Proceedings of ITC/ISHW2007

Density Collapse of Poloidally Rotating Plasma in TU-Heliac
Y. Tanaka, S. Kitajima, M. Sasao, H. Utoh, H. Aoyama, K. Iwazaki, H. Umetsu,
K. Ishii, A. Okamoto, T. Kobuchi, S. Inagakib, Y. Suzukia, and H. Takahashia
Department of Quantum Science and Energy Engineering, Tohoku University, Sendai 980-8579, Japana
National Institute for Fusion Science, Toki 509-5292, Japanb
Research Institute for Applied Mechanics, Kyushu University, Kasuga 816-8580, JapanThe ohmic heated plasma in TU-Heliac was biased by a hot-cathode and the E×B poloidal rotation was driven.
Coincident measurements of the line density and the ion saturation current revealed the existence of the density
collapse accompanied by the fluctuation in the poloidally rotating plasma. The power spectra were calculated from theion saturation current and the floating potential obtained by the high-speed triple probe. The density collapse
frequency was 1~10 kHz. The fluctuation frequency was 100~1000 kHz. The density radial profile at the moment
when the collapse occurred was estimated. The steep density gradient was vanished by the density collapse. The radial
profile of the fluctuation frequency was compared to that of the E×B poloidal rotation frequency. Both profiles had thesimilar radial dependence. From this comparison, the poloidal mode number of the fluctuation was estimated to be m =2 or 3. The collapse and the fluctuation localized in the core plasma region. This result suggested the existence of thecross-interaction between the density collapse and the fluctuation.
Keywords: heliac, stellarator, poloidal rotation, density collapse, fluctuation,

1. Introduction
H-mode was discovered in ASDEX Tokamak [1] andthen the mechanism of the improvement has been studied
for a long time. Recently it is considered that the plasma
rotation suppresses the anomalous transport. It is alsosuggested that a turbulent flow can drive the poloidal
rotation such as the zonal flow and that the poloidal shock
is formed at a moment when the poloidal mach number
exceeds unity [2]. Therefore, the understanding of theplasma rotation, especially in the super sonic regime, is
important.
Spontaneous E×B rotation is formed in the improved
plasma of the large device. An electrode biasing can drive
the E×B rotation in the small device and the confinement
improves. In Tohoku University Heliac (TU-Heliac), thenegative biasing experiment has been carried out for the
study of the transition phenomenon to the improved mode
[3-11]. A hot-cathode made of LaB6 was used for theelectron injection to the plasma and the negative potential
was formed. Typical behaviors of the improved mode were
the threefold increase in the density and the formation of
the radial electric field (2~4 kV/m). The E×B poloidal
rotation frequency exceeded 100 kHz. At the same time,the density and the potential fluctuations were observed in
the low frequency range (1~10 kHz) and the highfrequency range (100 ~ 1000 kHz) [6, 9, 11]. The highauthor’s e-mail: yutaka.tanaka@ppl2.qse.tohoku.ac.jp

frequency fluctuation burst and had the radial dependency.
In this work, the characteristics of the poloidally rotatingplasma are studied. Then the fluctuations are measured
coincidently and the radial profile of the high frequency
fluctuation is compared to that of the poloidal rotation.

2. Experimental Setup
TU-Heliac is a helical axis stellarator and has the bean
shaped flux surface [3]. Top view of TU-Heliac is shownin Fig. 1. Major radius is 0.48 m and minor radius is 0.06
m. Toroidal period number is 4. The standard magnetic
configuration was selected. The magnetic well depth at thelast closed flux surface (LCFS), the rotational transform at
the axis and the magnetic field were 2 %, 1.54 and 0.3 T,
respectively. Working gas was He. A plasma was producedby the low frequency alternate ohmic heating. The
frequency of the heating wave was 18.8 kHz. The plasma
current, the loop voltage and the absorbed power to theplasma were 200 A, 200 V and 2 kW, respectively. A
hot-cathode was used for the electron injection. The top
position of the hot-cathode was RHC = 86 mm. The origin
of RHC was the center of the center conductor coil. The
hot-cathode was biased against the vacuum vessel. The
bias voltage was -230 V and the electrode current was
about 4 A. The fluctuation was one of the important
plasma parameters and should be measured. In theProceedings of ITC/ISHW2007

Fig. 1 Top view of TU-Heliac

hot-cathode biased plasma, the E×B poloidal rotation
frequency exceeded 100 kHz. The fluctuation frequency
reached 400 kHz by the poloidal rotation. Langmuir probe
method had the advantage of spatial and time resolutions.
Therefore, the high-speed triple probe system (cutoff
frequency 1 MHz) was installed to TU-Heliac [11]. It wasinserted from the low field side. Its position was defined by
RTP as shown in Fig. 1. The magnetic axis corresponded to
RTP = 79 mm and the LCFS corresponded to RTP = 118 mm.
The 50 GHz microwave interferometer and the rake probe
were also used for the coincident measurement. The rake
probe had 3 tips and its tips were set radially. The length
between the top and bottom tips was 6.0 mm, which was
small compared to the minor radius.

