Convergence map with action-angle variables based on square matrix for nonlinear lattice optimization

To analyze nonlinear dynamic systems, we developed a new technique based on the square matrix method. We propose this technique called the “convergence map” for generating particle stability diagrams similar to the frequency maps widely used in accelerator physics to estimate dynamic aperture. The c...

Full description

Saved in:
Bibliographic Details
Published in:Physical review. Accelerators and beams Vol. 26; no. 5; p. 054002
Main Authors: Yu, Li Hua, Hidaka, Yoshiteru, Smaluk, Victor, Anderson, Kelly, Hao, Yue
Format: Journal Article
Language:English
Published: College Park American Physical Society 01.05.2023
Subjects:
Apertures
Computing time
Convergence
Dynamical systems
Fourier transforms
Iterative methods
Matrix methods
Nonlinear dynamics
Nonlinear equations
Nonlinear systems
Optimization
Particle accelerators
Particle tracking
Perturbation methods
ISSN:2469-9888, 2469-9888
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:To analyze nonlinear dynamic systems, we developed a new technique based on the square matrix method. We propose this technique called the “convergence map” for generating particle stability diagrams similar to the frequency maps widely used in accelerator physics to estimate dynamic aperture. The convergence map provides similar information as the frequency map but in a much shorter computing time. The dynamic equation can be rewritten in terms of action-angle variables provided by the square matrix derived from the accelerator lattice. The convergence map is obtained by solving the exact nonlinear equation iteratively by the perturbation method using Fourier transform and studying convergence numerically. When the iteration is convergent, the solution is expressed as a quasiperiodic analytical function as a highly accurate approximation and hence the motion is stable. The border of stable motion determines the dynamical aperture. As an example, we applied the new method to the nonlinear optimization of the NSLS-II storage ring and demonstrated a dynamic aperture comparable to or larger than the nominal one obtained by particle tracking. The computation speed of the convergence map is 30 to 300 times faster than the speed of the particle tracking, depending on the size of the ring lattice (number of superperiods). The computation speed ratio is larger for complex lattices with low symmetry, such as particle colliders.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
USDOE Office of Science (SC), High Energy Physics (HEP)
SC0012704; BNL LDRD 20-041; LDRD 20-041; SC0019403
ISSN:2469-9888
2469-9888
DOI:10.1103/PhysRevAccelBeams.26.054002