Latitudinal structures of discrete arcs resulting from viscous interaction between sheared plasma flows

Latitudinal structures of discrete arcs are modelled as a consequence of the quasi-steady magnetosphere-ionosphere coupling involving viscous interaction between sunward and anti-sunward plasma flows in the magnetosphere. The quasi-steady state in the magnetosphere and ionosphere coupling is described by the magnetospheric and ionospheric current conservation and the field-aligned currentpotential relation assuming adiabatic electron motion along field lines. The upward and downward fieldaligned currents are assumed to be stably maintained by vorticity-induced space charges in the region of plasma flow reversal, where divergence of the magnetospheric electric field E_⊥ is negative and positive, respectively. By introducing the effective conductance Σ_dc arising from the anomalous viscosity, a specific relation between the dc field-aligned current density J_∥ and the magnetospheric electric field E_⊥ is derived as $\text{J}{}_{\mathrm{\parallel }}\text{=?Σ}{}_{\mathrm{dc}}\text{div}\text{E}{}_{\mathrm{\perp }}$. Sufficiently large potential drops to accelerate auroral electrons are shown to exist along the auroral field lines originating from the flow reversal region with div $\text{E}{}_{\mathrm{\perp }}\text{< 0}$. It is shown that the latitudinal structure of a discrete arc is primarily determined by the magnetospheric potential structure and the characteristic width is on the order of 10 km at the ionospheric altitude.