Persistent homology of Hamiltonian orbits with applications to beam physics: Euler-Betti classification and topological chaos indicators
Abstract
Estimating the dynamic aperture of circular particle accelerators typically requires expensive long-term tracking. Using classical homology, we construct a two-dimensional theoretical classification of regular and chaotic orbits and use persistent homology for its numerical implementation on short orbit segments. In four dimensions, we introduce topological chaos indicators based on persistent homology and use normal-form theory to apply the classification to two symplectic-plane projections. The methods reproduce the expected organization of regular and chaotic motion in several canonical Hamiltonian systems. Applied to symplectified one-turn maps of a nonlinear lattice model of the Integrable Optics Test Accelerator, the results obtained from the first 200 turns identify the central connected stability region and its surrounding transition to chaos. They are consistent with the short-term dynamic aperture of the electron configuration obtained from 104 turns and the long-term dynamic aperture of the proton configuration obtained from 108 turns. For the configurations studied, persistent homology of short orbit segments predicts the dynamic aperture obtained by substantially longer tracking, potentially reducing the need for exhaustive simulations in studies of existing accelerators and the design of future facilities. The methods could also complement classical chaos indicators and modern approaches based on artificial intelligence.
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BibTeX
@misc{tinoco2026persistent,
title = {{Persistent homology of Hamiltonian orbits with applications to beam physics: Euler-Betti classification and topological chaos indicators}},
author = {D. Iglesias Tinoco and B. Erdélyi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.22412},
eprint = {2609.22412},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.22412},
}
RIS
TY - UNPB
TI - Persistent homology of Hamiltonian orbits with applications to beam physics: Euler-Betti classification and topological chaos indicators
AU - D. Iglesias Tinoco
AU - B. Erdélyi
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.22412
UR - https://arxiv.org/abs/2609.22412
AB - Estimating the dynamic aperture of circular particle accelerators typically requires expensive long-term tracking. Using classical homology, we construct a two-dimensional theoretical classification of regular and chaotic orbits and use persistent homology for its numerical implementation on short orbit segments. In four dimensions, we introduce topological chaos indicators based on persistent homology and use normal-form theory to apply the classification to two symplectic-plane projections. The methods reproduce the expected organization of regular and chaotic motion in several canonical Hamiltonian systems. Applied to symplectified one-turn maps of a nonlinear lattice model of the Integrable Optics Test Accelerator, the results obtained from the first 200 turns identify the central connected stability region and its surrounding transition to chaos. They are consistent with the short-term dynamic aperture of the electron configuration obtained from 10^4 turns and the long-term dynamic aperture of the proton configuration obtained from 10^8 turns. For the configurations studied, persistent homology of short orbit segments predicts the dynamic aperture obtained by substantially longer tracking, potentially reducing the need for exhaustive simulations in studies of existing accelerators and the design of future facilities. The methods could also complement classical chaos indicators and modern approaches based on artificial intelligence.
ER -