Poloidal eigenmode of the geodesic acoustic mode in the limit of high safety factor

The poloidal eigenmode of the geodesic acoustic mode (GAM) is studied in the limit of high safety factor. In this limit, the poloidal gyroradius cannot be treated as a perturbation or as an expansion parameter. Analytical expressions for the poloidal structure of the GAM potential, the radial wavenumber dependence of the frequency, the phase velocity, and the group velocity are obtained. The spatial structure of the poloidal eigenmode including the higher-order gyroradius effect is revealed theoretically.