First order tune shift calculations for transverse betatron dynamics

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An effective Hamiltonian, with non-linear magnetic multipole terms and momentum dispersion contributions, is used to obtain the first order tune-shift results for transverse betatron motion for protons in the Superconducting Super Collider (SSC). This Hamiltonian is represented in terms of action angle variables, and analytical results are obtained using symbolic algebra methods. Mathematical derivations of the transverse multipole expansion and of the transverse betatron equations, using an invariant action and curvilinear coordinates, are given in the appendices. Numerical and graphical tune-space results are given that illustrate the dependence of tune-shifts on injection amplitude and momentum spread. 10 refs., 7 figs.

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Pages: (36 p)

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Garavaglia, T. September 1, 1991.

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An effective Hamiltonian, with non-linear magnetic multipole terms and momentum dispersion contributions, is used to obtain the first order tune-shift results for transverse betatron motion for protons in the Superconducting Super Collider (SSC). This Hamiltonian is represented in terms of action angle variables, and analytical results are obtained using symbolic algebra methods. Mathematical derivations of the transverse multipole expansion and of the transverse betatron equations, using an invariant action and curvilinear coordinates, are given in the appendices. Numerical and graphical tune-space results are given that illustrate the dependence of tune-shifts on injection amplitude and momentum spread. 10 refs., 7 figs.

Physical Description

Pages: (36 p)

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OSTI; NTIS; INIS; GPO Dep.

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  • 1991 symposium on the Superconducting Super Collider (SSC), Corpus Christi, TX (United States), 13-17 Oct 1991

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  • Other: DE92000370
  • Report No.: SSCL-507
  • Report No.: CONF-9110225--1
  • Grant Number: AC35-89ER40486
  • Office of Scientific & Technical Information Report Number: 5334086
  • Archival Resource Key: ark:/67531/metadc1069441

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  • September 1, 1991

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  • Feb. 4, 2018, 10:51 a.m.

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  • March 2, 2018, 5:53 p.m.

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Garavaglia, T. First order tune shift calculations for transverse betatron dynamics, article, September 1, 1991; United States. (digital.library.unt.edu/ark:/67531/metadc1069441/: accessed October 15, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.