Orthogonal Electrodynamics in Multipole Magnetic Fields

Electrodynamics investigations of plasma-neutral interactions require basis vectors that bridge geographic and geomagnetic coordinates. We present the first orthogonal basis vectors and coordinates for multipole magnetic fields that facilitates mapping geophysical parameters along magnetic field-lines. The calculated zonal, field-aligned, and meridional directions physically organize electric fields and plasma motions in a locally orthogonal manner. The basis is optimized for electrodynamics as the meridional and zonal vectors are vertical and horizontal at the magnetic equator. To counter assumptions from previous solutions, we demonstrate that multipole magnetic fields intrinsically support orthogonal basis vectors. The new basis also satisfies the conservation of magnetic flux and yields a magnetic field with zero divergence. Comparison of two different basis derivations demonstrates low basis uncertainty. The mapping functionality is validated through analytical example and comparison to a novel electrostatic field-line model. Using the orthogonal basis vectors a new orthogonal magnetic coordinate system is created. The equations for electrodynamics are expressed and simplified by the new coordinates, including a novel two-dimensional variant. Using the orthogonal basis we create an optimal meridional-zonal grid plane for numerically solving electrodynamics equations. To support geophysical interpretation, the meridional-zonal grid is tested by calculating a global electrostatic potential and electric field distribution. The validated basis is compared to non-orthogonal solutions and models to demonstrate that previous solutions are geophysically inconsistent. While previous solutions only worked for dipole fields, the new basis supports multipole fields, enabling electrodynamics investigations and models that were previously impossible.