A unified theory of the diocotron, cyclotron maser, and negative-mass instabilities

A small-signal theory is developed which simultaneously includes the diocotron, negative mass, and cyclotron maser effects. The simple analysis is performed using a Pierce type approach for an axis encircling electron beam inside a circular waveguide. Relativistic, nonrelativistic, synchronous, and nonsynchronous limits are considered to recover the individual instabilities. It is found that the diocotron and the negative mass/cyclotron maser effect strengthen each other. At voltages higher than a few kiloelectron volt the relativistic negative mass/ cyclotron maser effects become dominant. However, the threshold beam voltage, which appears in gyrotron literature, for the onset of the cyclotron maser instability is found absent when the diocotron effect is taken into account. The feasibility of building a low-voltage tube is explored.