High Lundquist Number Resistive MHD Simulations of Magnetic Reconnection: Searching for Secondary Island Formation

TL;DR

This study conducts high Lundquist number resistive MHD simulations to investigate secondary island formation during magnetic reconnection, finding plasmoids form only under specific conditions and analyzing the reconnection rate scaling.

Contribution

It provides new high-resolution resistive MHD simulation results at high Lundquist numbers, exploring the conditions for secondary island formation and reconnection rate behavior.

Findings

Plasmoids form only with sufficient resolution or external noise.

Reconnection rate follows Sweet-Parker scaling without noise.

Reconnection rate becomes independent of Lundquist number with noise.

Abstract

Recently, secondary island formation due to the tearing instability of the Sweet-Parker current sheet was identified as a possible mechanism that can lead to fast reconnection (less sensitive dependence on Lundquist number $S$) both in numerical simulations using Particle-in-Cell (PIC) method [Daughton et al. 2009], as well as using resistive magnetohydrodynamics (MHD) [Lapenta 2008; Bhattacharjee et al. 2009]. This instability is thought to appear when $S$ is greater than a certain threshold. These recent results prompt us to perform more resistive MHD simulations of a basic reconnection configuration based on the island coalescence instability, using much higher resolutions and larger $S$. Our simulations are based on a fairly standard pseudo spectral code, which has been tested for accuracy, convergence, and compared well with codes using other methods [Ng et al. 2008]. In our simulations, formation of plasmoids were not found, except when insufficient resolution was used, or when a small amount of noise was added externally. The reconnection rate is found to follow the Sweet-Parker scaling when no noise is added, but increases to a level independent of $S$ with noise, when plasmoids form. Latest results with $S$ up to $2 \times 10^5$ will be presented.