Li, J. Wang, K.D. Yan, X.Q. Zhu, K. JACoW Publishing Geneva, Switzerland 978-3-95450-265-3 10.18429/JACoW-SAP2023-TUPB008 English 96-98 multipole HOM FFAG octupole controls Contribution to a conference proceedings 2024 2024-11 https://doi.org/10.18429/JACoW-SAP2023-TUPB008 https://jacow.org/sap2023/papers/tupb008.pdf The elliptical magnetic field zone is a useful tool for beam distribution homogenization and FFAG accelerators. Additionally, strongly curved magnets are studied for their application in beam transmission and nuclear fusion. However, traditional magnetic measurements, known as field harmonics, for straight magnets are not suitable for these two kinds of special magnets. In this article, advanced multipoles are used to characterize the fields of straight magnets with elliptical apertures and 2D axisymmetric enclosed curved magnets. The article provides a detailed analysis of magnetic fields using data from FEA or Biot-Savart law. Furthermore, the article discusses methods for characterizing the field quality of unclosed curved magnets used for gantry.