The chaotic dynamical aperture
Nonlinear magnetic forces become more important for particles in the modern large accelerators. These nonlinear elements are introduced either intentionally to control beam dynamics or by uncontrollable random errors. Equations of motion in the nonlinear Hamiltonian are usually non-integrable. Because of the nonlinear part of the Hamiltonian, the tune diagram of accelerators is a jungle. Nonlinear magnet multipoles are important in keeping the accelerator operation point in the safe quarter of the hostile jungle of resonant tunes. Indeed, all the modern accelerator design have taken advantages of nonlinear mechanics. On the other hand, the effect of the uncontrollable random multipoles should be evaluated carefully. A powerful method of studying the effect of these nonlinear multipoles is using a particle tracking calculation, where a group of test particles are tracing through these magnetic multipoles in the accelerator hundreds to millions of turns in order to test the dynamical aperture of the machine. These methods are extremely useful in the design of a large accelerator such as SSC, LEP, HERA and RHIC. These calculations unfortunately take tremendous amount of computing time. In this paper, we try to apply the existing method in the nonlinear dynamics to study the possible alternative solution. When the Hamiltonian motion becomes chaotic, the tune of the machine becomes undefined. The aperture related to the chaotic orbit can be identified as chaotic dynamical aperture. We review the method of determining chaotic orbit and apply the method to nonlinear problems in accelerator physics. We then discuss the scaling properties and effect of random sextupoles.
- Research Organization:
- Brookhaven National Laboratory, Upton, NY
- OSTI ID:
- 6190425
- Report Number(s):
- CONF-850504-; TRN: 86-004249
- Journal Information:
- IEEE Trans. Nucl. Sci.; (United States), Vol. NS-32:5; Conference: Particle accelerator conference, Vancouver, Canada, 13 May 1985
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
PARTICLE BEAMS
BEAM DYNAMICS
ACCELERATORS
APERTURES
BEAM FOCUSING MAGNETS
CALCULATION METHODS
HAMILTONIANS
MULTIPOLES
NONLINEAR PROBLEMS
ORBITS
TUNING
BEAMS
ELECTRICAL EQUIPMENT
ELECTROMAGNETS
EQUIPMENT
MAGNETS
MATHEMATICAL OPERATORS
OPENINGS
QUANTUM OPERATORS
430200* - Particle Accelerators- Beam Dynamics
Field Calculations
& Ion Optics