Experimental Observations of Zonal Flows and Turbulence in a Toroidal Plasma

A. Fujisawa, A. Shimizu, H. Nakano, S. Ohshima, K. Itoh, 1Y. Nagashima, 1S.-I. Itoh, H. Iguchi,
Y. Yoshimura, T. Minami, K. Nagaoka, C. Takahashi, M. Kojima, S. Nishimura, M. Isobe,
C. Suzuki, T Akiyama, T. Ido, K. Matsuoka, and S. Okamura
National Institute for Fusion Science, Oroshi-cho, Toki, 509-5292 Japan
1Research Institute for Applied Mechanics, Kyushu Univ., Kasuga, 816-8580, Japan
1. Introduction
In magnetically confined plasma, turbulence determines the plasma transports and the
resultant thermal structure. The extensive studies on transport barriers have shown that the
sheared structure of electric field can suppress the microscopic turbulence and the resultant
transport. The recent researches in simulation and theory have revealed that the turbulence
should generate mesoscopic structure, termed zonal flows [1], through nonlinear wave-wave
couplings. The zonal flows have a symmetric structure m=n=0 with a finite radial wave number,
thus, the zonal flows themselves do not contribute to any cross-field transport. However, the
zonal flows can control the transport through the energy exchanges with the turbulence, and the
zonal flows are quite important topics associated with the plasma confinement. This paper
describes the experimental results on the zonal flows in CHS. The topics include the following
three aspects; identification of zonal flows, their structure and dynamics, and their couplings
with turbulence.
2. Experimental Set-up
CHS is a toroidal helical device of which the major and averaged minor radii are R=1 m
and a=0.2 m, respectively. The device is equipped with two HIBPs to measure plasma potential
in different toroidal sections apart by 90 degree. Each HIBP has three channels to observe the
adjacent spatial points of the plasma. The local electric field can be directly evaluated by
making a difference between potentials of neighboring two channels. The target plasma for the
experiments is sustained with electron cyclotron resonance heating of ~ 200 kW. The magnetic
field strength of the discharges is B=0.88 T, and the density is kept constant at ne~ 5×1012 cm-3.
The signals are digitized in every 2μs (or 500 kHz sampling). The corresponding Nyquist
frequency is fN=250 kHz.
3. Observations of zonal flows
3-1. Identification of zonal flow and structure
The perpendicular flow to the magnetic field in magnetized plasmas is related to radial
electric field through ExB drift. Thus, the zonal flow can be detected by measuring the electric
field with HIBPs [2]. Figure 1 shows the spectrum of the electric field in CHS (the red line),
which is measured with the HIBP. The measured radial position is r~12cm where the signal-tonoise
ratio is the maximum. The blue line in Fig. 1a is the coherence between the electric fields
at two toroidal locations. The fluctuation in the low frequency regime less than ~1 kHz shows a
long-distance correlation, and the fluctuation has been confirmed to be the stationary zonal flow.
On the other hand, several coherent modes appearing (for example, at ~17 kHz) as sharp peaks
are considered to be the Geodesic acoustic modes (GAMs), oscillatory branch of the zonal flows.
These coherent modes are characterized by high coherence in potential fluctuations.
The radial structure of the stationary zonal flow is inferred by the phase difference
between electric fields in two locations. The phase variation of zonal flows between two radial
positions can be evaluated by varying the radial observation position of an HIBP, with fixing the
other. Figure 1b shows the correlation coefficient between the electric fields C(r1,r2), which
indicates the phase difference between two radial positions. The correlation analysis
demonstrates a radial structure changing sinusoidally with the wavelength of ~1.5 cm, that
corresponds to ~15ρi.

