A practical approach to extract symplectic transfer maps numerically for arbitrary magnetic elements

TL;DR

This paper presents a numerical method to accurately extract symplectic transfer maps for complex magnetic elements in particle accelerators, improving modeling of beam dynamics beyond simplified assumptions.

Contribution

It introduces a practical numerical approach to derive symplectic transfer maps from magnetic field data, applicable to complex and non-ideal magnetic elements.

Findings

Enables accurate modeling of beam dynamics with complex magnetic fields

Provides a method to extract transfer maps from simulation or measurement data

Improves the fidelity of accelerator design and optimization

Abstract

We introduce a practical approach to extract the symplectic transfer maps for arbitrary magnetic beam-line elements. Beam motion in particle accelerators depends on linear and nonlinear magnetic fields of the beam-line elements. These elements are usually modeled as magnetic multipoles with constant field strengths in the longitudinal direction (i.e., hard-edge model) in accelerator design and modeling codes. For magnets with complicated structures such as insertion devices or fields with significant longitudinal variation effects, the simplified models may not be sufficient to char- acterize beam dynamics behaviors accurately. A numerical approach has been developed to extract symplectic transfer maps from particle trajectory tracking simulation that uses magnetic field data provided by three-dimensional magnetic field modeling codes or experimental measurements. The extracted transfer maps can be used in linear optics design and nonlinear dynamics optimization to achieve more realistic results.