Abstract
The m=1 diocotron mode in non-neutral plasmas has long been thought of as a shifted equilibrium, and its frequency has been approximately calculated in this way by Fine and Driscoll [Phys. Plasmas 5, 601 (1998)]. This article shows that this idea can be coupled with a standard axisymmetric equilibrium calculation on a grid to calculate the frequency of this mode to very high precision including both finite-length and thermal effects, provided that the Debye length is small enough. As the Debye length begins to approach the plasma size not only does the shifted equilibrium calculation fail to predict correctly the frequency of the mode, but the idea that the mode is a simple shift of the original equilibrium also becomes invalid.
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