P1.24: Diocotron instability of a relativistic sheet electron beam

The diocotron instability of a relativistic sheet electron beam propagating through a uniform magnetic field is studied using a macroscopic cold fluid model. The general eigenvalue equation is obtained for low-frequency perturbations. In the limit of a long axial wavelength, a dispersion relation is derived for the special case of a sharp boundary density profile and used to study stability properties in the parameter regime where the plasma frequency is much smaller than the cyclotron frequency.