Nonlinear growth of zonal flows by secondary instability in general magnetic geometry

G G Plunk,A Bañón Navarro

doi:10.1088/1367-2630/aa5fdf

Abstract

We present a theory of the nonlinear growth of zonal flows in magnetized plasma turbulence, by the mechanism of secondary instability. The theory is derived for general magnetic geometry, and is thus applicable to both tokamaks and stellarators. The predicted growth rate is shown to compare favorably with nonlinear gyrokinetic simulations, with the error scaling as expected with the small parameter of the theory.

Highlights

The present work concerns the dynamics of zonal flows in magnetic confinement fusion devices, and in particular the three dimensional magnetic geometries of stellarators
The secondary mode can function more indirectly, by driving otherwise stable modes called zonal flows, that are involved in mode saturation by “backreaction” or shearing. This second scenario is of great importance in ion temperature gradient (ITG) turbulence in magnetic fusion devices, which is the motivation for the present work
We have presented a theory of nonlinear zonal flow growth in general magnetic geometry, and validated it using nonlinear gyrokinetic simulations

Summary

Introduction

The present work concerns the dynamics of zonal flows in magnetic confinement fusion devices, and in particular the three dimensional magnetic geometries of stellarators. In the theory of plasma turbulence, the notion of secondary instability, generally speaking, provides a useful tool for understanding the nonlinear processes that determine fluctuation amplitudes. The secondary mode can function more indirectly, by driving otherwise stable modes called zonal flows, that are involved in mode saturation by “backreaction” or shearing This second scenario is of great importance in ion temperature gradient (ITG) turbulence in magnetic fusion devices, which is the motivation for the present work. Some works on zonal flow growth have modeled the effect of magnetic geometry [9, 10], by deriving local fluid approximations of linear theory that, do not account for the variation of the linear modes within a flux surface.

Equations

Representing turbulence in general magnetic geometry

Derivation of the global secondary instability in general geometry

Numerical simulation of zonal flow growth by secondary instability

Conclusion