S-P6-4
Dynamics of global transport and turbulence noise force - an experimental
analysis on plasma turbulence
乱流ノイズ力と大域的輸送ダイナミクス―プラズマ乱流の実験解析
Yoshihiko Nagashima1, Sanae -I. Itoh1, Shigeru Inagaki1, Hiroyuki Arakawa2,
Naohiro Kasuya3, Akihide Fujisawa1, Kunihiro Kamataki1, Takuma Yamada4,
Shunjiro Shinohara5, Stella Oldenbürger1, Masatoshi Yagi1,2, Yuichi Takase4,Patrick H. Diamond6, and Kimitaka Itoh3
永島芳彦1，伊藤早苗1，稲垣滋1，荒川弘之2，糟谷直宏3，藤澤彰英1，鎌滝晋礼1，山田琢磨4，篠原俊二郎5，オルデンバーガーステラ1，矢木雅敏1,2，高瀬雄一4，
ダイアモンドヘンリーパトリック6，伊藤公孝3
1Kyushu University, 6-1 Kasugakoen, Kasuga 816-8580, Japan
Japan Atomic Energy Agency, 801-1 Mukoyama, Naka 311-0193, Japan
3
National Institute for Fusion Science, 322-6 Oroshi-cho, Toki 509-5292, Japan
4
The University of Tokyo, 5-1-5 kashiwanoha, Kashiwa 277-8561, Japan
5
Tokyo University of Agriculture and Technology, 2-24-16 Nakamachi, Koganei 184-8588, Japan
6
University of California San Diego, 9500 Gilman Drive, La Jolla, San Diego, CA 92093-0424, USA1
九州大学 〒816-8580 福岡県春日市春日公園6-1
2
日本原子力研究開発機構 〒311-0193 茨城県那珂市向山801-13核融合科学研究所 〒509-5292 岐阜県土岐市下石町322-64東京大学 〒277-8561 千葉県柏市柏の葉5-1-55
東京農工大学 〒184-8588 東京都小金井市中町2-24-166
カリフォルニア大学サンディエゴ校 〒92093-0424 米国加州サンディエゴ郡ラホヤ市ギルマン大通り9500
2Results from “extreme” measurement and analysis in a plasma turbulence are presented. Two azimuthalprobe arrays, which cover the whole area of azimuthal direction of an inhomogeneous magnetized plasma
column, realize simultaneous measurement of “dynamics” of global particle and momentum transports
driven by micro-scale turbulence for the first time. Non-Gaussian probability density functions (PDF) of
the azimuthally averaged transports are observed, and we confirm that the transition from the point-wise
PDFs to averaged ones. The change in the particle flux leads that in the momentum flux, demonstratingthat the momentum flux is induced by the relaxation of density gradient.

1. Introduction
Pursuit of the “extreme” in existing techniquesand methods sometimes explores new discovery
and opens the way to breakthrough of research
fields. This talk presents a challenge to “extreme”
experimental research on turbulence.
The research target is probability density
function (PDF) and dynamics of global transport
by plasma turbulence. Stochastic process ofturbulence fluctuation and transport often showsintermittent property and significant deviationfrom Gaussian PDF. It is considered that thenon-Gaussianity of the PDF of turbulence is oneof the key elements that characterize thefar-non-equilibrium states [1]. The intermittency
may play an important role in triggeringtransition phenomena [2]. Although progress ofstudy of the non-Gaussian PDF of point-wiseparticle flux has been noticeable in experiment[3], measurements of the global transport byturbulence are required because relaxation of theplasmas depends upon the global transport. Inaddition, the global momentum flux, essential forthe generation of global axial vector field byturbulence, is also important because the global
vector fields have considerable effect on therelaxation [4]. Furthermore, the momentum
transport may have the direct link to the particle
transport[5].
Therefore,
simultaneous
observations of statistics (PDF) and dynamics(fine time evolutions) of the global particle andmomentum transports are required to understandstructural formation in magnetized plasmas.
