# Fileset

[【Confidential】A final manuscript submitted to SuST.docx](https://mdr.nims.go.jp/filesets/d23ade4b-dba6-4952-8069-46605c95f2c0/download)

## Creator

[J Kováč](https://orcid.org/0000-0001-9127-9681), [P Kováč](https://orcid.org/0000-0003-1872-0359), M Búran, T Melišek, K Gažová, [A Kikuchi](https://orcid.org/0000-0002-5044-7156)

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[Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/)

## Other metadata

[DC and AC properties of 49-strand circular cables made of differently sheathed ultrafine MgB<sub>2</sub> superconducting wires](https://mdr.nims.go.jp/datasets/b0646397-c246-49ec-9ca5-d1fd3401dcff)

## Fulltext

(A final manuscript submitted to SuST (Confidential)DC and AC properties of 49-strand circular cables made of differently sheathed ultrafine MgB2 superconducting wiresJ. Kováč1, P. Kováč1*, M. Búran1, T. Melišek1, K. Gažová1 and A. Kikuchi2 1Institute of Electrical Engineering of SAS, 841 04 Bratislava Slovakia 2National Institute for Materials Science (NIMS), Tsukuba, Ibaraki 305-0028, JapanAbstractLow temperature properties of 49-strand circular cables made of ultrafine NIMS MgB2 wires has been studied. Critical currents of cables made from single-core MgB2 wires of diameter 0.050 mm and 0.022 mm and different sheath material (Cu, CuNi and Monel) have been measured at temperatures 4.2 – 35 K and external fields 0 – 8 T. In addition, magnetization AC losses were measured at 20 – 45 K, AC fields 1 – 100 mT and frequencies 72 Hz and 144 Hz. The presented experimental results show high engineering current densities in spite of very low filament size of 8.5 µm and also low AC losses due to well decoupled strands. It has been shown that total AC losses are not only affected by the filament size, but also by used sheath materials. Presented cables can be possibly used for small size windings with low AC losses.  *Corresponding author: Pavol Kováč, pavol.kovac@savba.skKey words: ultrafine MgB2 wires, circular cables, current densities, AC losses1. IntroductionHTS and MgB2 superconductors are well-established for DC applications due to high current densities at temperatures close to 20 K and no generation of heat. However, transitioning to AC applications (e.g. electric motors, transformers or AC power cables) leads to AC losses and heat generation when subjected to alternating currents and fields. Therefore, it is crucial to minimize the dissipative phenomena under AC conditions and to optimize the superconducting wires for such applications. In comparison to REBCO tapes, round MgB2 wires are more promising for AC windings as they can be manufactured with fine filaments and a tight twist pitch. For filamentary MgB2 wires, magnetization loss consists of four possible components: (i) hysteresis loss (Qh) in the superconducting filaments; (ii) coupling loss (Qc) in the resistive matrix due to coupling current circulating across the loops of the superconductor and the normal conductor; (iii) eddy current loss (Qe) induced by the presence of the conductive matrix; and (iv) additional ferromagnetic losses (Qf) arising from the magnetic sheath material. Terao et al have presented AC losses in 5 MW superconducting motor using 52.4 m filamentary MgB2 wire produced by Hyper Tech Research in which the loss ratio Qh/Qc was estimated to ~ 0.22 [1]. Qh and Qc loss components can be effectively reduced by the filament size and by twist pitch, respectively. Filament size bellow 15 m and twist pitch up to 10 mm have been presented for fine-filamentary MgB2 wires of Hyper Tech Research [2] and the minimal filament size of ~ 8.5 m have been reached recently for single-core wires made by NIMS [3]. Eddy current losses Qe can be reduced by more resistive sheath material, but, it also means reduced thermal stability of the composite wire [4]. Similarly, as for low temperature superconducting wires, AC loss reduction can be achieved for HTS and MgB2 conductors by a proper combination of filament size, twisting and by resistive barriers separating filaments [5-7]. Since there is a limit to reduce twist pitch of filamentary MgB2 composite [8], the increase of effective transfer resistivity is needed for further reduction of the eddy current loss. In the case of cables, the transfer resistivity among the individual MgB2 strands can be considerably increased and consequently the contribution of Qc effectively decreased [9-10]. The total AC loss is critical for applications and if the AC losses are too large, the cooling power must be increased and/or system may quench. To date, studies on AC loss in MgB2 wires towards real applications are not sufficient. New experimental and numerical AC loss data for MgB2 wires operating at realistic conditions are needed and interesting for all-superconducting motors [11]. In this work, we have studied in-field critical currents and magnetization AC loss of 49 strands circular cables made by NIMS from ultrafine MgB2 single-core wires with different metallic sheath. 