29pA01
ヘリカル・プラズマにおけるイオン温度勾配乱流輸送
Ion Temperature Gradient Turbulent Transport in Helical Plasmas
沼波政倫, 渡邉智彦，洲鎌英雄，田中謙治
Masanori Nunami, Tomo-Hiko Watanabe, Hideo Sugama, and Kenji Tanaka
核融合科学研究所 / 総合研究大学院大学
National Institute for Fusion Science / Graduate University for Advanced Studies

The anomalous transport has been considered to
be one of the most critical issues in magneticallyconfined fusion plasma researches. In the last
decades, large number of gyrokinetic simulation
studies has presented many significant results forthe anomalous transport physics. In order toimprove plasma confinement, it is very important toreduce the resultant levels of the turbulent transportthat are mainly caused by the micro-instabilities
such as the ion temperature gradient (ITG)
instability. Nowadays, according to great progressof the computational resources, direct comparisonsof numerical simulation results by the gyrokinetic
approaches with experimental data are stronglydemanded. While the studies in tokamaks havebeen extensively done to analyze turbulent
transport (for example, Ref. [1]), there are notmany studies for non-axisymmetric systems suchas the Large Helical Device (LHD) [2] to validate
the gyrokinetic simulation with the experimentalresults.
To demonstrate the comparisons between thesimulations and experiments in non-axisymmetricsystems, we focus on the LHD high ion temperature
discharge #88343 [3] and we employ thegyrokinetic Vlasov flux-tube code GKV-X [4]which is applicable to treat three-dimensional field
configurations. In the experiment, the density
fluctuations measured by two-dimensional phase
contrast imaging (2D-PCI) method [5] have large
amplitudes for the radial positions and the poloidalwavenumbers which correspond to the linear ITG
instabilities having large growth rates obtained
from the linear gyrokinetic analysis [6]. Applying
the GKV-X to the discharge, nonlinear ITG
turbulent transport simulations are performed [7].
Figure 1 shows a snapshot of the perturbed
electrostatic potentials obtained from the GKV-X
simulations in the discharge. The comparison
results of the ion heat flux obtained from thesimulations and the LHD experimental observation

Fig. 1 Color contours of the perturbed electrostatic

potentials obtained from GKV-X simulations in
the LHD high ion temperature discharge at threedifferent flux-surfaces, ρ=0.46, 0.65 and 0.83. The
plots show the snapshots at t = 60R0 / vti (ρ=0.65).

are plotted in Fig. 2. The simulation results areabout 15–50% lower than the experimental resultsthat includes not only the anomalous part but also
neoclassical contribution part to the total transport.
If the neoclassical part of the contributions is
subtracted from the total experimental observations,
it can be confirmed that the simulation results agree
well with the anomalous part of experimental
results. The wavenumber spectra of the turbulent
density fluctuation obtained from the PCI
measurement and the simulations are also compared.
Both spectra have a peak in a low wavenumber
region and similar shape in a high wavenumber
region. These reasonable agreements about the heat
flux and the turbulent spectrum between the LHD
experiment and the GKV-X simulations strongly
encourage us to pursue the gyrokinetic simulation
studies for the anomalous transport phenomena in
the helical or non-axisymmetric systems.
In general, the resultant turbulent transport isdetermined by the interaction between turbulencefluctuations and zonal flows. In our simulations, itFig. 2 Ion heat flux obtained from the LHD

experiment (dotted curve) and the GKV-X
simulations (open squares). The solid line
represents the anomalous part of theexperimental result.

is confirmed the spectral transfer of the fluctuations
into higher radial wavenumber region which isconsidered to be induced through the interaction
between the zonal flow and the turbulence as
discussed in Ref. [8]. In Fig. 3, by means of many
GKV-X simulation data, the correlations of the ITG
turbulent transport levels on the function of thesquared turbulent potential fluctuation ! ≡(1/2)∑!!,!!!! |!!!,!! |! , and the squared zonal flow
potential, ! ≡ (1/2)∑!! |!!!,０ |! , are examined.
Here, average along the field line is denoted by⋯ . One finds that the normalized ion heardiffusivity, !i /  !i GB , has strong correlation with !
and ! . In the plots, we also include the simulation
results in the vacuum field configuration with more
inward-shifted magnetic axis than the experimental
case, which is one of the optimized configurations
to reduce neoclassical transport [9]. Thus, all plots
including the case of inward-shifted configuration
are well represented by the simple relation despiteof the fact that a wide range of conditions for thedifferent flux surfaces, different field configurations,and different temperature/density gradient lengths
are included here. Therefore, we expect that thisobtained result can contribute to anomaloustransport modeling in helical plasmas. In fact, thenonlinear variables ! and ! are correlated withthe linear growth rates of the ITG mode and thelinear response function of the zonal flow potential.
Using the linear analyses, we can construct the ITG
turbulent transport model in the helical plasmas.
The details of the numerical modeling and current
issues of the turbulent transport simulations will bereported at the meeting.
Acknowledgments
The authors would like to thank the LHD

Fig. 3 Ion heat diffusivity in the gyro-Bohm unit!i /  !i GB versus the function of the squared
turbulent potential ! and the squared zonal flow
potential !.

experiment group for providing data and fruitful
discussions. This work is supported in part by theJapanese Ministry of Education, Culture, Sports,
Science and Technology, Grant (No. 22760660,21560861 and 24561030), in part by National
Institute for Fusion Science (NIFS) Collaborative
Research Program (KNST039 and KNXN229), andby use of Helios system at International Fusion
Energy Research Center (Project code: VLDGKand GTNAXIS).
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[2] A. Komori et al., Fusion Sci. Technol. 58(2010), 1.
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S2053.
[4] M. Nunami et al., Plasma Fusion Res. 5 (2010),
016.
[5] K. Tanaka et al., Rev. Sci. Instrum. 79 (2008),
10E702.
[6] M. Nunami et al., Plasma Fusion Res. 6 (2011),
1403001.
[7] M. Nunami et al., Phys. Plasmas 19 (2012),042504.
[8] M. Nakata et al., Phys. Plasmas 19 (2012),022303.
[9] S. Murakami et al., Nucl. Fusion 42 (2002),
L19.