The relevance of the self-field for the ‘peak effect’ in the transportJ_c(H) of iron-sheathed MgB₂wires

Abstract

A ferromagnetic sheath around a superconducting wire results in an unusual transport J c (H). For the field perpendicular to the current, there is a plateau in J c (H) at high temperatures and intermediate fields. This plateau develops into a peak at lower temperatures-resembling a 'peak effect'. A model based on cancellation of the self-field of the current and the external field within the iron sheath was proposed for the explanation of the plateau in J c (H). We test this model in three key experiments. Firstly, we show that the form of J c (H) for round MgB 2 /Fe wires is strongly temperature dependent. This is in contradiction with the model, because the properties of the iron sheath do not change in the measured temperature range. However, the temperature dependence of J c might still account for the change of J c (H). Secondly, the model requires a substantial component of the self-field to be parallel to the external field. Our measurements of J c (H) for a field parallel to the current show a peak in J c (H) at high temperatures and a pronounced plateau at low temperatures. The model cannot explain this because the self-field and external field are perpendicular in this experiment. Thirdly, the iron sheath was made thinner on one side of the wire, which should produce an asymmetry in J c (H) in the model for two different orientations of the external field. Such asymmetry was not observed. These experiments show that the effect of the self-field is of much lower importance than an as yet unknown effect that results in the observed plateau and peak in J c (H). Such an effect is likely to be based on a specific interaction between the superconductor and ferromagnet, perhaps similar to the overcritical state effect.

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.…”

“…Moreover, an intriguing and yet unexplained modification of the magnetic flux distribution within the SC core of Iron sheathed MgB 2 monocore wires has been experimentally observed by Magneto Optical Imaging techniques, which from the indirect calculation of the critical current density by magnetization measurements [39][40][41] , it was initially thought that the local deformation in the magnetic flux was caused by the occurrence of the somehow exotic overcritical current densities at the flux-free regions, similar to the concept of overcritical currents originally introduced for infinitely thin strips in the proximity of a SFM 24 , i.e, where apparently the SC can develop regions where without introducing additional pinning centres, the critical state Bean's law, J ≤ J c0 , with J c0 the critical current density at self-field conditions, is violated without destroying the SC state. Nevertheless, although it is true that the shielding properties of the SFM can enhance the critical current density of MgB 2 -Fe wires 42 , as MgB 2 is known to show a magnetic field dependence of the critical current density J c (H) that for perpendicular magnetic fields decreases as H increases 19 , these overcritical current densities have not been directly observed by magneto optical imaging methods 41,43,44 , neither by direct transport critical current density measurements 18 , precluding therefore their existence (at least) in this geometry. However, certain amount of magnetic field is observed in regions where no transport current is expected to flow under the critical state regime for bare SC at self-field conditions and also, a significant rise and drop of the local magnetic field within the SC core near the surface of the SFM sheath has been observed 41 , both being aspects that are intuitively in disagreement with the critical state theory and which have been remarkably challenging to convey within this qualitative framework, this despite the largely recognized success that from fundamental physical principles the critical state theory has reached for all known type-II superconductors 45,46 .…”

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] . Nevertheless, the influence of the physical coupling between the macroscopic electromagnetic properties of the SC and the SFM onto the hysteresis losses of these heterostructures is yet to be understood.…”

“…Nevertheless, although it is true that the shielding properties of the SFM can enhance the critical current density of MgB 2 -Fe wires 42 , as the MgB 2 is known to show a magnetic field dependence on the critical current density 19 , J c (H), these overcritical current densities have not been observed neither by MO techniques 41,43,44 nor by the direct measurement of J c0 by electric transport Pictorial representation of the analysed Superconducting (SC) -Soft-Ferromagnetic (SFM) metastructure. The main plot shows the distribution of current density, J, in the SC under self-field conditions for an applied transport current Itr = Ic sin (ωt), with ωt = π/4 (red shadowed area), and the relative coordinates for a finite-element Ji(ri, φi) as reference for Eqs.…”

“…The aforementioned problems have been somehow ignored, not only due to the engineering prospects of reducing the AC losses in multifilamentary superconductors by the magnetic screening effect of the SFM coatings, another problem that is still to be solved 19,[47][48][49][50][51][52] , but more importantly, it due to the intrinsic difficulty added by the uncertainty on the physical mechanism that couples the electromagnetic properties of SCs and SFMs at a local level (i.e., inside both materials but within a macroscopical approach). Even in the most ideal of the cases, a perfectly cylindrical type-II SC wire of infinite length obeying the general CST 45 , i.e., a case where a fully analytic solution for the time dynamics of the flux-front profiles exists 53 , it results apparently impossible to determine the cause of the increment in the AC-losses for a SC embedded within a closed SFM sheath.…”