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

Muhammad U Fareed,Harold S Ruiz

doi:10.3390/ma14206204

Abstract

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 , ranging from (NiZn ferrites) to = 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 . 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.

Highlights

Published: 19 October 2021Due 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]
We have shown that the counterintuitive increment in the alternating current (AC) losses of monocore SC-soft ferromagnetic material (SFM) metastructures, at self-field conditions, can be explained under the conventional framework of the general critical state theory without the need for the ansatz of overcritical currents
The variational formulation of the critical state theory (CST) introduced by Badía, López, and Ruiz [45], has been extended in such way that the corresponding magnetic vector potentials are written within the magnetic multipole approach commonly used for accelerator magnets [67,68,69,70]

Summary

Introduction

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]. 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) SC-SFM metastructures in self-field conditions can be affected by the amplitude of the transport current and the magnitude of the relative magnetic permeability of the SFM, as part of the main conclusions of this study (Section 5)

Multipole Expansion of the CST in Rounded SC-SFM Heterostructures

Findings

Conclusions