Finite-Larmor-radius-induced global geodesic acoustic modes—a two-fluid model

Abstract

A linear theory of ion finite-Larmor-radius (FLR)-induced global geodesic acoustic modes (GAMs) based on the electrostatic two-fluid model is developed, in which modest ion FLR effects are encompassed through polarization drifts. The radial differential equation obtained for the eigenmode is a type of generalized Schrödinger equation, in which the eigenfrequency is mixed with the potential term in a complex manner. By numerically solving this equation as a genuine boundary value problem, it is found that for typical equilibrium profiles, a series of global GAMs exist, with relatively higher frequencies that intersect with the GAM continuum. Those with frequencies in the intermediate range are forbidden by the singularity of the local dispersion function. When we restrict the poloidal θ harmonics up to m = ±1, we successfully interpret the bound-state profiles of global GAMs discovered in the simulation performed by Miyato et al (2006 Plasma Phys. Control. Fusion 48 A335). We also point out the limitation of their model.