Proceedings of ITC/ISHW2007

Study of toroidal current effect on rotational transform profile byMHD activity measurement in Heliotron J
G. Motojima, S. Yamamotoa, H. Okadab, S. Sakakibarac, K. Y. Watanabec, K. Nagasakib,
Y. Suzukic, T. Mizuuchib , S. Kobayashib, B. D. Blackwelld, Y. Nakamura,
K. Kondo, K. Hanatanib, H. Arimoto, S. Watanabe and F. Sanob
Graduate School of Energy Science, Kyoto University, Gokasho, Uji 611-0011, Japan
Kyoto University Pioneering Research Unit for Next Generation, Gokasho, Uji 611-0011, Japanb
Institute of Advanced Energy, Kyoto University, Gokasho, Uji 611-0011, JapancNational Institute for Fusion Science, 322-6 Oroshi-cho, Toki 509-5292, JapandPlasma Research Laboratory, Research School of Physical Sciences and Engineering, The Australian National University,Canberra, AustraliaaEffect of toroidal current on rotational transform has been investigated in Heliotron J by measuring
magnetohydrodynamic (MHD) activities at two configurations with rotational transform (ι/2π) close to 0.5. The
resonant mode has been observed in ECH + co-NBI plasma in the configuration with ι/2π = 0.48 at ρ = 0.7. This
result shows that the rotational transform is probably increased due to the toroidal current. The location of therational surface is determined at ρ = 0.8-0.9 by soft X-ray (SX) fluctuations related to the MHD mode. Equilibrium
calculation considering the toroidal current shows that the increase of the rotational transform by the toroidal
current is consistent with experimental results. The resonant mode structure has been investigated also in ECH +counter-NBI plasma at ι/2π = 0.50 configuration, and the location of the rational surface determined by SX signals
is not significantly changed compared to vacuum condition, suggesting that the change in the rotational transformprofile by the toroidal current is weak due to the balance between bootstrap current and counter-flowing NBcurrent.
Keywords: Bootstrap current, NB current, MHD instability, magnetic fluctuation, Heliotron J

Suppression of magnetohydrodynamic (MHD)
instability is one of the key issues for realization of highperformance plasma. In helical plasmas, stabilization ofpressure-driven modes such as ideal and/or resistive
interchange modes is a critical issue for high-β plasma.
Heliotron J is a low magnetic shear helical-axis heliotron
device with a magnetic well by which, it is considered that
MHD instability is expected to be avoided or stabilized [1].
However, MHD instabilities have been experimentallyobserved in electron cyclotron heating (ECH) and/or
neutral beam injection (NBI) heated plasmas of Heliotron J[2]. The m/n = 2/1 MHD instability exhibiting intense
magnetic fluctuations and low frequency (f < 10 kHz) has
been observed in the plasmas with the rotational transform
close to 0.5, where m and n are the poloidal and toroidal
mode
numbers,respectively.
Theequilibrium
configuration is changed by a toroidal current and aplasma pressure, and a low order resonant rational surface
can appear in the plasma. Toroidal currents such asbootstrap current, electron cyclotron (EC) current andneutral beam (NB) current have been examined in
Heliotron J [3,4]. They can modify MHD equilibrium andauthor’s e-mail:gen@center.iae.kyoto-u.ac.jp

stability due to the change in rotational transform (ι/2π)
profile. The effects of the toroidal current on MHD modes
have been investigated in CHS [5] and W7-AS [6]. Recent
experiment also indicates that the modification ofrotational transform by the toroidal current may induce aspontaneous transition in Heliotron J [7]. The objective of
this paper is to study the effect of toroidal current on therotational transform by measuring MHD activities inHeliotron J.

2. Experimental setup
0.55

(a)

(b)

0.50

ι/2π

1. Introduction

0.45
ι/2π = 0.48
ι/2π = 0.50

0.40
-0.05 0.00 0.05 0.10 0.15 0.20 0.25

<r> [m]Fig. 1 (a) Magnetic flux surface and 20 lines of sightin SX array are shown. Radial profiles ofrotational transform in vacuum condition areshown in (b).

