25C05
Gyrokinetic simulation study on ITG turbulent transport in LHD experiment
LHD実験におけるITG乱流輸送のジャイロ運動論的シミュレーション研究
Masanori Nunami, Tomo-Hiko Watanabe, Hideo Sugama and Kenji Tanaka
沼波政倫, 渡邉智彦，洲鎌英雄，田中謙治
National Institute for Fusion Science / Graduate University for Advanced Studies
322-6 Oroshi-cho, Toki, Gifu 509-5292, Japan
核融合科学研究所 / 総合研究大学院大学 〒509-5292 岐阜県土岐市下石町322-6
Gyrokinetic simulations are applied for ion temperature gradient (ITG) turbulent transport in the dischargeof Large Helical Device (LHD) experiment with high ion temperature. In the discharge, themicroturbulence spatial profiles are precisely measured by phase contrast imaging (PCI) method where themeasured fluctuations show some characteristics of the ITG instabilities. In the gyrokinetic nonlinear
simulations for the investigation of the turbulent transport triggered by the ITG modes and zonal flow
generations in the LHD experiment, we applied the GKV-X code which incorporates full geometricaleffects of non-axisymmetric field configuration corresponding to the discharge. The simulation results canreproduce the turbulent transport levels comparable to the experimental results. Furthermore, the resultant
transport levels at different flux surfaces are expressed in terms of a simple relation between the transportcoefficient and the ratio of the squared turbulent potential fluctuation to the averaged zonal flow amplitude.

1. Introduction
In the last decade, large number of gyrokinetic
simulation studies has presented many significant
results for the anomalous transport which is oneof critical issues in fusion plasma researches. In
order to improve plasma confinement, it is very
important to reduce the resultant transport levels
that are caused by competitive effect of zonal
flows and microinstabilities such as the ion
temperature gradient (ITG) modes. Nowadays,
direct comparison of numerical results ofgyrokinetic simulations with experimental data isstrongly demanded. For non-axisymmetricsystems such as Large Helical Device (LHD) [1],however, there are not many studies forvalidation of gyrokinetic simulation, althoughstudies in tokamaks have been extensively done
to investigate turbulent transport (for example,Ref. [2]). The present study is devoted to apply
the gyrokinetic simulations to evaluate thesaturation levels of the turbulent fluctuations,zonal flows, and ion heat transport in the LHD
discharge.
2. Ion heat transport and fluctuation spectra
In the LHD high ion temperature discharge#88343 [3], the density fluctuations measured byphase contrast imaging (PCI) method [4] have large
amplitudes for the radial positions and the poloidal
wavenumbers which correspond to ITG modes
having large growth rates obtained from the linear
gyrokinetic simulations [5]. Applying thegyrokinetic Vlasov flux-tube code GKV-X [6], inFig.1 Color contours of the perturbed electrostatic
potentials obtained from GKV-X simulations in
the LHD high ion temperature discharge at threedifferent flux-surfaces. The plots show thesnapshots at t = 80 R 0/vti(r=0.65).

present work, nonlinear flux-tube ITG turbulencesimulations are performed at different threeflux-surfaces in the discharge as shown in Fig.1.
Figure 2 shows the comparison results of the ionheat flux obtained from the simulations and theLHD experimental observation. The simulation
results are 15–50 % lower than that in theexperimental values which include both theanomalous and neoclassical contributions to thetransport. If the neoclassical part is subtracted fromthe experimental values, the simulation results
agree well with the anomalous part of experimentalresults. The wavenumber spectra of the turbulentχiGB = χ i / (ρti vti / R 0 )Experiment
AnomalousSimulation

2.0
1.0
0.0
0.0

0.2

0.4

r

0.6

0.8

1.0

6.0
2

1.0

0.0
0.0

0.5
kq rti1.0(b)
Simulation

1/2(a)( åkx á| nkx,ky/n0 | ñ )Fluctuation Amplitude (a.u.)

density fluctuation obtained from the PCI
measurement and the simulations are shown in
Fig.3. Both spectra have a peak in a low
wavenumber region and similar shape in a highwavenumber region. The reasonable agreements
between the LHD experiment and the simulations
strongly encourage us to pursue the gyrokinetic
simulation studies for the anomalous transport in
non-axisymmetric systems.
Experiment

4.0
2.0
0.0
0.0

0.5
ky rti500

ρ = 0.46
ρ = 0.65
ρ = 0.83
ρ = 0.65 (Inward)

100
1/2
T/Z

200

Fig.4 Lissajous plots of the ITG turbulence
1/2
simulations of the saturated phase in (T/ Z , ci)
space for the experimental case at three different
flux-surfaces and the inward-shifted LHD case.

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.

2.0

10 (c)

2Pi (MW)3.0

1.0

Fig.3 Wavenumber spectra for the fluctuation
amplitude obtained from (a) the experiment and (b)the GKV-X simulation. The dashed line in (a)represents the cutoff of the PCI measurement.

3. Relation between transport level, turbulent
fluctuation and zonal flow amplitude
The ITG turbulent transport is considered to be
determined by the interaction between turbulenceand zonal flows. Figure 4 shows the Lissajous plotsof the ITG turbulence simulations for the ion heatdiffusivity ciGB in the gyro-Bohm unit and the ratioof the squared turbulent potential T to the zonal
flow amplitude Z1/2. In the plots, we also show thesimulation result in the vacuum field configuration
with more inward shifted magnetic axis than theexperimental case, which is one of the optimized
configurations to reduce neoclassical transport [7].

While the transport level in the inward-shifted caseis lower than the experimental case, which isconsistent with our previous work [8], all plots
including the case of inward-shifted configuration
are well represented by a simple relation ciGB∝T/
Z1/2 despite of the fact that a wide range ofconditions for the different flux-surfaces and theinward-shifted case are included here. Therefore,
we expect that this newly obtained result cancontribute to anomalous transport modeling inhelical plasmas.
Acknowledgments
The authors would like to thank the LHD
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, and21560861, and in part by the NIFS Collaborative
Research
Programs,
NIFS11KNST017,
NIFS11KNXN229,
NIFS10KNTT003,
andNIFS10KNST006.
References[1] A. Komori et al., Fusion Sci. Technol. 58 (2010), 1.
[2] T. L. Rhodes et al., Nucl. Fusion 51 (2011), 063022.
[3] K. Tanaka et al., Plasma Fusion Res. 5 (2010),
S2053.
[4] K. Tanaka et al., Rev. Sci. Instrum. 79 (2008),
10E702.
[5] M. Nunami et al., Plasma Fusion Res. 6 (2011),
1403001.
[6] M. Nunami et al., Plasma Fusion Res. 5 (2010), 016.
[7] S. Murakami et al., Nucl. Fusion 42 (2002), L19.
[8] T.-H. Watanabe et al., Phys. Rev. Lett. 100 (2008)
195002.