Auroral arcs: Result of the interaction of a dynamic magnetosphere with the ionosphere

A model of auroral arcs is presented. It is assumed that the magnetic field lines into the auroral oval are loaded with kev electrons, that precipitating auroral electrons locally constitute a net field-aligned current, and that currents close in the outer magnetosphere by polarization currents. The model predicts that a flux tube convecting through the oval will undergo a highly nonlinear oscillation that produces standing waves, the auroral arcs. The conditions to be satisfied are (1) Ohm's law in the ionosphere, (2) electron number conservation in the ionosphere, (3) electric current continuity, (4) the tendency for electric fields to map between ionosphere and magnetosphere. The physics of condition 4 is not understood, but it is probable that arc-like solutions exist for several models. A specific model, including perfect mapping of electric fields, is studied. The solutions to this model closely resemble the arcs. Predicted in agreement with observation are arc thickness, inter-arc spacing, and the electric field behavior. The thickness and the spacing are functions of both the amplitude of the oscillation and the physical properties of the system. However, thickness times spacing is a function of the physical properties only, and the thickness divided by the spacing is a function of amplitude only. Presumably these and other quantitative relationships can be checked by observations.