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@inproceedings{lindberg:napac2022-tupa26, author = {R.R. Lindberg and M. Borland}, title = {{Fringe Field Maps for Cartesian Dipoles with Longitudinal and/or Transverse Gradients}}, & booktitle = {Proc. NAPAC'22}, booktitle = {Proc. 5th Int. Particle Accel. Conf. (NAPAC'22)}, pages = {401--404}, eid = {TUPA26}, language = {english}, keywords = {dipole, quadrupole, photon, focusing, lattice}, venue = {Albuquerque, NM, USA}, series = {International Particle Accelerator Conference}, number = {5}, publisher = {JACoW Publishing, Geneva, Switzerland}, month = {10}, year = {2022}, issn = {2673-7000}, isbn = {978-3-95450-232-5}, doi = {10.18429/JACoW-NAPAC2022-TUPA26}, url = {https://jacow.org/napac2022/papers/tupa26.pdf}, abstract = {{Fringe fields effects in dipoles can give rise to important linear and nonlinear contributions. This paper describes how to extend the classic results of Brown [1] and the more recent calculations of Hwang and Lee [2] to Cartesian dipoles with transverse and/or longitudinal gradients. We do this by 1) introducing a more general definition of the fringe field that can be applied to longitudinal gradient dipoles, 2) allowing for quadrupole and/or sextupole content in the magnet body, and 3) showing how to employ the resulting fringe field maps as a symplectic transformation of the coordinates. We compare our calculation results with tracking for longitudinal and transverse gradient dipoles planned for the APS-U.}}, }