2. Experimental49-strand circular cables were made of ultrafine NIMS MgB2 wires produced by in-situ PIT (Powder-In-Tube) process with pure Nb barrier and three different outer sheaths: OFHC (oxygen-free Cu), Cu10Ni and Monel [3]. The multiple cold wire drawing was performed to 0.05 mm and 0.022 mm. These ultrafine wires were used for the fabrication of 49-strand twisted cables in one step with the transposition length from 6.4 mm to13 mm, see Table 1. All cable samples were finally heat treated at 650 oC/30min in Ar gas atmosphere.Table 1. Description of 49 strands cable samples with different metallic sheaths.  Cable name Sheathmaterial Composition Ltrans.[mm] Dfil.[µm] NIMS1 OFHC  49 x 0.050 mm 8 18.2 NIMS2 Cu10Ni 49 x 0.050 mm 6.4 18.2 NIMS3 Monel 49 x 0.050 mm 8.7 18.2 NIMS4 Monel 49 x 0.022 mm 13 8.50Figure 1. The cross-section of MgB2/Nb/Monel wire of diameter 0.05 mm used for NIMS3 cable.Critical currents (Ic) of MgB2 cables were measured at liquid He temperature and external magnetic field between 2.0 T and 8.0 T using DC transport measurement of short samples (50 mm and 5 mm spacing of voltage taps).  In addition, Ic was of 70 mm long samples and 10 mm spacing of voltage were measured at elevated temperatures 10 – 35 K and external fields 0 – 3 T were also done. All measured samples were contacted by soldering and the criterion of 1 μVcm−1 was used for Ic estimation. Calibration-free method was applied for AC loss measurement and studies of magnetization losses at temperatures between 20 and 45 K, frequencies (72 Hz and 144 Hz) and field magnitudes (1 mT – 0.1 T), which allows to analyse the loss contributions more precisely [12]. Results and discussion2.1.  Current densities of cablesFigure 2(a) shows the critical currents of all cables measured at liquid He temperature. One can see clearly the effect of used outer sheath for cables NIMS1-3. The stronger the metallic sheath the higher is the density of Mg + B powder mixture in as-drawn wire, which has a positive effect on the creation of dense MgB2 phase with improved grain-connectivity. Cable NIMS4 has considerably lower currents due to thinner strands (0.022 mm). But, the comparison of engineering current densities (see Figure 2(b)) shows nearly the identical Je(B) dependences for NIMNS3 and NIMS4, which does not indicate any degradation of current density by wire drawing from 0.05 mm to 0.022 mm and confirms the excellent drawing process. The largest Je = 104Acm-2 is measured at B = 5.5 T for NIMNS3 and NIMS4, which allows possibly to make the coils generating field above 5 T, but around 4 T for NIMS1 with the softest Cu sheath.        Figure 2. Critical currents of four cables at 4.2 K (a) and corresponding engineering current densities (b).Figure 3 compares the critical currents of two cables NIMS2 (Figure 3(a)) and NIMS4 (Figure 3(b)) with different strand’s diameter and the transposition length, see Table 1. As one can see, the engineering current densities at higher temperatures are very similar, see Figure 3(c). While Je values at high temperatures of NIMS2 and NIMS4 are the same (at 24 K and 3 T and at 29 K for 1.5 T), the larger current densities are measured for NIMS2 cable at lower temperatures (10-24 K). It may indicate a slightly worsened grain connectivity for the thinnest MgB2 cores of NIMS4 with averaged diameter < 10 µm. Figure 3 shows also Je(3T) dependence of NIMS3 cable with the best in-field performance at temperatures 12-25 K, which correlates with the largest currents measured for this cable at 4.2 K (see Figure 2) and the best grain connectivity of MgB2 core inside the mechanically strong Monel sheath.    Figure 3. Critical currents of NIMS2 cable (a) and NIMS4 cable (b) at variable temperatures and fields and engineering current densities of three cables NIMS2-4 at variable external fields (c).2.2.  