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

Conference ·
OSTI ID:6042343
 [1]; ;  [2]
  1. Colorado Univ., Boulder, CO (USA). Dept. of Physics
  2. Stanford Linear Accelerator Center, Menlo Park, CA (USA)
+ Show Author Affiliations
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. 10 refs., 3 figs., 3 tabs.
Research Organization:
Stanford Linear Accelerator Center, Menlo Park, CA (USA)
Sponsoring Organization:
DOE/ER
DOE Contract Number:
AC03-76SF00515
OSTI ID:
6042343
Report Number(s):
SLAC-PUB-5414; CONF-9010270--3; ON: DE91007424
Country of Publication:
United States
Language:
English

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Related Subjects

43 PARTICLE ACCELERATORS
430200* -- Particle Accelerators-- Beam Dynamics
Field Calculations
& Ion Optics
657002 -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
BEAM DYNAMICS
BEAM OPTICS
CALCULATION METHODS
DEGREES OF FREEDOM
DIFFERENTIAL EQUATIONS
EQUATIONS
HAMILTON-JACOBI EQUATIONS
HAMILTONIANS
ITERATIVE METHODS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
NEWTON METHOD
NONLINEAR PROBLEMS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
PHASE SPACE
QUANTUM OPERATORS
SPACE
STORAGE RINGS
TORI