Mathematics
Scientific paper
Mar 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994soph..150..245f&link_type=abstract
Solar Physics, vol. 150, no. 1-2, p. 245-266
Mathematics
38
Current Sheets, Electric Current, Equilibrium Equations, Force-Free Magnetic Fields, Magnetic Energy Storage, Magnetic Field Reconnection, Magnetic Flux, Mathematical Models, Photosphere, Potential Fields, Solar Corona, Solar Flares, Solar Magnetic Field, Asymptotic Methods, Boundary Conditions, Catastrophe Theory, Cusps (Mathematics), Green'S Functions, Laplace Equation
Scientific paper
We determine the photospheric boundary conditions which maximize the magnetic energy released by a loss of ideal-magnetohydrodynamic (MHD) equilibrium in two-dimensional flux-rope models. In these models a loss of equilibrium causes a transition of the flux rope to a lower magnetic energy state at a higher altitude. During the transition a vertical current sheet forms below the flux rope, and reconnection in this current sheet releases additional energy. Here we compute how much energy is released by the loss of equilibrium relative to the total energy release. When the flux-rope radius is small compared to its height, it is possible to obtain general solutions of the Grad-Shafranov equation for a wide range of boundary conditions. Variational principles can then be used to find the particular boundary condition which maximizes the magnetic energy released for a given class of conditions. We apply this procedure to a class of models known as cusp-type catastrophes, and we find that the maximum energy released by the loss of equilibrium is 20.8% of the total energy release for any model in this class. If the additional restriction is imposed that the photospheric magnetic field forms a simple arcade in the absence of coronal currents, then the maximum energy release reduces to 8.6%
Forbes Terry G.
Isenberg Philip A.
Priest Eric R.
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