Computation of invariant tori in 2 1/2 degrees of freedom

Conference · Wed Jun 05 04:00:00 EDT 1991 · AIP Conference Proceedings (American Institute of Physics); (United States)

OSTI ID:5137503

Gabella, W E ^[1]; Ruth, R D; Warnock, R L ^[2]

---

1. Department of Physics, University of Colorado, Boulder, Colorado 80309 (United States)
2. Stanford Linear Accelerator Center, Stanford, California 94309 (United States)

Approximate invariant tori in phase space are found using a non-perturbative, numerical solution of the Hamilton-Jacobi equation for a nonlinear, time-periodic Hamiltonian. The Hamiltonian is written in the action-angle variables of its solvable part. The solution of the Hamilton-Jacobi equation is represented as a Fourier series in the angle variables but not in the time' variable. The Fourier coefficients of the solution are regarded as the fixed point of a nonlinear map. The fixed point is found using a simple iteration or a Newton-Broyden iteration. The Newton-Broyden method is slower than the simple iteration, but it yields solutions at amplitudes that are significant compared to the dynamic aperture.' Invariant tori are found for the dynamics of a charged particle in a storage ring with sextupole magnets.

• DOE Contract Number: FG02-86ER40302; AC03-76SF00515
• OSTI ID: 5137503
• Report Number(s): CONF-9010270--
• Conference Information: Journal Name: AIP Conference Proceedings (American Institute of Physics); (United States) Journal Volume: 230:1
• Country of Publication: United States
• Language: English

Related Subjects

43 PARTICLE ACCELERATORS
430200 -- Particle Accelerators-- Beam Dynamics
Field Calculations
& Ion Optics
661100* -- Classical & Quantum Mechanics-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BEAM DYNAMICS
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
EQUATIONS
HAMILTON-JACOBI EQUATIONS
ITERATIVE METHODS
MATHEMATICS
NEWTON METHOD
NONLINEAR PROBLEMS
NUMERICAL ANALYSIS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
STORAGE RINGS
TRAJECTORIES