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 α i =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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Melrose, D. Conservation of both current and helicity in a quadrupolar model for solar flares. Solar Physics 221, 121–133 (2004). https://doi.org/10.1023/B:SOLA.0000033358.64885.3a
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DOI: https://doi.org/10.1023/B:SOLA.0000033358.64885.3a