Saturation of the polar cap potential: Inference from Alfvén wing arguments

The cross polar cap potential varies roughly linearly with the solar wind electric field for nominal conditions but asymptotes to a constant value of order 200 kV for large electric field. When the impedance of the solar wind across open polar cap field lines dominates the impedance of the ionosphere, Alfvén waves incident from the solar wind are partially reflected, reducing the signal in the polar cap. Thus, the ratio of the cross polar cap potential to the potential imposed by the solar wind is 2Σ A /(Σ P + Σ A ), where Σ A is the Alfvén conductance of the solar wind (= ( ρ sw / μ o ) 1/2 / B sw ) to within a density‐dependent factor on average of order 1, Σ P is the Pedersen conductance of the ionosphere, and ρ sw ( B sw ) is the density (magnetic field magnitude) of the solar wind. For small B sw , the response is proportional to B sw . For large B sw , the cross polar cap potential depends only on the solar wind dynamic pressure (with small viscous and density‐dependent corrections). Quantitative estimates require knowledge of Σ P and the dependence of the potential imposed by the solar wind on its measured properties; standard assumptions yield saturation levels consistent with observations made during 13 storm intervals. Previous explanations of saturation have invoked changing reconnection efficiency, specific characteristics of the Region 1 current system, or the effect of the bow shock on the reconnecting plasma. Although our relation is mathematically similar to some previously proposed, our arguments place no constraints on reconnection efficiency or on magnetospheric geometry.