Limitation of accelerating process in the partly neutralized relativistic electron hollow beam

Abstract

A fluid-Maxwell thoery of the diocotron instability is developed for a relativistic electron hollow beam which is assumed in rigid-rotor and cold laminar flow equilibria. Stability analysis is performed for a sharp boundary electron density profile including the influence of positive ions which can accumulate in a long pulse device, and which form a partially neutralizing background. In the case of the strong magnetic field and tenuous electron beam (plasma frequency ωpb ≪gyrofrequency ωc) a partially neutralizing ion background staying uniformly within the beam annulus (R1<r<R2) has a stabilizing effect on the diocotron instability, R1 and R2 are the inner and outer radius of the annular hollow beam, respectively. However, the ions accumulating in the center of the beam (0<r<R1) have a destabilizing effect on the diocotron instability. Most importantly the kink mode becomes unstable with a growth rate several tenths of the diocotron frequency ωD ≡ ω2pb/2γ2ωc, where γ is the relativistic scaling factor.