Keyword: linear-dynamics
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MOPA81 Study of Nonlinear Dynamics in the 4-D Hénon Map Using the Square Matrix Method and Iterative Methods resonance, dynamic-aperture, lattice, sextupole 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.
poster icon 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
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TUZE3 Optimizing the Discovery of Underlying Nonlinear Beam Dynamics lattice, simulation, MMI, experiment 335
  • L.A. Pocher, T.M. Antonsen, L. Dovlatyan, I. Haber, P.G. O’Shea
    UMD, College Park, Maryland, USA
  Funding: Work supported by US DOE-HEP grants: DE-SC0010301 and DE-SC0022009
One of the DOE-HEP Grand Challenges identified by Nagaitsev et al. relates to the use of virtual particle accelerators for beam prediction and optimization. Useful virtual accelerators rely on efficient and effective methodologies grounded in theory, simulation, and experiment. This paper uses an algorithm called Sparse Identification of Nonlinear Dynamical systems (SINDy), which has not previously been applied to beam physics. We believe the SINDy methodology promises to simplify the optimization of accelerator design and commissioning, particularly where space charge is important. We show how SINDy can be used to discover and identify the underlying differential equation system governing the beam moment evolution. We compare discovered differential equations to theoretical predictions and results from the PIC code WARP modeling. We then integrate the discovered differential system forward in time and compare the results to data analyzed in prior work using a Machine Learning paradigm called Reservoir Computing. Finally, we propose extending our methodology, SINDy for Virtual Accelerators (SINDyVA), to the broader community’s computational and real experiments.
slides icon Slides TUZE3 [3.141 MB]  
DOI • reference for this paper ※ doi:10.18429/JACoW-NAPAC2022-TUZE3  
About • Received ※ 08 August 2022 — Accepted ※ 10 August 2022 — Issue date ※ 22 August 2022  
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WEPA34 Transfer Maps in the Hard-Edge Limit of Quadrupole and Bend Magnets Fringe Fields quadrupole, dipole, collider, space-charge 705
  • T.V. Gorlov
    ORNL, Oak Ridge, Tennessee, USA
  Funding: This work has been authored by UT-Battelle, LLC, under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy.
Beam dynamics of charged particles in the fringe field of a quadrupole and a dipole magnet is considered. An effective method for solving symplectic Lie map exp(:f:) in such cases has been developed. A precise analytic solution for nonlinear transverse beam dynamics in a quadrupole magnet with hard-edge fringe field has been obtained. The method of Lie map calculation considered here can be applied for other magnets and for soft edge type of fringe field.
DOI • reference for this paper ※ doi:10.18429/JACoW-NAPAC2022-WEPA34  
About • Received ※ 23 July 2022 — Revised ※ 29 July 2022 — Accepted ※ 07 August 2022 — Issue date ※ 12 August 2022
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WEPA80 Progress on Convergence Map Based on Square Matrix for Nonlinear Lattice Optimization lattice, dynamic-aperture, resonance, storage-ring 823
  • L.H. Yu, Y. Hao, Y. Hidaka, F. Plassard, V.V. Smaluk
    BNL, Upton, New York, USA
  • Y. Hao
    FRIB, East Lansing, Michigan, USA
  Funding: DOE.
We report progress on applying the square matrix method to obtain in high speed a "convergence map", which is similar but different from a frequency map. We give an example of applying the method to optimize a nonlinear lattice for the NSLS-II upgrade. The convergence map is obtained by solving the nonlinear dynamical equation by iteration of the perturbation method and studying the convergence. The map provides information about the stability border of the dynamical aperture. We compare the map with the frequency map from tracking. The result in our example of nonlinear optimization of the NSLS-II lattice shows the new method may be applied in nonlinear lattice optimization, taking advantage of the high speed (about 30~300 times faster) to explore x, y, and the off-momentum phase space.
poster icon Poster WEPA80 [5.392 MB]  
DOI • reference for this paper ※ doi:10.18429/JACoW-NAPAC2022-WEPA80  
About • Received ※ 19 July 2022 — Revised ※ 26 July 2022 — Accepted ※ 08 August 2022 — Issue date ※ 10 August 2022
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