Generalized Courant-Snyder theory and Kapchinskij-Vladimirskij distribution for high-intensity beams in a coupled transverse focusing lattice
- Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States)
- Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026 (China)
The Courant-Snyder (CS) theory and the Kapchinskij-Vladimirskij (KV) distribution for high-intensity beams in an 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 noncommutative. 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.
- OSTI ID:
- 21537906
- Journal Information:
- Physics of Plasmas, Vol. 18, Issue 5; Other Information: DOI: 10.1063/1.3574919; (c) 2011 American Institute of Physics; ISSN 1070-664X
- Country of Publication:
- United States
- Language:
- English
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Generalized Kapchinskij-Vladimirskij Distribution and Envelope Equation for High-Intensity Beams in a Coupled Transverse Focusing Lattice
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Related Subjects
70 PLASMA PHYSICS AND FUSION TECHNOLOGY
BOLTZMANN-VLASOV EQUATION
DISTRIBUTION FUNCTIONS
EXACT SOLUTIONS
FOCUSING
MATRICES
MAXWELL EQUATIONS
NONLINEAR PROBLEMS
PARTICLE BEAMS
BEAMS
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
MATHEMATICAL SOLUTIONS
PARTIAL DIFFERENTIAL EQUATIONS