Electrostatic Kelvin-Helmholtz instability produced by a localized electric field perpendicular to an external magnetic field

The evolution of a plasma with a localized electric field perpendicular to an external magnetic field is shown to be dominated by the Kelvin-Helmholtz instability. For small ion gyroradius, the instability is similar to the fluid mode. When the ion gyroradius is an appreciable fraction of the spatial extent of the electric field, the plasma is not in equilibrium, and the initial drift profile relaxes. Subsequent evolution still leads to vortex flows.