Propagation of ULF waves through the ionosphere: analytic solutions for oblique magnetic fields

The propagation of ultra low frequency (ULF; 1-100 mHz) waves from the magnetosphere to the ground is examined in the presence of oblique background magnetic fields. The problem is developed analytically for a thin sheet ionosphere, neutral atmosphere, and perfectly conducting ground. The cold plasma, ideal magnetohydrodynamic (MHD) Alfvén wave modes are assumed to propagate in the MHD medium above the ionosphere. A reflection and wave mode conversion coefficient matrix (RCM) is derived which describes mixing and conversion between shear Alfvén and fast mode energy when interacting with the ionosphere/atmosphere/ground system. The RCM is found to depend in a complicated way on the background magnetic field dip angle, the horizontal wave vector, and the conductivity of the ionosphere. For an oblique background magnetic field, →B₀ in the XZ plane, the perpendicular wave number, ky, is shown to be a critical parameter that determines reflection and mode conversion characteristics. This study also highlights the need for spatial information of ULF wave energy in order to interpret experimental ULF wave data recorded at ground level in terms of magnetospheric processes.