Small-Scale Heat Localization with Blowup in the Magnetic-Tube Cross Section During a Solar Flare

Abstract

We investigate the solutions of the nonlinear heat equation with a volume heat source and thermal conductivity dependent on a negative power of temperature. Properties of self-similar solutions are examined. Structures with contracting half-width evolve in the LS-regime with blowup. Self-similar analysis shows that the system attains a self-similar regime. The nonlinear heat equation is applied to model fast heating of the plasma in flares forming in a magnetic tube cross section, when heat is propagated by plasma ions across the magnetic field. Microflares are described by localized structures evolving in LS-regime with blowup. They may form thin hot filaments stretched in the direction of the magnetic field. The modeling results are consistent with experimental observations.