Betatron motion with coupling of horizontal and vertical degrees of freedom

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The Courant-Snyder parameterization of one-dimensional linear betatron motion is generalized to two-dimensional coupled linear motion. To represent the 4 x 4 symplectic transfer matrix the following ten parameters were chosen: four beta-functions, four alpha-functions and two betatron phase advances which have a meaning similar to the Courant-Snyder parameterization. Such a parameterization works equally well for weak and strong coupling and can be useful for analysis of coupled betatron motion in circular accelerators as well as in transfer lines. Similarly, the transfer matrix, the bilinear form describing the phase space ellipsoid and the second order moments are related to the eigen-vectors. ... continued below

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253 Kilobytes pages

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Bogacz, S. A. & Lebedev, V. A. November 21, 2002.

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The Courant-Snyder parameterization of one-dimensional linear betatron motion is generalized to two-dimensional coupled linear motion. To represent the 4 x 4 symplectic transfer matrix the following ten parameters were chosen: four beta-functions, four alpha-functions and two betatron phase advances which have a meaning similar to the Courant-Snyder parameterization. Such a parameterization works equally well for weak and strong coupling and can be useful for analysis of coupled betatron motion in circular accelerators as well as in transfer lines. Similarly, the transfer matrix, the bilinear form describing the phase space ellipsoid and the second order moments are related to the eigen-vectors. Corresponding equations can be useful in interpreting tracking results and experimental data.

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253 Kilobytes pages

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  • Snowmass 2001, Snowmass, CO (US), 06/30/2001--07/21/2001

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  • Report No.: FERMILAB-Conf-01/439
  • Grant Number: AC02-76CH03000
  • Office of Scientific & Technical Information Report Number: 804898
  • Archival Resource Key: ark:/67531/metadc739554

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  • November 21, 2002

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  • Oct. 18, 2015, 6:40 p.m.

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  • April 1, 2016, 5:16 p.m.

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Bogacz, S. A. & Lebedev, V. A. Betatron motion with coupling of horizontal and vertical degrees of freedom, article, November 21, 2002; Batavia, Illinois. (digital.library.unt.edu/ark:/67531/metadc739554/: accessed May 21, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.