Magnetic field induced by the ionospheric shell currents.

Recently, a model of the vertical profiles of shell currents and the magnetic field in the ionosphere has been developed (Romashets and Vandas, 2024). The distribution was determined for polar and equatorial regions. A global three-dimensional pattern of the shell-currents flow and its interconnections with the field aligned current (FAC) can be reconstructed. The magnetic field induced by the shell currents can produce at some locations a geomagnetic effect comparable to that of the ring current. The Biot-Savart integration over the entire ionosphere to derive the shell-currents induced magnetic field could be a challenging task. Here, we present an alternative method which utilizes spherical harmonics of different types for the inner and outer problems. The magnetic field inside the ionosphere is known, and outside of it is current-free and is represented as a gradient of a scalar potential, a sum of spherical harmonic functions with their coefficients. For the inner problem, only terms with (r/r0)^-n-1 are present in the sum, while the outer scalar potential contains only terms with (r/r0)ⁿ. Here 0<n<N, N=13, and r0 is the average distance from the Earth’s center to the ionosphere. Both the inner and outer problems for finding the induced magnetic field have only one condition: the magnetic field calculated with the scalar potential must be equal to the known magnetic field in the ionosphere. This research was supported by the NSF 2230363 and AVCR RVO:67985815 grants.

 

References.

• Romashets, M, Vandas, Determination of Vertical Profiles of Shell
  Currents in the Ionosphere, Annales Geophysicae, submitted, 2024.