Asymptotic Theory of Beam Break-Up in Linear Accelerators

Abstract

The phenomenon of radial beam break-up observed in terms of long, multi-section electron linear accelerators has been analyzed using a multi-cavity model. In this model the source of regeneration due to backward wave amplification is ignored. The dominant phenomenon involves build-up of radial modes in each cavity as coupled by the electron beam. The resulting differential equations are integrated by the method of steepest descent and by a numerical iteration method. Scaling laws in terms of the pulse length, beam intensity, energy gradient, and length of the structure are derived.