Saturation of the Polar Cap Potential: Inference from Alfvén Wing Arguments.

Details Saturation of the Polar Cap Potential: Inference from Alfvén Wing Arguments. Saturation of the Polar Cap Potential: Inference from Alfvén Wing Arguments.

Dec 2006

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006agufmsm22a..06k&link_type=abstract

American Geophysical Union, Fall Meeting 2006, abstract #SM22A-06

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2712 Electric Fields (2411), 2776 Polar Cap Phenomena, 2784 Solar Wind/Magnetosphere Interactions

Scientific paper

It is widely accepted that the polar cap potential (Vpc ) varies roughly linearly with the solar wind electric field (Esw) for nominal conditions but that it saturates at a level of order 200 kV as Esw becomes large. Explanations of the effect have invoked changes of the efficiency of reconnection or modifications of the characteristics of the Region 1 current system. Here we propose a very simple way of understanding the saturation effect as a result of the need to match impedances across open field lines from the polar cap into the solar wind. Using Alfvén wing theory as developed for the study of interactions of the moons of Jupiter with the plasma of Jupiter's magnetosphere and assuming that the solar wind field is purely southward oriented, we obtain the relation: Vpc=2 usw D (ρsw/μ_o)^{1/2} / [Σ_P +2 (ρsw/μo)^{1/2) / Bsw] where usw, ρsw, and Bsw are the solar wind velocity, density and magnetic field, respectively, D is the width of the region in the unperturbed solar wind that reconnects with the magnetosphere, and Σ_P is the Pedersen conductance of the ionosphere. In the limit of small Bsw, the expression is linear in Esw (uswBsw) but when Bsw exceeds (ρsw/μo)^{1/2)/Σ_P, the solar wind magnetic field no longer enters the relation, i.e. the polar cap potential saturates. Quantitative values from the equation rely on knowledge of the poorly constrained parameter, Σ_P, and the uncertain value of D, but for reasonable values of the parameters yields saturation levels consistent with observations. This expression relates closely to those proposed by other investigators, but the underlying two line derivation rests purely on the requirement that impedances match across transitions from one plasma regime to another and is independent of details of the magnetospheric geometry.

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