Proceedings of ITC/ISHW2007
Heliotron J is a medium-sized plasma experimental
device. The device parameters are as follows; its plasma
major radius R is 1.2 m, its averaged minor radius a is0.1-0.2 m, its rotational transform ι/2π is 0.3-0.8, and its
maximum magnetic field strength on the magnetic axis,
B0 is 1.5 T. The coil system is composed of an L = 1, M =4 helical coil, two types of toroidal coils A and B, andthree pairs of vertical coils. Here, L is the pole number ofthe helical coil and M is the pitch number of the fieldalong the toroidal direction. A wide variety of magnetic
configurations can be produced on the Heliotron J by
varying the current ratios in various coils. In this study,
two configurations with the rotational transform close to0.5 were selected, namely, ι/2π = 0.48 and 0.50 at ρ = 0.7
under vacuum condition while keeping magnetic fieldcomponents almost constant. In Fig. 1(a), the poloidal
cross-section for the ι/2π = 0.48 configuration is shown.
Figure 1(b) shows the rotational transform profiles in thevacuum condition. In this experimental condition, NB
was injected to the ECH plasma (ECH+NBI plasma).
Here, NB was injected to co-direction andcounter-direction for negative (counter-clockwise)
magnetic field and for positive (clockwise) magnetic field,respectively. The total toroidal current is measured by
Rogowski coils wound on the inner wall of the poloidal
cross-sections at two different toroidal angles. In order todetermine the geometric structure of magneticfluctuations accurately, 4 mirnov coils are installed in thetoroidal direction and 14 mirnov coils are set poloidally
on one poloidal cross section. The magnetic probes havethe frequency response of up to 500 kHz. A soft X-ray(SX) diode has 20 vertical viewing chords. Figure 1(a)also shows lines of sight of the SX diode.

magnetic fields using the following equations, since theflow direction of the bootstrap current, which depends on
B×∇B drift, is reversed by reversing the magnetic field,
while that of the NB current associated with the injecteddirection is not. Under the experimental conditions
discussed in this paper, the effect of the EC current isweak.

I BS =I NB =

I pcw − I pccw
2cw
I p + I pccw
2,,

where Ipcw and Ipccw are the toroidal currents in thepositive and negative magnetic field experiments,respectively. Here, we have assumed that each toroidal
current component of positive magnetic field is similar tothat of negative magnetic field. We confirmed the stored
energy between positive and negative magnetic field wasalmost identical. However, we should note that absorption
rate of NB is affected by the direction of magnetic field
due to the change in loss rate of high energy ions. Figure 2
shows the bootstrap current and the NB current roughly
evaluated. The bootstrap current is 1.5 ± 0.2 kA at ι/2π =0.48 case and 1.8 ± 0.3 kA at ι/2π = 0.50 case. While, the

3. Experimental results
3.1 Separation of bootstrap current and NB
current
In ECH + NBI plasmas, the toroidal current iscomposed of the bootstrap current and the NB current.
These currents can be evaluated by comparing theexperimental results obtained for positive and negative(e)I (kA)

3.0 Wp > 1.5 kJBSNBCD
2.0
1.0
0.0
-1.0
-2.0
0.47

0.48

0.49 0.50
ι/2π

0.51

0.52

Fig. 2 Estimated bootstrap current and NB current.

Fig. 3 Time evolution of an ECH + co- NBI plasma.
The (a) stored energy, (b) toroidal current, (c)magnetic fluctuation, amplitude of (d) m/n = 2/1 and(e) extended view from 200 msec to 250 msec of SXsignals.

Proceedings of ITC/ISHW2007
NB current is -1.0 ± 0.2 kA at ι/2π= 0.48 case and -0.8 ±0.3 kA at ι/2π = 0.50 case.

current of 1.5 kA and NB current of 1 kA flow in
co-direction, the rotational transform profile has therational surface of the m/n =2/1 around ρ = 0.8. The
location of the rational surface of the m/n =2/1 calculated
is consistent with that obtained by SX signals. The m/n =2/1 mode is not observed after 245 msec. The rationalsurface of the m/n =2/1 may disappear by the decrease ofrotational transform due to the decrease of the toroidal
current.
0.02

δIsx (a.u.)

