Mapping between the ionospheric and the tail electric fields in a time‐dependent Earth's magnetosphere

Abstract

In this paper we use the concept of the Faraday loop to connect the ionosphere and the tail along the geomagnetic field lines to study the coupling between ionospheric and magnetospheric electric fields. The formulation using the Faraday loop shows that the coupling consists of three contributions: One is the familiar mapping of the ionospheric field to the tail along equipotential magnetic field lines. The other two are parallel potential differences between the tail and the ionosphere distributed across the magnetic field lines and magnetic flux transport across the Faraday loop due to time evolution of the magnetic field, which gives rise to an inductive electric field perpendicular to the magnetic field. Application of this method requires a model for the ionospheric electric field, a model distribution of the parallel potential differences, and a time‐evolving magnetic field model. In the present study the ionospheric electric field pattern is described using a statistical model. The parallel potential differences are modeled by Gaussian distributions in latitude as narrow longitudinally elongated ridges. The magnetic field model describes the time evolution of the geomagnetic field during the substorm growth phase. We show that the effects of parallel potential differences and the inductive fields are of the same order as the mapped ionospheric field, and hence they must be taken into account when the large‐scale coupling is studied.