Speaker
Description
Previous gyrokinetic studies have shown that zonal flows (ZFs) can be driven by turbulent energy flux[1,2] and turbulent poloidal Reynolds stress[3]. Recently, several studies[4,5] show that the presence of impurities has very weak influence on the ratio of the residual to the initial zonal potential, $\delta\phi(\infty)/\delta\phi(0)$, driven by initial charge density perturbations in the long-wavelength limit. However, gyrokinetic theory[1] and simulations[2] indicate that the temperature perturbations induced by turbulent energy flux are important in driving ZFs. Therefore, it is important to investigate the effects of impurities on ZFs driven by temperature perturbations.
In this work, we investigate the effects of impurities on ZFs driven by ion density and temperature perturbations, which represent turbulent poloidal Reynolds stress and turbulent energy flux, respectively. By solving the Vlasov-Poisson problem in an axisymmetric system in the long-wavelength limit, the temporal asymptotic zonal potential $\delta\phi_k(\infty)$ can be written as
$\delta \phi_k(\infty) =\frac{\delta \phi_k(0)}{\epsilon_r}- \sum_{j=i,z}\frac{\rho_{\scriptscriptstyle M,j}}{\rho_{\scriptscriptstyle M}}\frac{\delta T_{j,k}(0)}{e_j},$
$\frac{\rho_{\scriptscriptstyle M}}{B^2} k_r^2 \delta \phi_k(0) = \sum_{j=i,z} e_j \delta n_{j,k}(0),$
with $\delta n_{j,k}(0)$ and $\delta T_{j,k}(0)$ denoting initial density and temperature perturbations, respectively. $\rho_{\scriptscriptstyle M}=\sum_{j=i,z}\rho_{\scriptscriptstyle M,j}=\sum_{j=i,z}n_jm_j$ is the total ion mass density. The results show that for ZFs driven by main ion density perturbations $\delta n_{i,k}(0)$, the presence of impurities has little effect on the neoclassical polarization shielding factor $\epsilon_r$. While for ZFs driven by main ion temperature perturbations $\delta T_{i,k}(0)$, the presence of impurities can decrease the main ion mass density fraction $\rho_{\scriptscriptstyle M,i}/\rho_{\scriptscriptstyle M}$, and thus decrease the amplitude of ZFs. Finally, the driving effects of impurity ion temperature perturbations $\delta T_{z,k}(0)$ on ZFs can be ignored, due to the low concentration of impurity ions.
Reference
[1] S. Wang, Phys. Plasmas 24, 102508 (2017).
[2] Z. Wang and S. Wang, Nucl. Fusion 65, 016034 (2025).
[3] D. Zhang, Y. Xu, Z. Dai, and S. Wang, Nucl. Fusion 60, 046015 (2020).
[4] W. Guo, L. Wang, and G. Zhuang, Nucl. Fusion 57, 056012 (2017).
[5] J. Seo, H. Jhang, and J.-M. Kwon, Phys. Plasmas 29, 052502 (2022).