Explicit symplectic representations of nonlinear dipole fringe field maps

The representation of beam transport through magnetic dipole fringe fields using effective "thin" maps has a long history. More recent work has extended the second-order Taylor model of Brown by providing Lie generators for symplectic maps that capture effects at higher order, expressed in terms of field integrals. These maps can be cumbersome to evaluate in an explicit symplectic form appropriate for particle tracking codes, and existing approaches often require additional approximations. We show how such maps can be recovered in a simple, explicit form as rational symplectic functions using a mixed-variable generating function approach.