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Hamiltonian maps and normal forms for intense beams

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Title: Hamiltonian maps and normal forms for intense beams
Authors: Turchetti, G.1 turchetti@bo.infn.it
Source: Nuclear Instruments & Methods in Physics Research Section A. Jun2006, Vol. 561 Issue 2, p151-157. 7p.
Subjects: Hamiltonian systems, Space charge, Electron beams, Adiabatic invariants
Abstract: Abstract: The dynamics of a beam in a ring with a localized multipolar nonlinearity is described by a polynomial one turn map. The space charge forces act continuously along the ring, but their effect can be included by replacing the linear tune with the depressed tune which depends on the Courant Snyder invariant. This approximation allows to use the normal forms to compute the nonlinear invariants, the nonlinear tune and the islands geometric parameters when a low order resonance is approached. [Copyright &y& Elsevier]
Copyright of Nuclear Instruments & Methods in Physics Research Section A is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 20923533
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Hamiltonian maps and normal forms for intense beams
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  Data: Abstract: The dynamics of a beam in a ring with a localized multipolar nonlinearity is described by a polynomial one turn map. The space charge forces act continuously along the ring, but their effect can be included by replacing the linear tune with the depressed tune which depends on the Courant Snyder invariant. This approximation allows to use the normal forms to compute the nonlinear invariants, the nonlinear tune and the islands geometric parameters when a low order resonance is approached. [Copyright &y& Elsevier]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Nuclear Instruments & Methods in Physics Research Section A is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1016/j.nima.2006.01.023
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      – Code: eng
        Text: English
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      – SubjectFull: Space charge
        Type: general
      – SubjectFull: Electron beams
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      – SubjectFull: Adiabatic invariants
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              Text: Jun2006
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