Dispersion relations for the Suydam problem

It is shown that three problems, namely the Suydam problem of the stabilization of a plasma placed in a gravitational field with shear the problem of Tokamak plasma stability concerning flute-mode perturbations, and the problem of dispersion of global Alfven modes with large poloidal wavenumbers, are described in a mathematical sense by the same Schrodinger equation. The energy spectrum of this equation is analyzed by using different asymptotic methods (the quasi-classical approximation, the perturbation method, and asymptotic matching of solutions). The results of these methods are in a good agreement. The analytical expressions obtained allow the authors to specify some well-known formulae and give a number of new expressions for the growth rates of the instabilities under consideration and the global Alfven-mode spectrum.