Investigation of the diocotron instability of an infinitely wide sheet electron beam by using the macroscopic cold-fluid model theory

This paper investigates the diocotron instability of an infinitely wide relativistic sheet electron beam in conducting walls propagating through a uniform magnetic field by using the macroscopic cold-fluid model theory. Assuming low-frequency perturbations with long axial wavelengths, the eigenvalue equation and the dispersion relation are acquired for a sheet electron beam with sharp boundary profile and uniform density. The results presented in this paper has developed the use of the macroscopic cold-fluid model theory by extending the parameter of the electron cyclotron frequency \omega _\rm c to a wider usage range, which is restricted to be much larger than the plasma frequency \omega _\rm p in the previous research work. Theoretical analyses and numerical calculations indicate that the transport of the sheet electron beam will be completely stabilized by augmenting the normalized beam thickness to a conductor gap larger than a threshold \lambda _\rm b , which is greatly dependent on the parameter \omega _\rm c /\omega _\rm p. The larger \omega_\rm c / \omega _\rm p is, the smaller \lambda _\rm b will be needed. Moreover, the system parameters, including the wave number k_x of the perturbations and the relativistic mass factor \gamma _\rm b , will also influence the growth rate of diocotron instability obviously.