Lie algebraic methods for particle tracking calculations
A study of the nonlinear stability of an accelerator or storage ring lattice typically includes particle tracking simulations. Such simulations trace rays through linear and nonlinear lattice elements by numerically evaluating linear matrix or impulsive nonlinear transformations. Using the mathematical tools of Lie groups and algebras, one may construct a formalism which makes explicit use of Hamilton's equations and which allows the description of groups of linear and nonlinear lattice elements by a single transformation. Such a transformation will be exactly canonical and will describe finite length linear and nonlinear elements through third (octupole) order. It is presently possible to include effects such as fringing fields and potentially possible to extend the formalism to include nonlinearities of higher order, multipole errors, and magnet misalignments. We outline this Lie algebraic formalism and its use in particle tracking calculations. A computer code, MARYLIE, has been constructed on the basis of this formalism. We describe the use of this program for tracking and provide examples of its application. 6 references, 3 figures.
- Research Organization:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of Maryland, College Park, MD (United States)
- DOE Contract Number:
- AC03-76SF00098
- OSTI ID:
- 5362638
- Report Number(s):
- LBL-16008; CONF-830822-49; ON: DE84004310
- Resource Relation:
- Conference: 12. international conference on high energy accelerators, Batavia, IL, USA, 11 Aug 1983
- Country of Publication:
- United States
- Language:
- English
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LIE GROUPS
ORBITS
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TRAJECTORIES
DATA
INFORMATION
MATHEMATICAL OPERATORS
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NUMERICAL DATA
QUANTUM OPERATORS
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