Resonant Alfvén waves on auroral field lines

It is shown that resonant Alfvén waves on dipole magnetic field geometry and plasma distributions suitable for auroral field lines can be conveniently treated in the theory of Mathieu functions. Resurgent interest in invoking large‐scale Alfvén waves to structure some elements of auroral electrodynamics calls for interpretation of measured perpendicular electric and magnetic disturbance fields in terms of Alfvén waves. The ability to express the resonant eigenmodes in closed form in terms of Mathieu functions allows for convenient tests of the Alfvén wave structuring hypothesis. Implications for current vector electric and magnetic disturbance measurements are discussed.