22S-R1-4
Modern View of Turbulence and Transport in Magnetized Plasmas
磁化プラズマの現代的描像について	 Akihide Fujisawa
藤澤	  彰英
Research Institute for Applied Mechanics, Itoh Research Center for Plasma Turbulence
６−１ Kasuga Kouen, Kasuga, Fukuoka 816-8580
九州大学応用力学研究所	  伊藤極限プラズマ研究連携センター	  〒816-8580 春日市春日公園６−１
The modern view of turbulence has been established due to the discovery of structures drift-waves generate, such as
zonal flows and streamers, providing a new framework for understanding turbulence-driven transport and structuralformation in magnetized plasmas. This paper presents recent development of laboratory experiments to have advanced
the understanding of plasma turbulence and transport, focusing on discoveries of mesoscale structures, such as zonal
flows and streamers, the analyzing techniques to quantify the couplings between different scale structures, and physics
of turbulence transport and barrier formation.

1. Introduction
Plasma is a state of matter extremely far fromequilibrium, and is a fundamental element forunderstanding the phenomena of our surroundings(the sun, aurora, the ionosphere, dynamo, etc.) andfor developing the modern technologies (nuclearfusion, display, plasma rocket, carbon nano-tube,etc.). Particularly, the plasma turbulence has been a
key issue for nuclear fusion, and extensive studiesof plasma turbulence over a half century have been
carried out from its infancy [1,2].
Thanks to the intensive efforts, recently, a newframework has been established for understandingof the plasma turbulence. In the modern view, theplasma turbulence is regarded as a system of drift
waves and structures that the drift-waves generate[3,4], while the plasma turbulence was simply
recognized as a system of drift waves after theconfirmation of the presence of drift waves inmagnetically confined plasmas [5,6]. This paper
introduces the modern view of the plasma
turbulence and resultant transport, focusing on theexperimental steps for accomplishing the modern
concept of plasma turbulence by introducing recent
examples of laboratory experiments.
2. Structures driven by drift-waves
At present it has been well recognized that the drift
wave can generate mesoscale structures such as
zonal flows, Geodesic Acoustic Modes (GAMs)
and streamer, which have been predicted bytheories and simulations. These structures havebeen identified in experiments to contribute to
making the modern view of plasma turbulence. Afew direct identifications of zonal flows have been
performed in CHS [7] and others [8-10], whilemuch more experimental results have been

available for studies of GAMs [11] after their first
identification [12,13]. As for streamers, a few
experiments have shown the signature of their
existence in toroidal experiments [14,15], while thecomplete identification has been done in a linearcylindrical device [16].
In addition to these mesoscale structures, anotherfluctuating structure driven by drift waves has been
recently found in electron temperature fluctuation
measurements in Large Helical Device (LHD)using electron cyclotron emission (ECE) [17]. The
discovered structure shows a long radial correlation
length comparable to the plasma minor radius,
therefore, this observation shows that the drift
waves should excite a linearly stable macroscopic
structure as well as those in mesoscale.
3. Mutual Interactions between
Recent developments of computer technologies
have made it easier to perform the analyses for
extracting the elemental processes of turbulence[18-20]. The bicoherence analysis is often used toshow the nonlinear couplings between turbulence
generated structures (e.g., zonal flows, GAMs andothers) and background waves in frequency domain[21,22]. The analysis have been extended towavenumber space to confirm the wavenumber
matching condition as well, i.e. k1 + k2 = k3 . In
linear cylindrical devices, LMD-U [23] andVINETA [24], a 64-channel azimuthal probe array
succeeded in resolving the nonlinear couplings
including the wavenumber space. Recently, thesimilar technique using the wavelet was applied on
temporal sequence of fast camera images in
MIRABELLE, demonstrating the ability to study
the temporal dynamics and spatial localization
where the couplings occur [25].

Moreover, the energy transfer direction between
the fluctuation components or structures can bededuced using the power transfer function (PTF)
analysis that was applied originally in the edge ofTEXT tokamak plasmas [26]. Nowadays, theanalysis is extended to be applied on 2D probe dataof the frequency and wavenumber space in TJ-K
torsatron, demonstrating the nonlocal energy
transfer from drift-waves to zonal flows [27]. Thecross-bicoherence analysis implied that the energy
exchange between zonal flows and local turbulence
should have spatial (or radial) dependence in
LMD-U [28]; the zonal flows lose their energy inthe edge but gain the energy in the core.
4. Turbulence Transport in Modern View
These structures and drift-waves have their own
contributions to plasma transport; the symmetricproperty of zonal flows causes no cross-fieldtransport. Therefore, an increase in the zonal flows
contributes to improving plasma confinement, andthe energy partition between these elemental
components in plasma turbulence should determine
the transport. The hypothesis has been verified inbiasing experiments performed in TJ-K stellarator[29] and TEXTOR tokamak [30]. The voltage isapplied on the biasing electrode to induce theplasma flows and result in the confinement
improvement in TJ-K and TEXTOR. The poloidally
symmetric fractions of electrostatic component, i.e.,zonal flows, are suggested to increase in theseexperiments. In CHS the energy partition between
the zonal flows and drift-waves is examined toconclude that the confinement is better in the casethat the energy fraction of zonal flows is larger [31].
This observation demonstrates that the plasmatransport is improved under the condition ofenhancing the zonal flows. The laws of energy
partition between the drift waves and theirgenerating structures are important to be pursued.
5. Future Direction
The outstanding progress has been made in thestudy of plasma turbulence by the remarkabledevelopment of diagnostics [32]. According to thenew paradigm, the plasma turbulence is maintained
through the spatiotemporal interactions all over thewhole plasma between the different scale
fluctuations, i.e., drift-waves (microscale), zonal
flows and streamers (mesoscale) and macroscopic
modes. For further understanding of the plasma
turbulence and transport, full dimensional
measurements, at least two-dimensional covering
the wide region of plasma, should be necessary to
clarify the spatial dynamics with extending theanalysis into the wavenumber domain, which
contributes to the first-principle understanding of
unsolved problems such as nonlocal transport.
Acknowledgements
This work is partly supported by the Grant-in-Aidsfor Scientific Research (No 23246162) and theGrant-in-Aids for Scientific Research (No21224014).
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