Title :
Resonance strength for the synchrotron Hamiltonian with RF phase modulation
Author :
Zhang, Yunkai ; Lee, S.Y.
Abstract :
RF phase modulation can be used to measure the beam transfer function in the study of wake field, machine impedance, and the characteristics of collective instabilities. The effect of RF phase modulation can be understood by employing the Hamiltonian analysis of resonance structure. For particle motion with a zero synchronous phase angle, the resonance strength can be analytically evaluated. This paper calculates and tabulates resonance strength functions with non-zero RF synchrotron phase angles. The expansion of the normalized off-momentum coordinates in action-angle phase space coordinates is derived. Our results are compared with that obtained from the canonical perturbation method. Implication of our work in the beam transfer function measurements will be discussed
Keywords :
accelerator RF systems; particle beam diagnostics; particle beam stability; perturbation theory; phase modulation; synchrotrons; RF phase modulation; action-angle phase space coordinates; beam transfer function measurement; beam transfer function measurements; canonical perturbation method; collective instabilities; machine impedance; off-momentum coordinates; particle motion; resonance strength; synchrotron Hamiltonian; wake field; zero synchronous phase angle; Impedance measurement; Motion analysis; Particle beam measurements; Perturbation methods; Phase measurement; Phase modulation; Radio frequency; Resonance; Synchrotrons; Transfer functions;
Conference_Titel :
Particle Accelerator Conference, 2001. PAC 2001. Proceedings of the 2001
Conference_Location :
Chicago, IL
Print_ISBN :
0-7803-7191-7
DOI :
10.1109/PAC.2001.987162