3. Density Collapse Accompanied by Fluctuation
The coincident measurements at the multi-position areimportant to understand the plasma physics. The positionsof the triple probe and the rake probe were calibrated using
the electron gun. These probes were set at ρ = 0.2 and thebiasing experiments were carried out, where ρ was thenormalized minor radius defined by ρ = <r>/a, <r> was theaverage radius of the flux surface and a was the minor
radius. ρ = 0.2 corresponded to RTP = 87 mm. Figure 2
shows the typical time traces of the line density nel and theion saturation current Is. The ion saturation current
suddenly decreased on the time scale of 0.01 ms (ex. time= 8.50, 8.65 and 8.81 ms). After the sudden decrease, it
slowly increased on the time scale of 0.1 ms.
Simultaneously the line density, which was measured
along the central chord as shown in Fig. 1, had the sametendency of increase and decrease, though it did not show
the sudden decrease because it was the integrated
parameter. Ion saturation current is proportional to density
and root of electron temperature. Increase and decrease of
the ion saturation current indicate that of the density. The

Fig. 2 Time traces of the line density nel and the ion
saturation current Is . The positions of the triple probe andthe rake probe were ρ ~ 0.2. The arrows indicate the timeof the density collapse.

sudden decrease of the density was observed in different
toroidal and radial positions. Therefore, this phenomenon
is considered the density collapse. In the sawtooth of CHS,
soft X-ray decreased at ρ < 0.5 and increased at ρ > 0.5[12]. In the density collapse of TU-Heliac, the difference
between the inside and the outside obtained by the rake
probe was not observed. This reason is considered that theprobe tips were close compared to the minor radius. Also
the fluctuation was observed in the ion saturation current,
though it was not observed in the line density because themicrowave interferometer could not measure the local
parameter. This fluctuation burst and had the simultaneous
characteristic between all signals. It did not appear in thephase of the density increased after the density collapse (ex.
time = 8.50~8.60 ms and 8.65~8.70ms). This result
suggests that the growth rate of the fluctuation has thedensity or the density gradient dependence.
The power spectra were calculated from the ion
saturation current Is and the floating potential Vf measured
by the triple probe as shown in Fig. 3. Fast Fourier
Transform was used in the calculation in spite of the burstof the fluctuation. Both spectra had the similar power
distribution. The density collapse frequency was 1~10 kHz.
Floating potential is determined by electron temperatureand space potential. The power of the floating potential
indicates that the electron temperature or the spacepotential also collapsed with the density. The fluctuation
frequency was 100~1000 kHz. The sharp peaks at 18 and
37 kHz were fundamental and second harmonic waves of
the alternate ohmic heating. The peak at 3 MHz was thenoise of the isolation amplifier.
The density radial profile at the moment when thecollapse occurs is required for the understanding of thecollapse, though it can not be measured by the present
diagnostic system in TU-Heliac. The triple probe wasProceedings of ITC/ISHW2007

Fig. 4 Radial profile of the ion saturation current obtainedby the triple probe. Low pass filter of 18.0 kHz was used
to remove the 18.8 kHz ohmic heating wave. In RTP =76~87 mm, the ion saturation current decreased about
40 % after the collapse.

Fig. 3 Power spectra of (a) the ion saturation current Is and(b) the floating potential Vf. Probe position was ρ = 0.2. The
density collapse frequency was 1~10 kHz and the fluctuation
frequency was 100~1000 kHz.

moved its radial position shot by shot. The data of the ion
saturation current was obtained moving its position every 1
mm. Digital low pass filter of 18.0 kHz was used toremove the 18.8 kHz ohmic heating wave and to pick up
only the frequency corresponded to the collapse. The dataobtained by 47 shots were plotted as shown in Fig. 4. The
magnetic axis corresponded to RTP = 79 mm and the LCFS
corresponded to RTP = 118 mm. The estimation of thedensity profile at the moment when the collapse occurred
was possible from this figure. The maximum and theminimum in the ion saturation current indicated the density
profiles before and after the collapse. The triple probe
position in Fig. 2 was RTP = 87mm. Before the collapse,
steep gradient existed in RTP = 83~90 mm. After thecollapse, the ion saturation current decreased about 40 % in
RTP = 76~87 mm. The steep gradient was vanished by thecollapse. This result suggests that the density gradienttriggers the collapse.
The poloidal momentum balance between Jr×B
driving force, ion viscosity and ion friction determines thepoloidal rotation speed. We can control the friction term byfilling the working gas because the friction results fromcharge exchange between ions and neutral particles. The
radial profiles of the power spectra are shown in fig. 5.
These were calculated from the ion saturation current
obtained by the triple probe. Working gas pressure (a)1.3x10-2 Pa, (b) 3.5x10-2 Pa were selected. Fig. 5 (a) lacks
the high field side spectra. The triple probe was inserted
from the low field side and the measurement of the highfield side was restricted by the disturbance from the probe

