuki Hosakab, Shiori Miharab,Nobuhiro Nishinoc, Takashi Minamid, Yousuke Nakashimae, Yasuhiro Suzukid, Sadayoshi Murakamif,
Kiyomasa Watanabed, Masayuki Yokoyamad, Yuji Nakamurab, Kiyoshi Hanatani, Katsumi Kondob,
Shoichi Okamurad, Fumimichi Sano
Institute of Advanced Energy, Kyoto University, Gokasho, Uji 611-0011, Japan
Kyoto University Pioneering research Unit for Next Generation, Gokasho, Uji 611-0011, Japanb
Graduate School of Energy Science, Kyoto University, Gokasho, Uji, 611-0011, Japanc
Graduate School of Engineering, Hiroshima University, Higashi-Hiroshima 739-8527, Japand
National Institute for Fusion Science, 322-6 Oroshi-cho, Toki 509-5292, Japane
Plasma Research Center, University of Tsukuba, Tsukuba, Ibaraki 305-8577, Japanf
Graduate school of Engineering, Kyoto university, Kyoto 606-8501, Japana(Received day month year / Accepted day month year)
The transition to an improved confinement mode in NBI-only plasma is investigated in Heliotron J, focusing on
the onset condition of the transition. The transition, identified by a drop in the Hα intensity and an increase in thestored energy, the line-averaged electron density, has been observed in the Co-injection case. The experiment shows(1) the delay time between the NBI turned-on and the drop of the Hα intensity decreases with the power, and (2) thetransition occurs at a certain toroidal current (bootstrap current and NBCD current). The critical current depends onthe vacuum rotational transform. The free-boundary equilibrium calculation predicts that the rotational transformand the shape of the magnetic surface, especially in the outer region, can be modified asymmetrically to the current
direction.
Keywords: Heliotron J, rotational transform, effect of non-inductive plasma current, transition of confinement mode,
NBI plasma

1. Introduction
Heliotron J [1, 2] is a low-magnetic-shear device
with an L/M = 1/4 helical coil (R0 = 1.2 m, B0 ≤ 1.5 T)
based on the helical-axis heliotron concept [3], where thebumpiness, εb, is introduced as a new control knob offield configuration in addition to the other major fieldharmonics, helicity and toroidicity. One of the major
objectives of Heliotron J project is to examine the effectsof the new field parameters on the plasma performanceand to experimentally explore this advanced concept. The
configuration control studies are essential parts of the
Heliotron J experiment.
The study of εb-control effects on the bulk plasma
confinement and behavior of fast-ions were initiallyperformed for ECH plasmas selecting three different εbconfigurations with the same rotational transform at thelast closed flux surface (LCFS), ι(a)/2π in the vacuum
condition (i.e. no plasma effects) [4, 5 ]. As for theauthor’s e-mail: mizuuchi@iae.kyoto-u.ac.jp

εb-effect on the fast-ion behavior, which was examined bysuperimposing an NBI or ICRF pulse on ECH target
plasmas, the higher εb configuration is preferable for theconfinement of low- and high-pitch angle fast-ions. Theseobservations are qualitatively consistent with the drift
optimization viewpoint. On the other hand, as for the
global energy confinement, the dependence is not sosimple and we have tried to understand the observations
based on the discussion of the effective ripple modulation
amplitude, εeff. The preliminary analysis suggests that thelower εeff configuration seems to be preferable for the
global confinement for ECH-only plasma Theseexperiments have expanded to NBI-only plasmas [6],where the difference of τEexp in high- and medium-εb
configurations is not clear compare to that for ECH-onlyplasma. These observations suggest the possibility ofdifferent εb-dependence of the global energy confinement
time between ECH-only and NBI-only plasmas.
On the other hand, as experimentally demonstrated

