On field line resonances of hydromagnetic Alfvén waves in dipole magnetic field

Using the dipole magnetic field model, we have developed the theory of field line resonances of hydromagnetic Alfvén waves in general magnetic field geometries. In this model, the Alfvén speed thus varies both perpendicular and parallel to the magnetic field. Specifically, it is found that field line resonances do persist in the dipole model. The corresponding singular solutions near the resonant field lines as well as the natural definition of standing shear Alfvén eigenfunctions have also been systematically derived.