A generalized model for parametric coupling of longitudinal modes in synchrotrons

Author

Colestock, Patrick L. ; Klamp, Linda

Author_Institution

Fermi Nat. Accel. Lab., Batavia, IL, USA

fYear

1993

fDate

17-20 May 1993

Firstpage

3384

Abstract

Observations of nonlinear coupling of longitudinal modes in the Fermilab Tevatron have been recently identified as a manifestation of parametric coupling. In this model, a spatially uniform, finite-amplitude, longitudinal perturbation is applied to the beam, which then decays into two or more daughter waves as a result of this coupling. Selection rules are derived which are based on frequency and phase matching conditions. These selection criteria are obtained using a multiple time-scale expansion of the weakly non-linear Vlasov equation governing longitudinal motion

Keywords

Vlasov equation; beam handling techniques; particle beam diagnostics; perturbation theory; proton accelerators; synchrotrons; Fermilab Tevatron; daughter waves; finite-amplitude perturbation; frequency matching; longitudinal modes; longitudinal motion; longitudinal perturbation; multiple time-scale expansion; nonlinear coupling; parametric coupling; phase matching; selection rules; spatially uniform perturbation; synchrotrons; weakly nonlinear Vlasov equation; Dispersion; Frequency conversion; Nonlinear equations; Optical coupling; Particle beams; Scattering; Signal analysis; Synchrotrons; Transfer functions; Voltage;

fLanguage

English

Publisher

ieee

Conference_Titel

Particle Accelerator Conference, 1993., Proceedings of the 1993

Conference_Location

Washington, DC

Print_ISBN

0-7803-1203-1

Type

conf

DOI

10.1109/PAC.1993.309658

Filename

309658