Proceedings of ITC/ISHW2007
in W7-AS [7] and Heliotron J [8], the value of the edge
rotational transform ι(a)/2π is essential for the good
plasma confinement in a low magnetic-shear device,including L-H transition and MHD activities. The effectsof rational surfaces in the core region have been studiedin many tokamaks and helical devices from the viewpointof MHD activities. Recently the effects of low-orderrational surfaces have been discussed from the viewpointof the appearance of external/internal transport barriers orenhanced confinement modes in helical devices [9, 10].
In addition, the edge rotational transform is also closely
related with the field topology for so-called a “built-in”
divertor in heliotron/stellarator systems.
The initial study of rotational transform effects on
the global confinement in Heliotron J were performed byfor ECH-only plasma [11]. Since the transition to theimproved confinement mode (H-mode) was discovered in
Heliotron J, the accessibility condition to the transition
has been experimentally investigated for different
configurations labeled by the vacuum edge rotationaltransform ι(a)/2π|vac [8]. ECH- and ECH+NBI
experiments indicate the existence of ι(a)/2π|vac-windows
for the high quality H-mode (τΕexp/(f×τISS04) > 1.5) close
to the low-mode rational numbers of ι(a)/2π|vac. Here,τISS04 and f are the global energy confinement time by theinternational (inter-machine) stellarator scaling and a new
configuration-descriptive re-normalization factor driven
for each configuration subgroup of the experimental
database, respectively [12, 13]. Figure 1 shows such
ι(a)/2π|vac-dependence for ECH+NBI plasmas [8]. The

power and density thresholds of the H-mode are observed
to depend on the configuration (i.e. ι(a)/2π|vac), but thesystematic dependences between them are not fully
understood. It might have to consider the influence of the
topology (“shape”) of the magnetic surfaces on thepoloidal viscous damping rate, which influences theformation of the radial electric field through the plasma
poloidal rotation [14]. The poloidal viscous damping ratedepends also on the existence of the rational surface [15].
Even for non-Ohmic heating plasmas in a helicaldevice, non-inductive plasma current can be driven by thepressure-gradient (bootstrap current), ECCD and NBCD.
The modification of ι(r)/2π due to such non-inductive
plasma current can create new rational surfaces in thecore region. In the edge region, the change of therotational transform can modify the divertor plasma
distribution in a low-shear device. In the Heliotron J
experiments, it is experimentally confirmed that thebootstrap current and ECCD can be controlled by thebumpiness tailoring [16]. A tangential NBI system [17]can also control the direction and intensity of NBCD
current by selecting the beam lines and by controlling theinjection power. Experimentally, the effects of the plasma
current and its radial profile on the edge field topology
and divertor plasma distribution have been investigated in
Heliotron J from viewpoints of divertor control and balkplasma confinement [18]. An experimental detection of
the rotational transform modification during a discharge
has been tried in Heliotron J by using the sensitivity of
MHD activities on the rational surfaces [19].
This paper reports recent experimental investigation
into the effects of the non-inductive plasma current (orresultant modification of ι(r)/2π) on the onset of the
ECH

Diamagnetic
loop

Ip

BL2
Ｏ

Rogowskii
Coil

SX

Puff

BL1

Bp

Bt
(Normal)Hα ArrayFig.2 Top view of the Heliotron J device.
In the case of the “normal” operation, the direction of
the magnetic field is clockwise, where the toroidal
current flowing in the counter-clockwise direction
enhances the poloidal magnetic field strength.
(“additive current”)

Fig. 1 Configuration effect on the normalized global
energy confinement time of for ECH+NBI plasma.
Each configuration is labeled by ι(a)/2π|vac.
The window for the high quality H-mode (hatchingzone) is observed close to the low-mode rational
numbers of ι(a)/2π|vac [8].
2Proceedings of ITC/ISHW2007
Heliotron J (vacuum)

