<title>Pierce-type dispersion relation for an intense relativistic electron beam interacting with a slow-wave structure</title>

Abstract

A Pierce-type dispersion relation is derived from field theory which describes the interaction of an intense relativistic electron beam with a cylindrical slow-wave structure of arbitrary corrugation depth. It is shown that near a resonance the Pierce parameter can be expressed in terms of the vacuum dispersion function and the space-charge parameter is proportional to a fill factor. The dispersion relation is valid in both the low-current (Compton) regime and the high-current (Raman) regime. The dispersion characteristics of the interaction, such as the linear instability growth rate and bandwidth, are analyzed in both regimes.