3D Modeling of the Magnetization of Superconducting Rectangular-Based Bulks and Tape Stacks

In recent years, numerical models have become popular and powerful tools to investigate the electromagnetic behavior of superconductors. One domain where this advances are most necessary is the 3D modeling of the electromagnetic behavior of superconductors. For this purpose, a benchmark problem consisting of superconducting cube subjected to an AC magnetic field perpendicular to one of its faces has been recently defined and successfully solved. In this work, a situation more relevant for applications is investigated: a superconducting parallelepiped bulk with the magnetic field parallel to two of its faces and making an angle with the other one without and with a further constraint on the possible directions of the current. The latter constraint can be used to model the magnetization of a stack of high-temperature superconductor tapes, which are electrically insulated in one direction. For the present study three different numerical approaches are used: the Minimum Electro-Magnetic Entropy Production (MEMEP) method, the $H$-formulation of Maxwell's equations and the Volume Integral Method (VIM) for 3D eddy currents computation. The results in terms of current density profiles and energy dissipation are compared, and the differences in the two situations of unconstrained and constrained current flow are pointed out. In addition, various technical issues related to the 3D modeling of superconductors are discussed and information about the computational effort required by each model is provided. This works constitutes a concrete result of the collaborative effort taking place within the HTS numerical modeling community and will hopefully serve as a stepping stone for future joint investigations

3D Modelling and Validation of the Optimal Pitch in Commercial CORC Cables

Conductor on a rounded core (CORC\textsuperscript{\textregistered}) cables with current densities beyond 300 A/mm$^{-2}$ at 4.2 K, and a capacity to retain around 90 $\%$ of critical current after bending to a diameter of 3.5 cm, make them a strong candidate for high field power applications and magnets. In this paper, we present a full 3D-FEM model based upon the so-called H-formulation for commercial CORC\textsuperscript{\textregistered} cables manufactured by Advanced Conductor Technologies LLC. The model presented consists of tapes ranging from 1 up to 3 SuperPower 4mm-width tapes in 1 single layer and at multiple pitch angles. By varying the twist pitch, local electromagnetic characteristics such as the current density distribution along the length and width are visualized. Measurements of macroscopical quantities such as AC-losses are disclosed in comparison with available experimental measurements. We particularly focused on the influence of the twist pitch by comparing the efficiency and performance of multiple cables, critically assessing the optimal twist pitch angle.Comment: 9 pages, 3 figures, CEC/ICMC'21 Conference, IOP Conference Series: Materials Science and Engineering, Advances in Cryogenic Engineerin

Cross-field demagnetization of stacks of tapes: 3D modeling and measurements

Abstract: Stacks of superconducting (SC) tapes can trap much higher magnetic fields than conventional magnets. This makes them very promising for motors and generators. However, ripple magnetic fields in these machines present a cross-field component that demagnetizes the stacks. At present, there is no quantitative agreement between measurements and modeling of cross-field demagnetization, mainly due to the need for a 3D model that takes the end effects and real micron-thick SC layer into account. This article presents 3D modeling and measurements of cross-field demagnetization in stacks of up to 5 tapes and initial magnetization modeling of stacks of up to 15 tapes. 3D modeling of the cross-field demagnetization explicitly shows that the critical current density, Jc, in the direction perpendicular to the tape surface does not play a role in cross-field demagnetization. When taking the measured anisotropic magnetic field dependence of Jc into account, 3D calculations agree with measurements with less than a 4% deviation, while the error of 2D modeling is much higher. Then, our 3D numerical methods can realistically predict cross-field demagnetization. Due to the force-free configuration of part of the current density, J, in the stack, better agreement with experiments will probably require measuring the Jc anisotropy for the whole solid angle range, including J parallel to the magnetic field

Computational Modelling of Russia's First 2G-HTS Triaxial Cable

A better understanding of the interaction between three phases is required when developing superconducting cables for high voltage AC systems. With a particular focus on the energy losses of real power transmission cables, in this paper we utilize the so-called H-formulation of Maxwell equations to devise a 2D model for superconducting triaxial cables. The major aim of this model is to comprehend and reproduce the experimental observations reported on the first triaxial prototype cable developed by SuperOx and VNIIKP. The computationally modelled and prototyped cable is made of up to 87 tapes of 4 mm width SuperOx tape arranged across the three phases. Our computational results are compared to the experimental measurements performed by VNIIKP with the electrical contact method, showing a high degree of accuracy over the outer phase of the cable, whilst revealing technical issues with the experimental measurements at the inner phases. Thus, in consultation with VNIIKP it has been concluded that for the actual experimental measurement of the AC losses at the inner phases, and consequently of the overall cable, a sophisticated calorimetric setup must be built. Still our model is capable to provide an independent assessment of the VNIIKP-SuperOx cable design, by investigating the magnetic profiles per phase in the time domain. In this sense, we confirm that the unbalanced arrange of currents and distancing between the phases affirmatively lead to no magnetic leakages, and therefore to an adequate balance of the cabling inductance.Comment: 9 pages, 3 figures, CEC/ICMC'21 Conference, IOP Conference Series: Materials Science and Engineering, Advances in Cryogenic Engineering (Accepted, Ref. M3Po1A-03, 11 January 2022

Maximum reduction of energy losses in multicore MgB2 wires by metastructured soft-ferromagnetic coatings.

