Mathematical Modeling of the Dynamics of Plasma Heating in a Magnetic Tube During Solar Flares

Abstract

A mathematical model describing the initial phase of flare heating in the solar corona is proposed. The model is based on the nonlinear heat equation with a sign-changing volume source, which is obtained by reduction of the stationary- plasma energy equation. Flares are assumed to arise as a result of sausage-type instabilities in magnetic tubes and formation of collapsing magnetic traps. A source function is chosen, and model parameters are fitted. Calculations are performed, and the formation of thermal structures under supercritical perturbations against a homogeneous temperature background is studied. It is shown that, during the flare, structures are created in which the energy release half-width shrinks over time. The decrease of the emission measure observed in the early phase of the flare is associated with the decrease of the flare filling factor due to the decrease of structure half-widths.