Eigenmode analysis of field line oscillations interacting with the ionosphere-atmosphere-solid earth electromagnetic coupled system

In order to understand the effect of ionosphere on the localized toroidal magnetic shell oscillation (field line oscillation), we have constructed a rectangular box model for the magnetosphere-ionosphere-solid earth system including the anisotropically conducting ionosphere and performed the eigenmode analysis of the magnetohydrodynamic (MHD) waves in the model. We have found that the eigenmodes of field line oscillation are effectively controlled by the height-integrated Pedersen and Hall conductivities, meaning that the field-aligned current (FAC) in the magnetosphere is closed to both the Pedersen current and the Hall current. The divergent Hall current, that is, the Hall current, which closes the FAC, is a newfound current that is driven by the Hall effect of the ionospheric inductive (rotational) electric field. The divergent Hall current brings into sharp relief by considering the ionosphere to be inductive, and it inevitably requires the electromagnetic coupling between the magnetosphere, ionosphere, atmosphere, and solid earth. The nature of the ionospheric current associated with the standing shear Alfvén mode is also analyzed in detail by using the concept of wave reflection and mode conversion at the inductive ionosphere. In particular, we emphasize that the magnetic flux sustained by the rotational Hall current, that is, accompanied by the radiation of fast magnetosonic wave to the magnetosphere and atmospheric poloidal magnetic wave to the atmosphere, should be taken into account for magnetosphere-ionosphere coupling of FAC.