Tearing and Kelvin-Helmholtz dynamics in fully kinetic particle-in-cell simulations of electron-scale current sheets

Abstract

We investigate the stability and nonlinear evolution of localized electron-scale current sheets using fully kinetic, electromagnetic particle-in-cell (PIC) simulations in two and three dimensions. By varying the current-sheet thickness, we examine how it influences the dominant instability and subsequent nonlinear dynamics. In two dimensions, the evolution is governed by electron inertial tearing, with growth rates in good agreement with linear electron magnetohydrodynamics (EMHD) predictions. In three dimensions, however, a thickness-dependent transition emerges. For wider current sheets, a velocity-shear-driven Kelvin-Helmholtz-type instability dominates the early and intermediate evolution, leading to vortex formation and strong modulation of the current layer, followed by the re-emergence of tearing at later times. In contrast, thinner sheets remain tearing-dominated throughout, with no transition to a shear-driven regime, although their effective growth rate is reduced relative to linear predictions, suggesting the influence of mode coupling and three-dimensional effects. These results establish a thickness-dependent transition from tearing-dominated to shear-driven dynamics and reveal a nonlinear sequence of instability evolution in fully kinetic systems, providing new insight into the competition between curvature-driven and shear-driven instabilities in electron-scale current sheets.