Abstract
The longitude independent wave equation for the poloidal or isotropic magnetohydrodynamic resonances of a plasma magnetized by a dipole field is solved under the assumption of an Alfvén velocity increasing linearly with radial distance and retaining the latitude dependence of the magnetic field. Such a radial dependence is the only case in which the equation is separable in spherical coordinates and the solution possesses several advantages: the radial functions are particularly simple, the eigenfrequencies are derivable from an algebraic equation, and the contribution of the magnetic field's polar angle dependence can be clearly obserued.
