S5-2
New transport picture in turbulent plasma introduced by novel measurementsof turbulence
先進プラズマ乱流計測が描く新乱流輸送像	 
S. Inagaki1,2)
稲垣滋1,2)
1) Research Institute for Applied Mechanics, Kyushu University, 6-1 Kasuga-Koen, Kasuga 816-8580, Japan
九州大学応用力学研究所 〒816-8580	  春日市春日公園6-1
2) Research Center for Plasma Turbulence, Kyushu University, 6-1 Kasuga-Koen, Kasuga 816-8580, Japan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
Here we report research methods of plasma turbulence and turbulence transport. Development ofadvanced data analysis methods and novel diagnostic tools will propel us to quantify elementary processesof plasma turbulence. (i) Cross-correlation between heterogeneous diagnostic signals succeeded to discovera new fluctuating structure with a long distance radial correlation. (ii) Conditional averaging technique isused to extract the dynamic response of turbulence and turbulence transport precisely and allows us toobserve the hysteresis in the flux-gradient relation. (iii) Utilization of the microwave frequency comb
technique is very promising for developing the spatiotemporal structure of turbulence withultra-high-spatial- and temporal-resolutions. These results shift the picture of plasma turbulence to the new
one in which multi-scale fluctuations coexist and interact each other. This picture calls for a conceptual
breakthrough for the control algorithm of plasma dynamics in future fusion reactors.

1. Introduction
In magnetized plasmas, micro-turbulence
excited by the steep pressure gradient can drive
fluxes of particle, heat and momentum acrossclosed magnetic flux surfaces [1]. A local diffusive
picture of transport in which the transport flux is
expressed in terms of mean parameters and their
spatial derivatives at the same location has been
widely believed. For more than 20 years, however,dynamic behavior of magnetized plasma has
indicated limitations of such diffusive picture [2].
The local closures of turbulence and transport (i.e.,
formulation in terms of local parameters) are notsufficient to describe turbulent transport. In themodern view of plasma turbulence, the couplings
between different spatial-scale fluctuations could
provide a possible link between turbulence at two
distant radial positions in plasmas [3, 4]. Recently,
the existence of macroscopic fluctuations couplingwith micro-turbulence was discovered andconsidered to play important role on turbulencetransport dynamics [5]. More recently, new global
hysteresis in the flux-gradient relation wasdemonstrated [6]. The existence of hysteresis meansthat the heat flux is a multiple-valued function ofgradient, so that the transport dynamics is quite far
from that predicted by a simple diffusive transport,
in which the heat flux is a single-valued function ofgradient. These qualitative differences of transport
picture have a critical impact on the predictivecapability of temporal evolution of future burning
plasmas and thus should be clarified.

We developed new analysis methods for a
dynamic response of plasma by using of the linear
plasma device PANTA. Then we applied theseanalysis methods extensively to LHD experiments
and results made establish a research method ofplasma turbulence transport. Furthermore, wedeveloped a novel measurement tool forobservation of the multi-scale plasma turbulence.
2. Correlation hunting
Identification of all the possible fluctuations
and three-dimensional structure of them in confinedplasmas remains an urgent issue. There are many
experimental evidences for meso-scale andmicro-scale fluctuations (e.g. zonal flows and drift
waves, respectively). However, the knowledge offluctuations, which have very long radial
correlation lengths, was limited except in MHD
modes. In addition, there are a few experimental
observations
concerning
totwoorthree-dimensional
structureofturbulence.
Correlation is very powerful tool to identify weaksignals. In fact, the zonal flow is discovered by
two-point two-time correlation analysis of dual
HIBPsignals.
Herea
cooperation
ofcross-correlation analyses by use of heterogeneous
diagnostics (microwave reflectometer, array ofmagnetic probes and so on) is proposed to identify ahidden structure in turbulence. This approach isalso valid for the evaluation of the two-dimensional
turbulence structure. For example, a macro-scale
fluctuation is discovered and the toroidal andpoloidal mode numbers of it are measured by thecross correlation between a signal from ECE andmagnetic probe arrays [6]. Correlation between themacro-fluctuation and the envelope of the
micro-fluctuations is very useful to observe thenon-linear parametric coupling between them. The
cross-bi-coherence analysis also supports theexistence of the disparate-scale coupling in themulti-scale turbulence.
3. Conditional averaging technique
Periodical and quasi-periodical changes ofsignals of interest can be extracted statistically byconditional averaging technique. If the signal ofinterest is some sort of incoherent wave, theenvelope of wave is often used. In this technique,the periodical/quasi-periodical reference trigger isrequired. The signal is extracted for each timeinterval of trigger and averaged. This approach has
been applied to turbulent plasmas in the LMD-U
and PANTA device, and this has led toidentification of large-amplitude solitary wave
structures [7]. In the toroidal plasma experiments,
the spike-like Hα signal during ELMs can be used
to observe the H-mode transition dynamics. The
spike-like blob signal in the SOL probe itself is
frequently used to evaluate the spatiotemporal
behavior of blobs. In the LHD, the spatiotemporal
structure of heat pulse under modulated heating
source is extracted precisely [6]. The averaged
low-noise signals allow us to evaluate a temporal
evolution of heat flux and an associated change ofthe micro-fluctuation amplitude. The difference inthe time scales between responses in the gradientsand the response in the heat flux to the heat source
modulation clearly indicates that there is ahysteresis in the flux-gradient relation. On the other
hand, the heat flux is proportional to the local
micro-fluctuation intensity. This fact indicates thatthe turbulence intensity and heat flux aredetermined by the local temperature gradient only.
The theoretical study proposed a new
thermodynamical force in phase space anddemonstrated the strong impact of it on theturbulence dynamics. The impact of structures inphase-space (phase-space turbulence) is a new areaof theoretical and experimental study on turbulence.
4. Microwave frequency comb reflectometer
Global non-linear turbulence simulation codes
predict that large-amplitude corrugations in theprofile (e.g. ExB staircase) evolve dynamically[3,8,9]. To observe such corrugations, which can beessential to the dynamical response of turbulent
plasmas, it is necessary to simultaneously measure

the mean profile and its fluctuations precisely.
Microwave frequency comb technique isaccelerated over the past few years and thistechnique is applied to the reflectometry for coreplasma diagnostic in fusion plasma. Microwave
frequency comb reflectometer is a possible
candidate to measure the density profile as acontinuous function of radius with high temporal
resolution. We used an ultra-high speed digital
storage oscilloscope, which allow us to realize"digital mixer" for incident and reflect waves. We
have developed a method to reconstruct the density
profile as a continuous function of radius with atemporal resolution of 1 µs by using the conditional
averaging technique. The new reflectometer is very
promising for developing the physics of plasma
turbulence and transport.
5. Summary
This study established experimental methods forgeneralization of (1) flux-gradient relation toreplace Fick's law of diffusion and (2) non-local
and non-linear coupling between multi-scale
fluctuations. The resulting new picture of
turbulence and turbulence transport will have deep
impact on our predictability of evolution ofturbulent plasmas, and provide a sophisticatedcontrolling parameter of the burning plasmas, suchas ITER.
Acknowledgments
This work is partly supported by theGrant-in-Aid for Scientific Research of JSPF, Japan(21224014, 23244113, 23360414) and by thecollaboration
programsofNIFS(NIFS13KOCT001) and of the RIAM of Kyushu
University and Asada Science Foundation.
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