Computation of error effects in nonlinear Hamiltonian systems using Lie algebraic methods

Journal Article · Mon Jun 01 00:00:00 EDT 1992 · Journal of Mathematical Physics (New York); (United States)

DOI:https://doi.org/10.1063/1.529670· OSTI ID:7114310

Healy, L M ^[1]; Dragt, A J; Gjaja, I M ^[2]

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1. Naval Center for Space Technology, Naval Research Laboratory, Code 8242, Washington, DC 20375 (United States)
2. Center for Theoretical Physics, Department of Physics, University of Maryland, College Park, Maryland 20742 (United States)

There exist Lie algebraic methods for obtaining transfer maps around any given trajectory of a Hamiltonian system. This paper describes an iterative procedure for finding transfer maps around the same trajectory when the Hamiltonian is perturbed by small linear terms. Such terms often result when an actual system deviates from an ideal one due to errors. Two examples from accelerator physics are worked out. Comparisons with numerical computations, and in simple cases exact analytical calculations, demonstrate the validity of the procedure.

• DOE Contract Number: AS05-80ER10666
• OSTI ID: 7114310
• Journal Information: Journal of Mathematical Physics (New York); (United States), Vol. 33:6; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Ta
BEAM DYNAMICS
ERRORS
CLASSICAL MECHANICS
ACCELERATORS
ALGORITHMS
BEAM FOCUSING MAGNETS
BEAM OPTICS
CHARGED PARTICLES
CHARGED-PARTICLE TRANSPORT
HAMILTONIAN FUNCTION
LIE GROUPS
SERIES EXPANSION
TRAJECTORIES
ELECTRICAL EQUIPMENT
ELECTROMAGNETS
EQUIPMENT
FUNCTIONS
MAGNETS
MATHEMATICAL LOGIC
MECHANICS
RADIATION TRANSPORT
SYMMETRY GROUPS
661100* - Classical & Quantum Mechanics- (1992-)
661220 - Particle Beam Production & Handling
Targets- (1992-)