The diocotron instability of a general relativistic electron beam

The diocotron instability of a general relativistic electron beam is studied using a macroscopic, cold fluid model. In contrast with the previous treatments where the theoretical analyses are carried out for an annular electron beam in a guided magnetic field, such that plasma frequency ≪ cyclotron frequency, the restriction on the magnitude of the beam density and guiding magnetic field is removed in deriving and solving the general eigenvalue equation. In the limit of long axial wavelengths, a dispersion relation is extracted for the special case of a sharp boundary density profile. The stability properties are investigated for a broad range of beam parameters. The results show that the kink mode can be unstable as the plasma frequency approaches the cyclotron frequency.