AC lossesGenerally, the total AC losses of MgB2 composite wires and cables are the sum of all dissipative contributions: Q = Qh + Qc + Qe  + Qf. While Qh and Qc (hysteretic and coupling) loss components are measured only below the critical temperature, Qe and Qf (eddy-current and magnetic) are contributing into the total Q(T) of composite wire in the whole range of measured temperatures. Mentioned above loss components are affected by the frequency, temperature and applied external field differently. In addition, they could be affected also by the penetration of external magnetic field into MgB2 filaments due to shielding effects [5]. Figure 4 shows the total AC losses of four cable samples measured at temperatures 20 - 45 K, two frequencies 72 Hz and 144 Hz and the constant external field of 100 mT. As one can see, quite similar Q(T) dependences are measured for NIMS1 and NIMS2, see Figure 4(a).       Figure 4. Magnetization AC losses of cables NIMS1-3 versus temperature at the constant magnetic field of 100 mT and two frequencies 72 and 144 Hz (a) and comparison of Q(T) of NIMS 3 with NIMS4 (b).Slightly larger losses of NIMS1 at temperatures T < 28 K can be due to some contribution of eddy currents in well conductive OFHC copper sheath in comparison to more resistive Cu10Ni of NIMS2. The loss maximum at T  28 K corresponds to dominating hysteretic loss component Qh, which is decreasing with lowered temperature due to increased current density in MgB2 cores and subsequent expulsion of magnetic field from its volume. The effect of doubled frequency is apparent and the total loss at 20 K is increased by  33 % for non-magnetic sheath and by  29 % for magnetic one, see arrow in Figure 4(a). Hysteretic loss per cycle is independent on frequency, but, the eddy current and coupling loss per cycle are linearly dependent on frequency [5]. In the case of NIMS3, only small loss maximum of hysteretic loss and nearly constant losses for lowered temperature (< 30 K) are visible due to magnetic shielding of MgB2 cores, which correlates well with our previous studies performed on MgB2 wire with Monel sheath [12]. Non-zero losses above the critical temperature (Tc  36.2 K) measured for all cables correspond to eddy current and magnetic loss components inside the used metallic sheaths. Figure 4(b) compares Q(T) dependences of NIMS3 and NIMS4 with Monel sheath differing only by used wire’s size (0.050 mm and 0.022 mm) and by transposition length (8.7 mm and 13 mm), see Table 1. It is apparent that Q(T) of these two cables have similar shape and the same effect of frequency, but, the total loss is reduced considerably (by ~50 %) for the smaller MgB2 core size of NIMS4. AC losses measured above the critical temperature (Qe + Qf) are also measurable for both cables, but, the reduced wire size is responsible for the lowest losses generated in metallic components of NIMS4 cable.    Figure 5. Comparison of Q(T) at low magnetic field of 13 mT and frequency 144 Hz (a) and corresponding Q(B) dependences at 20 K (b).Figure 5(a) shows the total AC losses of all cable samples at low external field 13 mT and frequency 144 Hz. As one can see, the loss maximum at T  34 K corresponding to maximal contribution of Qh is totally missing for NIMS3 and NIMS4 due to full magnetic shielding of MgB2 cores in low external field by the Monel sheath [12]. Figure 5(b) shows the same log-log Q(B) characteristics proportional to B2 for NIMS1-3, but half in magnitude for NIMS4 with thinnest strands. Q(B)  B2 in the whole range of field confirms the dominating contribution of Qc, Qe and Qf loss components.     Figure 6. Comparison of Q(T) (a) and Q(B) (b) for NIMS2 cable (see red circles) and 54 filament Hyper Tech wire (see blue stars).   Figure 6 compares Q(T) and Q(B) of 49 strands NIMS2 cable of diameter 0.41 mm with 54 filaments Hyper Tech wire of 0.39 mm (Hy Tech 54f), which have comparable filament sizes of 18.2 µm and 22 µm, respectively. In addition, these conductors have the same content of MgB2 phase, which is 15% [11]. Figure 6(a) shows that total AC losses of NIMS2 cable are lower than for Hyper Tech wire bellow the critical temperature, but, losses in metallic elements (above 37 K) are in the opposite ratio. While the ratio of Qmax/Q40K = 3 is obtained for Hy Tech 54f, it is only 1.2 for NIMS2 cable. The effect of increased frequency on the total loss at 20 K is also different: increased by  33 % for NIMS2 and by  22 % for Hy Tech 54f, which can be ascribed by lower losses generated in the metallic components of filamentary