Explicit symplectic integrator for s-dependent static magnetic field.

This paper reports our recent work on explicit symplectic integration techniques for the charged particle motion in an s-dependent static magnetic field. Using the extended phase space, symplectic integrators can be developed for Hamiltonians with or without the paraxial approximation using either the space or time as an independent variable. This work extends the successful element-by-element tracking method for studying single-particle nonlinear dynamics to a set of s-dependent magnetic elements. Important applications of this work include the studies of the charged particle dynamics in a storage ring with various insertion devices, superconducting magnets, large aperture magnets with significant fringe fields, and solenoid magnets in the interaction region. Consequently, this work is expected to make an impact on design and optimal operation of existing and future light source rings and high energy physics accelerators.