Plasma and Fusion Research: Regular Articles

Volume 14, 3401081 (2019)

Intermittent Magnetic Fluctuations Associated withHigh-Temperature Bubbles in an ECR Plasma∗)Shinji YOSHIMURA, Kenichiro TERASAKA1) and Masayoshi Y. TANAKA1)
National Institute for Fusion Science, National Institutes of Natural Sciences, 322-6 Oroshi, Toki 509-5292, Japan1)
Interdisciplinary Graduate School of Engineering Science, Kyushu University,
6-1 Kasuga-koen, Kasuga 816-8580, Japan(Received 10 January 2019 / Accepted 15 March 2019)
Magnetic probe measurement has been performed in a cylindrical electron cyclotron resonance plasma inwhich localized high temperature electron region, i.e. high-temperature bubble, has been generated intermittently.
It is found that the high-temperature bubble is accompanied by a pulsed magnetic fluctuation perpendicular to
the external magnetic field. Polarities of the magnetic fluctuation suggest that it should be induced by a transient
upstream electric current. This hypothesis has been validated by a simultaneous increase of electron flux in thedownstream direction. No enhancement of electron flux in the upstream direction has been observed even underthe existence of the bubbles. The result suggests that the electron velocity distribution function in the bubble
should be an asymmetric one, which gives rise to an eﬀective upstream electric current.
c 2019 The Japan Society of Plasma Science and Nuclear Fusion Research

Keywords: intermittency, high-temperature bubble, magnetic fluctuation, electron cyclotron resonance plasma,
HYPER-I device
DOI: 10.1585/pfr.14.3401081

1. Introduction
Intermittent and bursty behavior is a manifestation ofnonequilibrium and nonlinear nature of plasmas, and it is
an important research topic in plasma physics.
Recently, we have reported intermittent generationof high-temperature bubbles [1] in an electron cyclotron
resonance (ECR) plasma. This phenomenon was firstrecognized as spontaneous excitation of sporadic largeamplitude negative spikes in the floating potential signal
measured with a Langmuir probe [2, 3]. Although floating
potential is generally used as a substitute of space potential in the case of constant electron temperature, it is also
very sensitive to a change in electron temperature. This isbecause the abrupt change in electron temperature breaks
the balance between electron current and ion current flowing into the probe electrode from which the floating potential is determined. In our previous experiment, thecurrent-voltage characteristics taken by conditional sampling method revealed that the electron temperature inside
the bubble (32 eV) was about three times higher than thatoutside the bubble (11 eV) [1]. Higher electron temperature increases electron influx by thermal diﬀusion, and thefloating potential becomes more negative to draw more ion
current. Therefore, the negative spikes in floating potential
signal indicate the generation of high-temperature bubbles.
The cross-sectional structure of the high-temperature
bubble can be visualized by two-dimensional measurement
author’s e-mail: yoshimura.shinji@nifs.ac.jp∗) This article is based on the presentation at the 27th International Toki
Conference (ITC27) & the 13th Asia Pacific Plasma Theory Conference(APPTC2018).

of floating potential using the high-impedance wire grid(HIWG) detector [4]. It was shown that the bubble hasa circular cross-section of which diameter defined by fullwidth at half maximum is typically 30 mm. This result wasalso confirmed by a line-emission intensity profile of He I
at 668 nm taken by an ICCD camera, in which the floating potential of a reference Langmuir probe was used asa trigger signal. The image of He I line emission clearly
showed a circular high intensity region of which diameter
was about 30 mm. It should be mentioned that a similar result was obtained when the feeding gas was changed fromhelium to neon [5]. The high-temperature bubbles havebeen observed not only in helium gas discharge but in various gas discharges such as argon, neon and xenon.
Statistical analysis of floating potential time series revealed the randomness of high-temperature bubbles [6].
The probability density function of the waiting time [7]that is defined by a time interval between two consecutive
bubble events was well fitted by an exponential distribution. This result indicates that the bubble is generated at aconstant probability. In other words, the high-temperature
bubble generation is a stationary Poisson process.
We have so far investigated many properties of hightemperature bubbles by means of electrical measurementsuch as Langmuir probes. In order to gain a much deeper
understanding of the phenomenon, magnetic measurement
using magnetic probes should be performed.
In this paper, we report the first observation ofintermittent magnetic field fluctuations associated withthe high-temperature bubbles and discuss the generation

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c 2019 The Japan Society of Plasma
Science and Nuclear Fusion Research

Plasma and Fusion Research: Regular Articles

Volume 14, 3401081 (2019)mechanism of them based on electron flux measurements
using a directional Langmuir probe (DLP) [8]. The experimental device and diagnostic methods are described inSec. 2. The experimental results of magnetic probe measurement are presented in Sec. 3. We discuss the generation mechanism of the magnetic field fluctuation in Sec. 4.
The conclusion is given in Sec. 5.

