Proceedings of ITC/ISHW2007

Effects of Rotating Magnetic Islands Driven by External
Perturbation Fields in TU-Heliac
S. Kitajima, H. Umetsu, M. Sasao, A. Okamoto, T. Kobuchi, Y. Tanaka, H. Utoh, H. Aoyama,
K. Iwazaki, S. Inagakia, M. Takayamab, A. Komoric, K. Nishimurac, Y. Suzukic,
M. Yokoyamac, H. Takahashic
Department of Quantum Science and Energy Engineering, Tohoku University, Sendai 980-8579, Japana

Research Institute for Applied Mechanics Kyushu University, 6-1 Kasuga-kouen, Kasuga, Fukuoka 816-8580, JapanbcAkita Prefectural University, Honjyo, Akita 015-0055, Japan

National Institute for Fusion Science, 322-6 Oroshi-cho, Toki 509-5292, Japan

New method of rotating the magnetic islands by the external perturbation fields was proposed. The perturbation
fields were produced by 4 pairs of cusp field coil, in which the alternating currents flowed and the currents had the/2 phase shift. The phase shifter for the coil currents was designed and constructed. The phase difference in the
floating potential signals measured by the two Langmuir probes confirmed that the rotation of the magnetic islandsin the counterclockwise direction (c/c) direction. The clockwise (c/w) rotation was also observed in the plasma
biased by the hot cathode electrode. These experimental results suggest the ability of the plasma poloidal rotation
driven by rotating islands.
Keywords: stellarator, heliac, magnetic islands, poloidal rotation, perturbation field, electrode bias

1. Inroduction
Study of magnetic island effects on the transport inhelical devices is important, because it leads to theadvanced control method for a plasma periphery in afusion reactor. For the research on island effects onconfinement modes, the Tohoku University Heliac(TU-Heliac) has advantages that (1) the position of arational surface is changeable by selecting the ratio of coilcurrents, (2) the island formation can be controlled byexternal perturbation field coils, (3) a radial electric fieldand particle transport can be controlled by the electrodebiasing. In TU-Heliac the improved mode transition has
been triggered by electrode biasing using a hot cathodemade of LaB6. The driving force J x B for a plasma
poloidal rotation was externally controlled and the poloidalviscosity was successfully estimated from the external
driving force [1-3]. In recent experiments the ion viscosity
in the biased plasma with islands was roughly estimated. It
suggested that the ion viscosity increased according to theincrease of the magnetic island width [4]. Therefore it isexpected that plasma poloidal rotation will be driven by thepoloidal rotation of the island. The purposes of thisexperiment are, to propose the new method of rotatingislands by the external perturbation fields, to survey theability of the plasma poloidal rotation driven by rotatingislands and, to study the rotating island effects on
confinement modes in TU-Heliac.
sumio.kitajima@qse.tohoku.ac.jp

2. Experimental Setup
2.1. TU-Heliac
The TU-Heliac is a 4-period heliac (major radius,0.48 m; average plasma radius, 0.07 m). The heliac
configurations were produced by three sets of magnetic

Fig. 1 Bird’s eye-view of TU-Heliac and 4 pairs ofupper and lower external perturbation field coils. 4
pairs of coils were divided into two groups (thefirst group consists of 1U1D and 3U3D, thesecond group of 2U2D and 4U4D).

Proceedings of ITC/ISHW2007

2.2. External Perturbation Coils
In TU-Heliac we selected the current ratio to locate arational flux surface (n/m = 5/3) in the plasma periphery.
The efficient configuration of perturbation coils forgenerating islands (m = 3) has been searched. We decided
4 pairs of upper and lower external perturbation field coils,
which located at the toroidal angle  = 0°, 90°, 180° and
270°, and generated cusp field at each toroidal angle asshown in Fig. 1. We explored the possibility of the poloidal
rotation of islands by changing the phase of the each
perturbation coil current. We tried the method that,
dividing perturbation coils into two groups (the first groupconsists of 1U1D and 3U3D, the second group of 2U2D
and 4U4D), changing perturbation current separately, one

