Electrical and mechanical limits of ex situ MgB2 wires for cabling

One of the objectives of the SCARLET project is to develop and industrially manufacture superconducting MgB2 cables cooled by liquid hydrogen. The ex situ powder-in-tube MgB2 wires manufactured by ASG are considered for the cable design that can carry DC current of 20 kA. These braided superconducting wires, containing brittle filaments, require high current. Thus, the study of the electro-mechanical properties of MgB2 wires is crucial for the cable design and its functional use. Superconducting wires have to withstand all the stresses applied during the cabling process, installation, and operations at the temperature of around 20 K. Hence, several configurations of MgB2/Ni/Monel composite wires have been subjected to detailed electrical and mechanical characterizations, which allow the estimation of the stress limits during the manufacturing of the designed cable. These experiments demonstrated that the maximal tensile stress applied to the wire at room temperature should be below 180–200 MPa, and safety bending observed for the outer filament strains was below 0.3%–0.35%. It is also revealed that the limit of acceptable torsion (expressed by the twist pitch to wire diameter L t/d w) is affected by the filament architecture and wire diameter. This limit should be above 100 for 1 mm wire and above 150 for 1.53 mm wire.


Introduction
MgB 2 tapes and wires have been developed by using the ex situ powder-in-tube (PIT) process [1] and are commercially available in kilometers of lengths since 2003 by Columbus Superconductors (now ASG).Such wires were already used for manufacturing low and high voltage power cables [2][3][4].MgB 2 wires are foreseen to be a key and low-cost technology for sustainable electrical grids, thus offering an attractive solution for the extremely high direct current distribution.Long aging of these wires in LH 2 or cold gas H 2 Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. has also been already performed and it did not show any degradation of the superconducting properties of the material [2].Since superconductors require cryogenic temperatures, thus, to ensure material reliability, good thermal stability must be assured.This includes better management of the energy dissipation by the present thermal properties of all the used materials in both the superconducting state and the cases of faults.A superconducting wire carries a high current compared to normal conductors and must support energy disturbances when a fault occurs, which may cause the transition of the superconductor to the normal state (quench) [5].If this transition is not well managed, it may result in an irreversible damage to the superconductor.Therefore, the superconducting wire must be designed with appropriate cryogenic stabilization to prevent failure under normal operating conditions.To improve the thermal stability of superconducting wires, most applications also require the use of a stabilizer, which is, generally, a layer or matrix of metals with high thermal and electrical conductivities, such as Cu or Ag, in proximity to the superconductor [6].The ex situ PIT wires contain brittle MgB 2 filaments; therefore, their handling is limited.Considering the multiple steps during cabling, and subsequent ones (spooling/unspooling/handling), the stresses and strains applied on the MgB 2 strands shall be below the irreversible limits; for example, the minimum bending radius that the wire can withstand without the degradation of its superconducting performance [7,8].Due to the high temperatures applied at the final annealing and softened metallic sheaths, ex situ PIT MgB 2 wires have lower irreversible limits than in situ ones [9,10].The idea of MgB 2 cables cooled by liquid hydrogen was first presented by Trevisani et al [11].For an optimized cable design, the MgB 2 wire should present the highest possible critical current I c in the stable regime at low magnetic fields (0.5-0.8 T) and temperatures around 20 K, which allow to minimize the number of superconducting strands.A small diameter wire (1-1.5 mm) is also desired to allow for a reduced cable size.The aim of the SCARLET project [12] is to develop and industrially manufacture a superconducting cable cooled by liquid H 2 .An efficient and safe solution for the distribution of hydrogen is to deliver it in its high-density liquid phase at 20-25 K (−250 • C) under low pressure (<20 bar).In addition, liquid hydrogen is a cryogen with a very high cooling capacity of 446 kJ kg −1 compared to liquid helium with only 20.3 kJ kg −1 [2].Inserting a superconducting cable in the LH 2 pipeline network offers a unique way to benefit from an existing cryogenic pipe network and simultaneously distribute electricity and hydrogen.
The aim of this work is to analyze the electrical and mechanical characteristics of ex situ MgB 2 /Ni/Monel wires.We also show that the estimated limits of tension, bending and torsion stress should be considered for the cable design.

