Title :
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
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;
Conference_Titel :
Particle Accelerator Conference, 1993., Proceedings of the 1993
Conference_Location :
Washington, DC
Print_ISBN :
0-7803-1203-1
DOI :
10.1109/PAC.1993.309658
