Collisionless zonal-flow dynamics in quasisymmetric stellarators

TL;DR

This paper investigates the collisionless plasma response to zonal-density perturbations in quasisymmetric stellarators, revealing how geometric factors influence oscillations and residual flows, with implications for turbulence regulation.

Contribution

It provides an analytic expression for the geometric factor affecting residual flow in quasisymmetric stellarators and compares it with gyrokinetic simulations, highlighting the role of geometric symmetry errors.

Findings

Geodesic-acoustic-mode oscillations are absent in quasi-helically symmetric configurations with small safety factor.

The Rosenbluth--Hinton residual flow is scaled by a geometric factor $\\mathcal{C}$, derived analytically.

Good agreement between theory and simulation occurs when quasisymmetry errors are minimal.

Abstract

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.