0.60

obtain a prospect of the deformation of the configurationby plasma pressure and/or current, and to understand theexperimental observations.
Figures 4 and 5 show an example of such calculation
obtained by using HINT2 [20] for the STD configuration.
Here, we assume rather peaked plasma pressure- andcurrent-profiles: β(s) = β0×(1-s)2 with β0 = 0.5%, jp(s) =j0×(1-s)2, where s denotes toroidal flux corresponding to
the square of the normalized minor radius (= ρ2). In Fig. 4,“vacuum” means no plasma condition (i.e. β = 0 %, the

8/13

ι/2π

4/7

0.55
0.50

12/22
8/15
12/23
4/8
8/17

0.00

0.10
0.20
<r> (m)Fig. 3 Radial profile of the vacuum rotationaltransform for several configuration. The horizontal
dashed lines indicate some low-mode rationals.

vacuum0kAtransition event.

2. Experimental setup
The details of the Heliotron J device is described in[1, 2]. Figure 2 schematically shows the top view of
Heliotron J with the main heating and diagnostic systems.
The initial plasma is produced by the 70GHz second
harmonic X-mode ECH system launched from a top port
located at the straight section of Heliotron J. The
hydrogen neutral beam (30 keV, 0.7 MW/beam-line) is
injected using two tangential beam-lines facing eachother (BL1 and BL2). Selecting one of the beam-line orchanging the direction of the confinement field, Co- or
CTR-injection is performed. The working gas ishydrogen or deuterium.
The configuration of the confinement field is
controlled using the five types of the external coils, thehelical coil, two individual sets of the toroidal coils (TAand TB) and two sets of the vertical coils (AV and IV).
The major part of the field configuration is determined by
the helical and toroidal coil currents. The bumpiness ismainly controlled by changing the coil current ratio of TA
and TB coils, ITA and ITB, respectively. Trimming of othercoil currents, it is possible to control εb within tolerable
change in the other major Fourier components of theconfinement field (helicity and toroidicity), ι(a)/2π|vac, theplasma volume and the major radius [4]. On the other
hand, ι(r)/2π|vac can be controlled by mainly changing thecurrent ratio of the helical coil to the toroidal coils. Here,it is possible to minimize the change of the bumpiness bykeeping the current ratio of ITA:ITB to be constant. Some
examples of radial profile of the rotational transform in
the vacuum condition are shown in Fig. 3. The εb at ρ =2/3 and ι(a)/2π|vac for the standard (STD) configuration of
Heliotron J are ≈ 0.06 (ITA:ITB = 5:2) and ≈ 0.56,
respectively.

ad. 1kA

sub. 1kA

ad. 2kA

sub. 2kA

Fig.4.

Effects of plasma pressure and current
on the configuration.
HINT2

0.60

Ip = ad. 2kA

ι/2π

0kA

vacuum0

Fig.5.

A free-boundary equilibrium calculation is useful to3

ad. 1kA

4/7

sub. 2kA

12/22
8/15
12/23

sub. 1kA

0.50

3. Numerical study of plasma current effects on
the field configurationβ(s)=b0(1-s)2 , β 0=0.5 %jp(s)=j0(1-s)2
8/13

4/8

0.1
0.2
<r> (m)Effects of plasma pressure and current on therotational transform.

Proceedings of ITC/ISHW2007
sustained by Co-NBI (BL2, Pinj ~ 0.46 MW/28kV). Here,“Co-”means the NBCD current increases the vacuum
rotational transform (“additive” current). At t ~ 206 ms, asudden drop of Hα intensity and increases of the stored
energy and line-averaged density were observed, indicating
the onset of transition to an improved confinement mode.
The changes in the radial profile of SX-intensity and theion saturation current in the scrape-off region (not shown)indicate that this phenomenon is an edge relating event.
The Hα intensity was rapidly increased from ~ 220 ms,
and finally the back transition occurred followed by thedecrease of the stored energy. It is interesting to note that
there is some time delay between the start of NBI and thedrop of the Hα intensity. This delay time is longer than the“build-up time” of NBI-only plasma (~16 ms (from t ~186
to t ~102 ms) in this particular shot).
As shown in the previous section, the toroidal current
and plasma pressure (<β> ~ 0.2 % in this shot) can modify
the rotational transform profile and the shape of LCFS.

