Electric Field and Energy Losses of Rounded Superconducting / Ferromagnetic Heterostructures at Self-Field Conditions

The ac losses induced by an alternating transport current in type-II superconductors is a well-known phenomenon, which still attracts much attention because of its intrinsic relevance for the proper development of practical applications. In the case of single core superconducting cables of cylindrical cross-section, it is possible to find exact analytical solutions at self field conditions, and it has been believed for nearly two decades that the use of an ideal soft ferromagnetic sheath with negligible magnetization losses will not affect the electromagnetic properties of the superconducting wire, and on the contrary due to the shielding magnetic properties of the ferromagnet, the total ac losses of the SC wire have to be reduced or as maximum they must be equal to the one for the bare superconductor at self-field conditions, what contraries the experimental evidences that show a non-negligible increase on the ac losses. In this paper, we explain the physical nature of this mysterious increase in the ac losses for rounded superconducting/ferromagnetic heterostrutures, which for the sake of generality, has been solved within the critical state theory, and a magnetic multipolar expansion that enables the direct coupling of the magnetostatic properties of the superconductor and an ideal soft ferromagnet. A significant increase in the transient electric field during excitation period has been observed, which might have utter implications on the adequate selection of insulation materials for superconducting/ferromagnetic heterostructures.