Plasma shaping effects on the geodesic acoustic mode in toroidally axisymmetric plasmas

The geodesic acoustic mode (GAM) is studied in noncircular, finite aspect ratio, toroidal plasmas with a gyrokinetic theory and a local magnetohydrodynamics equilibrium model. Dependencies of the GAM frequency on finite aspect ratio and elongation are investigated when trapped particle effects are neglected in the large aspect ratio limit. It is found that the GAM frequency sharply decreases with an increasing elongation by dependence of [2∕(κ2+1)]1∕2 and slightly decreases with an increasing inverse aspect ratio by dependence of about 1−3ε2∕4, where κ and ε are the plasma elongation and inverse aspect ratio. The elongation dependence comes from the modification of classical ion polarization balanced by that of curvature drift polarization while the aspect ratio dependence is due to the former in the leading order.