Current Sheets Formation in Tangled Coronal Magnetic Fields

TL;DR

This study explores how current sheets form in tangled magnetic fields of the solar corona, identifying a magnetic intensity threshold that determines whether current sheets develop rapidly or are suppressed.

Contribution

It introduces a threshold criterion for current sheet formation in coronal magnetic fields using reduced magnetohydrodynamic models, highlighting the role of magnetic intensity and scale ratios.

Findings

Current sheets form rapidly above a specific magnetic threshold.

Below the threshold, magnetic tension prevents current sheet formation.

Current sheet thickness decreases exponentially over time in ideal conditions.

Abstract

We investigate the dynamical evolution of magnetic fields in closed regions of solar and stellar coronae. To understand under which conditions current sheets form, we examine dissipative and ideal reduced magnetohydrodynamic models in cartesian geometry, where two magnetic field components are present: the strong guide field $B_0$, extended along the axial direction, and the dynamical orthogonal field $\mathbf{b}$. Magnetic field lines thread the system along the axial direction, that spans the length $L$, and are line-tied at the top and bottom plates. The magnetic field $b$ initially has only large scales, with its gradient (current) length-scale of order $\ell_b$. We identify the magnetic intensity threshold $b/B_0 \sim \ell_b/L$. For values of $b$ below this threshold, field-line tension inhibits the formation of current sheets, while above the threshold they form quickly on fast ideal timescales. In the ideal case, above the magnetic threshold, we show that current sheets thickness decreases in time until it becomes smaller than the grid resolution, with the analyticity strip width $\delta$ decreasing at least exponentially, after which the simulations become under-resolved.