SYMPLECTIC INTERPOLATION.

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It is important to have symplectic maps for the various electromagnetic elements in an accelerator ring. For some tracking problems we must consider elements which evolve during a ramp. Rather than performing a computationally intensive numerical integration for every turn, it should be possible to integrate the trajectory for a few sets of parameters, and then interpolate the transport map as a function of one or more parameters, such as energy. We present two methods for interpolation of symplectic matrices as a function of parameters: one method is based on the calculation of a representation in terms of a basis ... continued below

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5 pages

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MACKAY, W.W. & LUCCIO, A.U. June 23, 2006.

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It is important to have symplectic maps for the various electromagnetic elements in an accelerator ring. For some tracking problems we must consider elements which evolve during a ramp. Rather than performing a computationally intensive numerical integration for every turn, it should be possible to integrate the trajectory for a few sets of parameters, and then interpolate the transport map as a function of one or more parameters, such as energy. We present two methods for interpolation of symplectic matrices as a function of parameters: one method is based on the calculation of a representation in terms of a basis of group generators [2, 3] and the other is based on the related but simpler symplectification method of Healy [1]. Both algorithms guarantee a symplectic result.

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5 pages

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  • 10TH BIENNIAL EUROPEAN PARTICLE ACCELERATOR CONFERENCE (EPAC); EDINBURGH, UK; 20060626 through 20060630

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  • Report No.: BNL--75463-2006-CP
  • Grant Number: DE-AC02-98CH10886
  • Office of Scientific & Technical Information Report Number: 884999
  • Archival Resource Key: ark:/67531/metadc876792

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  • June 23, 2006

Added to The UNT Digital Library

  • Sept. 21, 2016, 2:29 a.m.

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  • Dec. 12, 2016, 8:18 p.m.

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MACKAY, W.W. & LUCCIO, A.U. SYMPLECTIC INTERPOLATION., article, June 23, 2006; [Upton, New York]. (digital.library.unt.edu/ark:/67531/metadc876792/: accessed November 18, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.