Selected MgB 2 wires
Three MgB 2 wires with 6 or 36 filaments embedded in an Ni matrix and an outer Monel sheath manufactured by ASG superconductors [13,14] have been selected for electrical and mechanical characterizations.These wires are briefly described in table 1, and their corresponding cross-sections are shown in figure 1.The main differences are in the fill factor (17% or 26%) and wire diameter (1.0-1.53 mm).Each filament is surrounded by Ni.Due to no diffusion barrier, a reactive interface layer of thickness of around 5 µm is created during the final heat treatment, which corresponds to 4.8% of the total area for the wire W36-1.0 and 2% for W6-1.5.

Electrical and mechanical measurements
The R(T) characteristics of the wires were measured using a standard four-probe method in a temperature range of 25-300 K at the constant DC current magnitude of 100 mA and with voltage taps separated by 20 mm.
Transport critical current (I c ) measurements were performed for short straight wire samples of 50-70 mm with a  criterion of 1 µV cm −1 at liquid He temperature and external magnetic fields of up to 8 T generated by a split-coil superconducting magnet.The current leads were soldered at 5 mm from the end of each wire, and the voltage taps were located at the center of the sample, separated from each other by 5 mm.Critical currents at higher temperatures, 10-36 K, were measured for wire samples inside the sub-cooled water ice [15].The I-V curves, far above the critical current criterion, were acquired at a constant current ramping of 0.43 As −1 up to the quenched current value (I q ), at which the current is fully expelled from MgB 2 filaments into the metallic sheath.
A simple torsion test equipment, with variable twist pitch (L t ), has been used for short samples (≈70 mm) that are cut from the wires W36-1.0 and W6-1.5.This system is based on two grips: a rotated grip driven by a stepping motor and a static one fixed against the rotation [16].Critical currents of twisted samples were measured at liquid He temperature and compared with the non-twisted ones.Stress-strain characteristics of selected wires were obtained initially by tension at room temperature.The sample's length between the grips was 50 mm, and the elongation of the sample was measured by using a single Nyilas extensometer [17] with a gauge length of 25 mm.The axial tensile load was then applied up to certain stress/strain limits.The sample was unloaded and mounted on a sample holder for the I c measurement at 4.2 K and an external field (5-8 T) to quantify any irreversible degradation.Critical current degradation due to bending was measured for wires bent to variable diameters at room temperature; consequently, I c measurements were performed at 4.2 K as for tensioned samples [18].

R(T) dependence
Figure 2(a) shows ρ(T) characteristics of the wires W6-1.5 and W36-1.0 measured between 25 K and 300 K with a slightly higher resistivity for W6-1.5 due to a higher content of the MgB 2 phase (26%) and smaller amounts of metallic elements (table 1). Figure 2(b) compares the resistive transitions below 40 K showing the on-set critical temperature T c-on = 39.23 K for both wires and slightly lowered T c-low = 37.65 K and wider transition for W6-1.5 with ∆T c equal to 1.58 K. Lower T c-on = 38.5 K and comparable transitions (∆T c = 1.6-2.1 K) were measured for in situ MgB 2 wires with 114-342 filaments manufactured by Hyper Tech Research, Inc [19].MgB 2 in situ wires with 6-54 filaments, manufactured by Sam Dong, also present a lower critical temperature T c-on = 37 K [20], see the green characteristic in figure 2(b).The higher critical temperatures of ex situ made ASG wires ∼39 K offer a larger temperature window for practical applications.

