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.