Fig. 5 Radial profile of the power spectra calculated fromthe ion saturation current at working gas pressure (a)pHe=1.3x10-2 Pa, (b) pHe=3.5x10-2 Pa. The lines show thepoloidal rotation frequency calculated by Eq. (1). The
arrows indicate the magnetic axis and LCFS.

to the plasma. The fluctuation had the large power in RTP =85~95 mm in both pressure conditions and it had
symmetry against the magnetic axis in the high-pressure
condition. There was a hole on the magnetic axis, in which
the fluctuation did not exist. The fluctuation had the radial
dependence such as 1/r. The frequency in the low-pressure
condition was 2 times higher than that in the high-pressure
condition. The fluctuation frequency might be determinedby the poloidal rotation frequency. Then the comparison
between these frequencies is important. The E×B poloidal
rotation frequency fEB can be estimated from the radial
profile of the floating potential and is written as

Proceedings of ITC/ISHW2007

dV f d r,
f EB =
2" r B#(1)

where Bφ is the toroidal magnetic field. Essentially the
space potential should be used for the calculation of the!rotation frequency though it has too large error near themagnetic axis and can not be used. This may be consideredthat the size of the triple probe (5 mm) is comparable to theradius of the flux surface. Eq. (1) approximately represents
the correct rotation characteristic because it largely
depends on <r> in the denominator. The frequency of mfEB
was also plotted in Fig. 5, where m was the positive integer.
m = 1 line indicated the poloidal rotation frequency and it
increased as it got close to the magnetic axis. It reached
150 kHz in the low-pressure condition. The fluctuations inboth gas conditions had the similar radial dependence to m
= 2~3 line. The physical meaning of m is the poloidal
mode number. The fluctuation poloidal mode is estimatedto be m = 2 or 3. It also showed the surprising result. The
fluctuation burst simultaneously in the different radial
positions as shown the rake probe in Fig. 2. On the other
hand, the fluctuation frequency had the radial dependence.

4. Discussion
It was observed that the density profile wasasymmetry against the magnetic axis as shown in Fig. 4. It
may represent the plasma compressibility. To satisfy thecontinuity equation under the E×B poloidal rotation, theplasma is compressed at the certain poloidal angle. Ions try
to remove the density anisotropy by the parallel thermal
motion. Poloidal Mach number Mp is useful to estimate theplasma compressibility. Mp means the ratio of the parallel
diffusion time by the ion thermal motion to the E×B
poloidal rotation time. Mp is written as,#1

M p = q"#1v t v EB ,(2)where q is the safety factor, ε = <r>/R is the toroidal ripple,
vt is the ion thermal velocity and vEB is the E×B poloidal!velocity. Eq. (2) is rewritten to the convenient form as,"1

M p = qRv t # EB ,(3)

where ωEB is the E×B poloidal rotation frequency
calculated by Eq. (1). Substituting ωEB into Eq. (3),!poloidal Mach number was calculated as Mp ~ 10. This
result shows that the ion diffusion is not sufficient against
the ion compression by the E×B poloidal rotation. Thenthe asymmetry of the ion saturation current suggests thecompressibility of the plasma.
The density collapse and the fluctuation wereobserved in the core region of the plasma. The steep
density profile was vanished by the density collapse. The
fluctuation did not appear in the phase of the density
increase after the collapse. These results suggest theexistence of the cross-interaction between the density
collapse and the fluctuation. The frequencies of thepoloidal rotation and the fluctuation reached 15 % and30~40 % of the ion cyclotron frequency. There ispossibility of the electromagnetic wave such as Alfven
wave. The magnetic fluctuation should be measured for theunderstanding of this phenomenon.

5. Summary
The hot-cathode biasing experiment was carried out in
TU-Heliac. Coincident measurements of the line density
and the ion saturation current revealed the existence of thedensity collapse accompanied by the fluctuation in thepoloidally rotating plasma. The power spectra of the ion
saturation current and the floating potential showed that thedensity collapse frequency was 1~10 kHz and that thefluctuation frequency was 100~1000 kHz. The steep
density gradient was vanished by the density collapse. The
radial profile of the fluctuation frequency was compared tothat of the E×B poloidal rotation frequency. Both profiles
had the similar radial dependence. From this comparison,
the poloidal mode number of the fluctuation was estimatedto be m = 2 or 3. The poloidal mach number reached 10
and suggested the plasma compressibility.

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

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