Transport and modulation of relativistic electron beams by periodic ion channels

Abstract

A theoretical investigation of an intense relativistic electron beam propagating in a periodic ion channel is presented. Analytic expressions for the electric field are found for the case of a cosine modulation of the channel ion density. Two different types of channels are considered: (i) periodic beam‐induced ionization channels, and (ii) periodic channels created by an external source. Analytical conditions are derived for the matched radius of the beam and for approximate envelope motion using the ‘‘smooth’’ approximation. Numerical solutions to the envelope equation show that by changing the period or the space‐charge neutralization fraction of the channel the beam can be made to focus and diverge or to undergo stable, modulated transport. It is shown that the results are qualitatively similar to previous work concerning periodic magnetic and electrostatic focusing.