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

Hong Qin, Moses Chung, and Ronald C. Davidson

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

DOI  :  10.2172/969304
RP-ID  :  PPPL-4471
PID  :  OSTI ID: 969304
Others  :  TRN: US1000270

学科分类：原子、分子光学和等离子物理

美国|英语

来源: SciTech Connect

【 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.