Diocotron instability of a relativistic sheet electron beam propagating through a rectangular conducting wall

Abstract

Properties of the diocotron instability in a relativistic sheet electron beam propagating through a rectangular conducting wall are investigated within the framework of a macroscopic cold fluid model. The electron beam is assumed to be partially neutralized by the positive immobile ions with the fractional charge neutralization f. The eigenvalue equation is obtained for low-frequency perturbations in standing waves. The dispersion relation of the diocotron instability is derived and used to investigate stability properties for a broad range of system parameters including the ratio a/d of the beam thickness (2a) to the conductor gap (2d) and the charge neutralization f. The dispersion relation indicates that the system is stabilized by increasing the neutralization f to 1/γ2b, where γb is the characteristic value of the beam relativistic factor. It is also shown that the diocotron perturbations are completely stabilized by increasing the beam thickness to more than one-half the conductor gap (i.e., a/d≳0.5) for f=0. The growth rate of instability is a substantial fraction of the diocotron frequency if the system is unstable.