Analytical Solution for Space-Charge Waves in a Two-Stream Cylindrical Electron Beam

TL;DR

This paper develops an analytical approach to determine the eigenmodes and electric fields of space-charge waves in a two-stream cylindrical electron beam, considering interactions with the beam tunnel wall.

Contribution

It extends Ramo's analytical model to two streams, enabling analysis of two-stream instability and plasma frequency effects in cylindrical geometries.

Findings

Analytical expressions for wavenumbers and electric fields of eigenmodes.

Modeling of two-stream instability in cylindrical electron beams.

Insights into plasma frequency reduction effects.

Abstract

We present an analytical method to compute the wavenumbers and electric fields of the space-charge-wave eigenmodes supported by a two-stream electron beam, consisting of a solid inner cylindrical stream and a coaxial outer annular stream, both contained within a cylindrical metallic tunnel.We extend the analytical model developed by Ramo to the case of two streams. The method accounts for the interaction between the two streams with the presence of the beam-tunnel wall; it can be used to model the complex wavenumbers associated with the two-stream instability and the plasma frequency reduction effects in vacuum electronic amplifiers and other vacuum electronic devices.