Refinement of the Hamilton-Jacobi solution using a second canonical transformation

Conference · Wed May 01 00:00:00 EDT 1991

OSTI ID:5730961

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

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1. Colorado Univ., Boulder, CO (USA). Dept. of Physics
2. 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

Related Subjects

43 PARTICLE ACCELERATORS
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
& Ion Optics
990200 - Mathematics & Computers