Explosive Instability and Coronal Heating

The observed energy-loss rate from the solar corona implies that the coronal magnetic field has a critical angle at which energy is released. It has been hypothesized that at this critical angle an "explosive instability" would occur, leading to an enhanced conversion of magnetic energy into heat. In earlier investigations, we have shown that a shear-dependent magnetohydrodynamic process called "secondary instability" has many of the distinctive features of the hypothetical "explosive instability." In this paper, we give the first demonstration that this "secondary instability" occurs in a system with line-tied magnetic fields and boundary shearing—basically the situation described by Parker. We also show that, as the disturbance due to secondary instability attains finite amplitude, there is a transition to turbulence which leads to enhanced dissipation of magnetic and kinetic energy. These results are obtained from numerical simulations performed with a new parallelized, viscoresistive, three-dimensional code that solves the cold plasma equations. The code employs a Fourier collocation—finite difference spatial discretization, and uses a third-order Runge–Kutta temporal discretization.