Generalized Courant-Snyder Theory and Kapchinskij-Vladimirskij Distribution For High-intensity Beams In A Coupled Transverse Focusing Lattice
Authors: Hong QIn
Abstract:
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.
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Submitted to: Physics of Plasmas (December 2010)
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Download PPPL-4638 (pdf KB pp)
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