The zonal-flow residual does not tend to zero in the limit of small mirror ratio

TL;DR

This paper examines the behavior of the zonal-flow residual in magnetic confinement devices at small mirror ratios, revealing that it does not tend to zero as previously assumed, especially influenced by barely passing particles.

Contribution

It provides an analytical estimate of the residual in the small mirror ratio limit and clarifies its relationship with the geodesic acoustic mode, extending understanding beyond the quadratic approximation.

Findings

Residual remains finite at small mirror ratios.

Barely passing particles significantly influence the residual.

Residual is smallest in the core of quasi-axisymmetric fields.

Abstract

The intensity of the turbulence in tokamaks and stellarators depends on its ability to excite and sustain zonal flows. Insight into this physics may be gained by studying the ''residual'', i.e. the late-time linear response of the system to an initial perturbation. We investigate this zonal-flow residual in the limit of a small magnetic mirror ratio, where we find that the typical quadratic approximation to RH (Rosenbluth & Hinton, 1998) breaks down. Barely passing particles are in this limit central in determining the resulting level of the residual, which we estimate analytically. The role played by the population with large orbit width provides valuable physical insight into the response of the residual beyond this limit. Applying this result to tokamak, quasi-symmetric and quasi-isodynamic equilibria, using a near-axis approximation, we identify the effect to be more relevant (although small) in the core of quasi-axisymmetric fields, where the residual is smallest. The analysis in the paper also clarifies the relationship between the residual and the geodesic acoustic mode, whose typical theoretical set-ups are similar.