Three-dimensional tearing instability of flux-tube-like magnetic fields

Abstract: Magnetic reconnection, a fundamental plasma process, is pivotal in understanding energy conversion and particle acceleration in astrophysical systems. While extensively studied in two-dimensional (2D) configurations, the dynamics of reconnection in three-dimensional (3D) systems remain under-explored. In this work, we extend the classical tearing mode instability to 3D by introducing a modulation along the otherwise uniform direction in a 2D equilibrium, given by $g(y)$, mimicking a flux tube-like configuration. We perform linear stability analysis (both analytically and numerically) and direct numerical simulations to investigate the effects of three-dimensionality. Remarkably, we find that a tearing-like instability arises in 3D as well, even without the presence of guide fields. Further, our findings reveal that the 3D tearing instability exhibits reduced growth rates compared to 2D by a factor of $\int g(y)^{1/2} dy~/\int dy$, with the dispersion relation maintaining similar scaling characteristics. We show that the modulation introduces spatially varying resistive layer properties, which influence the reconnection dynamics.