Figure 3 shows a discharge with ECH + co-NBI at
ι/2π = 0.48 configuration. The ECH power of 208 kW is
injected from 165 msec to 265 msec. The NB
port-through power of 573 kW is injected in theco-direction from 175 msec to 265 msec into the target
plasma. The net toroidal current is increased up to 2.5 kA.
The m/n = 2/1 mode with low frequency (3 kHz) isobserved from 225 msec to 245 msec. The m/n =2/1
mode rotates in the electron diamagnetic direction. TheSX signal synchronizes with the magnetic fluctuations
with the low frequency. Figure 4(a) shows the relative
amplitude of the fluctuations observed in the SX signal.
The peaks are observed at 5 ch (ρ = 0.90), 15ch (ρ =0.45) and 18ch (ρ = 0.80). Figure 4(b) shows the phasedifference among SX channels for the mode. The derived
phase relation indicates the ‘even’ or ‘odd’ character ofthe m number, that is, the phase difference between theSX channels is ~ 2π (~π) for an even (odd) m number.
The phases of 5ch and 18ch are almost same and it isconsistent with the m = 2 determined using the magnetic
probe arrays. Therefore, they correspond to the locationof the resonant surface of the m/n =2/1 mode. In vacuum
magnetic surface of ι/2π = 0.48 configuration, there is norational surface of the m/n = 2/1, however, the rotationaltransform is affected by the plasma pressure andco-flowing toroidal current, resulting in crossing therational surface of the m/n = 2/1. In order to clarify theeffect of the toroidal current on the equilibrium, fixedboundary VMEC calculations considering toroidal
current were carried out [10]. We assume that bootstrap
current density is given by j = j0(s-s2), and NB current isgiven by j = j0(1-s)2, where s denotes the normalized
toroidal flux, and the relationship of s = ρ2 holds. The
total amount of these toroidal currents was chosen to beconsistent with the experimental value evaluated in Fig. 2.
The electron density is given by ne = 2×1019(1-s3) m-3,
and electron and ion temperature are given by Te = 0.45×(1-s)2 keV and Ti = 0.15× (1-s)2 keV. Figure 5 shows theradial profile of the rotational transform calculated byVMEC code with toroidal current. When the bootstrap

180#25921 0.228-0.229 (sec)(a)
Phase (degree)

3.2 ECH + co-NBI plasma

0.01

0.00

010Ch20#25921 0.228-0.229 (sec)(b)

0-18001020ChFig. 4 Radial profile of (a) SX fluctuation
amplitude and (b) phase difference among SXchannels.

3.3 ECH + counter-NBI plasma
Figure 6 shows a discharge in ECH + counter-NBIwith ι/2π = 0.50 configuration. The ECH pulse with thepower of 312 kW is injected from 165 msec to 290 msec.
The NB with the port-through power of 561 kW is
injected in the counter-direction from 170 msec to 290
msec. The net toroidal current is increased up to 1 kA.
The total toroidal current during counter-NBI injection issmaller than that during co-NBI injection, since the NB
current flows in counter-direction against the bootstrap
current. The m/n = 2/1 mode with low frequency (5 kHz)is observed from 165 msec to 280 msec. The mode
rotates in electron diamagnetic direction. The SX signal
synchronizing with the magnetic fluctuations of low
frequency is observed. Figure 7 shows the relative
amplitude of the fluctuations observed in the SX signal at280 msec when the m/n = 2/1 mode is strongest. The peak
19-3

6

n=2*10 (m )*(1-ρ )2 2

T =0.45(keV)*(1-ρ )eCurrent Density

1.00

(a)

2 2j(ρ)=(1-ρ )2j(ρ)=ρ -ρ0.80

Rotational Transform

0.52

2 2

T =0.15(keV)*(1-ρ )iβ(0)=0.25 %

(b)

0.51

42j(ρ)=1+4ρ -5ρ

40.50

0.60
j

ι/2π

0.49

0.40

0.48
0.47

0.00
0.00

2 2j(ρ)=(1-ρ ) (1kA)
20.20

0.46

0.20

0.40

0.60
ρ

0.80

1.00

0.45
0.00

4j(ρ)=ρ -ρ (1.5kA)
24j(ρ)=1+4ρ -5ρ (2.5kA)
vacuum

0.20

0.40

0.60

0.80

1.00

ρ

Fig. 5 (a) Toroidal current profile and (b) radial profile of rotational transform deduced from VMEC calculation withthe effect of toroidal current and plasma pressure.

