Collisionless zonal flow damping in quasisymmetric stellarators

Quasisymmetric stellarators are similar to tokamaks in radial particle drift and flow damping, but exhibit zonal flow oscillations and the residual zonal flow R_ZF -> 0 as radial wavenumber k_x -> 0 due to deviations from perfect quasisymmetry. In collisionless linear calculations, damped GAM oscillations settle to a long-time zonal flow residual. This often describes the strength of zonal flows in tokamaks, and thus their effect on turbulence saturation. In stellarators, long-time damping and zonal flow oscillations complicate this simple picture. We present calculations of zonal flow damping in realistic geometry from the National Compact Stellarator eXperiment and symmetric and broken-symmetry configurations of the Helically Symmetric eXperiment. Using GENE and EUTERPE, a comparison of flux tube, flux surface, and full volume geometry representations demonstrates that a local flux tube captures the zonal flow residual, but that full volume simulations are required for damping at small k_x. The zonal flow residual does not correlate to reduced heat flux in nonlinear simulations, but the oscillation and short-time damping may provide a proxy.