Plasma and Fusion Research: Regular Articles

Volume 14, 2402036 (2019)

Spatiotemporal Structure of Hα Emission fromthe Detached Plasma in GAMMA 10/PDX∗)
Hirohiko TANAKA, Mizuki SAKAMOTO1) , Naomichi EZUMI1) , Akihiro TERAKADO1) ,Kunpei NOJIRI1) , Tomohiro MIKAMI1) , Yosuke KINOSHITA1) , Kaede KOBAYASHI1) ,Masayuki YOSHIKAWA1) , Junko KOHAGURA1) and Noriyasu OHNO
Graduate School of Engineering, Nagoya University, Chikusa-ku, Nagoya 464-8603, Japan
Plasma Research Center, University of Tsukuba, 1-1-1 Tennodai, Tsukuba 305-8577, Japan1)(Received 6 September 2018 / Accepted 10 January 2019)
High-speed camera measurement was performed for analyses of detached plasma fluctuation in the GAMMA
10/PDX tandem mirror device. Significant spectral peaks at frequencies of 1.5 and 3 kHz were observed to haveseveral local maxima along the vertical, near the entrance of the V-shaped target. Wavelet analysis indicatedthat 1.5- and 3-kHz fluctuations became non-simultaneously strong. Their phase relationships demonstrated
inversion-symmetric and symmetric features with respect to the midplane. Such spectral patterns were interpreted
as the line-integral of odd- and even-mode structures. It is suspected that the vertical edge part was due to radiallyelongated structures with an azimuthal phase shift.
c 2019 The Japan Society of Plasma Science and Nuclear Fusion ResearchKeywords: fluctuation, plasma detachment, high-speed camera, frequency analysis, GAMMA 10/PDX
DOI: 10.1585/pfr.14.2402036

1. Introduction
Plasma detachment is sought so as to achieve a suﬃcient reduction in divertor heat load by promoting radiation
and recombination processes via plasma-neutral gas interactions. Recently, enhanced non-diﬀusive transport thatbroadens the plasma profile across the magnetic field wasobserved under the detached divertor condition in several
magnetic confinement devices [1–3]. As the profile broadening contributes to the peak-flux reduction in addition to
the conventional detachment theory, our understanding of
the transport mechanism becomes more valuable.
For the GAMMA 10/PDX tandem mirror device, a recent study shows that blob-/hole-like isolated high-/lowdensity structures appeared at the radial outer-side edge
inside the “divertor simulation experimental module (Dmodule)” [4]. By using Langmuir probes in the D-moduleand upstream microwave interferometers, it was observedthat blob-/hole-like structures were outstanding during thetransient state between the attached and detached divertor
states. Further, these structures rotated in the azimuthal direction together with the rotation of a few mode-numberstructures. In this previous research, although multipoint
fluctuation characteristics were clarified with intrinsic highspatial resolution of Langmuir probes, dependencies in radial and axial directions cannot be separately discussed dueto the structure arrangement.
The high-speed camera is an eﬀective solution formeasuring wide-range fluctuation without any disturbanceauthor’s e-mail: h-tanaka@ees.nagoya-u.ac.jp∗) This article is based on the presentation at the 12th International Conference on Open Magnetic Systems for Plasma Confinement (OS2018).

in observed plasma parameters. In this study, we applieda high-speed camera viewing inside the D-module andfirst investigated the fluctuation characteristics of the detached plasma emission in GAMMA 10/PDX. Fourier andwavelet analyses demonstrated vertical locations of several
anomalous spectral peaks that were attributed to the lineintegral eﬀect. To interpret the obtained frequency characteristics, synthetic data based on a simplified model wasgenerated and compared.
In Sec. 2, experimental setup is described. In Sec. 3,frequency analysis is presented and compared with synthetic patterns. Finally, in Sec. 4, we discuss our experimental results and summarize our study.

