Propagation of ULF waves through the ionosphere: inductive effect for oblique magnetic fields

Solutions for ultra-low frequency (ULF) wave fields in the frequency range 1–100mHz that interact with the Earth's ionosphere in the presence of oblique background magnetic fields are described. Analytic expressions for the electric and magnetic wave fields in the magnetosphere, ionosphere and atmosphere are derived within the context of an inductive ionosphere. The inductive shielding effect (ISE) arises from the generation of an "inductive" rotational current by the induced part of the divergent electric field in the ionosphere which reduces the wave amplitude detected on the ground. The inductive response of the ionosphere is described by Faraday's law and the ISE depends on the horizontal scale size of the ULF disturbance, its frequency and the ionosphere conductivities. The ISE for ULF waves in a vertical background magnetic field is limited in application to high latitudes. In this paper we examine the ISE within the context of oblique background magnetic fields, extending studies of an inductive ionosphere and the associated shielding of ULF waves to lower latitudes. It is found that the dip angle of the background magnetic field has a significant effect on signals detected at the ground. For incident shear Alfvén mode waves and oblique background magnetic fields, the horizontal component of the field-aligned current contributes to the signal detected at the ground. At low latitudes, the ISE is larger at smaller conductivity values compared with high latitudes.