Comparative study of the axial and azimuthal bunching mechanisms in electromagnetic cyclotron instabilities

A comparative study is presented of the axial and azimuthal bunching mechanisms of the electromagnetic electron cyclotron instability. Axial bunching can be described with a nonrelativistic treatment, but azimuthal bunching is relativistic in origin. As is well known, the axial bunching mechanism drives the Weibel-type instability while the azimuthal bunching mechanism drives the electron cyclotron maser instability. For an electron ensemble of cold helical trajectories, a unified physical interpretation of both instabilities is presented. It is shown that the two bunching mechanisms are actually simultaneously present in either instability and compete with one another. As a result, the dominant mechanism determines the type of instability. A criterion for distinguishing the two types of instabilities is derived. It is shown that the energy of the electrons plays an insignificant role in the criterion and, hence, should not be a factor in the justification of a nonrelativistic treatment. Regimes of validity of nonrelativistic models are defined, however. Applications to gyrotron experiments are discussed.