Rings of vorticity and current density and associated linear stability criteria. Panel a: vorticity and current density for both viscosity models at t = 3 and z = 0. Panel b: linear stability measures as functions of radius at t = 6. The switching model permits rings of greater radial extent and notably stronger vorticity, resulting in a current-vortex sheet that is linearly unstable to the KHI. The thin dashed grey line Λ = 1 is the boundary between the KHI and the tearing instability from the 2D linear analysis of Einaudi & Rubini (1986).