Computation of invariant tori in 2 1/2 degrees of freedom
- Department of Physics, University of Colorado, Boulder, Colorado 80309 (United States)
- 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-; CODEN: APCPC
- Journal Information:
- AIP Conference Proceedings (American Institute of Physics); (United States), Vol. 230:1; Conference: Joint Institute for Fusion Theory (JIFT) workshop on nonlinear dynamics and acceleration mechanisms, Tsukuba (Japan), 22-25 Oct 1990; ISSN 0094-243X
- Country of Publication:
- United States
- Language:
- English
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