Asymmetric Hopf bifurcation for proton beams with electron cooling

Author

Kang, X. ; Ball, M. ; Brabson, B. ; Budnick, J. ; Caussyn, D.D. ; Colestock, P. ; East, G. ; Ellison, M. ; Hamilton, B. ; Hedblom, K. ; Lee, S.Y. ; Li, D. ; Liu, J.Y. ; Ng, K.Y. ; Pei, A. ; Riabko, A. ; Syphers, M. ; Wang, L. ; Wang, Y.

Author_Institution

Cyclotron Facility, Indiana Univ., Bloomington, IN, USA

Volume

5

fYear

1995

fDate

1-5 May 1995

Firstpage

2934

Abstract

We observed maintained longitudinal limiting cycle oscillations, which grew rapidly once a critical threshold in the relative velocity between the proton beam and the cooling electrons was exceeded. The threshold for the bifurcation of a fixed point into a limit cycle, also known as a Hopf bifurcation, was found to be asymmetric with respect to the relative velocity. This asymmetry of Hopf bifurcation was found to be related to the electron beam alignment with respect to the stored proton beam

Keywords

beam handling techniques; bifurcation; proton accelerators; storage rings; asymmetric Hopf bifurcation; cooling electrons; electron beam alignment; electron cooling; longitudinal limiting cycle oscillations; proton beam; proton beams; stored proton beam; Bifurcation; Cooling; Damping; Electron beams; Laboratories; Limit-cycles; Particle beams; Physics; Protons; Synchrotrons;

fLanguage

English

Publisher

ieee

Conference_Titel

Particle Accelerator Conference, 1995., Proceedings of the 1995

Conference_Location

Dallas, TX

Print_ISBN

0-7803-2934-1

Type

conf

DOI

10.1109/PAC.1995.505742

Filename

505742