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Since the magnetic field strength is not constant on the magnetic flux surface, theflow also varies so that the density compression occurs along the poloidal direction. Since the inhomogeneousflow causes the density compression in the poloidal direction, the parallel flow is also perturbed. In this study, we investigate the effects of the parallel flow perturbation on the geodesic acoustic mode (GAM) when it is described by the kinetic approach. Using the continuity equation, it is shown that the flow perturbation in the geodesic curvature direction is balanced by the lowest-order term of the density perturbation in, and the flow perturbation in the parallel direction is balanced by the higher-order terms of the density perturbation. Since the density perturbation includes both the perpendicular and parallel flow perturbation contributions, the GAM frequency obtained by the kinetic approach has the parallel flow perturbation contribution, which is 1/term in the GAM frequency equation. The low frequency branch of the dispersion relation is also discussed to demonstrate the connection between the GAM theory and neoclassical theory for the first time. It is shown that the flow perturbation in the geodesic curvature direction is balanced mostly by the parallel flow perturbation. It means that the flow in the flux surface is divergence free approximately as in the usual transport ordering. Thus, the poloidal flow goes to the neoclassical flow when the low frequency branch is taken.

Relation Between the Low Frequency GAM and the Neoclassical Flow