Colloquium
Parker spontaneous current-sheets in topologically untwisted magnetic fields

Abstract

A continuous magnetic field evolving under the hydromagnetic frozen-in condition preserves its field topology. Depending on that field topology, the evolving field may inevitably develop electric current-sheets, i.e., magnetic tangential discontinuities, in the course of nonlinear fluid-field interaction. This inevitability obtains for all field topologies one could prescribe for the field, except those of a special subset of measure zero. This theory of Eugene Parker is based on demonstrating that a field endowed with a fixed topology cannot generally find an equilibrium state in which the field is everywhere spatially continuous. I will discuss a recent development of this magnetostatic problem from an intuitive point of view, giving a basic understanding of why current sheets not only form easily but do so throughout a magnetic field. Parker’s theory explains the heating of the solar corona, to million-degree temperatures, in terms of spontaneous current sheets that must form because of high electrical conductivity, and, yet, must dissipate in spite of that high (but finite) conductivity. This process may be the fundamental reason for the high-temperature plasmas found almost everywhere in the astrophysical universe