Proceedings of ITC/ISHW2007#26308 0.287-0.288 (sec)

180(a)
Phase (degree)δIsx (a.u.)

0.02

0.01

0.00

010(b)

0-18020#26308 0.287-0.288 (sec)

0Ch

1020ChFig. 7 Radial profile of (a) SX fluctuation amplitude and(b) phase difference among SX channels.
current is increased up to 2.5 kA. The rotationaltransform is probably increased by the toroidal current,
resulting in crossing the rational surface. Measurement ofthe mode structure using a 20 channel SX detector arrayshowed that the rational surface was located around ρ =0.8-0.9. The increase of the rotational transform by thetoroidal current is consistent with the equilibrium
calculation.
The m/n = 2/1 mode was observed also in ECH +counter-NBI plasma with ι/2π = 0.50 configuration. By
SX measurement, the rational surface was determined at
the position which is not changed from that of vacuumcondition. Equilibrium calculation also shows that there
is no significant change in the rotational transform profileby the toroidal current. These results suggest that thechange in the rotational transform profile by the toroidal
current is weak in ECH + counter-NBI plasma due to thebalance between bootstrap current and counter-flowing
NB current.

Fig. 6 Time evolution of an ECH + counter-NBI plasma.
The (a) stored energy, (b) toroidal current, (c) magnetic
fluctuation and amplitude of (d) m/n = 2/1.
is observed at 3 ch and 19 ch. The phases of 3ch and 19ch
are almost same and it is consistent with the m = 2
identified by magnetic probes. The positions are almost
similar to the rational surface of 0.5 in vacuum condition.
The VMEC calculations were performed in the same way
as in the previous section. The profiles of toroidal
currents and plasma pressure were similar to that of Sec
3.2. Figure 8 shows the calculated rotational transformprofile with toroidal current. There is no significant
difference between the rotational transform profile
considering the toroidal currents and that of vacuum
condition, compared with ECH + co-NBI plasma. These
results suggest that the change in rotational transformprofile by toroidal current is weak due to the balance
between the bootstrap current and counter-flowing NB
current.

References
[1]
[2]
[3]
[4]
[5]
[6]
[7]

4. Conclusion
The effect of toroidal current on the rotationaltransform has been studied in Heliotron J by measuring
MHD activities. In ECH + co-NBI plasma with ι/2π =0.48 configuration, the m/n = 2/1 mode with low
frequency was observed when the co-flowing toroidal[8]

T. Obiki, et al., 2001 Nuclear Fusion 17 611
S. Yamamoto, et al., 2007 Fusion Sci. Technol. 51 92
G. Motojima, et al., 2007 Nuclear Fusion 47 1045
G. Motojima, et al., 2007 Fusion Sci. Technol. 51 122S. Sakakibara, et al., 1995 Jpn. J. Appl. Phys. 34 L252
E. Sallander, et al., 2000 Nuclear Fusion 40 1499
S. Kobayashi, et al., Proc. 34th EPS Conf. , Warsaw,Poland, 2007
Hirshman S.P. and Betancourt O. 1991 J. Comput. Phys.
96, 9919-3

6

n=2*10 (m )*(1-ρ )2 2

T =0.45(keV)*(1-ρ )e

2 2current density

1.50(a)2 2j(ρ)=(1-ρ )1.00

2j(ρ)=ρ -ρ0.52

j(ρ)=-1+8ρ -7ρ

T =0.15(keV)*(1-ρ )iβ(0)=0.25 %(b)0.51

42Rotational Transform

40.50

0.50

ι/2πj

0.49
0.00
-0.50

0.47

2 2j(ρ)=(1-ρ ) (-0.8 kA)
2-1.00
-1.50
0.00

0.48

0.46
0.20

0.40

0.60
ρ

0.80

1.00

0.45
0.00

4j(ρ)=ρ -ρ (1.8 kA)
24j(ρ)=-1+8ρ -7ρ (1.0 kA)
vacuum

0.20

0.40

0.60

0.80

1.00

ρ

Fig. 8 (a) Toroidal current profile and (b) Radial profile of rotational transform deduced from VMEC calculation
with the effect of toroidal current and plasma pressure.