3-2. Spatial structure of GAMs
Further experimental observations were performed to investigate the coherent mode
structures conjectured as GAMs [3]. In the experiments, the coherent modes are observed at 8,
16, 18 and 35 kHz, and the long-distance correlation is confirmed for the potential fluctuations
at these frequencies between two toroidal locations. The radial structure of the coherent modes
can be inferred, similarly to the previous case, by varying an observation point shot by shot in
every 1 mm, with fixing the other as the reference to correct the variation of the mode intensity
between shots. Figure 2 shows the potential fluctuation powers at the four frequencies as a
Figure 1. (a) Power spectra of potential difference, and coherence between potential differences at the
two toroidal locations. The electric field fluctuation ranging from 0.3 kHz to 1 kHz shows longdistance
correlation. (b) Radial structure of zonal flow. The structure is estimated from correlation
between electric fields at different toroidal locations. In this experiment, the observation radius of the
second HIBP is varied around r2=12 cm with the observation point of the first HIBP being fixed at
r1=12 cm. The closed circles represent traditional correlation coefficient as a function of observation
radius of the second HIBP.
function of radius. Obviously from Fig. 2a, the power of the lowest frequency mode at 8 kHz
increases toward the edge, while that of the other higher mode at 35 kHz increase toward the
core where the electron temperature is higher. On the other hand, the power profiles at the
frequencies of 16 and 18 kHz are shown in Fig. 2b. The power at 16 kHz has a maximum
around r=12 cm, while the other increases toward the plasma core. The dependence of the
frequency on the temperature is qualitatively consistent with the theoretical prediction of GAM;
fGAM~cs/2πR where cs and R are the ion sound velocity and the major radius, respectively.
However, definite identification needs to confirm the following issues at least; the axi-symmetry
(m=n=0) of electric field fluctuation, the asymmetry (m=1/n=0) of density fluctuation, and a
significant causal relation of the modes with the background turbulence [4].

3-3. Impacts of zonal flow on turbulence and transport
The effects of zonal flow on turbulence-driven transport are examined. The HIBP can
measure simultaneously density and potential fluctuations. This ability makes it possible to
evaluate the particle flux as a function of each frequency of turbulence. In addition, the
application of a wavelet analysis can extract the intermittent behavior of the particle flux.
Figure 3 shows the comparison between temporal patterns of the evaluated particle flux density
and the zonal flow or low pass filtered potential difference [5]. In Fig. 3, similar activities could
be seen in the patterns of the zonal flow and the particle flux density.
In order to quantify the correlation of turbulence and zonal flow, the wavelet spectra are
evaluated for periods discriminated by the phase of the zonal flow. Figure 3b shows the
conditional averages of the wavelet spectra of density and potential fluctuations, using the zonal
flow phase as a condition. Around ~ 50 kHz and ~ 120 kHz, the fluctuation power in the
minimum phase of zonal flow is stronger than that in the maximum phase of zonal flow. In
addition, the power spectra at the intermediate (or zero) phase show the mean values between
Figure 2. Potential fluctuation powers of the four coherent modes as a function of radius. (a)
The powers at 8kHz and 35 kHz, and (b) the powers at twin peaks of 16 and 18 kHz. These
two modes show quite different characteristics in their radial distributions.
mean existence of two individual modes in the narrow frequency range. A tendency
is found that the higher frequency modes are localized in higher temperature region.
the two (maxima and minima). The result, therefore, provides evidence to show a causal linkage
between turbulence and zonal flow.
4. Summary
The experiments confirmed, using twin heavy ion beam probes, the existence of
mesoscopic fluctuating structure characterized by a long-distance correlation (or symmetric
nature) with a finite radial wave number. The diagnostics could reveal nonlinear or causal
linkage between turbulence and zonal flows. The time-dependent analysis using a wavelet
showed that the zonal flows should affect the turbulence and the resultant transport. The
experimental observations presented in this paper really support that the zonal flows are the new
important players in the plasma transport. The laboratory experiments of magnetically confined
plasma have been recently entered into the stage of clarifying the mechanisms of plasma
structural formation through the observation on different scales of fluctuations, micro, meso and
macro scales. The laboratory plasma experiments will contribute to the understanding of
structure or phenomena related to turbulence is ubiquitous in nature, e.g., band-like structure in
rotational planets, jet stream, solar tacocline (momentum transport barrier) and so on.
REFERENCES
[1] P. H. Diamond, K. Itoh, S.-I. Itoh, Plasma Phys. Control. Fusion 47 R35 (2005)
[2] A. Fujisawa et al., Phys. Rev. Lett.93 165002 (2004)
[3] A. Fujisawa et al., Plasma Phys. Control. Fusion 48 S31 (2006).
[4] Y. Nagashima et al., Phys. Rev. Lett. 95 095002 (2005).
[5] A. Fujisawa et al., Plasma Phys. Control. Fusion 48 S205 (2006).

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