net current Ip = 0 kA). The case of “additive current”
direction (i.e. the current increases ι/2π|vac) is indicated as“ad. *kA” and the opposite case is “sub. *kA” in the
figure. Figure 5 shows the effects on the rotationaltransform obtained by the same calculations for Fig. 4. As
shown in Figs. 4 and 5, the plasma current can modify not
only the rotational transform but also the “shape” of thelast closed flux surface. Moreover, as discussed in [18],even for the same net-current value, the difference incurrent profile j(s) has important effects on themodification. It should be noted that the effects are notsymmetry to the net current direction. The effect of theplasma pressure can be somewhat compensated by thesubtractive current. Moreover, the “proximity” to therational number, 4/7 for the STD configuration, is
important since the low-mode resonance has an importantrole on the field topology,. The vacuum rotationaltransform at the edge is about 0.56 (i.e. less than therational number 4/7) in the standard configuration,
ι(a)/2π become close to the rational by the additive
current, but the subtractive current increase the distancefrom the resonance condition.

4.1. Differences between Co- and CRT-NBI
The Co- and CTR-NBI plasmas are compared in thesame vacuum configuration with ι(a)/2π|vac ≈ 0.54 [21],where a natural resonance of m/n = 15/8 exists at ρ ≈ 0.87
in vacuum. Figure 7 shows the time traces of some plasma
parameters for CO- and CTR-NBI plasmas. In thisexperiment, only the beam-line of BL1 was injected into
D+ plasma initiated by ECH. By changing the field
direction, Co- and CTR-injections were examined. The
port-through NB powers (Pinj) are 0.58 and 0.56 MW for
Co- and CTR-injection cases, respectively. Although theevaluation of the absorption efficiency of CTR-injection
NBI is an on-going task, the stored energy and theline-averaged density for the both discharges have similar

4. Transition in NBI-only plasmaECH

C o -N B

19

19

m

-3

I (kA)

G a s P u ff

C T R -N B
NBI

0
2
0
2

Cad.
o

0

p

0
8
Hα

-2
6

I

(A .U .)
200
220
t im e ( m s )

240

Hα

180

I (A.U.)

0

2 ECH

e

x1 0

n

e

0
3

W(kJ)

#11948-3

3

C o n f ig . ; ι ( a ) /2 π = 0 . 5 4# 2 5 8 9 2 (C o -N B ), # 2 5 9 8 9 (C T R -N B )C o -N B

n (x10 m )W(kJ)In this study, we focus on the NBI-only plasmas tosimplify the situation and to take advantage of current
controllability of NBCD in the density region higher thanthe empirical critical (lower-limit) density for thetransition [8].
Figure 6 shows an example of the time traces for thestored energy, line-averaged density and Hα intensity froman NBI-only plasma in the STD configuration, where thedirection of the confinement field is the normal direction
and the working gas is hydrogen. The plasma initiation was
performed by using a short pulse (~ 6ms) of the 70GHz 2X
ECH microwaves. After that, the plasma was heated andFig.6. Typical example of NBI-only plasma showing
the transition. Time trace of the stored energy (top), theline-averaged density (middle) and the intensity of Hα(bottom) are plotted.

