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
Phys. Rev. Lett. 103, 224802 – Published 25 November 2009

Abstract

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.

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  • Received 26 August 2009

DOI:https://doi.org/10.1103/PhysRevLett.103.224802

©2009 American Physical Society

Authors & Affiliations

Hong Qin1, Moses Chung2, and Ronald C. Davidson1

  • 1Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543, USA
  • 2Accelerator Physics Center, Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA

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Issue

Vol. 103, Iss. 22 — 27 November 2009

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