Global geodesic acoustic mode in an ideal magnetohydrodynamic tokamak plasma

A concise and transparent second order ordinary differential equation (ODE) describing the radial structure of the global geodesic acoustic mode (GAM) is analytically presented in a low-beta tokamak plasma. The large-aspect-ratio and circular cross section are assumed to linearize the ideal magnetohydrodynamic equations. We show clearly how finite beta-dependent terms affect the global GAM frequency and radial mode structure. A typical Wentzel-Kramers-Brillouin form of solution is found for some reversed shear equilibria. For some other equilibria with lower beta, even also in a reversed shear tokamak, the GAM continuum is upraised by the high order beta-dependent terms so that its maximum is beyond omega(G), where omega(G) is the classical local frequency of GAM. As a result, no self-consistent solution to the ODE can be found. Published under license by AIP Publishing.