Csub.
TR

4
2
0

180

200
220
t im e ( m s )240

Fig.7. Comparison of Co- (red) and CTR-NBI(green) plasmas in the same vacuum configuration.
4

Proceedings of ITC/ISHW2007
values, respectively, at least for the time interval of 200
ms < t < 220 ms. The direction of the plasma current is
consistent with the expectation from the NBCD scenario
but the intensity is not the same for the both discharges.
Since the bootstrap current IBS always flows to theadditive direction in this configuration, NBCD current in
the CTR-NBI case is somewhat compensated by IBS. Thiscancellation effect usually becomes large in higher
density (or stored energy) range since IBS is an increasing
function of the pressure gradient.
As shown in Fig. 7, the decrease in the Hα intensity
and increase in the growth rate of the stored energy areobserved in the Co-NBI case, but no clear change in Ha
intensity or change in the “growth rate” of the stored
energy were observed in the CTR-NBI case. In otherconfigurations with different ι(a)/2π|vac or the bumpiness,
the transition event has not been observed for CTR
NBI-only plasma in the range of Pinj ~ 0.25-0.6 MW.
In the Co-NBI case, the changes in Hα and thestored energy were observed at three timing (t ~ 204, 214
and 225 ms), indicating repetitive L-H-L sequences inthis discharge. In next subsection, we will discuss thedelay time between the start of NBI and the onset timingof the transition (determined by the drop of Hα intensity),
we focus on the first event since for later event it is not soeasy to control the density by gas-puffing.

2

50

(a)

40

(b)

30

1
20
High εb1000High εMedium ε

b

200
P

400
(kW)

600

0
0

b

Medium εb

200
P

PortThrough

400
(kW)

600

PortthroughFig.8. Power dependences of the delay time (a) andthe plasma current at the onset timing of the transition(b) for high (red) and medium (blue) bumpiness
configuration.
and it elongates to Δt ~ 40 ms at ~ 0.3 MW.
From the viewpoint of the configuration effect on
the transition, it is interesting to check the value of theplasma current at the onset timing of the transition event
since the plasma current modifies the field configuration
as shown in Section 3. Figure 8(b) shows the toroidal
current at the onset timing as a function of Pinj. It isclearly shown that the transition happens when thetoroidal current reaches a critical Ip value which depends
on the configuration; 0.7±0.1kA for the medium-εb
1.3±0.2kA for the high-εb configurations, respectively.
4.3. Configuration effects on the critical current
The effects of the plasma current on the field
configuration should depend on the vacuum rotationaltransform. In order to investigate the effect of ι(a)/2π|vacon the critical current discussed in the previous
subsection, the ι(a)/2π|vac-scan experiment was performed
for NBI-only plasma by changing the coil current ratio of
the helical coil to the toroidal coils with the fixed ITA:ITB
ratio. (ITA:ITB = 5:2, medium-εb). Figure 9 shows thetoroidal current at the onset timing as a function of

4.2. Heating power dependence of the delay time
The delay time between the start of NBI and the dropof the Hα intensity was investigated by changing theheating power for two vacuum configurations with εb =0.06 (medium εb) and 0.15 (high εb), where ι(a)/2π|vac wasset at almost the same value of 0.56. The experiment was
performed under the reversed field direction with thebeam-line BL1 (Co-injection for this field direction). Since
the density was controlled in the range of 1.5−2.0×1019 m-3
in this experiment, the absorption efficiency of NBI isconsidered to be almost the same (~ 30%) for the bothconfigurations. This density range is higher than theempirical critical (lower-limit) density for the transition
obtained from the previous experiments. The similar
NBI-only plasma experiment was also performed for thevacuum configuration with εb = 0.01 (low εb) andι(a)/2π|vac ≈ 0.56. However no clear transition event wasobserved for the low-εb configuration even in the same
experimental conditions of the injection power and theplasma density. It should be noted that for ECH+NBI
plasmas, the transition was rather easily observed in theprevious experiment although the improvement factor
was low compared to that for the medium-εb case [4].
Figure 8(a) shows the delay time Δt as a function of
Pinj for the high- and medium-εb configurations. The delay
time for each configuration is almost the same value anddepends on the injected power; Δt ~ 20 ms at Pinj ~ 0.6 MW,

12/23 12/22

8/17 4/8 8/15

4/7

8/13

(High εb)Ip (kA) (kA)
Ip@transition

2

1

0
0.45

0.5
0.55
0.6
ι(0)/2π (=1/q)

