Short quadrupole parametrization

The Enge function can be used to parametrize any element with well-defined edges. If an element is too short, however, there is no unambiguous definition of the effective edge. We first demonstrate that very little fringe field detail is needed to obtain accurate maps even up to fifth order. Then we go on to show a simple fitting algorithm that works well for short as well as long quadrupoles. The results are true whether the quads are magnetic or electrostatic.