Generalized Kapchinskij-Vladimirskij distribution and envelope equation for high-intensity beams in a coupled transverse focusing lattice.
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.
Qin
Hong
H
Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543, USA.
Chung
Moses
M
Davidson
Ronald C
RC