A theory of two‐stream instability in two hollow relativistic electron beams

Abstract

Stability properties of two‐stream instability of two hollow electron beams are investigated. The equilibrium configuration consists of two intense relativistic hollow electron beams propagating through a grounded conducting cylinder. Analysis of the longitudinal two‐stream instability is carried out within the framework of the linearized Vlasov–Maxwell equations for the equilibrium distribution function, in which beam electrons have a Lorentzian distribution in the axial momentum. Dispersion relation of the longitudinal two‐stream instability is derived. Stability criteria from this dispersion relation indicate that the normalized velocity difference Δβ between the beams should be within a certain range of value to be unstable. Growth rate of the instability is a substantial fraction of the real frequency, thereby indicating that the longitudinal two‐stream instability is an effective means of beam current modulation. Transverse instability of hollow electron beams is also investigated. Dispersion relati...