Destabilization of them=1Diocotron Mode in Non-neutral Plasmas

The theory for a Penning-Malmberg trap predicts $m\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ diocotron stability. However, experiments with hollow profiles show robust exponential growth. We propose a new mechanism of destabilization of this mode, involving parallel compression due to end curvature. The results are in good agreement with the experiments. The resulting modified drift-Poisson equations are analogous to the geophysical shallow water equations, and conservation of line integrated density corresponds to that of potential vorticity. This analogy predicts Rossby waves in non-neutral plasmas and an $m\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ instability in fluids.