Symmetry properties of a symplectic transport matrix and Twiss parameterization of a fully coupled motion

Twiss parameterization proposed by Courant and Snyder is a keystone of accelerator physics. Several authors have extended it later to the case of the fully coupled betatron motion and synchrobetatron motion of a coasting beam. A few proposals have been made as well how to construct a parameterizatio...

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Main Author: Sergei Glukhov
Format: Article
Language:English
Published: American Physical Society 2025-08-01
Series:Physical Review Accelerators and Beams
Online Access:http://doi.org/10.1103/3ld3-dmmv
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author Sergei Glukhov
author_facet Sergei Glukhov
author_sort Sergei Glukhov
collection DOAJ
description Twiss parameterization proposed by Courant and Snyder is a keystone of accelerator physics. Several authors have extended it later to the case of the fully coupled betatron motion and synchrobetatron motion of a coasting beam. A few proposals have been made as well how to construct a parameterization which is fully symmetric with respect to all three spatial degrees of freedom. The key point for each of them is to find a similarity transformation which turns the transport matrix into a block-diagonal form with 2×2 cells. In the present work, this approach has been considered in detail. It is based on the idea initially proposed by Mais and Ripken for transport matrix eigenvalue calculation only. It shows how to introduce a symmetric Twiss-like parameterization and an emittance concept for an arbitrary symplectic 6×6 matrix. The resulting parameterization can be reduced to the well-known Lebedev-Bogacz parameterization in case of 4×4 matrix. Special attention has been paid to the intrinsic ambiguity existing in the Twiss parameterization of a coupled motion.
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spelling doaj-art-2aca6ec145c94ee98362d55e88843bde2025-08-20T03:43:55ZengAmerican Physical SocietyPhysical Review Accelerators and Beams2469-98882025-08-0128808400110.1103/3ld3-dmmvSymmetry properties of a symplectic transport matrix and Twiss parameterization of a fully coupled motionSergei GlukhovTwiss parameterization proposed by Courant and Snyder is a keystone of accelerator physics. Several authors have extended it later to the case of the fully coupled betatron motion and synchrobetatron motion of a coasting beam. A few proposals have been made as well how to construct a parameterization which is fully symmetric with respect to all three spatial degrees of freedom. The key point for each of them is to find a similarity transformation which turns the transport matrix into a block-diagonal form with 2×2 cells. In the present work, this approach has been considered in detail. It is based on the idea initially proposed by Mais and Ripken for transport matrix eigenvalue calculation only. It shows how to introduce a symmetric Twiss-like parameterization and an emittance concept for an arbitrary symplectic 6×6 matrix. The resulting parameterization can be reduced to the well-known Lebedev-Bogacz parameterization in case of 4×4 matrix. Special attention has been paid to the intrinsic ambiguity existing in the Twiss parameterization of a coupled motion.http://doi.org/10.1103/3ld3-dmmv
spellingShingle Sergei Glukhov
Symmetry properties of a symplectic transport matrix and Twiss parameterization of a fully coupled motion
Physical Review Accelerators and Beams
title Symmetry properties of a symplectic transport matrix and Twiss parameterization of a fully coupled motion
title_full Symmetry properties of a symplectic transport matrix and Twiss parameterization of a fully coupled motion
title_fullStr Symmetry properties of a symplectic transport matrix and Twiss parameterization of a fully coupled motion
title_full_unstemmed Symmetry properties of a symplectic transport matrix and Twiss parameterization of a fully coupled motion
title_short Symmetry properties of a symplectic transport matrix and Twiss parameterization of a fully coupled motion
title_sort symmetry properties of a symplectic transport matrix and twiss parameterization of a fully coupled motion
url http://doi.org/10.1103/3ld3-dmmv
work_keys_str_mv AT sergeiglukhov symmetrypropertiesofasymplectictransportmatrixandtwissparameterizationofafullycoupledmotion