Unified linear response function for zonal flows with full finite orbit effects

Abstract

A new formulation of the linear response function of electrostatic potential to nonlinear drive (due to turbulence) is presented in this paper; zonal flows play important roles in the self-regulation of turbulence and their basic physics are contained in response functions. Two branches of zonal flows [stationary zonal flow and geodesic acoustic mode (GAM)] are known to exist in the low and high frequency ranges. However, they have been analyzed separately using different approximations due the difference in their frequency ranges. This paper visits this problem and gives a unified expression of the response function by taking full account of finite orbit effects. The drift kinetic equation is integrated along particle orbits by expanding them in Fourier series. Thus, a separate handling of passing and trapped particles is facilitated revealing some important aspects of zonal flows: (1) neoclassical poloidal mode coupling due to finite orbit effects, (2) enhancement of the nonuniform potential field due to reduced parallel transport, and (3) the presence of two propagation bands of GAM as the quadratic dispersion relation is solved.