Allowing for hysteresis in the calculation of fields in the elements of accelerator magnetic systems

Iron magnetic circuit residual magnetization may contribute as much as several Gs to the magnetic field in charged-particle accelerators. This contribution depends on the magnetization “history”. It is not taken into account in most of the existing software that uses the main magnetization curve. Therefore, an error in field calculations usually exceeds 1%, which is unacceptable for accelerators. In this article, a simple phenomenological magnetic-hysteresis model that is suitable for numerical computations is suggested. Approximations based on the proposed model are compared to the results of measurements on partial hysteresis cycles in a steel ring.