On the Stability of the Linearized Kapchinskij-Vladimirskij Equations

C. Xu, E. Schuster, and C.K. Allen

Particle Accelerators Conference

Albuquerque, NM, USA, June 25-29, 2007

Abstract

We discuss the stability of the linearized Kapchinskij-Vladimirskij (KV) equation around a matched solution, which is a linear periodic Hamiltonian system. By using the averaging method and asymptotic analysis, we find stability boundaries for the linearized beam envelope system without integrating the KV equation numerically.