The Tearing Order

Thin current sheets in plasmas are unstable. The tearing instability — where magnetic field lines reconnect across the sheet — is the textbook mechanism for current sheet disruption. The instability tears the sheet into magnetic islands, converting magnetic energy into kinetic energy and heat. In 2D simulations, tearing dominates across a wide range of current sheet thicknesses, consistent with the standard theoretical framework.

Mishra and Gaur (arXiv:2603.27173, March 2026) show that in 3D, the instability order reverses for wider current sheets. Wider electron-scale current sheets are initially dominated not by tearing but by the Kelvin-Helmholtz instability — a velocity-shear-driven instability that creates vortex structures along the sheet. The Kelvin-Helmholtz instability, normally considered secondary to tearing at electron scales, wins the competition when the third dimension is available for vortex rollup.

The mechanism is geometric. In 2D, the Kelvin-Helmholtz instability is confined to the plane of the sheet — it can create waves along the current sheet but cannot form the three-dimensional vortex tubes that represent its most unstable mode. In 3D, the vortex tubes extend along the third dimension, accessing a larger volume of the shear flow and growing faster than the tearing mode. For thin sheets, tearing still dominates because the reconnection rate is fast enough to outcompete the vortex growth. For wider sheets, tearing is slower (the reconnection timescale increases with sheet thickness) while the Kelvin-Helmholtz growth rate is enhanced by the greater shear volume.

The tearing mode re-emerges at later times. The Kelvin-Helmholtz vortices create secondary current sheets at the edges of the vortex structures, and these secondary sheets are thin enough for tearing to dominate. The final state involves tearing, but the pathway to that state goes through an intermediate Kelvin-Helmholtz phase that 2D simulations miss entirely.

The structural observation: the dominant instability of a current sheet depends on the dimensionality of the simulation. A 2D study predicts tearing; a 3D study predicts Kelvin-Helmholtz first, then tearing. The physics is not wrong in 2D — tearing does operate — but it misses the faster instability that the third dimension enables. The simplification of reducing to 2D does not merely approximate the 3D answer; it changes which answer appears first.