2. Experimental Setup
The experiments were performed with the HYPER-I
device [9] at the National Institute for Fusion Science. The
HYPER-I device consists of a cylindrical vacuum chamber (30 cm in diameter and 2.0 m in axial length) and ten
magnetic field coils. A schematic drawing of the HYPERI device is shown in Fig. 1. The coordinate system usedin this study is also shown in Fig. 1. The origin of z-axis
is set to the vacuum side surface of the quartz window
for microwave injection, and the origin of x- and y-axis
is set to the center of circular cross-section of the vacuum chamber. The plasma is produced by ECR heatingwith a 2.45 GHz microwave injected from the high-fieldside of the weakly-diverging magnetic field configuration.
The helium gas operation pressure and the microwave input power in this experiment were 1.5 mTorr and 21 kW,
respectively. Under these externally controlled parameters,
the high-temperature bubbles are spontaneously generated
in the plasma. Typical electron temperature outside thehigh-temperature bubbles was 10 eV, and typical electron
density 1018 m−3 .
A DLP, which was originally developed to measure
angle-resolved ion saturation current, was used to measure
the change of angle-resolved electron flux in the present
experiment, and magnetic probes (MPs) were used to measure magnetic fluctuations. Figure 2 shows schematic
drawings of DLP and MP. The DLP consists of a tungsten
electrode (1.5 mm in diameter) covered with an alumina
insulating tube (3.0 mm in diameter) of which side surface
has a hole (1.0 mm in diameter) to collect plasma particles. In order to detect the change in electron flux, the DLP
was connected to the ground through 50 Ω resistor to ensure frequency response, and the voltage across the resistor
was measured. For the correspondence to change in floating potential, the DLP was not connected to a DC power
supply. In the present experiment, the plasma potential
was +30–40 V, and the floating potential +15–20 V. Therefore, the DLP received ion current in steady state. However, when the high-temperature bubble was generated, thefloating potential sharply dropped to a negative value (upto −20 V) due to an abrupt increase in electron flux eventhough the plasma potential remained the same. Then, theDLP received electron current, and the voltage across theresistor showed a negative spike, which was used as anindex of high-temperature bubble generation in this experiment. The DLP was installed on a radial port located atz = 1.175 m. Note that when the hole faces to upstream

Fig. 1 Schematic drawing of the HYPER-I device with a typical magnetic field configuration. A directional Langmuirprobe (DLP) and two magnetic probes (MP1 and MP2)
are located at z = 1.175 m and z = 1.555 m, respectively.

Fig. 2 Schematic drawings of DLP and MP.

(downstream) direction, the DLP detects electron flux inthe downstream (upstream) direction. The MP has a 100turn loop pick-up coil made of polyimide wire of whichdiameter is 0.1 mm. The pick-up coil is covered by aninternal stainless-steel tube to prevent damage from heat,
which has a 1 mm slit to allow the magnetic flux to passthrough the coil. The stainless-steel tube is covered withan alumina insulating tube (8 mm in diameter). Since theoutput signal of MP is proportional to the time derivativeof magnetic flux density, the signal should be numericallyintegrated when the amplitude of magnetic flux density isneeded. The MP was calibrated by a preliminary experiment using a Helmholtz coil to obtain absolute value ofmagnetic fluctuation strength. Two MPs facing each otherwere installed at z = 1.555 m.

3. Experimental Results
At first, we measured the z-component (Bz ) and ycomponent (By ) of magnetic fluctuation by setting the normal vector of the pick-up coil parallel to and perpendicular to the external magnetic field. Figure 3 (a) shows

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Fig. 3 (a) z-component and (b) y-component of magnetic fluctuation measured at x = −20 mm, y = 0 mm. Solid-line
squares (blue online) indicate the positive polarity, andbroken one (red online) the negative polarity.

that no distinct Bz fluctuation was excited in the plasma.
On the other hand, Fig. 3 (b) clearly shows that By fluctuations were excited intermittently with unequal time intervals. Typical amplitude and duration of By fluctuations
were about 40 µT and 10 µs, respectively. These results indicate that the magnetic fluctuations are excited by electric
current parallel to external magnetic field in z-direction.
Moreover, it should be pointed out that the By fluctuations
include a mix of positive (marked by solid-line square) andnegative (marked by broken-line square) polarities as seenfrom Fig. 3 (b).
In order to investigate the direction and the positionsof electric current that induces magnetic fluctuations, measurement with two MPs located at x = +20 mm (MP1) andx = −20 mm (MP2) was performed. Combinations of possible magnetic fluctuation polarities and conceivable electric current directions are illustrated in Fig. 4 (a), where +θdirection is defined as a counterclockwise direction seenfrom the end of the vacuum chamber. Figure 4 (b) shows
the results of simultaneous Bθ measurement with two MPs,
where the detection threshold was set to 9.9 µT. Each quadrant in Fig. 4 (b) corresponds to the situation illustrated in
the same quadrant in Fig. 4 (a). Since no data is plotted in
the first quadrant in Fig. 4 (b), it is concluded that there isFig. 4 (a) Illustrations of magnetic fluctuation directions andconceivable electric currents. (b) Relation between Bθ,MP1
and Bθ,MP2 , which were simultaneously measured withMP1 and MP2.

no downstream electric current that induces +θ-direction
magnetic fluctuations for both MPs at the same time. Inaddition, as seen from the second and the forth quadrants,
it is more reasonable that the Bθ fluctuations are excited by
upstream electric current because of the disparity of Bθ amplitudes. For example, the number of large Bθ,MP1 is greaterthan that of Bθ,MP2 in the second quadrant. Therefore, theelectric current must be passing through near MP1, which
agrees with the case of upstream current (the right-handside arrow in the figure).
It should be mentioned that the result of Fig. 4 (b) does
not mean the third quadrant case is the dominant one, because we set a threshold value condition to pick up Bθ data.
When the upstream electric current passes through outside
the MP1 (MP2), Bθ,MP2 (Bθ,MP1 ) can be small due to thedistance from the current and be smaller than the thresholdvalue.

