Chaotic dynamical aperture

Conference · Tue Jan 01 04:00:00 EST 1985

OSTI ID:5674111

Lee, S Y; Tepikian, S

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 designs 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 a tremendous amount of computing time. In this review the method of determining chaotic orbit and applying the method to nonlinear problems in accelerator physics is discussed. We then discuss the scaling properties and effect of random sextupoles.

• Research Organization: Brookhaven National Lab., Upton, NY (USA)
• DOE Contract Number: AC02-76CH00016
• OSTI ID: 5674111
• Report Number(s): BNL-36565; CONF-850504-159; ON: DE85013285
• Country of Publication: United States
• Language: English

Related Subjects

43 PARTICLE ACCELERATORS
430200* -- Particle Accelerators-- Beam Dynamics
Field Calculations
& Ion Optics
ACCELERATORS
APERTURES
BEAM DYNAMICS
CYCLIC ACCELERATORS
DIFFERENTIAL EQUATIONS
EQUATIONS
EQUATIONS OF MOTION
HAMILTONIANS
MAGNETIC FIELDS
MATHEMATICAL OPERATORS
NONLINEAR PROBLEMS
OPENINGS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM OPERATORS
RESONANCE
TRAJECTORIES