NAPAC2022 - List of Authors (Anderson, K.J.)

Paper	Title	Page
MOPA81	Study of Nonlinear Dynamics in the 4-D Hénon Map Using the Square Matrix Method and Iterative Methods	232
	K.J. Anderson, Y. Hao FRIB, East Lansing, Michigan, USA L.H. Yu BNL, Upton, New York, USA
	Funding: Accelerator Stewardship program under award number DE-SC0019403 US Department of Energy, Office of Science, High Energy Physics under award number DE-SC0018362 and Michigan State University The Hénon Map represents a linear lattice with a single sextupole kick. This map has been extensively studied due to its chaotic behavior. The case for the two dimensional phase space has recently been revisited using ideas from KAM theory to create an iterative process that transforms nonlinear perturbed trajectories into rigid rotations. The convergence of this method relates to the resonance structure and can be used as an indicator of the dynamic aperture. The studies of this method have been extended to the four dimensional phase space case which introduces coupling between the transverse coordinates. Hao, Y., Anderson, K., & Yu, L. H. (2021, August). Revisit of Nonlinear Dynamics in Hénon Map Using Square Matrix Method. https://doi.org/10.18429/JACoW-IPAC2021-THPAB016
	Poster MOPA81 [3.103 MB]
DOI •	reference for this paper ※ doi:10.18429/JACoW-NAPAC2022-MOPA81
About •	Received ※ 19 July 2022 — Revised ※ 04 August 2022 — Accepted ※ 15 August 2022 — Issue date ※ 26 August 2022
Cite •	reference for this paper using ※ BibTeX, ※ LaTeX, ※ Text/Word, ※ RIS, ※ EndNote (xml)

Paper

Title

Page

Study of Nonlinear Dynamics in the 4-D Hénon Map Using the Square Matrix Method and Iterative Methods

232

K.J. Anderson, Y. Hao
FRIB, East Lansing, Michigan, USA
L.H. Yu
BNL, Upton, New York, USA

Funding: Accelerator Stewardship program under award number DE-SC0019403 US Department of Energy, Office of Science, High Energy Physics under award number DE-SC0018362 and Michigan State University
The Hénon Map represents a linear lattice with a single sextupole kick. This map has been extensively studied due to its chaotic behavior. The case for the two dimensional phase space has recently been revisited using ideas from KAM theory to create an iterative process that transforms nonlinear perturbed trajectories into rigid rotations*. The convergence of this method relates to the resonance structure and can be used as an indicator of the dynamic aperture. The studies of this method have been extended to the four dimensional phase space case which introduces coupling between the transverse coordinates.
*Hao, Y., Anderson, K., & Yu, L. H. (2021, August). Revisit of Nonlinear Dynamics in Hénon Map Using Square Matrix Method. https://doi.org/10.18429/JACoW-IPAC2021-THPAB016

Poster MOPA81 [3.103 MB]

DOI •

reference for this paper ※ doi:10.18429/JACoW-NAPAC2022-MOPA81

About •

Received ※ 19 July 2022 — Revised ※ 04 August 2022 — Accepted ※ 15 August 2022 — Issue date ※ 26 August 2022

Cite •

reference for this paper using ※ BibTeX, ※ LaTeX, ※ Text/Word, ※ RIS, ※ EndNote (xml)