Bibliographic Citation
| Document | For copies of Journal Articles, please contact the Publisher or your local public or university library and refer to the information in the Resource Relation field. For copies of other documents, please see the Availability, Publisher, Research Organization, Resource Relation and/or Author (affiliation information) fields and/or Document Availability. |
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| Title | A Hamiltonian-free description of single particle dynamics for hopelessly complex periodic systems |
| Creator/Author | Forest, E. (Exploratory Studies Group, Accelerator and Fusion Research Division, Lawrence Berkeley Laboratory, 1 Cyclotron Road, MS 47-112, Berkeley, California 94720 (USA)) |
| Publication Date | 1990 May 01 |
| OSTI Identifier | OSTI ID: 6944092 |
| DOE Contract Number | AC03-76SF00098 |
| Other Number(s) | Journal ID: ISSN 0022-2488; CODEN: JMAPA |
| Resource Type | Journal Article |
| Resource Relation | Journal Name: Journal of Mathematical Physics (New York); (USA); Journal Volume: 31:5 |
| Subject | 43 PARTICLE ACCELERATORS; CHARGED PARTICLES; DYNAMICS; MAGNETIC FIELDS; DESIGN; STELLARATORS; FLOQUET FUNCTION; HAMILTONIANS; IRREDUCIBLE REPRESENTATIONS; LIE GROUPS; MAPPING; NONLINEAR PROBLEMS; TIME DEPENDENCE; TRANSFORMATIONS; USES; CLOSED PLASMA DEVICES; FUNCTIONS; MATHEMATICAL OPERATORS; MECHANICS; QUANTUM OPERATORS; SYMMETRY GROUPS; THERMONUCLEAR DEVICES |
| Description/Abstract | A picture of periodic systems that does not rely on the Hamiltonian of the system, but on maps between a finite number of time locations, is developed. Moser or Deprit-like normalizations are done directly on the maps, thereby avoiding the complex time-dependent theory. Linear and nonlinear Floquet variables are redefined entirely in terms of maps. This approach relies heavily on the Lie representation of maps introduced by Dragt and Finn (J. Math. Phys. {bold 20}, 2649 (1979); J. Geophys. Res. {bold 81}, 13 (1976)). One might say that although the Hamiltonian is not used in the normalization transformation, Lie operators are used, which are themselves, in some sense, pseudo-Hamiltonians for the maps they represent. The techniques find application in accelerator dynamics or in any field where the Hamiltonian is periodic, but hopelessly complex, such as magnetic field design in stellarators. |
| Country of Publication | United States |
| Language | English |
| Format | Medium: X; Size: Pages: 1133-1144 |
| System Entry Date | 2008 Feb 08 |
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Last Updated: 11/19/2009