Magnetohydrodynamic simulations of transient transpolar potential responses to solar wind density changes

Magnetohydrodynamic (MHD) simulations are used to examine the response of the transpolar potential (ΦTP) to changes in the solar wind density during periods of constant solar wind electric field. For increases (decreases) in the solar wind density ΦTP responds immediately by increasing (decreasing) from the steady state values. In both cases the response of ΦTP is transient, decaying to near initial steady state values even when the density change persists. The magnitude of the ΦTP response is proportional to both the rate of erosion of the dayside magnetopause and the ionospheric Pedersen conductance. In our MHD simulations ΦTP is driven entirely by the dayside merging rate and is insensitive to changes in the nightside reconnection rate. The observed relationship between the modeled dayside merging rate and ΦTP is well characterized by an L‐R circuit equation derived from integrating Faraday's Law around the Region 1 current loop. The inductive time constant for variations in the transpolar potential was found to be 6.5 (13) minutes for simulations using ionospheric Pedersen conductances of 6 (12) mhos. This corresponds in both cases to a magnetosphere‐ionosphere inductance of 65 Henries. Observations of the transpolar potential derived using the assimilative mapping of ionospheric electrodynamics (AMIE) model are presented and shown to be consistent with the simulation results.