Simple macroscopic theory of cyclotron maser instabilities

The stability of an annular layer of relativistic electrons, guided by a uniform magnetic field inside a circular waveguide, is analyzed using a fluid dynamical treatment. The simple theory presented here is aimed at providing some perspective of the cyclotron maser instability which traditionally has required an analysis in phase space. The same dispersion relationship is recovered from the macroscopic fluid model. Thus in addition to the usual interpretation in terms of phase bunching in the electronic motions, the cyclotron maser instability may also be regarded simply as a growing space-charge wave in a relativistic beam which is in sychronism with the surrounding structure, or as due to current bunching, or even as an instability of the shear flow of a rotating relativistic electron fluid. Such a variety of interpretations emerges because the cyclotron maser instability is recently identified as the negative mass instability in rotating relativistic beams. The ac space-charge effects are completely accounted for in the present study. The theory presented here follows closely the treatment of classical electron tubes, and is valid even for nonsynchronous interactions. The threshold beam voltage required for the onset of cyclotron maser instability may also be derived using the fluid dynamical approach. The effects of axial bunching are analyzed. This macroscopic theory may be applied to various geometrical configurations.