Invited paper. Cyclotron maser instability as a resonant limit of space charge wave†

In place of a treatment in phase space, we present in this paper a macroscopic, fluid-like, description of cyclotron maser instabilities in a simple geometrical configuration. The approach follows that commonly used in conventional microwave devices. The usual dispersion relationship for cyclotron maser instability is recovered by considering the synchronous interaction between the space charges on the relativistic beam with the surrounding electromagnetic structure. The charge bunching processes are described. This analyis is also valid for non-synchronous interactions.