Analyzing charged particle beams using lie transform perturbation theory

This paper briefly reviews the use of Lie transform perturbation theory applied to the dynamics of charged particle beams. Several details not provided here can be found in [1] and [2]. The work analyzes influences due to nonlinear components in external focusing of beams, a regime where the Courant-Snyder invariants are broken [3] for single particle dynamics. The Lie transform analysis is also used to analyze beams with space charge effects, which satisfy the Vlasov -Poisson system of equations. Equilibrium distributions may be obtained even in the nonlinear focusing regime, where simple solution such as the Kapchinskij-Vladimirskij [4] are no longer valid. The work utilizes results that were obtained earlier as part of the research activities of Prof. Allan Kaufman and members of his group.