Effects of toroidal rotation and ion collisional viscosity on low-frequency zonal flow in tokamak plasma

Theoretical investigations are conducted to examine the impact of toroidal rotation and ion collisional viscosity on low-frequency zonal flow (LFZF) in a tokamak plasma with the fluid model. The results indicate that while the frequency of LFZF remains unchanged during an isothermal process with γ=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma { = }1$$\end{document}, its damping rate is influenced by both toroidal rotation and ion collisional viscosity. Specifically, as the ion collisional viscosity increases, so does the damping rate of LFZF; conversely, as the toroidal rotation As its Mach number rises, its damping rate decreases. For a non-isothermal process with γ>1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma \, > 1$$\end{document} (such as γ=5/3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma = 5/3$$\end{document}), the damping rate and frequency of LFZF are influenced by both toroidal rotation and ion collisional viscosity. It has been demonstrated that when the toroidal rotation Mach number surpasses a certain threshold, the frequency transitions from zero to a finite value, while the damping rate decreases as the toroidal rotation Mach number increases for LFZF. Furthermore, it has been observed that the damping rate of LFZF increases while the frequency decreases with an increase in ion collisional viscosity. Moreover, when the ion collisional viscosity surpasses a certain threshold, the frequency of LFZF drops to zero.