H. Sugama

K." Tanaka

M. "Nunami

T.-H. Watanabe

National Institute for Fusion Science (NIFS-Repository)

In recent LHD experiments, high ion temperature(high-Ti) discharges have been realized by the high powerneutral beam injection, and the spatial distributions ofthe density ﬂuctuations have been also measured by thetwo-dimensional phase contrast imaging. In the mea-surements in the shot number 88343 1, 2), the large-amplitude ﬂuctuations observed in the plasma frame,propagates in the direction of the ion diamagnetic ro-tation and the amplitude increases as the ion temper-ature gradient increases. The peak of the ﬂuctuationamplitude is found at region of ρ ∼ 0.6-0.8 in the radialspace, and kρti ∼ 0.45 in the perpendicular wavenumberspace, where ρ is the normalized minor radius and ρti isthe ion thermal gyroradius. These facts of the observa-tions seem to show the features of the ion temperaturegradient modes (ITG modes), therefore, the ﬂuctuationsobserved in the experiment are considered to be drivenby the ITG modes.We performed the linear gyrokinetic Vlasov simula-tions 3) for the ITG modes and zonal ﬂows for the high-Tidischarges, utilizing GKV-X code 4) under the experi-mental conditions of density, temperature, and VMECequilibrium conﬁguration in the discharge, with the as-sumptions of ni/ne = 1, Ti/Te = 1, collisionless, adi-abatic electrons, and zero-beta limit. The simulationresults show that the ITG mode in the conﬁguration ismost unstable at ρ = 0.65 in radial space (see Fig. 1),and kyρti = 0.35 in the space of the poloidal wavenumberky. Comparing the results with the ﬂuctuation measure-ments in the LHD discharge, it is found that the regionsof the experimental ﬂuctuation peaks are located aroundthe positions where the linear ITG modes are most un-stable in radial and wavenumber spaces. Then, takingaccount of the error-bars of the experimental data, wethought that the density ﬂuctuations observed in theLHD experiments are attributed to the ITG modes.To ﬁnd the critical ion temperature gradient for theITG mode in the high-Ti discharge, we investigate thedependence of the ITG mode growth rates on the tem-perature gradient. Then, we obtain the critical values ofR0/LT i where the growth rate vanishes. Figure 2 showsthe critical values for the high-Ti phase, as a functionof ρ. From the plot, we ﬁnd that γmax given by Fig. 1peaks at a radial position where the deviation of the tem-perature gradient from the critical value is largest. Thecritical value is higher than the experimental value forρ <∼ 0.2 where γmax of Fig. 1 vanishes.The linear response of the zonal ﬂow potential in theconﬁguration is also investigated. In the investigations,it is observed that the damping of the geodesic acous-tic mode (GAM) oscillations in the lower safety factoris faster than those in the higher one. The evolution ofthe GAM-averaged response kernel shows that the ini-tial behavior does not change for diﬀerent perpendicu-lar wavenumbers, but is inﬂuenced by the equilibriumconﬁguration. The residual levels are enhanced by in-creasing the radial wavenumber and are also inﬂuencedby the helical Fourier components which depend on theradial position and the Ti proﬁle. These results are con-sistent with the analytical conclusions for the zonal ﬂowresponses 5).0.0 0.2 0.4 0.6 0.8 1.00.00.10.20.3ργ max[vti/R0]High−TiFig. 1: Radial proﬁle of the growth rate of the ITGmode for the LHD high-Ti discharge.0.0 0.2 0.4 0.6 0.8 1.00.010.020.0R 0 / L TiρHigh−TiExperiment (High− Ti)Fig. 2: Radial proﬁle of the critical ion temperaturegradient obtained by GKV-X simulations (black circles),and the bold curve represents the experimental proﬁle ofR0/LT i in the LHD high-Ti discharge.1) K. Ida, M. Yoshinuma, M. Osakabe et al., Phys. Plas-mas 16 (2009), 056111.2) K. Tanaka, C. A. Michael, L. N. Vyacheslavov et al.,Plasma Fusion Res. 5 (2010), S2053.3) M. Nunami, T.-H. Watanabe, H. Sugama andK. Tanaka, Plasma Fusion Res. 6 (2011), 1403001.4) M. Nunami, T.-H. Watanabe and H. Sugama, PlasmaFusion Res. 5 (2010), 016.5) H. Sugama and T.-H. Watanabe, Phys. Plasmas 13(2006), 012501.190§4. Gyrokinetic Simulations for Ion Temperature Gradient Mode and Zonal Flows in LHD High Ion Temperature DischargeNunami, M., Watanabe, T.-H., Sugama, H., Tanaka, K.

Gyrokinetic Simulations for Ion Temperature Gradient Mode and Zonal Flows in LHD High Ion Temperature Discharge

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