Relation between current sheets and vortex sheets in stationary incompressible MHD

TL;DR

This paper explores the relationship between current sheets and vortex sheets in stationary incompressible MHD, highlighting how variations in the Alfven-Mach number influence their alignment and existence in space plasma boundary layers.

Contribution

It introduces a theoretical framework linking current and vortex sheets through the Alfven-Mach number profile, applicable to both small and large Mach numbers, with implications for space plasma phenomena.

Findings

Current and vortex sheets can be aligned or separate depending on the Alfven-Mach number profile.

Special density distributions can produce current sheets without vortex sheets.

Vortex sheets can exist without strong current sheets in low Mach number limits.

Abstract

Magnetohydrodynamic configurations with strong localized current concentrations and vortices play an important role for the dissipation of energy in space and astrophysical plasma. Within this work we investigate the relation between current sheets and vortex sheets in incompressible, stationary equilibria. For this approach it is helpful that the similar mathematical structure of magnetohydrostatics and stationary incompressible hydrodynamics allows us to transform static equilibria into stationary ones. The main control function for such a transformation is the profile of the Alfven-Mach number M_A, which is always constant along magnetic field lines, but can change from one field line to another. In the case of a global constant M_A, vortices and electric current concentrations are parallel. More interesting is the nonlinear case, where M_A varies perpendicular to the field lines. This is a typical situation at boundary layers like the magnetopause, heliopause, the solar wind flowing around helmet streamers and at the boundary of solar coronal holes. The corresponding current and vortex sheets show in some cases also an alignment, but not in every case. For special density distributions in 2D it is possible to have current but no vortex sheets. In 2D vortex sheets of field aligned-flows can also exist without strong current sheets, taking the limit of small Alfven Mach numbers into account. The current sheet can vanish if the Alfven Mach number is (almost) constant and the density gradient is large across some boundary layer. It should be emphasized that the used theory is not only valid for small Alfven Mach numbers M_A<<1, but also for M_A~1. Connection to other theoretical approaches and observations and physical effects in space plasmas are presented. Differences in the various aspects of theoretical investigations of current sheets and vortex sheets are given.