Three‐Dimensional Closure of Field‐Aligned Currents in the Polar Ionosphere

Using a simplified three‐dimensional Hall‐magnetohydrodynamics simulation, we investigated the current closure of field‐aligned currents (FACs) in the polar ionosphere. Ion‐neutral collision was taken into consideration. To excite a pair of FACs, an electric field perturbation is applied to the upper boundary of the simulation box. The flow shear propagated downward accompanied with the FACs. When the electron density was initially uniform, most of the FACs are connected with the Pedersen current due to electrostatic processes. Some of them are connected with the Hall current due to inductive processes. When the density was initially enhanced in a longitudinally elongated region (high‐density band), overflow of the Hall current takes place near the edge of the high‐density band. Additionally, localized FACs appear to bridge between the Pedersen current layer (high altitude) and the Hall current layer (low altitude). The formation of the additional FACs is closely associated with the field‐aligned gradient of ∇∙ E , where E is the electric field. We compared the current lines with those evaluated by the traditional thin‐layer assumption. The current closure obtained by the thin‐layer assumption is fully different from that obtained by the three‐dimensional model. In the full three‐dimensional simulation, a current line flowing in the Hall layer can pass underneath the current flowing in the Pedersen layer. Such “intersection” is not allowed in the thin‐layer assumption. We believe that the three‐dimensional model offers advantages for fully understanding the closure of the FACs together with the current closure on the magnetospheric side.