Euler Potentials for Dungey Magnetosphere With Axisymmetric Ring and Field‐Aligned Currents

Abstract

Euler potentials are found for the magnetic field in the inner magnetosphere, consisting of the Earth's dipole field, the Dungey term, ring current (RC), and field‐aligned current (FAC). The magnetic field in this approximation is axially symmetric. One Euler potential for the dipole, Dungey term, and RC is the same, while that for the magnetic field induced by FAC is different and calculated in this work under the condition that all four field contributions have the same second Euler potential. The Euler potentials are determined for quiet, severe, and superstorm geomagnetic conditions. The restriction of the model is its axial symmetry, so changes of the location and intensity of the currents with azimuthal angle are not explicitly present. On the other hand, these parameters can be changed in the model, and one can study local distributions.

Exact Alpha‐Beta Mapping of IGRF Magnetic Field in the Ionosphere

“…The first Euler potential, α , is a function of $${B}_{r}^{2}$$, and β will be determined from the integrations of the basic functions in the volume and solving corresponding matrix equation. For spherically symmetric model magnetospheric magnetic field, when β can be chosen as β = − φ , this problem was solved in Romashets and Vandas (2022).…”

“…The Euler potentials for the Earth's dipole magnetic field, field‐aligned currents, and the ring current were found in Romashets and Vandas (2020). The Dungey (Dungey, 1963) term was added into the consideration in Romashets and Vandas (2022).…”