Explicit formulas for 2nd-order driving terms due to sextupoles and chromatic effects of quadrupoles. Metadata

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  • Main Title Explicit formulas for 2nd-order driving terms due to sextupoles and chromatic effects of quadrupoles.


  • Author: Wang, C-X. (Accelerator Systems Division (APS))
    Creator Type: Personal


  • Sponsor: United States. Department of Energy. Office of Science.
    Contributor Type: Organization


  • Name: Argonne National Laboratory
    Place of Publication: United States
    Additional Info: Argonne National Laboratory (ANL)


  • Creation: 2012-04-25


  • Other


  • Content Description: Optimization of nonlinear driving terms have become a useful tool for designing storage rings, especially modern light sources where the strong nonlinearity is dominated by the large chromatic effects of quadrupoles and strong sextupoles for chromaticity control. The Lie algebraic method is well known for computing such driving terms. However, it appears that there was a lack of explicit formulas in the public domain for such computation, resulting in uncertainty and/or inconsistency in widely used codes. This note presents explicit formulas for driving terms due to sextupoles and chromatic effects of quadrupoles, which can be considered as thin elements. The computation is accurate to the 4th-order Hamiltonian and 2nd-order in terms of magnet parameters. The results given here are the same as the APS internal note AOP-TN-2009-020. This internal nte has been revised and published here as a Light Source Note in order to get this information into the public domain, since both ELEGANT and OPA are using these formulas.


  • Keyword: Light Sources
  • Keyword: Storage Rings
  • STI Subject Categories: 43 Particle Accelerators
  • Keyword: Quadrupoles
  • Keyword: Optimization
  • Keyword: Magnets
  • Keyword: Hamiltonians


  • Name: Office of Scientific & Technical Information Technical Reports
    Code: OSTI


  • Name: UNT Libraries Government Documents Department
    Code: UNTGD

Resource Type

  • Report


  • Text


  • Report No.: ANL/APS/LS-330
  • Grant Number: DE-AC02-06CH11357
  • DOI: 10.2172/1039519
  • Office of Scientific & Technical Information Report Number: 1039519
  • Archival Resource Key: ark:/67531/metadc843515