The second-order tune shift with amplitude for octupole-induced resonances in storage ring

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Description

The purpose of this note is to analyze the octupole-induced resonances, to lowest order, in a synchrotron and storage ring. When the Hamiltonian with octupole term is transformed to action-angle variables, it is found that the amplitude-dependent tune shift terms are composed of two types: terms of second-order in betatron oscillation amplitude of a particle and terms of fourth-order in oscillation amplitude. Obtaining fourth-order terms requires complicated analysis even with the first-order perturbation theory employed. Treatment of this analysis will be the subject of a subsequent note. Second-order terms are straightforward and simple to calculate, and therefore they treat them ... continued below

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5 p.

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Yoon, M. September 1, 1988.

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Description

The purpose of this note is to analyze the octupole-induced resonances, to lowest order, in a synchrotron and storage ring. When the Hamiltonian with octupole term is transformed to action-angle variables, it is found that the amplitude-dependent tune shift terms are composed of two types: terms of second-order in betatron oscillation amplitude of a particle and terms of fourth-order in oscillation amplitude. Obtaining fourth-order terms requires complicated analysis even with the first-order perturbation theory employed. Treatment of this analysis will be the subject of a subsequent note. Second-order terms are straightforward and simple to calculate, and therefore they treat them here first.

Physical Description

5 p.

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OSTI as DE96015140

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  • Other Information: PBD: Sep 1988

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  • Other: DE96015140
  • Report No.: LS--126(ANL)
  • Grant Number: W-31109-ENG-38
  • DOI: 10.2172/378885 | External Link
  • Office of Scientific & Technical Information Report Number: 378885
  • Archival Resource Key: ark:/67531/metadc674830

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  • September 1, 1988

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  • July 25, 2015, 2:20 a.m.

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  • Dec. 16, 2015, 3:51 p.m.

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Yoon, M. The second-order tune shift with amplitude for octupole-induced resonances in storage ring, report, September 1, 1988; Illinois. (digital.library.unt.edu/ark:/67531/metadc674830/: accessed September 25, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.