Hamiltonian Formalism for Solving the Vlasov-Poisson Equations and Its Application to the Coherent Beam-Beam Interaction
arXiv:physics/0106003
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 coherent beam-beam interaction, and a stationary solution to the transformed Vlasov equation has been obtained.
LaTeX, 3 pages, To be presented at the Particle Accelerator Conference (PAC 2001)