0.65

ι(a)/2π

Fig.9. ι(a)/2π|vac-dependence of the critical toroidal
current for the transition in NBI-only plasmas.
Major low-mode rational numbers are also indicated.
5

Proceedings of ITC/ISHW2007
ι(a)/2π|vac. The density and NBI power range are the sameas that for Fig. 8 in this experiment, and the data from Fig.
8(b) for the high-εb case is also plotted as a reference.
Although we tried Co- and CTR-injection experiments inthe same configurations, no transition has been observedin the CTR-injection NBI-only plasmas under the present
experimental conditions and selected ι(a)/2π|vac-values.
Therefore, the plots in Fig. 9 are all additive current data.
As shown in the figure, the critical current exists for all
configurations and its value systematically decreases asincrease of ι(a)/2π|vac.

the bumpiness, but is independent of Pinj.
As for the H-mode in tokamaks, the effects ofplasma rotation are discussed. We should take care of theeffect of different momentum input direction from Coand CTR-NBI. In order to obtain the toroidal/poloidal
rotation velocity, we are preparing the diagnostic systemof the charge exchange recombination spectroscopy.

Acknowledgments
The authors are grateful to the Heliotron J
supporting group for their excellent arrangement of theexperiments. They would also like to acknowledge Profs.
T. Fukuda, T. Isobe, T. Mutoh, C. Suzuki, Y. Takeiri,
N. Tamura, E. Ascasibar, B. Blackwell, C. Hidalgo,
Q. Yang, B. Zurro for valuable discussions. This work is
performed with the support and under the auspices of the
Collaboration Program of the Laboratory for Complex
Energy Processes, IAE, Kyoto University and Kyoto
University 21st century COE Program “Establishment of
COE on Sustainable Energy System”, the NIFS
Collaborative Research Program (NIFS04KUHL001-005,
NIFS05KUHL007, NIFS06KUHL007, NIFS06KUHL
009-010, NIFS06KUHL011, NIFS06KUHL 014-015) as
well as and the Formation of International Network for
Scientific Collaborations..

5. Discussions
Under the present experimental condition (Pinj andmagnetic configuration), no transition has been observedin the CTR-injection NBI-only plasmas. The Pinj-scanexperiment shows the power dependence of the delay
time after the NBI turned-on to the onset of the transition.
This might indicate that the effective heating power Pheat
was too low for the CTR-injection to make the transition.
However, it is natural to consider that Pheat is not so
different between Co- and CTR-cases since almost thesame stored energy as that in Co- NBI plasma was
obtained in the CTR-NBI plasma (Fig. 7).
In this study, we found out the existence of thecritical current for the onset of the transition. In the
CTR-injection case, since the current direction of NBCD
is opposite to that of the bootstrap current, the total
current becomes lower than that in Co- injection case andthe current profile would be different. The free-boundary
equilibrium calculation predicts that the rotationaltransform and the shape of the magnetic surface can be
modified asymmetrically to the current direction (Fig. 4).
As shown in Fig. 9, the examined values of ι(a)/2π|vac in
this study were located at smaller side of the nearest
low-mode rational number. Therefore, roughly speaking,the additive current increase the edge rotational transformand approach to the low-mode rational number, but thesubtractive current has the opposite effect. It is not easy
to directly explain the ι(a)/2π|vac–dependence of thecritical current by this simple idea, but the rational near
the plasma edge would have some important effect on thetransition event. Similar power dependence of delay timefor ETB event is reported [22] in a high shear device,
CHS. Here the delay time decreases as getting close
ι(a)/2π|vac to 1.

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6. Summary
[18]
[19]
[20]
[21]

The transition to an improved confinement mode in
NBI-only plasma is investigated in Heliotron J, focusing
on the onset condition of the transition. In this study, we
found out the existence of the critical current for the onsetof the transition in NBI-only plasma. This critical current
depends on the vacuum field configuration, ι(a)/2π|vac and

[22]

6

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