  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.
