Magnetization Profiles of AC Type-II Superconducting Wires Exposed to DC Magnetic Fields

Abstract

The macroscopic electromagnetic behaviour of a type-II superconducting wire for alternating current power transmission under constant magnetic field conditions is captured by the numerical solution of the Maxwell equations under the framework of the critical state principle and the so-called integral formulation, also known as J-formulation. Time-dependent distributions for the flux front profiles of local current density, magnetic flux, and cycles of magnetic moment are presented. We have found that, regardless of the intensity of the applied magnetic field, the first cycle of Itr(t) defines the period of magnetic stabilization of the SC wire where two plateaus with constant magnetic moment can be measured. Then, a cyclic monotonic behaviour with well-defined flux-front boundaries has been identified, with clear signatures of current-like and field-like flux front profiles. This observation has allowed us to establish semi-analytical approaches of flux-tracking for the local dynamics of current density of AC SC wires immersed in a constant transverse magnetic field, from which all the macroscopical electromagnetic quantities of interest such as the magnetic field, magnetic moment, and power density of energy losses can be calculated. The observations reported for a rounded SC wire, define an adequate benchmark for the implementation of flux-tracking approaches in other 2D symmetries, such as SC strips, where the flux-front profile for isolated excitations can be formulated by exact geometrical expressions.

Flux front dynamics and energy losses of magnetically anisotropic 2G-HTS pancake coils under prospective winding deformations

“…As previously mentioned, although the numerical computing time for our models could be strongly reduced by simplifying the number of elements inside of each one of the superconducting domains (or HTS coil turns), by allowing a 1D strip symmetry for each one of the HTS layers, therefore eliminating the aspect-ratio problem, this comes under the expense that the physical nature of the local profiles of current density could not be observed within this approach. However, it is well know that the electromagnetic properties of type-II superconductors such as the ReBCO materials used for the manufacturing of 2G-HTS tapes are, strongly affected by the intensity and direction of externally applied magnetic fields [19,31,32], which can diminish the intensity of the critical current density, J c (B, θ) [20], or lead to rather complicated distributions of current density profiles inside the superconducting material [14,[33][34][35][36]. In fact, in order to understand the physical nature and time dependence of the local profiles of current density, which determine the overall electromagnetic properties of the coil, it is necessary to model each one of the HTS layer as a 2D system with a minimum of 2 sub-layers across their thickness, such that opposite magnetization currents can appear within each one of the HTS domains.…”

“…denotes a full cycle of the time-varying electromagnetic sources after the magnetic relaxation period, i.e., after the first half cycle of the applied transport current in absence of an external magnetic field. Otherwise, if the situation considers an applied magnetic field which change of direction along the cycle, the magnetic relaxation period can take several cycles to accommodate the local consumption of magnetization currents, by the concomitant action of the transport current in cross-field and rotating field configurations [14,33,34,41]. However, although the pancake coils studied in this paper are subjected only to an AC transport current, therefore reducing the number of cycles needed for the overall calculation of the AC-losses, the critical aspect behind Eq.…”

“…Within these kind of studies, one of the most determining factors which needs to be considered when fostering a superconducting application is the actual estimation of its AC losses, as it utterly defines the optimal design, performance, and cost assessment of a superconducting machine [12]. However, it is well-known that the type-II superconducting materials used for the fabrication of 2G-HTS tapes are extremely prone to be affected by external and induced changes in the electromagnetic excitations, what results in very complex local distributions of current density and flux front profiles, both being the physical source of the hysteresis losses [13,14]. In fact, in the case of a superconducting coil, each one of its turns which carries a certain amount of current, then affects the electromagnetic performance of the other turns by magnetic induction where not only profiles of transport current must appear, but also local profiles with magnetization currents.…”

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

“…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 ].…”

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

“…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.…”