Conservation of both current and helicity in a quadrupolar model for solar flares |
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Authors: | Melrose Don |
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Institution: | (1) School of Physics, University of Sydney, NSW, 2006, Australia |
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Abstract: | A model for a solar flare, involving magnetic reconnection transferring flux and current between current-carrying magnetic
loops connecting two pairs of footpoints, is generalized to include conservation of magnetic helicity during reconnection,
as well as conservation of current at all four footpoints. For a set of force-free loops, with the ith loop having flux F
i and current I
i, the self and mutual helicities are proportional to the self and mutual inductances with the constant of proportionality
determined by αi=F
i/μ0
I
i. In a constant-α model, the change in magnetic energy is proportional to the change in helicity, and conservation of helicity
implies conservation of magnetic energy, so that a flare cannot occur. In a quadrupolar model, with α1>α2 initially, α1 increases and α2 decreases when flux and current are transferred from loops 1 and 2 to loops 3 and 4. A model that conserves both current
and helicity is constructed; it depends on the initial αs, and otherwise is somewhat simpler than when helicity is neglected. |
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Keywords: | |
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