On the possibility of electric-current sheets in dense formation

Abstract

This is a mathematical study of the formation of tangential discontinuities, or current sheets, in a magnetic field evolving in an electrically perfectly conducting fluid in response to deformation of its domain, an effect first treated by Hahm and Kulsrud [Phys. Fluids 28, 2412 (1985)]. Explicit examples are presented of three-dimensional, untwisted fields, anchored to the boundary, that cannot assume a force-free state in the absence of current sheets. The underlying physics of this process is as described by the Parker theory of spontaneous current sheets, namely, that for most continuous magnetic fields in complex three-dimensional geometry, there is an incompatibility between the preservation of field topology and point-by-point force balance to achieve equilibrium. This incompatibility is removed through discontinuous plasma displacements that produce magnetic tangential discontinuities. In contrast to the twisted magnetic fields central to the Parker theory, fixing the connectivity between the anchored magnetic footpoints alone is sufficient to lead to current-sheet formation in untwisted fields. This mode of sheet formation may produce spatially dense multitudes of sheets to heat a plasma throughout its macroscopic volume such as implied by several phenomena in the solar corona.