Skip to content

Coupled lattice analysis #60

Open
Open

Description

@austin-hoover

This would complement the current MATRIX_Lattice class, which computes parameters for uncoupled lattices. Unlike the 2D case, there are multiple parameterizations of the 4D or 6D transfer matrix, so it would make sense to support these different parameterizations. Options include Lebedev-Bogacz [1], Edwards-Teng [2], Wolski [3], and Qin-Davidson [4]. Some of these apply also to non-periodic lattices.

Some work to this end is here, which analyzes the one-turn transfer matrix in the Lebedev-Bogacz framework. I did not implement tracking of the parameters throughout the lattice. I'm not sure if this is the best way to include these parameterizations.

[1] Lebedev, Valeri A., and S. A. Bogacz. "Betatron motion with coupling of horizontal and vertical degrees of freedom." Journal of Instrumentation 5.10 (2010): P10010. (https://arxiv.org/pdf/1207.5526)

[2] Edwards, D. A., and L. C. Teng. "Parametrization of linear coupled motion in periodic systems." IEEE Transactions on nuclear science 20.3 (1973): 885-888. (https://accelconf.web.cern.ch/p73/PDF/PAC1973_0885.pdf)

[3] Wolski, Andrzej. "Alternative approach to general coupled linear optics." Physical Review Special Topics—Accelerators and Beams 9.2 (2006): 024001. (https://journals.aps.org/prab/pdf/10.1103/PhysRevSTAB.9.024001)

[4] Qin, Hong, et al. "Analytical methods for describing charged particle dynamics in general focusing lattices using generalized Courant-Snyder theory." Physical Review Special Topics-Accelerators and Beams 17.4 (2014): 044001. (https://journals.aps.org/prab/pdf/10.1103/PhysRevSTAB.17.044001)

Activity

  1. changed the title [-]Add coupled linear lattice analysis[/-] [+]Coupled lattice analysis[/+] on Apr 8, 2025
  2. austin-hoover commented on Sep 4, 2025

    @austin-hoover
    ContributorAuthor
  3. austin-hoover commented on Sep 15, 2026

    @austin-hoover
    ContributorAuthor

    I think it would make sense to add to/rewrite MATRIX_Lattice rather than creating a new class.

  4. austin-hoover commented on Oct 9, 2026

    @austin-hoover
    ContributorAuthor

    This has been started with PR #151, which calculates eigentunes from the transfer matrix eigenvalues.

Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment

Metadata

Metadata

Assignees

No one assigned

    Labels

    No labels
    No labels

    Type

    No type

    Projects

    No projects

      Milestone

      No milestone

      Relationships

      None yet

      Development

      No branches or pull requests

      Issue actions