Magnetic dissipation: Spatial and temporal structure

Abstract

A magnetically dominated plasma driven by motions on boundaries at which magnetic field lines are anchored is forced to dissipate the work being done upon it, no matter how small the electrical resistivity. Numerical experiments have clarified that dissipation is achieved through the formation of a hierarchy of electrical current sheets. The probability distribution function of the local winding of magnetic field lines is nearly Gaussian, with a width of the order unity. The dissipation is highly irregular in space and time, but the average level of dissipation is well described by a scaling law that is independent of the electrical resistivity. If the boundary driving is suspended for a period of time the magnetic dissipation rapidly drops to insignificant levels, leaving the magnetic field in a nearly force-free state. Renewed boundary driving leads to a quick return to dissipation levels compatible with the rate of boundary work, with dissipation starting much more rapidly than when starting from idealized initial conditions with a uniform magnetic field. Application of these concepts to the solar corona lends credibility to realistic, three-dimensional numerical models that predict emission measures, coronal structures, and heating rates compatible with observations.