Analytical solutions for global geodesic acoustic modes in tokamak plasmas

Analytical solutions for global geodesic acoustic modes in the plasma of a tokamak with circular concentric magnetic surfaces are obtained. In the framework of ideal magnetohydrodynamics, an integral equation for eigenvalues (dispersion relation) taking into account toroidal coupling between electrostatic perturbations and electromagnetic perturbations with the poloidal mode number |m| = 2 is derived. In the absence of such coupling, the dispersion relation yields only the standard continuous spectrum. The existence of a global geodesic acoustic mode is analyzed for equilibria with both on-axis and off-axis maxima of the local geodesic acoustic frequency. The analytical results are compared with results of numerical calculations.