Open AccessGeneralized Kapchinskij-Vladimirskij Distribution and Envelope Equation for High-intensity Beams in a Coupled Transverse Focusing Lattice
Author(s) -
and Ronald C. Davidson Hong Qin Moses Chung
Publication year - 2009
Language(s) - English
Resource type - Reports
DOI - 10.2172/969304
Subject(s) - transverse plane , physics , lattice (music) , nonlinear system , beam (structure) , ellipse , classical mechanics , quantum mechanics , optics , structural engineering , astronomy , acoustics , engineering
In an uncoupled lattice, the Kapchinskij-Vladimirskij (KV) distribution function first analyzed in 1959 is the only known exact solution of the nonlinear Vlasov-Maxwell equations for high- intensity beams including self-fields in a self-consistent manner. The KV solution is generalized here to high-intensity beams in a coupled transverse lattice using the recently developed generalized Courant-Snyder invariant for coupled transverse dynamics. This solution projects to a rotating, pulsating elliptical beam in transverse configuration space, determined by the generalized matrix envelope equation