Overlapping resonances and chaos in halo formation

Journal Article · Sat Jun 01 04:00:00 EDT 1996 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.51069· OSTI ID:390433

Riabko, A; Lee, S Y ^[1]

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1. Department of Physics, Indiana University, Bloomington, Indiana 47405 (United States)

The {open_quote}{open_quote}particle-core{close_quote}{close_quote} model in the framework of Kapchinskij-Vladimirskij (KV) distribution function approach is used in order to study dynamics of a test particle in a space charge dominated beam propagating through time-dependent FOFO focusing channel. A simple analytical method is suggested in order to find a closed orbit solution for the envelope; the question about stability of small amplitude oscillations of weakly mismatched beam around the closed orbit solution is considered. The test particle motion is described by the methods of Hamiltonian dynamics; it is shown that a set of parametric resonances of the particle Hamiltonian can be generated by mismatched envelope oscillations in the time-dependent focusing channel. It is demonstrated that the onset of global chaos in the particle phase space exhibits a sharp transition when the amplitude of envelope oscillations is larger than some critical value. Implications caused by the time dependence of the linear focusing field are discussed. The relation between the critical envelope mismatch for the halo formation and the space charge perviance is obtained numerically and explained qualitatively for few values of the linear focusing field amplitude of the FOFO channel. {copyright} {ital 1996 American Institute of Physics.}

• Research Organization: Indiana University
• DOE Contract Number: FG02-93ER40801
• OSTI ID: 390433
• Report Number(s): CONF-9510361--
• Journal Information: AIP Conference Proceedings, Journal Name: AIP Conference Proceedings Journal Issue: 1 Vol. 377; ISSN 0094-243X; ISSN APCPCS
• Country of Publication: United States
• Language: English

Related Subjects

43 PARTICLE ACCELERATORS
BEAM DYNAMICS
FOCUSING
HAMILTONIAN FUNCTION
PARTICLE BEAMS
SPACE CHARGE
STABILITY
TIME DEPENDENCE