Energy Storage and Current Sheets in a Quadrupolar Corona

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Scientific paper

We consider magnetic energy storage in a force-free model corona with quadrupolar boundary conditions at the coronal base. Our broad goal is to explore the energetics of the corona prior to coronal mass ejections. Specifically, we compare the maximum possible energy with that of a fully open field with the same boundary conditions; Aly and Sturrock have conjectured that the latter is the upper bound on the energy of force-free fields without detached flux. As found earlier for dipolar and other bipolar boundary conditions, it is possible in the quadrupolar case to develop solutions with detached flux ropes, whose energy exceeds the open-field energy. The excess energy in this case of a more confined magnetic structure proves greater than with bipolar fields. We also present a method for calculating the non-trivial configuration of the open-field current sheet in this case where it is not obvious from symmetry, and we use the result to determine the open-field energy.

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