Numerical Simulation of Current Sheet Formation in a Quasi-Separatrix Layer using Adaptive Mesh Refinement

TL;DR

This study uses adaptive mesh refinement in numerical MHD simulations to investigate the formation and evolution of thin current sheets in magnetic quasi-separatrix layers, revealing unarrested collapse to very small scales and high current densities.

Contribution

The paper introduces the application of adaptive mesh refinement to simulate the detailed evolution of current sheets in QSLs, extending previous work and capturing smaller scales and higher current densities.

Findings

Current sheets can collapse to scales much smaller than previously reported.

High current densities are generated without signs of saturation.

The current sheet moves upward during thinning, following magnetic structure expansion.

Abstract

The formation of a thin current sheet in a magnetic quasi-separatrix layer (QSL) is investigated by means of numerical simulation using a simplified ideal, low-$\beta$, MHD model. The initial configuration and driving boundary conditions are relevant to phenomena observed in the solar corona and were studied earlier by Aulanier et al., A&A 444, 961 (2005). In extension to that work, we use the technique of adaptive mesh refinement (AMR) to significantly enhance the local spatial resolution of the current sheet during its formation, which enables us to follow the evolution into a later stage. Our simulations are in good agreement with the results of Aulanier et al. up to the calculated time in that work. In a later phase, we observe a basically unarrested collapse of the sheet to length scales that are more than one order of magnitude smaller than those reported earlier. The current density attains correspondingly larger maximum values within the sheet. During this thinning process, which is finally limited by lack of resolution even in the AMR studies, the current sheet moves upward, following a global expansion of the magnetic structure during the quasi-static evolution. The sheet is locally one-dimensional and the plasma flow in its vicinity, when transformed into a co-moving frame, qualitatively resembles a stagnation point flow. In conclusion, our simulations support the idea that extremely high current densities are generated in the vicinities of QSLs as a response to external perturbations, with no sign of saturation.