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

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 Helically Symmetric eXperiment (HSX), a broken HSX, quasi-axial geometry National Compact Stellarator (NCSX). Zonal flow oscillations long-time affect evolution, residual goes to zero small radial wavenumber. oscillation frequency rate depend on bounce-averaged particle drift accordance with theory. While each flux tube surface unique, several different tubes HSX or NCSX can reproduce flux-surface calculation given an adequate parallel extent. flux-tube calculations accurately moderate $k_x$, but time scales longer local representations, particularly $k_x$ approaching system size.