2. Experimental Setup
GAMMA 10/PDX equips the D-module in the westend cell with a divergent magnetic field, to study divertor
physics [5]. To evaluate the divertor plasma characteristics, there are several measurement systems inside the Dmodule, e.g., Langmuir probes, a spectrometer, and a highspeed camera [6].
Figure 1 shows a snapshot of 2D images on the xz plane viewed from the north side of the D-module. In
this study, a movie data of the Hα emission intensity, IHα ,which is proportional to the product of neutral and electron densities, was obtained using an optical filter. Theframe rate and shutter speed were 20 kHz and 10 µs, respectively. Although this frame rate was insuﬃcient for
detecting blob- and hole-like structures [4], the measured
region covered a wide area inside the D-module and mode

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

Volume 14, 2402036 (2019)

Fig. 1 Snapshot of Hα emission movie at t = 350 ms with theV-shaped target and Langmuir probes.

structures at several kilohertz could be captured. The amplitude resolution was 8 bits (256 tonal values for eachpixel) and the frame size was 240 × 320 pixels. The approximate position of the V-shaped target with Langmuirprobes (#1 - #5) is also depicted in Fig. 1. The inner angleof the V-shaped target was set to 45◦ . At the same time,probe #17 was located almost upstream of probe #5 along
the magnetic field with a slight deviation in the azimuthal
direction. Ion saturation current (Isat ) fluctuations were acquired at a sampling frequency of 500 kHz.
In this study, we mainly analyzed IHα fluctuations inside the vertically elongated rectangle area (100 × 4 pixels)
near the entrance of the V-shaped target, which avoids
the non-uniform reflection from backstructures such asa flange and bolt holes (see Fig. 1). To reduce noise
and increase amplitude resolution, IHα was averaged at
4 × 4 pixels, which corresponds to an ∼8.8 × 8.8 mm2 areaon the x-z plane, in the undermentioned analyses. Thus,
25 sets of time-series data resized from the rectangular
100 × 4 pixels will be investigated below.

3. Measurement and Analysis
A transient discharge from the attached to detachedstates was analyzed (shot number: 243740). Plasma wassustained with the ion cyclotron range of frequency waves.
This discharge is the same as that in the previous study [4]where the high-speed camera data had not yet been analyzed.

3.1

Time series in the transient discharge

Figure 2 shows the time series of the diamagnetism(DMCC ), the electron line density (NLCC ) in the central
cell, Isat at probes #1, #5, and #17, and IHα at three diﬀerent z positions (A, B, and C) at x ∼ 0 (see Fig. 1). In thisdischarge, H2 gas was puﬀed with a plenum pressure of800 mbar in the middle of a 400-ms pulse discharge. Fromt ∼ 150 ms, Isat and IHα increase due to the gas injection.
A little later, DMCC and NLCC start to get aﬀected slightly.

Fig. 2 Time series of (a) DMCC (dashed line), NLCC (solid line),(b) Isat at probes #1, #5, and #17, and (c) raw IHα at threepositions (A, B, and C in Fig. 1).

On the V-shaped target, we can observe the rollover of Isat
after t ∼ 200 ms. This results from plasma detachment. Att > ∼300 ms, the decreasing and increasing tendencies ofIsat and IHα , respectively, weaken.
Hereafter, a quasi-steady-state detached period withlarge-amplitude IHα at the entrance of the V-shaped target(t = [320, 380] ms) will be investigated in detail.

3.2 Frequency characteristics
Figure 3 (a) shows the Fourier power spectra of IHα asfunctions of the frequency, f , and x, demonstrating a seemingly strange pattern. There are spectral peaks at f ∼ 1.5
and 3 kHz with diﬀerent x locations. In addition, a smalleramplitude peak is confirmed at 4.5 kHz. Figure 3 (b) shows
the vertical distribution of the standard deviation (σ) ofIHα1 , IHα2 , and IHα3 . Here, IHα1 , IHα2 , and IHα3 are defined as the band-passed signals of IHα at f1 = [1, 2] kHz,f2 = [2.5, 3.5] kHz, and f3 = [4, 5] kHz, respectively. The
standard deviations of IHα1 and IHα3 have a local minimum
at x = 0, while σ of IHα2 has a local maximum at the same
position. It should be noted that these distributions have4 - 5 local maxima along x with large amplitudes near thecenter and small amplitudes at the edge.
To detect appearances of these periodic fluctuations intime, the wavelet transform was applied with the Morlet
mother wavelet [7]. Figures 3 (c) and (d) show the absolute values of the wavelet coeﬃcients at f = 1.5 and3 kHz, respectively, as functions of t and x. The former

