Gyrokinetic simulation of Alfvénic ion temperature gradient instabilities in the presence of impurities

Abstract The impurity effects on Alfvénic ion temperature gradient (AITG) instabilities in toroidal magnetic configurations are widely studied, utilizing a complete gyrokinetic approach for main and impurity ions. Two independent instability branches, i.e. the electromagnetic AITG mode and the essentially electrostatic ITG mode, can exist and even coexist with finite- $\beta$ effects included. The contributions from Shafranov shift and electromagnetic effects on two different instability branches are identified and compared in detail. The results indicate that the electromagnetic stabilizing effects dominate and even can completely stabilize ITG modes. However, the strong stabilizing influences of Shafranov shift dominate on AITG modes and hence the electromagnetic destabilizing influences are suppressed by the Shafranov shift for high $\beta_e$ or $\alpha$ regions. The presence of impurity ions with both positive and negative density gradient profiles can stabilize AITG modes. In contrast, for ITG modes, the impurities with negative (positive) gradient parameter $R / L_{n z}$ have destabilizing (stabilizing) influences. Such distinct responses to the injected impurities are demonstrated to be associated with their different instability essences and influencing mechanisms. i.e. for the former, the instability is sensitive to the Shafranov shift parameter $\alpha$ ($\alpha$ varies with $R / L_{n z}$) regions, while for the later, the impurity effects mainly rely on the competition between the destabilizing influence of the impurity density gradients and the stabilizing influence caused by main ion dilution from impurities. Significantly, high concentration, steep positive $R / L_{n z}$, and high mass number of impurities as well as effective charge number $Z_{\text {eff }}$ are conducive to the stabilization of AITG modes. The unstable window in $\hat{s}$ space of AITG modes is much wider than that of ITG modes, and the effects of safety factor $q$ on the former is more significantly pronounced.