Anomalous fractional magnetic field diffusion through cross-section of a massive toroidal ferromagnetic core

Abstract Toroidal massive ferromagnetic cores are used in a wide range of electromagnetic applications, such as current sensors, inductances, static converters and filters. Growing interest exists in the industrial field with regards simulation tools to reduce experimental campaigns and improve product knowledge and performance. Accurate simulation results require a consideration of precise electromagnetic laws, such as the exact non-linear magnetic behavior of toroidal magnetic cores. Under the influence of an external surface magnetic field that was created by a surrounding coil, the local magnetic state through a ferromagnetic core cross-section was ruled by a combination of magnetic domain kinetics and external magnetic field diffusion. Conventional methods to simulate magnetic behavior are based on a separation of magnetic contributions, where microscopic Eddy currents from domain wall motions and macroscopic currents from external magnetic field variations are considered separately. This separation is artificial, because both loss mechanisms occur simultaneously and interact. In this study, an alternative solution was proposed through the resolution of a two-dimensional anomalous fractional magnetic field diffusion. The fractional order constitutes an additional degree of freedom in the simulation scheme, which can be identified by comparison with the experimental results. By adjusting this order, accurate local and global simulation results can be obtained on a broad frequency bandwidth and allow for the precise prediction of the dynamic magnetic behavior of a toroidal massive magnetic core.