Explicit Higher Order Symplectic Integrator for s-Dependent Magnetic Field

(Dated: June 16, 2001) We derive second and higher order explicit symplectic integrators for the charged particle motion in an s-dependent magnetic field with the paraxial approximation. The Hamiltonian of such a system takes the form of H = P k(pk − ak(~q, s)) + V (~q, s). This work solves a long-standing problem for modeling s-dependent magnetic elements. Important applications of this work include the studies of the charged particle dynamics in a storage ring with strong field wigglers, arbitrarily polarized insertion devices, and super-conducting magnets with strong fringe fields. Consequently, this work will have a significant impact on the optimal use of the above magnetic devices in the light source rings as well as in next generation linear collider damping rings.