Marginal Stability of Sweet-Parker Type Current Sheets at Low Lundquist Numbers

TL;DR

This paper investigates the stability of Sweet-Parker current sheets at low Lundquist numbers using 2D MHD simulations and linear stability analysis, revealing the stabilizing effects of outflows and initial conditions on tearing mode instabilities.

Contribution

It provides a detailed analysis of how background flows and initial perturbations influence the stability threshold of current sheets at low Lundquist numbers, extending understanding beyond previous models.

Findings

Outflows stabilize the current sheet by stretching magnetic islands.

The linear theory matches simulations for S > 1000.

Initial perturbation location affects the stability threshold.

Abstract

Magnetohydrodynamic simulations have shown that a non-unique critical Lundquist number $S_c$ exists, hovering around $S_c \sim 10^4$, above which threshold Sweet-Parker type stationary reconnecting configurations become unstable to a fast tearing mode dominated by plasmoid generation. It is known that the flow along the sheet plays a stabilizing role, though a satisfactory explanation of the non-universality and variable critical Lundquist numbers observed is still lacking. Here we discuss this question using 2D linear MHD simulations and linear stability analyses of Sweet-Parker type current sheets in the presence of background stationary inflows and outflows at low Lundquist numbers ($S\le 10^4$). Simulations show that the inhomogeneous outflow stabilizes the current sheet by stretching the growing magnetic islands and at the same time evacuating the magnetic islands out of the current sheet. This limits the time during which fluctuations which begin at any given wave-length can remain unstable, rendering the instability non-exponential. We find that the linear theory based on the expanding-wavelength assumption works well for $S$ larger than $\sim 1000$. However we also find that the inflow and location of the initial perturbation also affect the stability threshold.