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

Improving our understanding of the physical coupling between type-II superconductors (SC) and soft ferromagnetic materials (SFM) is the root for progressing to the application of SC-SFM metastructures in scenarios such as magnetic cloaking, magnetic shielding, and power transmission systems. However, in the latter, some intriguing and yet unexplained phenomena occurred, such as a noticeable rise in the SC energy losses, and a local but not isotropic deformation of its magnetic flux density. These phenomena, which are in apparent contradiction with the most fundamental theory of electromagnetism for superconductivity, that is, the critical state theory (CST), have remained unexplained for about 20 years, given the acceptance of the controversial and yet paradigmatic existence of the so-called overcritical current densities. Therefore, aiming to resolve these long-standing problems, we extended the CST by incorporating a semi-analytical model for cylindrical monocore SC-SFM heterostructures, setting the standards for its validation with a variational approach of multipole functionals for the magnetic coupling between Sc and SFM materials. It is accompanied by a comprehensive numerical study for SFM sheaths of arbitrary dimensions and magnetic relative permeabilities μr, ranging from μr=5 (NiZn ferrites) to μr = 350,000 (pure Iron), showing how the AC-losses of the SC-SFM metastructure radically changes as a function of the SC and the SFM radius for μr≥100. Our numerical technique and simulations also revealed a good qualitative agreement with the magneto optical imaging observations that were questioning the CST validness, proving therefore that the reported phenomena for self-field SC-SFM heterostructures can be understood without including the ansatz of overcritical currents.

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

Understanding the physical coupling between the macroscopic electromagnetic properties of type II superconductors (SC) and soft ferromagnetic materials (SFM), is root for progressing onto the application of SC-SFM metastructures in scenarios such as magnetic cloaking, magnetic shielding, and loss free current transmission systems. However, in the latter case understanding the origin of the rise in the hysteresis losses of the superconductor by effect of the coupling with the SFM has historically resulted in a notable challenge, it because this rise in the AC losses is simply counterintuitive due to the fact that the SFM itself does not add magnetization losses to the system and furthermore, there is no evidence of electrical current sharing between these two materials. Thus, aimed to resolve this long-standing problem, in this paper, we present a semi-analytical model for monocore SC-SFM heterostructures of cylindrical cross-section and self-field conditions, showing the first known map of AC-losses for SC-SFM magnetically shielded wires, with magnetic relative permeabilities for the SFM ranging from mur=5 (NiZn ferrites) to mur =350000 (pure Iron). The distribution of current density and magnetic field inside the SC-SFM metastructure is shown in great detail, revealing a remarkable agreement with the intriguing magneto optical imaging observations that were originally questioning the validness of the critical state theory. In this sense, we have extended the critical state theory within its variational formalism, incorporating a multipole functional approach which allows the direct finding of the coupling terms between a SC current and a SFM sheath, proving that all reported phenomena for the self-filed hysteretic behavior of SC-SFM heterostructures can be understood within the classical critical state model without the need to recur to the ansatz of overcritical currents.