On vertical spinning Alfven waves in a magnetic flux tube

The Alfven-wave equation is derived for an atmosphere in the presence of a non-uniform vertical magnetic field and the Hall effect, allowing for Alfven speed and ion gyrofrequency that may vary with altitude; the pair of coupled second-order differential equations for the horizontal wave variables, namely magnetic field or velocity perturbations, is reduced to a single complex second-order differential equation. The latter is applied to spinning Alfven waves in a magnetic flux tube, in magnetohydrostatic equilibrium, in an isothermal atmosphere. (Author)