7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

Geodesic Curvature Dependence of Zonal Flow in the LHD

S. Nishimoto1, K. Nagaoka1, 2, M. Nakata2, 3, M. Yokoyama2, 3, K. Tanaka3,4,
LHD Experimental Group2
1
Department of physics, Nagoya University, 2National Institute for Fusion Science, 3SOKENDAI,
4Kyushu University
e-mail (speaker): nishimoto.shu@nifs.ac.jp
Control of turbulent transport is one of the mostimportant issues in the core plasma of the magneticallyconfined fusion research. It is well known that zonal flow,which is driven by nonlinear coupling in turbulence, may
suppress the turbulent transport. Therefore, the impact of
the zonal flow on turbulent transport have been
intensively studied[1].
Recently, theoretical research showed the zonal flow
dependence on the geodesic curvature of the magnetic
field line[2]. The geodesic curvature is proportional to theradial excursion for trapped particles, which may shield
the zonal flow potential, in other words, may be a zonal
flow damping effect. In this study, the geodesic curvaturedependence on the ion heat transport was experimentallyinvestigated and the zonal flow effect is discussed.
The experiment was carried out on the Large HelicalDevice (LHD). The geodesic curvature 〈𝜅𝑔 〉 iscontrolled by the radial position of the plasma axis. We
investigated parameters dependence of ion heat transportwith Akaike Information Criterion (AIC). For every caseof number of parameters, nonlinear multi regression
analyses for the selected parameters were carried out,
which is summarized in table 1. The geodesic curvaturedependence is the most crucial for the heat transport andthe dependence is qualitatively consistent with thetheoretical study[2].
Another approach was also carried out using thereduced transport model [3]𝜒i turb
𝜒i GBGB=𝐶1 𝒯̅ 𝛼𝐶2 +𝒵̅ 1/2⁄𝒯̅,intensity, and zonal flow intensity, respectively. The𝜒i turb /𝜒i GB and 𝒯̅ were evaluated by the experimental
observation, then the zonal flow effect 𝒵̅ 1/2 ⁄𝒯̅ can beobtained, which are shown in figure 1. The similar
dependence on the geodesic curvature was also observed.
These analyses indicate crucial importance of geodesiccurvature to suppress turbulent transport and thedependence may be effective for the application to theturbulent transport optimization in three-dimensional
torus plasma design.

Figure 1. Geodesic curvature dependence of zonal
flow effect ( 𝒵̅ 1/2 ⁄𝒯̅ ), turbulence ( 𝒯̅ ), andturbulent transport coefficient normalized bygyro-Bohm diffusion coefficient (𝜒i turb ⁄𝜒i GB ).
[1] A. Fujisawa, Proc. Jpn. Acad., Ser. B 97, 103 (2021)[2] M. Nakata, PFR, 17, 1203078 (2022)[3] M. Nunami et al., Phys. Plasmas, 20, 092307 (2013)

Where 𝜒i
, 𝜒i , 𝒯̅ , 𝒵̅ are turbulent transportcoefficient, gyro-Bohm diffusion coefficient, turbulenceturbln 𝜒i /𝜒i GB= 𝑎0+ 𝑎1 ln 𝑥1+ 𝑎2 ln 𝑥2
+⋯

AICc
499.8
354.4
264.6
218.6
219.2
250.5

Parameters and coefficients〈𝜅𝑔 〉𝑇e ⁄𝑇i𝑅 ⁄𝐿𝑛 + 𝑅 ⁄𝐿 𝑇i

𝑅 ⁄𝐿 𝑇e

𝜈ii ∗𝑛̃e ⁄𝑛e

1.46
1.25
1.53
1.85
1.77
1.78

1.37
1.21
1.64
1.68
1.62

-0.428-0.469-0.421-0.427-0.960-0.948-0.9870.06300.07470.0752

Table 1. Amount of AICc and coefficients for nonlinear multi regression analysis of ion-heat transportcoefficient normalized by gyro-Bohm diffusion coefficient. The best parameter selection is yellow
hatched column, where the AICc has the minimum number. The coefficients are represented as
numbers in the cells.