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 ?c to a wider usage range, which is restricted to be much larger than the plasma frequency ?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 ?b, which is greatly dependent on the parameter ?c/?p. The larger ?c/?p is, the smaller ?b will be needed. Moreover, the system parameters, including the wave number kx of the perturbations and the relativistic mass factor ?b, will also influence the growth rate of diocotron instability obviously.