Waves in a cold pure electron plasma of finite length

A theory for low-frequency electrostatic modes of a finite length pure electron plasma column is presented. The plasma is modeled as a cold uniform density cylinder with flat ends. An interesting result is that the diocotron mode can have an axial wavelength that is much larger than the plasma length. Also, for particular values of the plasma density, the axial magnetic field, and the dimensions of the plasma, the diocotron mode is degenerate with a plasma mode and this results in a strong mixing of the modes.