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Plasma and Fusion Research: Regular Articles

Volume 14, 2402036 (2019)ponent is strong in the latter period, as shown in Fig. 3 (e).
Here, IHα m means the simple moving average of IHα over200 points (10 ms), mainly consisting of low-frequency
components at f < 100 Hz. These figures show wire-meshlike features with diﬀerent inclined angles around the midplane.
Figures 4 (c)(d) and (e)(f) show IHα1 and IHα2 , respectively. It can be confirmed that IHα1 in the former and IHα2
in the latter periods are strong. From Fig. 4 (c), IHα1 atx ∼ +18 and −18 pixels are observed to be anti-phase.
Further, IHα1 at x ∼ ±18 pixels seem to be anti-phase toIHα1 at x ∼ ±40 pixels. On the contrary, IHα2 at x ∼ 0
and ±28 pixels are anti-phase, and IHα2 at x ∼ ±28 and±44 pixels are anti-phase.
Considering the line-integral eﬀect of the high-speed
camera measurement, odd- and even-mode structures
should become weak and strong at x = 0, respectively.
Therefore, fluctuations at 1.5 and 3 kHz must be attributed
to odd and even modes, respectively. This presumption
agrees with the supposition from the microwave interferometer and the segmented central limiter measurements inthe previous study [4] where the azimuthal mode numbers(m) of 1.5- and 3-kHz fluctuations were supposed to bem = 1 and 2, respectively.

3.4 Synthetic patterns based on a simplified
modelFig. 3 (a) Fourier power spectra of IHα at t = [320, 380] ms
as functions of f and x. (b) σ of IHα1 (solid line), IHα2(dashed line), and IHα3 (dotted line) along x. The absolute values of the wavelet coeﬃcients of (c) IHα at 1.5 kHzand (d) 3 kHz as functions of t and x, and (e) Isat at probe#17 as functions of t and f .

fluctuation seems to appear frequently at t < ∼360 ms.
On the contrary, the latter fluctuation largely occurs att > ∼345 ms. These fluctuations are thought to be strong
non-simultaneously. Figure 3 (e) shows the absolute valueof the wavelet coeﬃcient of Isat at probe #17 versus t andf . Amplitudes of f = 1.5 and 3 kHz components in theIsat fluctuation show similar temporal tendencies with thoseof IHα .

3.3

Phase relationship along the x direction

To interpret the periodic fluctuations shown in Fig. 3,
the spatiotemporal behavior of the phase relationship wasinvestigated. Figures 4 (a) and (b) show fluctuation components (IHα − IHα m ) as functions of t and x at t =[337, 339] ms and [363, 365] ms. In the former period, the1.5-kHz fluctuation is dominant, whereas the 3-kHz com-

