From pulsar scintillations to coronal heating: discontinuities in magnetohydrodynamics

Abstract: From pulsar scintillations we infer the presence of sheet-like structures in the ISM; it has been suggested that these are current sheets. Current sheets probably play an important role in heating the solar corona, and there is evidence for their presence in the solar wind. Such magnetic discontinuities have been found in numerical simulations with particular boundary conditions, as well as in simulations using an incompressible equation of state. Here, I investigate their formation under more general circumstances by means of topological considerations as well as numerical simulations of the relaxation of an arbitrary smoothly-varying magnetic field. The simulations are performed with a variety of parameters and boundary conditions: in low, high and of-order-unity plasma-$\beta$ regimes, with periodic and fixed boundaries, with and without a friction force, at various resolutions and with various diffusivities. Current sheets form, over a dynamical timescale, under {\it all} conditions explored. At higher resolution they are thinner, and there is a greater number of weaker current sheets. The magnetic field eventually relaxes into a smooth minimum energy state, the energy of which depends on the magnetic helicity, as well as on the nature of the boundaries.