When compared with rare-earth coated conductors, magnesium diboride superconducting cables are known to show significant advantages by cost and easy production. However, the inherent difficulty for achieving a significant reduction of their magnetization losses in multifilamentary wires, without degrading the high critical current density that is so characteristic of the monowire, is considered as one of the major drawbacks for their practical use in high power density applications. Being this one of the major markets for superconducting cables, from fundamental principles and computational optimization techniques, in this paper we demonstrate how the embedding of the superconducting filaments into soft-ferromagnetic metastructures can render to their full magnetic decoupling, and therefore, to the maximum reduction of the energy losses that can be achieved without deteriorate the critical current density of the cable. The designed multifilamentary metastructure is made of NbTi coated MgB2 superconducting filaments in a Cu-matrix, serving as a reference for validating our model with actual experimental measurements in monowires and multifilamentary wires. The novelty in our computationally aided multifilamentary wires, is that each one of the filaments is embedded within a thin metastructure made of a soft-ferromagnetic layer and a resistive layer. We have found that for soft-ferromagnetic layers with magnetic permeabilities in the range of μr = 20-100, nearly a full magnetic decoupling between the superconducting filaments can be achieved, leading to efficiencies higher than 92%, and an overall reduction of the AC-losses (including eddy currents at the Cu-matrix) higher than 50%.</p

Impact of the Magneto Angular Dependence of the Critical Current Density in CORC Cables

With the advent of CORC cables as one of themost suitable conductor technologies for the development of ultra high magnetic field applications, the understanding of their physical properties at a local level and how these influence the macroscopically averaged quantities such as the AC losses, is of the utmost importance as their ulterior optimization and further engineering development depends on it. In this sense, within the electromagnetic scenario, in this paper we present a thorough discussion on how the distribution of critical current and critical current density inside the multiple tapes of a CORC cable can be predicted by three-dimensional finite element methods, and how these diverge when most simple scenarios such as a constant Jc equivalent to the self-field critical current condition for straight tapes, or a Jc(B) function like the Kim’s model, are both contrasted with the most realistic Jc(B,θ) function which encompasses the magneto angular dependence of the HTS tapes. Clearly distinctive features have been found between these three approaches, revealing an anisotropic distribution of the critical current density along the helix tapes when the magneto angular dependence is considered, but with equivalent distribution of magnetization currents, and therefore responding equally in terms of the calculated hysteretic losses when the CORC cable is subjected to an applied magnetic field in perpendicular direction to the cable’s former

Hand Pulling Following Mowing and Herbicide Treatments Increases Control of Spotted Knapweed (\u3ci\u3eCentaurea stoebe\u3c/i\u3e)

Extensive areas in the upper Midwest have been invaded by spotted knapweed, and effective management strategies are required to reestablish native plant communities. We examined effects of mowing, mowing plus clopyralid, or mowing plus glyphosate in factorial combination with hand pulling and burning on knapweed abundances on a knapweed-infested site in western Michigan. We applied mowing and herbicide treatments in summer 2008, and seeded all plots with native grasses and forbs in spring 2009. We conducted the knapweed pulling treatment from 2009 to 2012 in July. The prescribed burn was conducted in April 2012. By 2012, hand pulling reduced adult knapweed densities to 0.57 ± 0.12 m−2 (0.053 ± 0.011 ft−2) (mean ± SE), which was 5.8% of nonpulled treatments, juvenile densities to 0.29 ± 0.07 m−2 (2.1% of nonpulled treatments), and seedling densities to 0.07 ± 0.06 m−2 (2.6% of nonpulled treatments). After 3 yr, hand pulling reduced seed bank densities to 68 ± 26 m−2 as compared to 524 ± 254 m−2 in nonpulled treatments and 369 ± 66 m−2 in adjacent untreated areas of the study site. Without hand pulling, effects of mowing or mowing plus glyphosate were short-lived and allowed knapweed to rapidly resurge. In comparison, although a single mowing plus clopyralid treatment maintained significantly reduced densities of knapweed for 4 yr, by 2012 knapweed biomass in the nonpulled clopyralid treatment was approximately 60% of that in the other nonpulled treatments. Burning had minimal impacts on knapweed densities regardless of treatment combination, probably as a result of low fire intensity. Results demonstrated that persistent hand pulling used as a follow-up to single mowing or mowing plus herbicide treatments can be an effective practice for treating isolated spotted knapweed infestations or for removing small numbers of knapweed that survive herbicide applications

Cross-field demagnetization of stacks of tapes: 3D modeling and measurements

Abstract: Stacks of superconducting (SC) tapes can trap much higher magnetic fields than conventional magnets. This makes them very promising for motors and generators. However, ripple magnetic fields in these machines present a cross-field component that demagnetizes the stacks. At present, there is no quantitative agreement between measurements and modeling of cross-field demagnetization, mainly due to the need for a 3D model that takes the end effects and real micron-thick SC layer into account. This article presents 3D modeling and measurements of cross-field demagnetization in stacks of up to 5 tapes and initial magnetization modeling of stacks of up to 15 tapes. 3D modeling of the cross-field demagnetization explicitly shows that the critical current density, Jc, in the direction perpendicular to the tape surface does not play a role in cross-field demagnetization. When taking the measured anisotropic magnetic field dependence of Jc into account, 3D calculations agree with measurements with less than a 4% deviation, while the error of 2D modeling is much higher. Then, our 3D numerical methods can realistically predict cross-field demagnetization. Due to the force-free configuration of part of the current density, J, in the stack, better agreement with experiments will probably require measuring the Jc anisotropy for the whole solid angle range, including J parallel to the magnetic field