Resistively-limited current sheet implosions in planar anti-parallel (1D) and null-point containing (2D) magnetic field geometries

TL;DR

This study investigates the long-term evolution of resistively-limited current sheet implosions in 1D and 2D magnetic fields, revealing how halting mechanisms and post-implosion dynamics influence energy release and shock formation.

Contribution

It provides a detailed analysis of the nonlinear evolution and halting mechanisms of current sheet implosions in resistive MHD, including the scaling laws and shock structures in 2D.

Findings

Halting occurs rapidly after reaching the diffusion scale due to Ohmic heating.

Post-implosion expansion leads to shock waves and current sheet growth.

In 2D, expansion stalls due to outflow in reconnection jets.

Abstract

Implosive formation of current sheets is a fundamental plasma process. Previous studies focused on the early time evolution, while here our primary aim is to explore the longer-term evolution, which may be critical for determining the efficiency of energy release. To address this problem we investigate two closely-related problems, namely: (i) 1D, pinched anti-parallel magnetic fields and (ii) 2D, null point containing fields which are locally imbalanced ('null-collapse' or 'X-point collapse'). Within the framework of resistive MHD, we simulate the full nonlinear evolution through three distinct phases: the initial implosion, its eventual halting mechanism, and subsequent evolution post-halting. In a parameter study, we find the scaling with resistivity of current sheet properties at the halting time is in good agreement - in both geometries - with that inferred from a known 1D similarity solution. We find that the halting of the implosions occurs rapidly after reaching the diffusion scale by sudden Ohmic heating of the dense plasma within the current sheet, which provides a pressure gradient sufficient to oppose further collapse and decelerate the converging flow. This back-pressure grows to exceed that required for force balance and so the post-implosion evolution is characterised by the consequences of the current sheet `bouncing' outwards. These are: (i) the launching of propagating fast MHD waves (shocks) outwards and (ii) the width-wise expansion of the current sheet itself. The expansion is only observed to stall in the 2D case, where the pressurisation is relieved by outflow in the reconnection jets. In the 2D case, we quantify the maximum amount of current sheet expansion as it scales with resistivity, and analyse the structure of the reconnection region which forms post-expansion, replete with Petschek-type slow shocks and fast termination shocks.