A simple model is presented of a finite length electron plasma column supporting a small amplitude diocotron wave with mode number m=1. The electrons are contained inside conducting cylinders in an axial magnetic field, with negative voltages on end cylinders providing axial containment. The m=1 diocotron mode is the E×B drift orbit of an offset electron column around the cylinder axis, due to radial electric fields from image charges on the wall. The model predicts that the mode frequency will be higher than that of an infinitely long column due to θ-drifts from the radial containment fields at the plasma ends. The predicted dependencies on plasma length, radius, and temperature agree well with experiments, where frequency increases up to 2.5× are observed. For very short plasmas, these containment fields predominate over the image charge fields, and the plasma orbit is called the “magnetron” mode. The shift in the magnetron frequency due to image charges is also calculated.

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