Comparison of local and global gyrokinetic calculations of collisionless zonal flow damping in quasi-symmetric stellarators

TL;DR

This paper compares local and global gyrokinetic calculations of collisionless zonal flow damping in quasi-symmetric stellarators, revealing how local models approximate global behavior with some differences in oscillation and damping times.

Contribution

It provides a detailed comparison between local flux-tube, flux-surface, and full-volume gyrokinetic calculations of zonal flow damping in quasi-symmetric stellarators, highlighting the conditions under which local models are accurate.

Findings

Flux-surface and flux-tube calculations can replicate full-volume residuals for moderate wavenumbers.

Local models show longer oscillation and damping times, especially at small wavenumbers.

Zonal flow damping depends on bounce-averaged radial particle drift, consistent with theory.

Abstract

The linear collisionless damping of zonal flows is calculated for quasi-symmetric stellarator equilibria in flux-tube, flux-surface, and full-volume geometry. Equilibria are studied from the quasi-helical symmetry configuration of the Helically Symmetric eXperiment (HSX), a broken symmetry configuration of HSX, and the quasi-axial symmetry geometry of the National Compact Stellarator eXperiment (NCSX). Zonal flow oscillations and long-time damping affect the zonal flow evolution, and the zonal flow residual goes to zero for small radial wavenumber. The oscillation frequency and damping rate depend on the bounce-averaged radial particle drift in accordance with theory. While each flux tube on a flux surface is unique, several different flux tubes in HSX or NCSX can reproduce the zonal flow damping from a flux-surface calculation given an adequate parallel extent. The flux-surface or flux-tube calculations can accurately reproduce the full-volume long-time residual for moderate $k_x$, but the oscillation and damping time scales are longer in local representations, particularly for small $k_x$ approaching the system size.