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General Theory of the Diocotron Instability of a 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 a teneous electron beam in a strong magnetic field, i.e., plasma frequency << cyclotron frequency, the restriction on the magnitude of the beam density and guiding magnetic field is removed in deriving the general eigenvalue equation. In the limit of long axial wavelengths, a dispersion relation is extracted for a special case of a sharp boundary density profile. The stability properties for various rotating beams 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.