On the role of topological complexity in spontaneous development of current sheets

Abstract

The computations presented in this work aim to asses the importance of field line interlacing on spontaneous development of current sheets. From Parker's magnetostatic theorem, such development of current sheets is inevitable in a topologically complex magnetofluid, with infinite electrical conductivity, at equilibrium. Relevant initial value problems are constructed by superposition of two untwisted component fields, each component field being represented by a pair of global magnetic flux surface. The intensity of field line interlacing is then specified by the relative amplitude of the two superposed fields. The computations are performed by varying this relative amplitude. Also to have a direct visualization of current sheet formation, we follow the evolution of flux surfaces instead of the vector magnetic field. An important finding of this paper is in the demonstration that initial field lines having intense interlacing tend to develop current sheets which are distributed throughout the computational domain with no preference for topologically favorable sites like magnetic nulls or field reversal layers. The onsets of these current sheets are attributed to favorable contortions of magnetic flux surfaces where two oppositely directed parts of the same field line or different field lines come to close proximity. However, for less intensely interlaced field lines, the simulations indicate development of current sheets at sites only where the magnetic topology is favorable. These current sheets originate as two sets of anti-parallel complimentary field lines press onto each other.