Equilibrium and tearing stability of thin current layers in magnetic arcades

Abstract

The MHD equilibrium of a thin, force-free current layer in a magnetic arcade is solved analytically. Various approximations are made in order to achieve a lowest order description that is physically relevant as well as mathematically tractable: The arcade is assumed to emanate from feet that are well localized, the current emanates from a localized sheet within the feet and is relatively weak. The resulting expressions for B (sup arrow) are relatively simple and natural flux coordinates are identifiable. The stability of such a current sheet to resistive filamentation is then investigated