Lower bound on the critical energy for the onset of chaos and the chaotic dynamical aperture of large accelerators
- Department of Natural Sciences, Baruch College of The City University of New York, 17 Lexington Avenue, New York 10010 (United States)
- Center for Theoretical Physics, Sloane Physics Laboratory, Yale University, New Haven, Conneticut 06511 (United States) Nuclear Structure Laboratory, Yale University, New Haven, Connecticut 06511 (United States)
A generic nonintegrable Hamiltonian system is characterized by a critical energy above which chaotic motion sets in. A general method of finding a lower bound to this critical energy that does not require a solution of the equations of motion is discussed. Below the critical energy, the motion is regular everywhere on the energy surface and no instabilities can develop. The method is applied to a practical situation encountered in modern large accelerators, where the transverse motion of the particles in an arrangement of quadrupole, sextupole, and octupole magnetic elements may become chaotic. The chaotic dynamical aperture of the beam is calculated as a function of a dimensionless strength parameter. The estimated critical energy is compared with that obtained from detailed studies of the Poincare sections of the above system at various energies.
- DOE Contract Number:
- FG02-91ER40608
- OSTI ID:
- 7206196
- Journal Information:
- Physical Review A. General Physics; (United States), Vol. 45:4; ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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GENERAL PHYSICS
43 PARTICLE ACCELERATORS
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BEAM DYNAMICS
BEAM OPTICS
APERTURES
CLASSICAL MECHANICS
ENERGY
HAMILTONIAN FUNCTION
MAGNETS
MULTIPOLES
PARTICLE BEAMS
PHASE SPACE
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FUNCTIONS
MATHEMATICAL SPACE
MECHANICS
OPENINGS
SPACE
661100* - Classical & Quantum Mechanics- (1992-)
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Field Calculations
& Ion Optics