Alfvénic field line resonances in arbitrary magnetic field topology

In this paper we present a general covariant–contravariant formalism suitable for describing standing shear Alfvén waves in a general magnetic field topology. We define a non-orthogonal field-aligned coordinate system based on Euler potentials and compute the metric tensor coefficients for these coordinates numerically. An eigenvalue problem for the system of four ordinary equations is then solved to compute the eigenfrequency and polarization of the standing Alfvén wave for a given field line. As examples, dipole and Tsyganenko 96 magnetic field models are used. The results are compared to the predictions of older models based on either dipole or axisymmetric magnetic fields.