To understand detailed mode structures, we generated
a similar plot from a simplified artificial mode function
considering the line-integral eﬀect. Figure 5 shows thesynthetic patterns calculated from the modeled signals asfunctions of t and x. In this calculation, we assumed thata mode has an amplitude with sin(2πm frot t − mθ), whereθ is the azimuthal angle, existing on a single circle withradius R0 , and it rotates with a frequency of frot . At anx-position where the mode intensities at forward and backsides in the line of sight are in-phase/anti-phase, IHα becomes strong/weak. In addition, IHα at |x| ∼ R0 becomesstrong due to the line-integral of a self-structure.
Mode structures at m = 1 and m = 2 rotating withfrot = 1.5 kHz could reproduce the experimentally observed phase relationships around x = 0, as shown inFigs. 5 (a) and (b). However, in the far-edge region at|x| > R0 , there is no structure unlike Figs. 4 (c) and (f).
To obtain the far-edge structures with a single mode on acircle, m = 3 and 4 were employed, as shown in Figs. 5 (c)and (d). When higher-order modes are used, experimentally observed inclined angles of in-phase region aroundx = 0 can be obtained when frot = 0.5 kHz for m = 3and frot = 0.75 kHz for m = 4. Although center- andedge-phase relationships are reproduced, an alternate appearance of m = 3 and 4 structures of varying rotationalfrequencies is unnatural.
One of the possible reasons that the far-edge structures
cannot be reconstructed from m = 1 and 2 modes in the2402036-3

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Volume 14, 2402036 (2019)

Fig. 4 (a)(b) IHα − IHα m , (c)(d) IHα1 , and (e)(f) IHα2 as functions of t and x at (a)(c)(e) t = [337, 339] ms and (b)(d)(f) [363, 365] ms.

Fig. 5 Synthetic patterns from modeled signals with (a) m = 1, (b) 2, (c) 3, and (d) 4. frot was calculated as the peak frequency divided
by m. R0 was determined from the peak position of σ in Fig. 3 (b).

above calculation is attributed to the assumption that themode exists on a single circle. A mode structure shouldhave a finite size and it could have an azimuthal phase shift
in the radial direction. For example, if a mode structure hada spiral shape like Refs. [8, 9], the phase relationship could
have an anti-phase structure in the far-edge region.

4. Summary and Discussion
High-speed camera measurement of the detachedplasma fluctuation was performed using GAMMA
10/PDX. To investigate spatiotemporal patterns of themode structures, Fourier and wavelet transforms were applied. In addition, band-passed signals were plotted to understand the phase relationship in the vertical direction. It
was clarified that odd- and even-mode structures were detected as the spectral peaks at f = 1.5 and 3 kHz. If theirrotation frequencies were the same, azimuthal mode numbers were m = 1 and 2. However, it was also observedthat a low-m structure on a single circle cannot reproduce
the experimentally observed far-edge phase pattern. Theremight be radially elongated structures with an azimuthal
phase shift. To clarify the shapes of the mode structures, acomparison between the emission signals and other fluctu-2402036-4

Plasma and Fusion Research: Regular Articles

Volume 14, 2402036 (2019)ations that have no line-integral eﬀect would be eﬀective.
We are now planning to use a reciprocating probe just in
front of the D-module in addition to the high-speed camera and Langmuir probes on the V-shaped target.
Because the blob- and hole-like structures reported inRef. [4] lay in the f > 10-kHz frequency range and theNyquist frequency of the above-described high-speed camera measurement was 10 kHz, we could not detect thesestructures in this study. In future, we should capture withhigher temporal resolution. Furthermore, the instability
type should be clarified with the radial electric field measurement, among others.

Acknowledgments(16H06139, 16H02440), the NIFS Collaboration Researchprogram (NIFS17KUGM120, NIFS17KUGM130), andthe NINS program of Promoting Research by Networking
among Institutions (01411702).
[1] H. Tanaka et al., Phys. Plasmas 17, 102509 (2010).
[2] D. Carralero et al., Nucl. Fusion 58, 096015 (2018).
[3] H. Tanaka et al., Plasma Phys. Control. Fusion 60, 075013(2018).
[4] H. Tanaka et al., Phys. Plasmas 25, 082505 (2018).
[5] Y. Nakashima et al., Nucl. Fusion 57, 116033 (2017).
[6] A. Terakado et al., AIP Conf. Proc. 1771, 050008 (2016).
[7] N. Ohno et al., Contrib. Plasma Phys. 44, 222 (2004).
[8] S. Inagaki et al., Nucl. Fusion 52, 023022 (2012).
[9] H. Tanaka et al., Contrib. Plasma Phys. 50, 256 (2010).

This research was supported by JSPS KAKENHI

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