Stability theorem for off-axis states of a non-neutral plasma column

A sufficient condition is given for the stability of a long non-neutral plasma column that obeys two-dimensional E×B dynamics. The column is confined by a uniform magnetic field and bounded by a conducting cylinder aligned with the field. The variational approach used here generalizes the well-known stability of a centered, axisymmetric column, whose density is a monotonically decreasing function of radius. Displacement of such a column away from the axis by excitation of an l=1 diocotron mode yields a dynamical equilibrium stationary in a frame rotating with the mode. This new equilibrium is shown to be stable if the column is not too large. The analysis may explain, in part, the remarkable longevity observed for l=1 diocotron modes in experiments.