Collisionless zonal-flow dynamics in quasisymmetric stellarators

The linear collisionless plasma response to a zonal density perturbation in quasisymmetric stellarators is studied, including the initial geodesic-acoustic-mode oscillation frequency and the final Rosenbluth--Hinton residual-flow level. While the geodesic-acoustic-mode oscillations in quasiaxisymmetric configurations are similar to tokamaks, they become almost nonexistent in quasi-helically symmetric configurations when the effective safety factor is small. Compared with concentric circular tokamaks, the Rosenbluth--Hinton residual is also found to be multiplied by a geometric factor C that arises from the flux-surface averaged classical polarization. Using the near-axis-expansion framework, we derive an analytic expression for C, which varies significantly among different configurations. These analytic results are compared with numerical simulation results from the gyrokinetic particle-in-cell codes GTC and XGC-S, and good agreement in the 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 possible relation between the transport level and the stellarator geometric parameters via nonlinear interactions with zonal flows.