Refinement of the Hamilton-Jacobi solution using a second canonical transformation
- Colorado Univ., Boulder, CO (USA). Dept. of Physics
- Stanford Linear Accelerator Center, Menlo Park, CA (USA)
Two canonical transformations are implemented to find approximate invariant surface for a nonlinear, time-periodic Hamiltonian. The first transformation is found from the non-perturbative, iterative solution of the Hamilton-Jacobi equation. The residual angle dependence remaining after performing the transformation is mostly eliminated by a second, perturbative transformation. This refinement can improve the accuracy, or the speed, of the invariant surface calculation. The motion of a single particle in one transverse dimension is studied in a storage ring example where strong sextupole magnets are the source of nonlinearity. The refined transformation to action-angle variables, and the corresponding invariant surface, can attain accuracy similar to that of a good non-perturbative transformation in half the computation time. 3 refs., 2 figs., 1 tab.
- Research Organization:
- Stanford Linear Accelerator Center, Menlo Park, CA (USA)
- Sponsoring Organization:
- USDOE; USDOE, Washington, DC (USA)
- DOE Contract Number:
- AC03-76SF00515; FG02-86ER40302
- OSTI ID:
- 5730961
- Report Number(s):
- SLAC-PUB-5565; CONF-910505-104; ON: DE91012965
- Resource Relation:
- Conference: 1991 Institute of Electrical and Electronics Engineers (IEEE) particle accelerator conference (PAC), San Francisco, CA (USA), 6-9 May 1991
- Country of Publication:
- United States
- Language:
- English
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99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
BEAM DYNAMICS
HAMILTON-JACOBI EQUATIONS
CANONICAL TRANSFORMATIONS
HAMILTONIANS
ITERATIVE METHODS
MAGNETIC FIELDS
NONLINEAR PROBLEMS
PERTURBATION THEORY
STORAGE RINGS
DIFFERENTIAL EQUATIONS
EQUATIONS
MATHEMATICAL OPERATORS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM OPERATORS
TRANSFORMATIONS
430200* - Particle Accelerators- Beam Dynamics
Field Calculations
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990200 - Mathematics & Computers