Hamiltonian formalism for solving the Vlasov-Poisson equations and its application to the coherent beam-beam interaction

Author

Tzenov, Stephan I. ; Davidson, Ronald C.

Author_Institution

Plasma Phys. Lab., Princeton Univ., NJ, USA

Volume

3

fYear

2001

fDate

2001

Firstpage

2075

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

Keywords

Poisson equation; Vlasov equation; integral equations; particle beam dynamics; transforms; Hamiltonian formalism; Vlasov-Poisson equations; charged particle beam evolution; coherent beam-beam interaction; collective self-field excitations; equilibrium beam densities; nonlinear canonical transformation; nonlinear integral equations; radiation effects; storage rings; Ear; Laboratories; Maxwell equations; Particle accelerators; Particle beams; Perturbation methods; Physics; Plasma applications; Poisson equations; Storage rings;

fLanguage

English

Publisher

ieee

Conference_Titel

Particle Accelerator Conference, 2001. PAC 2001. Proceedings of the 2001

Conference_Location

Chicago, IL

Print_ISBN

0-7803-7191-7

Type

conf

DOI

10.1109/PAC.2001.987281

Filename

987281