Magnetic Field Topology in Solar Active Regions

Abstract

In solar active regions, over extended periods of time the plasma-magnetic field configuration evolves quasistatically through a sequence of nearly force-free equilibrium states. This evolution may be understood as the continual distortion of an existing equilibrium by wavelike disturbances propagating upward from the photosphere and subsequent fast relaxation to a new, neighbouring equilibrium. In the present paper the build-up of magnetic energy, which is presumably necessary for flares and other explosive events, during a quasistatic evolution is considered. If during the slow evolution the magnetic energy is increased, then the relaxation processes represent inverse cascades of energy. We study the conditions under which such cascades are possible within the framework of mean-field MHD. In contrast to the convection zone, where the dynamo for the global magnetic field of the Sun works, the solar atmosphere is convectively stable and the first order smoothing approximation justified. It turns out then that current helicity (B.∇ × B) is an important quantity decisive for whether magnetic energy can be built up.