As a result of “extreme” experiment, we show
the first simultaneous observation of statistics anddynamics of the azimuthally averaged particle
and momentum fluxes by turbulence inmagnetized plasmas [6]. We made efforts to
prepare “extreme” number of electrodes/probes tofulfill the observation. Measurement of spatiallyminute structure of turbulence transport requires
fine spatial arrangement of electrodes in theprobes. The “global” flux measurements also
require that the probes cover the whole azimuthal
range of the two-dimensional plasma turbulence.
In addition, to detect small probability ofintermittent flux events with sufficiently highprecision, we paid attention on obtaining“extremely” large amount of data.
2. Experiment
The target plasma is fully-developed drift-wave
turbulence in a linear device (the Large Mirror
Device-Upgrade, LMD-U [7]). Magnetic fieldstrength is fixed at 0.09 T in the center of the vessel,
and the ion cyclotron frequency is ~ 34 kHz. (Thesampling rate is 1 MHz.) Auto-power spectra of theion saturation current and floating potential
fluctuations have broadband property at 7 - 8 kHz(fundamental drift-wave) [8]. Two probe arrays
were used to measure the momentum and particle
fluxes, respectively. The radii of the observation
with the two arrays are fixed at r = 4 cm where thelocal momentum transport had a maximum. (Radiusof the cylindrical plasma is 5 cm.) Our maininterest is origin of the momentum flux, therefore,
we chose the radius r = 4 cm as the observation
location. The momentum flux (Reynolds stress, RS)
was measured with 16 channel RS probe array(16ch-RSP) [9]. The 16ch-RSP has 16 units, andthe units are arranged approximately at regularintervals in the azimuthal direction. The particle
flux was simultaneously measured with the 64ch
azimuthal probe array [10]. Average ion saturation
current has finite radial gradient around r = 4cm.
Turbulent fluxes are mainly driven by fluctuationsin the frequency range less than 10 kHz.
3. PDF analysis
First, we describe results of observed PDFs of theglobal particle and momentum transports. Theobserved PDFs of the fluxes are characterized bynon-Gaussianity featured with the positive tail. Inparticular, the difference between the local PDFs
and azimuthally-averaged PDFs was significant.
We obtained the tail exponent of the PDF of theazimuthally-averaged RS as 1.208. The PDF tailfollows the stretched Gaussian law (deviated fromthe Gaussian, where the exponent is 2). In theexponent calculation, the probability covers three orfour orders of magnitude as a result of the large
amount of data, thus the exponent is preciselydetermined. We also found that the tail exponentsof the PDF varied from 0.6 (point-wise) to 1.2(averaged), as the spatial length of averaging

became longer. When the spatial range is close tohalf wavelength of the fundamental drift-wave, thetail exponent starts to converge. The origin of thedifference between the local PDF and the spatiallyaveraged PDF is the internal structure of the flux
event. This is the evidence that the local turbulencetransport events are not independent, and have longrange correlation. This result demonstrates that themixing of these microscopic dynamics constitutes
the PDF for the azimuthally averaged flux.
4. Correlation between the both fluxes
Next, to investigate the dynamical link between
the global particle and momentum transports, weshow the results from correlation analysis between
the both transports. The time delay from thecorrelation analysis may provide clues to originof the momentum transport and causalrelationship between the flux events in particle andmomentum. The particle flux mainly leads the RS
by 25x10-6 s, higher than the time resolution of thesampling rate. Time delay caused by the differenceof locations between the two probe arrays isnegligible. Therefore, the observation of thesignificant time delay of 25x10-6 s shows the causal
relationship between the particle and themomentum fluxes in this plasma turbulence. We
have confirmed that the change in the particle
fluxes leads that in the momentum flux,demonstrating that the momentum flux is inducedby the relaxation of density gradient.
Acknowledgments
This work was partially supported by
Grant-in-Aids for Specially-Promoted Research(16002500) of MEXT, Grants-in-Aids for Young
Scientists (B) (18760637), for Scientific Research(S) (21224014), and for Scientific Research (B)(23360409) of JSPS, Japan
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