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Fig. 5 (a) End-view image of the experimental arrangement.
DLP is located at z = 1.175 m and x = 0 mm. MPs are located at z = 1.555 m and x = ± 20 mm. (b) Typical probe
signals associated with a high-temperature bubble.

Fig. 6 (a) Cross-sectional view of DLP and coordinate system.
ϕ is the angle of normal vector of probe surface with respect to z-axis. ϕ = 0 is set to upstream direction. (b) Angle dependence of the ratio of number of large amplitude
negative spikes in DLP signal (N_DLP spike ) to the numberof large amplitude magnetic fluctuations (N_MP fluctuation ).

4. Discussion
From the results shown in Sec. 3, we can build ahypothesis that the magnetic fluctuations are excited bytransient upstream electric current flowing in the hightemperature bubble. In order to confirm the hypothesis,
we performed a simultaneous measurement of electron flux
and magnetic fluctuations. The experimental arrangementof a DLP and two MPs is shown in Fig. 5 (a), where thehole of the DLP was positioned at x = 0 mm and faced toupstream so as to detect the change in downstream electron
flux, and two MPs were located at x = ±20 mm. Typicalprobe signals of single bubble event is shown in Fig. 5 (b).
The polarities of magnetic fluctuations agree with the situation illustrated in the third quadrant of Fig. 4 (a). Moreover, a transient increase in downstream electron flux simultaneously takes place as seen in the bottom panel ofFig. 5 (b), which generates an eﬀective upstream electriccurrent. Although the change in ion flux was not measured in this experiment, it is not plausible that the ion
flux plays an important role in the current that generates
magnetic fluctuations discussed here. It is because the ion
current measured with a Langmuir probe negatively biasedat −90 V showed no noticeable change under the existenceof the bubbles.
Next, we performed angle-resolved measurement ofintermittent electron flux associated with magnetic fluctuation of which amplitude was larger than 40 µT by rotat-ing the shaft of DLP as shown in Fig. 6 (a). The verticalaxis of Fig. 6 (b) is the ratio of the number of large amplitude negative spikes in DLP signal to the number of large
amplitude magnetic fluctuations simultaneously detectedby two MPs. The detection threshold for the DLP signal
was set to −30 mV (−0.6 mA). For each angle, the resultsof five diﬀerent 100 ms time series were averaged. The
typical number of large amplitude magnetic fluctuations in
100 ms time series was about 250, and the dispersion wasless than 2%. When the angle ϕ = 0◦ , the hole of DLP
faced to upstream so that downstream electron flux can bedetected. Figure 6 (b) clearly shows that all large amplitude magnetic fluctuations were accompanied by large amplitude negative spikes in DLP signal. However, there isno negative spikes, i.e. intermittent enhancement of electron flux, when the hole of DLP faced to downstream (ϕ= 180◦ ) even though the large amplitude magnetic fluctuations were excited. Slight spread of count seen within± 45◦ is attributable to the aspect ratio of the hole (1 mm indiameter and 0.7 mm in depth) of DLP. Therefore, we canconclude that the magnetic fluctuations associated with thehigh-temperature bubbles are generated by the enhancement of downstream electron flux that forms an eﬀective
upstream current. This result also suggests that the velocity distribution function in the bubble is not symmetric one

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but an asymmetric one. Integrating this asymmetric velocity distribution function gives net downstream electron fluxin the bubble.

5. Conclusion
We have observed magnetic fluctuations that are associated with high-temperature bubbles in an ECR plasma
by magnetic probes. Relation between the polarities ofmagnetic fluctuations measured with two magnetic probes
suggested that they were induced by upstream electric current. Angle-resolved measurement of electron flux usinga directional Langmuir probe has revealed that enhancement of downstream electron flux takes place in the hightemperature bubble. This flux enhancement leads to aneﬀective upstream current that induces magnetic fluctuations. Asymmetry of transient electron velocity distribution function has also been suggested. It is concluded thatmagnetic probe measurement in the present experiment hasrevealed a dynamic aspect of high temperature bubbles.

Acknowledgments
The authors thank Mr. K. Kanamoto (Kyushu Univ.),
Mr. K. Furuta (Nagoya Univ.), Mr. Y. Kato (KyushuUniv.), and Mr. E. Tanaka (Kyushu Univ.) for useful
discussion and experimental assistance. This work wassupported by JSPS KAKENHI (Grant No. 24540554) andNIFS Collaboration Research Program NIFS13KBAP016.
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