Hamiltonian Formalism for Solving the Vlasov-Poisson Equations and Its Applications to Periodic Focusing Systems and the Coherent Beam-Beam Interaction

Abstract

A Hamiltonian approach to the solution of the Vlasov-Poisson equations has been developed. Based on a nonlinear canonical transformation, the rapidly oscillating terms in the original Hamiltonian are transformed away, yielding a new Hamiltonian that contains slowly varying terms only. The formalism has been applied to the dynamics of an intense beam propagating through a periodic focusing lattice, and to the coherent beam-beam interaction. A stationary solution to the transformed Vlasov equation has been obtained.

REVTEX, 19 pages, Submitted to the Physical Review Special Topics - Accelerators and Beams

References in corpus (2)

• Simulation of the Beam-Beam Effects in $e^{+}{e}^{-}$ Storage Rings with a Method of Reducing the Region of Mesh
• Collision Integrals and the Generalized Kinetic Equation for Charged Particle Beams