Title :
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
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;
Conference_Titel :
Particle Accelerator Conference, 1995., Proceedings of the 1995
Conference_Location :
Dallas, TX
Print_ISBN :
0-7803-2934-1
DOI :
10.1109/PAC.1995.505742
