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.

Figures (10)

• Figure 1: Schematic of the simulation geometry. The equilibrium magnetic field $\mathbf{B}_{\mathrm{eq}}$ is along $y$ and varies across $x$, forming a localized current sheet. The equilibrium electron flow $\mathbf{v}_{\mathrm{eq}}$ is along $z$. The $x$-direction is the gradient (inflow) direction, and $y$ corresponds to the magnetic field (outflow) direction.
• Figure 2: The equilibrium magnetic field (top row) and velocity (bottom row) profiles for two values of the $\epsilon = 0.3$ (left panel) and $\epsilon = 0.9$ (right panel).
• Figure 3: Variation of the quantity $B_0 B_0"$ across the current sheet for (top) $\epsilon=0.3$ and (bottom) $\epsilon=0.9$. Regions with $B_0 B_0"<0$ correspond to tearing-favorable locations, while $B_0 B_0">0$ identifies regions where surface-preserving EMHD modes may develop. The stronger curvature for $\epsilon=0.3$ indicates enhanced susceptibility to non-tearing dynamics.
• Figure 4: Temporal evolution of the logarithm of perturbed total energy $E_{\mathrm{pert}}$ for $\epsilon=0.3$ (top panels) and $\epsilon=0.9$ (bottom panels) in two-dimensional (left) and three-dimensional (right) simulations. Dashed lines denote slopes corresponding to linear EMHD growth rates. The 2D results exhibit exponential growth consistent with electron inertial tearing in both cases. In contrast, the 3D evolution shows a thickness-dependent modification: the thin sheet remains tearing-dominated with reduced effective growth, while the wide sheet exhibits faster growth associated with the onset of shear-driven (Kelvin–Helmholtz) dynamics.
• Figure 5: Evolution of the out-of-plane magnetic field $B_z$ in the 2D simulation for $\epsilon=0.9$ (wide sheet), with in-plane magnetic field lines superimposed.