Stability of orbits in nonlinear mechanics for finite but very long times
In various applications of nonlinear mechanics, especially in accelerator design, it would be useful to set bounds on the motion for finite but very long times. Such bounds can be sought with the help of a canonical transformation to new action-angle variables (J, {Psi}), such that action J is nearly constant while the angle {Psi} advances almost linearly with the time. By examining the change in J during a time T{sub 0} from many initial conditions in the open domain {Omega} of phase space, one can estimate the change in J during a much larger time T, on any orbit starting in a smaller open domain {Omega}{sub 0} {contained in} {Omega}. A numerical realization of this idea is described. The canonical transformations, equivalent to close approximations to invariant tori, are constructed by an effective new method in which surfaces are fitted to orbit data. In a first application to a model sextupole lattice in a region of strong nonlinearity, we predict stability of betatron motion in two degrees of freedom for a time comparable to the storage time in a proton storage ring (10{sup 8} turns). 10 refs., 6 figs., 1 tab.
- Research Organization:
- Stanford Linear Accelerator Center, Menlo Park, CA (USA)
- Sponsoring Organization:
- DOE/ER
- DOE Contract Number:
- AC03-76SF00515
- OSTI ID:
- 6649870
- Report Number(s):
- SLAC-PUB-5304; CONF-9004230-2; ON: DE90016685; TRN: 90-028703
- Resource Relation:
- Conference: Workshop on non-linear problems in future particle accelerators, Capri (Italy), 19-25 Apr 1990
- Country of Publication:
- United States
- Language:
- English
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