A magnetohydrodynamic theory for the lunar response to time variations in a spatially uniform ambient magnetic field
An analytic theory based on principles of magnetohydrodynamics is derived for interpreting the lunar magnetic response to magnetic field fluctuations in the lobes of the geomagnetic tail. Only the case of magnetic perturbations parallel to a spatially uniform ambient magnetic field is treated. The theoretical frequency-dependent MHD transfer function depends on both the lunar electrical conductivity profile and the Alfven speed of the tail lobe plasma. For circular frequencies much less than the Alfven speed/lunar radius, the MHD transfer function reduces to the vacuum transfer function, while at higher frequencies the finite propagation speed of magnetic disturbances affects the response. These characteristics of the MHD transfer function are in qualitative agreement with observation. A carefully selected set of magnetic field transient events could be used together with this theory to infer lunar electrical conductivity profiles and the tail lobe plasma density (via its dependence on the Alfven speed).