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

Abstract

The AC losses induced by an alternating transport current in type-II superconductors is a well known phenomena which still attracts much attention due to its intrinsic relevance for the proper development of practical applications. In the case of single core superconducting cables of cylindrical crosssection, 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 on the AC losses for rounded superconducting/ferromagnetic heterostructures, which for the sake of generality, it has been solved within the critical state theory and, a magnetic multipolar expansion which enables the direct coupling of the magnetostatic properties of the superconductor and an ideal soft ferromagnet. A significant increase on the transient electric field during the excitation period has been observed, which might have utter implications on the adequate choosing of insulation materials for superconducting/ferromagnetic heterostructures.

Critical State Theory for the Magnetic Coupling between Soft Ferromagnetic Materials and Type-II Superconductors

“…Due to the novel phenomena and applications that can be envisaged by the use of metamaterials, in recent years the developing of superconducting-ferromagnetic metastructures has been the object of considerable attention [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 ]. Particular focus has been played onto the magnetization and demagnetization properties of type-II superconductors (SC) surrounded or in the near proximity of a soft ferromagnetic material (SFM) [ 11 , 12 ], the study of magnetic cloaking heterostructures [ 4 , 5 , 6 , 7 , 8 ], and their magnetic shielding properties [ 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 ].…”

“…However, it is precisely for this geometry where a certain amount of magnetic field has been observed in regions where no transport current is expected to flow, at least under the classical conception of the CST regime for a bare SC at self-field conditions. A significant rise and drop of the local magnetic field within the SC core near the surface of the SFM sheath has also been observed [ 41 ], both of these features being in apparent disagreement with the CST, despite its largely recognized success for all known type-II superconductors [ 10 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 ].…”

“…Therefore, inspired by the pioneering research on circular magnets for high-energy particle accelerators at CERN [ 67 , 68 , 69 , 70 ] and the general CST by Badía, López and Ruiz [ 45 ], in this paper we included a multipole expansion in the integral formulation of the CST for type-II SC rounded wires [ 10 , 46 , 47 , 48 , 49 , 50 , 51 , 52 ], allowing a direct inclusion of the magnetostatic coupling between the SC and a rounded SFM sheath ( Section 2 ). In this way, we disclose the electromagnetic behavior of the current density and magnetic field resulting from the coupling of the SC and the SFM in Section 3 , explaining with semi-analytical and numerical methods the actual causes behind the increment of the AC losses in an SC-SFM cylindrical metastructure in Section 4 .…”

Why energy lossless ferromagnetic materials can add energy losses onto type-II superconductors?

“…Due to the novel phenomena and applications that can be envisaged by the use or devising of metamaterials, the developing of Superconducting-Ferromagnetic heterostructures have been the focus of considerable attention in recent years. [1][2][3][4][5][6][7][8][9][10][11] Particular focus has been played to the role of magnetization and demagnetization properties of these kind of systems 11,12 , as well to the study of their magnetic cloaking features [4][5][6][7][8] , and the shielding properties of type II superconductors (SC) surrounded or in the near proximity of a soft ferromagnetic material (SFM) [13][14][15][16][17][18][19][20][21][22] . However, the influence of the physical coupling between the macroscopic electromagnetic properties of these materials on the overall hysteresis losses of SC/SFM heterostructures for AC applications is yet to be understood.…”

“…al. 10,[55][56][57][58][59][60][61] , in this paper we extend the integral formulation of the critical state theory introduced in Ref. 45, by including a multipole fields expansion which enables the straightforward inclusion of the magnetostatic coupling between a SC and a rounded SFM sheath (Sec.…”