Analytic studies of the long range beam-beam tune shifts and chromaticities

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A formula is derived, which allows efficient analytical evaluation of the long range beam-beam tune shifts and chromaticities with amplitude. It assumes that the beams are infinitely short, oppositely charged, and with Gaussian transversal profile. The formula employs an infinite sum with favorable convergence rates, making it well suited especially for the long range case. For a deeper understanding of the beam-beam effects, the structure of the formula was analyzed. It is shown that the tune shifts and chromaticities change sign at certain values of the separation and/or amplitude, and folds in the footprints are predicted. Some special cases were ... continued below

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1140 Kilobytes pages

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Erdelyi, Bela & Sen, Tanaji May 29, 2002.

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Description

A formula is derived, which allows efficient analytical evaluation of the long range beam-beam tune shifts and chromaticities with amplitude. It assumes that the beams are infinitely short, oppositely charged, and with Gaussian transversal profile. The formula employs an infinite sum with favorable convergence rates, making it well suited especially for the long range case. For a deeper understanding of the beam-beam effects, the structure of the formula was analyzed. It is shown that the tune shifts and chromaticities change sign at certain values of the separation and/or amplitude, and folds in the footprints are predicted. Some special cases were studied in more detail. Applications to the Tevatron are presented, including some proposed compensation schemes.

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1140 Kilobytes pages

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  • Other Information: PBD: 29 May 2002

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  • Report No.: FERMILAB-TM-2171
  • Grant Number: AC-2-76CH03000
  • DOI: 10.2172/794463 | External Link
  • Office of Scientific & Technical Information Report Number: 794463
  • Archival Resource Key: ark:/67531/metadc735134

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  • May 29, 2002

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  • Oct. 19, 2015, 7:39 p.m.

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  • April 1, 2016, 3:36 p.m.

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Erdelyi, Bela & Sen, Tanaji. Analytic studies of the long range beam-beam tune shifts and chromaticities, report, May 29, 2002; Batavia, Illinois. (digital.library.unt.edu/ark:/67531/metadc735134/: accessed August 20, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.