Asymmetric eigenmodes in a simple model plasmasphere with non-uniform Alfvén speed

Abstract A previous study of non-axisymmetric eigenmodes in a simple model plasmasphere is extended to a case in which the Alfven speed varies across the magnetic field lines. An approximate ordinary differential equation is derived, and this contains a logarithmic singularity closely analagous to a result obtain by Tamao (1965). The singularity is found to lie close to the resonant lines of force for a hypothetical torsional oscillation. Some valid eigenfrequencies are stated for a region with appropriate further boundaries.