On the spontaneous formation of electric current sheets above a flexible solar photosphere

Abstract

This paper treats the general tendency for a magnetic field in an electrically perfectly conducting plasma to seek an equilibrium state with embedded electric current sheets or magnetic tangential discontinuities. This property is simplest to demonstrate theoretically with two-dimensional force-free magnetic fields in the infinite half-space above a plane boundary where magnetic footpoints are rigidly anchored. The principal results of recent treatments of this simple model are summarized and extended to clarify their basic physics in order to answer the criticism of this model by Karpen et al. (1990). These authors have concluded that the formation of current sheets in this model depended on the use of rigid boundary conditions to the extent that current sheets would not form if the boundary is not rigid but is replaced by a gravitationally stratified photosphere of finite thickness. It is shown that the conclusion of these authors is not valid, based on a physical analysis and an explicit magnetostatic construction of a possible equilibrium state in which a current sheet has formed in the presence of a flexible photosphere.