Algebraic instability of hollow electron columns and cylindrical vortices

An axisymmetric, amgnetically confined electron column, in which the {bold E}{times}{bold B} rotation frequency is not a monotone function of radius, is linearly unstable to two-dimensional, electrostatic disturbances with azimuthal mode number {ital l}=1. The perturbation density is asymptotically proportional to {radical}{ital t} and may be described as a shift of the core of the column. A particle-in-cell simulation indicates that harmonics grow rapidly and that there are secondary instabilities. An identical instability arises in hollow circular vortex columns in an inviscid, incompressible neutral fluid.