Lie algebraic methods for particle tracking calculations

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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 ... continued below

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Pages: 5

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Douglas, D.R. & Dragt, A.J. August 1, 1983.

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Description

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.

Physical Description

Pages: 5

Notes

NTIS, PC A02/MF A01.

Source

  • 12. international conference on high energy accelerators, Batavia, IL, USA, 11 Aug 1983

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  • Other: DE84004310
  • Report No.: LBL-16008
  • Report No.: CONF-830822-49
  • Grant Number: AC03-76SF00098
  • DOI: 10.2172/5362638 | External Link
  • Office of Scientific & Technical Information Report Number: 5362638
  • Archival Resource Key: ark:/67531/metadc1066979

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Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.

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  • August 1, 1983

Added to The UNT Digital Library

  • Feb. 4, 2018, 10:51 a.m.

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  • April 2, 2018, 1:14 p.m.

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Douglas, D.R. & Dragt, A.J. Lie algebraic methods for particle tracking calculations, report, August 1, 1983; United States. (digital.library.unt.edu/ark:/67531/metadc1066979/: accessed April 20, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.