90° phase shifter
10 m
12 μF

1U

1D0,18090,2700E

I (A)field coils: 32 toroidal field coils, a center conductor coil,and one pair of vertical field coils as shown in Fig. 1.
Three capacitor banks consisting of two-stage pulse
forming networks separately supplied coil currents of 10
ms flat top [5]. The target plasma for external perturbation
fields was He plasma produced by low frequency joule
heating (f = 18.8 kHz, Pout ~ 35 kW). The joule heating
power was supplied to one pair of poloidal coils woundoutside the toroidal coils [6]. The vacuum vessel was filledwith fueling neutral He gas and sealed from the evacuation
system before every discharge. The electron density andtemperature measured by a Langmuir probe (triple probe)
were ~ 6 x 1017 m-3 and ~ 20 eV at the magnetic axis andthe magnetic field strength at the axis was 0.3 T.

3030.53131.532

Time (ms)Fig. 3 Perturbation coil currents measured by theRogowsky coils. Two group coil currents have /2phase shift and same values.

is the average radius of the rational flux surface (n/m = 5/3)
and m is the mode number of magnetic islands. The
poloidal rotation velocity can be changeable by thefrequency . Furthermore we can select the poloidal
rotation direction (clockwise c/w or counterclockwise
direction c/c) by changing the polarity of the phase shift.
Here the c/c direction means the ion diamagnetic direction.
In the experiment we adopted the phase shifter shownin Fig. 2, which consisted of precisely tuned capacitors andresister. The perturbation field coil current was 1.2 kAT
and the frequency was 2.515 kHz. The current and thefrequency were selected to perform the preliminaryexperiments and we have the plan of increase in current
and frequency. Figure 3 shows the perturbation coilcurrents measured by the Rogowsky coils. We can see thattwo group coil currents have /2 phase shift and samevalues.
Figure 4 shows the magnetic surfaces with m = 3
magnetic islands which were produced by the external
perturbation fields. The m = 3 magnetic islands rotated by

13.38 μF

2UV

2D

2.515 kHz
3U

3D

Fig.2 Schematic
perturbation coils.

4U

4D

circuitfortheexternalgroup’s current was Iex = I0sin(t) and other was Iex =I0sin(t - /2). Each coil produces an alternating cusp fieldwith the frequency . The result of magnetic surface
calculations suggested that islands rotate to poloidaldirection with the poloidal velocity of <r>/m. Here, <r>Fig. 4 Cross section of magnetic surfaces with m = 3
magnetic island. Two Langmuir probes on the magnetic
surface at the positions which were separated about ahalf of the poloidal length of the island.

Proceedings of ITC/ISHW2007

3. Phase shift in Probe Measurements
To check experimentally the effect of the external
perturbation field, we measured the floating potential by aLangmuir probe (high speed triple probe [7, 8]), which wasinserted from the low field side at the toroidal angle  = 0°.
In Fig. 5 it is clear that the floating potential signal has thefrequency component of the perturbation fields (lowertrace) and the phase shift to the external perturbation coil-25
Perturbation Coil Current

Vf (V)

-30
-35
-40
30

3132

33

3435

Time (ms)Fig. 5 External perturbation coil current and thefloating potential measured by a Langmuir probe(high speed triple probe).

current (upper trace). Then we measured the radial profileof the FFT power spectrum in the floating potential signals.
Figure 6 shows the relation between the power spectrum of
the floating potential and the radial position of theLangmuir probe. Figure 6 clearly shows that the frequencyof the perturbation field coil current (f = 2.515 kHz) was
excited around the m = 3 magnetic island.
In order to confirm the rotation of magnetic islands
we set two Langmuir probes on the magnetic surface at thepositions which were separated about a half of the poloidal

