Generalized Courant-Snyder Theory and Kapchinskij-Vladimirskij Distribution For High-intensity Beams In A Coupled Transverse Focusing Lattice

Hong QIn, Ronald Davidson

关键词: BOLTZMANN-VLASOV EQUATION;    CONFIGURATION;    DIFFERENTIAL EQUATIONS;    DISTRIBUTION;    DISTRIBUTION FUNCTIONS;    EXACT SOLUTIONS;    FOCUSING;    GEOMETRY;    ROTATION;   

DOI  :  10.2172/1028187
RP-ID  :  PPPL-4638
PID  :  OSTI ID: 1028187
Others  :  TRN: US1106006

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 】

The Courant-Snyder (CS) theory and the Kapchinskij-Vladimirskij (KV) distribution for high-intensity beams in a uncoupled focusing lattice are generalized to the case of coupled transverse dynamics. The envelope function is generalized to an envelope matrix, and the envelope equation becomes a matrix envelope equation with matrix operations that are non-commutative. In an uncoupled lattice, the 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 to high-intensity beams in a coupled transverse lattice using the generalized CS invariant. This solution projects to a rotating, pulsating elliptical beam in transverse configuration space. The fully self-consistent solution reduces the nonlinear Vlasov-Maxwell equations to a nonlinear matrix ordinary differential equation for the envelope matrix, which determines the geometry of the pulsating and rotating beam ellipse. These results provide us with a new theoretical tool to investigate the dynamics of high-intensity beams in a coupled transverse lattice. A strongly coupled lattice, a so-called N-rolling lattice, is studied as an example. It is found that strong coupling does not deteriorate the beam quality. Instead, the coupling induces beam rotation, and reduces beam pulsation.