wire. The position of Qmax is observed at 33 K for Hy Tech 54f, but for 28 K in NIMS2, which indicates different critical temperatures (Tc) and current densities (Jc) of these wires. Tc = 36.2 K was measured for 0.05 mm NIMS wire [3]. Figure 6(b) shows Q(B) at 20 K and 72 Hz proportional to B2 for Hy Tech 54f wire as also for NIMS2 cable with the total loss lowered by 60 %. Because of direct effect current density on AC loss, the engineering current densities (Je) measured at 4.2 K and 20 K for compared above conductors are shown by Figure 7.Figure 7. Comparison of in-field engineering current densities of NIMS2 (circle-points) and Hy Tech 54f (star-points) at 4.2 K and 20 K.  Engineering current density (Je) of Hy Tech 54f wire is estimated as the ratio of its critical current (Ic) to the area of wire 0.39 mm in diameter and Je of NIMS2 is calculated as Ic/area for 49 wires of 0.05 mm (see empty circles).  While Je of Hy Tech 54f are lower than that of NIMS2 at 4.2 K, differences in Je(B) are smaller at 20 K. As one can see, there is even the cross-over of Je(20K) at ~1.25 T, and bellow this field the current density of Hy Tech 54f wire is larger and increasing more rapidly. Consequently, the larger current densities at fields applied for AC measurements (0.01 - 0.1 T) have increased AC losses of Hy Tech 54f at 20 K (see Figure 6). ConclusionsCritical currents and AC losses of circular cables made from single-core MgB2 wires of diameter 0.050 mm and 0.022 mm and different sheath material have been measured. Engineering current density of presented cables Je =104 Acm-2 measured at 4.2 K and external field  5.5 T confirms the excellent deforming process applied for thin wires of diameters 0.05 mm and 0.022 mm with not reduced current density. AC losses of present cables are affected by the used metallic sheaths due to different conductivities and magnetic properties. Especially the shielding by magnetic Monel affects the measured temperature dependences of AC loss. Comparison of AC losses in circular cable with losses of filamentary MgB2 wire has shown that cabling of thin single-core MgB2 wires with low filament size is effective way for reduction of coupling current losses. AcknowledgementThis work was supported by the Collaborative Research Agreement between NIMS and IEE of SAS and by the Slovak Scientific Agency under VEGA-2/0017/22. References[1] Terao Y, Seta A, Ohsaki H, Oyori H and Morioka N 2019 Lightweight design of fully superconducting motors for electrical aircraft propulsion systems, IEEE Trans. Appl. Supercond. 29 5202305 [2] Kováč J, Kováč P, Rindfleisch M and Tomsic M 2023 Magnetization AC losses of MgB2 wires with thin filaments and resistive sheath, Supercond. Sci. Technol. 36 095009 [3] Kikuchi A, Iijima Y, Kumakura H, Yamamoto M, Kawano M and Otsubo M 2024 Development of the Ultrafine MgB2 Superconducting Wires and Flexible Cables, IEEE Trans. Appl. Supercond. 34 6200104[4] Búran M, Kováč P, Kopera L and Hušek I 2023 Thermal stability of 6-filament MgB2 wire with resistive CuNi sheath cooled by liquid He and water ice, Cryogeneics 133 103694 [5] Wilson M N, Superconducting magnets, 1 ed, New York: Oxford University Press 1983[6] Banno N, Amemiya N, 1999 IEEE trans. Appl. Supercond. 9 2561-2564 [7] Kwasnitza K, Clerc S, Flükiger R, Huang Y 1999 Cryogenics 39 829-841[8] Kováč P, Hušek I, Kopera L and Melišek T 2011 Filamentary MgB2 wires twisted before and after heat treatment, Sup. Sci. and Technology 24 115006[9] Kováč P, Kopera L, Melišek T, Hain M, Kováč J, Kulich M and Hušek I 2018 Rutherford cable made of IMD MgB2 wires sheathed with Al-Al2O3 particulate metal matrix composite, Sup Sci and Technology 31 015015[10] Kováč J, Kulich M, Kopera L and Kováč P 2018 AC losses of Rutherford MgB2 cables made by PIT and IMD process, Sup Sci and Technology 31 125014 [11] Qiao Y,  Ainslie M, Sun Y, Badcock R. A,  Strickland N. M and Jiang Z 2025, 3D numerical simulation of magnetization loss in multifilamentary MgB2 wires at 20 K, Supercond. Sci. Technol. 38 015024[12] Kováč J, Šouc J, Kováč P and Hušek I 2015 AC losses of single-core MgB2 wires with different metallic sheaths Physica C 519 95-992image2.tiffimage3.tiffimage4.tiffimage5.tiffimage6.emf8 10 12 14 16 18 20 22 24 26 28 30 32 34103104105B = 0.5 TB = 3.0 T  engineering current density [Acm-2]temperature [K] NIMS3 NIMS2 NIMS4B = 1.5 T(c)oleObject1.binimage7.tiffimage8.tiffimage9.tiffimage10.tiffimage11.tiffimage12.tiffimage13.tifimage1.jpg