Generalized Kapchinskij-Vladimirskij Distribution and Envelope Equation for High-intensity Beams in a Coupled Transverse Focusing Lattice

[摘要] 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.

[发布日期] 2009-11-20

[学科分类] 原子、分子光学和等离子物理

[关键词] BOLTZMANN-VLASOV EQUATION;CONFIGURATION;DISTRIBUTION;DISTRIBUTION FUNCTIONS;EXACT SOLUTIONS;FOCUSING