Geodesic acoustic mode frequency and the structure of Alfvén continuum in toroidal plasmas with high q2β

It is shown that conventional expressions for the frequencies of the geodesic acoustic mode (GAM) and the gaps in the Alfvén continuum of toroidal plasmas are valid only when q2β ≪ 1, where q is the safety factor and β is the ratio of the plasma pressure to the magnetic field pressure. Expressions, which are relevant to plasmas with , where , cs is the sound velocity, vA is the Alfvén velocity) and convenient for practical use, are obtained for the GAM frequency and the characteristic values of the frequencies of gap modes (toroidicity-induced Alfvén eigenmodes, ellipticity-induced Alfvén eigenmodes and noncircularity-induced Alfvén eigenmodes). It is found that at any the Alfvén continuum in the near-axis region is described by Mathieu's equation. Due to this, simple expressions are also obtained for the limit case of .