Fringe field maps for symplectic models of general Cartesian dipoles

We present a framework with which to analyze the effects of magnetic fringe fields. The theory defines the fringe field to be the transition between two regions of nearly constant field, and can incorporate constant multipoles in the magnet body. We then analyze Cartesian dipoles and derive symplectic fringe field maps that are applicable to longitudinal and/or transverse gradient dipoles. We verify the fringe maps with tracking, and show how we incorporated the theory into the tracking code ELEGANT. The resulting elements and several supporting scripts are now available for users, and we conclude with several predictions relevant to the APS Upgrade project.