length of the island. These probes were set at the same
meridian plane at the toroidal angle  = 0° as shown in Fig.
4. We measured the phase shift in the frequency of theperturbation fields (f = 2.515 kHz) between two probe
signals. Figure 7 shows the difference of the phase between
the floating potential signals at the three radial points. The
open symbols and closed symbols denote the c/w and c/c
directions of the rotating islands which were expected by
the calculations. We can confirm that at the inside the m =3 islands the phase difference was about  in the c/c
direction case, which was consistent with the calculation
results and suggested the rotation at the inside of the island(R = 102 mm), and corresponded to the poloidal rotation
velocity of ~ 0.2 km/s. These experimental results suggest
the ability of the plasma poloidal rotation driven byrotating islands. However in the c/w case the phasedifference had the small positive values, which wereinconsistent with the calculation, because it should be -.
In these experiments the target plasma had the weak
positive radial electric fields (Er ~ 2 kV/m), thus the bulk
plasma rotated in the c/c direction by the E x B rotation.
Therefore we can explain that there are some restrictions
on the rotation of the islands in the direction which is
opposite to the natural direction of the bulk plasma rotation(c/c direction).

4c/c rotation
c/w rotation

phase shift (rad)the alternating perturbation fields.

20-2-480

m=3island

LCFS

Magnetic Axis

90

100

110

120

R (mm)
Fig. 7 Difference of the phase between the
floating potential signals at the three radial points.
The open symbols and closed symbols denote thec/w and c/c directions of the rotating islands
which are expected by the calculations.

Fig. 6 Relation between the FFT power spectrumof floating potential and the radial position of theLangmuir probe.

In TU-Heliac we can bias the potential to the plasma
by the hot cathode electrode made of LaB6. We can control
the negative radial electric field externally by the electrodebiasing. The hot cathode (diameter, 10 mm; length, 17Proceedings of ITC/ISHW2007mm) was inserted horizontally into the plasma from thelow magnetic field side at a toroidal angle  = 270°. Them = 3 islands were formed at the outside of the hot cathode.
The direction of the E x B rotation was the c/w direction,
thus we can decelerate the natural c/c plasma rotation. Here
E is the radial electric field made from the biasing. We
tried to apply the external perturbation fields to rotate theislands in the biased plasma. Figure 8 shows the relation
between the differences of the phase in two floating
potential signals and the electrode current used for theplasma biasing. The increase in the electrode current
means the increase in the c/w plasma rotation velocity. We
showed again the results without the electrode biasing (IE =0 A) shown in Fig. 7. Before the application of the external
perturbation fields we tried to measure the velocity of thec/c rotation
c/w rotation

phase shift (rad)4R = 102 mm

24. Summary
We proposed the method to rotate the magnetic
islands by the external perturbation fields which wereproduced with 4 pairs of cusp field. The alternating
currents for the perturbation coils have the /2 phase shift.
We designed and constructed the phase shifter for the coilcurrents and we measured the phase difference in thefloating potential signals by two Langmuir probes, which
confirmed that the rotation at the inside of the magnetic
islands in the c/c direction. Furthermore the c/w rotation
was also observed in the plasma biased by the hot cathodeelectrode. These experimental results suggest the ability ofthe plasma poloidal rotation driven by rotating islands,
though the island rotation was affected by the rotation of
the target plasma. We can expect the higher poloidal
rotation velocity by increasing in the frequency of theperturbation coil current.

Acknowledgment
This work was supported by a Grant-in-Aid from theMinistry of Education, Science and Culture of Japan (No.
17360439).

References

0-2-4012IE (A)Fig. 8 Relation between the differences of thephase in two floating potential signals and theelectrode current. The increase in the electrodecurrent means the increase in the velocity of thec/w bulk plasma rotation.

plasma poloidal rotation by the phase velocity of highfrequency fluctuations in floating potential [2, 9]. From
this results the plasma poloidal rotation disappeared in thecase which the electrode current was about 2 A. In Fig. 8
we can see that in the c/w island rotation case the phasedifference had about -2 rad at IE = 2 A, which wasconsistent with the calculations and suggested the rotationof the magnetic island, although in the c/c island rotation
cases the phase difference decreased compared with theexperimental results in Fig. 7. This suggested that the bulk
plasma rotation by the biasing was overdriven.

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