Collisionless zonal-flow dynamics in quasisymmetric stellarators

The linear collisionless plasma response to a zonal-density perturbation in quasisymmetric stellarators is studied, including the geodesic-acoustic-mode oscillations and the Rosenbluth--Hinton residual flow. While the geodesic-acoustic-mode oscillations in quasiaxisymmetric configurations are similar to tokamaks, they become non-existent in quasi-helically symmetric configurations when the effective safety factor in helical-angle coordinates is small. Compared with concentric circular tokamaks, the Rosenbluth--Hinton residual is also found to be multiplied by a geometric factor $\mathcal{C}$ that arises from the flux-surface averaged classical polarization. Using the near-axis-expansion framework, we derive an analytic expression for $\mathcal{C}$, which varies significantly among different configurations. These analytic results are compared with numerical simulation results from the global gyrokinetic particle-in-cell code GTC, and good agreement with the theoretical Rosenbluth--Hinton residual level is achieved only when the quasisymmetry error is small enough. Since zonal flows can be important for regulating turbulent transport, these results suggest a possible relation between the transport level and the stellarator geometric parameters via nonlinear interactions with zonal flows.