Ionospheric depletion in auroral downward currents

The auroral downward field‐aligned current is mainly carried by electrons of ionospheric origin accelerated into the magnetosphere along the Earth's high‐latitude field lines. The ionosphere is a finite source of electrons: Thus, if a current is to continue to flow, it is natural to assume that the current region must broaden to access more current carriers. In this paper, we present an Alfvén wave model of magnetosphere‐ionosphere interaction to describe the evolution of ionospheric E region number density under the influence of a downward current. The behavior of the system falls into two regimes depending upon whether the quantity = j 0/ α en e 2 h is greater or less than unity (where j 0 is initial current density, α is the recombination coefficient, n e is background E region number density, and h is E region height): If the current density is smaller than a critical current density, j c = αen e 2 h (i.e., < 1), then the E region only depletes within the original current region, and there is sufficient photoionization to feed the current to the magnetosphere; if the required current density is larger than j c (i.e., > 1), then the current region is forced to broaden in order to access sufficient electrons. On the dayside, where a typical E region number density is ∼10 11 m −3 , broadening only occurs for very strong current densities ∼10 μ A m −2 ; on the nightside, however, where E region number densities can fall by a factor of 10, broadening occurs for any current density greater than ∼0.1 μ A m −2 . From this model, we derive expressions for the final depletion width (generally ∼1–10 times the width of the original current region) and for the characteristic timescale of depletion (typically ∼10–100 s).