A mathematical model is proposed describing the initial phase of solar flare heating in the corona. The model is based on the nonlinear heat equation with a sign-alternating volume source, which is derived from the energy equation of the electron component of stationary plasma. Flares are assumed to arise as a result of sausage-type instabilities of a magnetic tube and creation of collapsing magnetic traps. A source function is chosen and the model parameters are fitted. Thermal structures arising under supercritical perturbations in a homogeneous temperature background are calculated and their specific features are examined. With nonclassical heat conduction, flares produce structures for which the half-width of the energy release region shrinks over time. The effect of “emission measure reduction” observed in the early phase of the flare is associated with the decrease of the flare filling factor due to the decrease of the structure half-width.
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Translated from Prikladnaya Matematika i Informatika, No. 45, 2014, pp. 15–31.
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Kurkina, E.S., Kuretova, E.D. & Kovalev, V.A. Formation of Thermal Structures with Blowup During Solar Flares. Comput Math Model 26, 144–155 (2015). https://doi.org/10.1007/s10598-015-9262-5
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DOI: https://doi.org/10.1007/s10598-015-9262-5