I-V curves
I-V curves of W36-1.0 measured up to quench currents at external fields of 3-8 T and temperature of 4.2 K are shown in figure 3(a).These measurements allow us to study the behaviors of current redistribution into the multi-filamentary wire up to the quench and/or transition to the normal state at over-current (I > > I c ).Although fluent I-V curves can be measured for lower critical currents (∼1 A) in the range of voltages between 0.1 µV and 0.01 V, resistive tails at voltages between 10 −7 and 10 −5 V and also quenches between 10 −4 and 10 −3 V are observed for higher critical currents (10-200 A).Resistive tails presented by the voltage increase between 10 −7 and 10 −5 V are caused by the current transfer through the short (5 mm) current leads and only 5 cm length of the measured sample.Figure 3(b) shows 7 -cm-long W36-1.0piecesample I-V curves measured at an external field of 2 T and in water-ice-cooled temperatures ranging between 20 K and 30 K, where no resistive tails above 10 −7 V were observed.
Fluent transition of superconducting current from MgB 2 filaments into Ni/Monel sheath is observed up to the critical current value of 10 A. For I c ⩾ 30 A, the current is suddenly expelled as shown in figure 3(b).Although the quenches measured at 4.2 K close to I c = 100 A are followed by an immediate thermal runaway, figure 3(b) shows a stable behavior after the quench and well measurable I-V points on the resistive (dashed) line representing the resistance of metallic sheaths.
To improve the thermal stability of MgB 2 /Ni/Monel wires, a Cu layer of 33 µm was added electro-chemically on the wire's surface.The effect of improved stabilization of W6-1.5 in the field of 6 T, and W36-1.0 in 4.5 T, is shown in figure 4(a),  where I-V curves of both wires with identical critical currents at 4.2 K (before and after Cu addition) are plotted.The fluent current redistribution for wires with Cu layer is apparent in comparison to the sudden quenching observed for non-Cu ones.One can see that the quench and the thermal runaway of non-stabilized W6-1.5 wire occurs at I q /I c ratio of 1.18, while the same occurs at I q /I c = 1.45 for Cu stabilized W6-1.5-Cu without any runaway up to the transport current of 147 A and 6 T. In addition, W6-1.5 wire quenched at the power of only 43.6 mW, whereas the same at 96.9 mW for W6-1.5-Cu, and a stable I-V curve was measured up to the power of 580 mW.Similar relations are observed for W36-1.0-Cumeasured at 4.5 T (figure 4(a)).
Figure 4(b) shows how the I q /I c ratio of W36-1.0 wire at 4.2 K is drastically decreased with increased critical current.I q /I c ∼ 1.1 for I c ∼ 100 A expresses a low thermal stability of MgB 2 /Ni/Monel wires cooled by liquid He.Although the electroplated Cu layer represents only 4.2% of whole W6-1.5-Cuwire area, the I q /I c ratio at I c = 100 A is increased by 23% (see the open-blue-star (non-Cu) and filled red-star point (with Cu) in figure 4(b)).In the case of 19-filament Ni sheathed ASG tape, stabilized by a highly conductive Cu strip of 0.2 × 3 mm 2 taking 28.5% of the whole tape area, a considerably higher I q /I c of 2.64 was measured for I c of 109 A (see the blacksquare point in figure 4(b)) [6].In the case of 6-54 filament stabilized in situ Sam Dong wires by 26%-28.5% of Cu [20], the I q /I c ratio is higher by 43%-100% compared to that of the non-Cu W36-1.0 wire.As shown above, composite superconductors with proper conductive materials offer improved thermal stability, as well as, effective protection against their possible destruction during the quench, which is important for the safety performance of superconducting MgB 2 cables.

Critical currents
The transport critical currents of W36-1.0,W36-1.3, and W6-1.5 measured at 4.2 K are shown in figure 5(a).Due to the different wire diameters and contents of the MgB 2 phase (table 1), I c values of W6-1.5 are larger than both W36-1.0 and W36-1.3.Engineering critical current density J e = 10 4 Acm −2 of W6-1.5 wires is measured at field above 5 T, and only at 4 T for W36-1.0 and W36-1.3, as shown in figure 5(b).In contrast, the J e (B) slope is less steep for W6-1.5 than for W36-1.0 and W36-1.3 (the blue-dashed line in figure 5(b)) due to the different precursor powders used.Figure 5(b) also shows J e (B) of 18 filaments in situ Sam Dong wire with 18.1% of the MgB 2 phase [20], which crosses the current density of W6-1.5 at external field of 5 T and has higher J e above 5 T.
The critical currents of W6-1.5 and W36-1.0 wires at external fields 0-5 T and temperatures 10-37 K are shown in figures 6(a) and (b).Similarly, as observed at 4.2 K, infield I c values of W6-1.5 are larger than for W36-1.0 due to the increased total filament area.Figure 6(c) shows engineering current densities (J e ) of W6-1.5, W36-1.3, and W36-1.0 compared with 18-filament SamDong in situ wire [20].The self-field J e of all three PIT MgB 2 ex situ wires are very similar, with values between 35 and 36 K, but SD18-0.8 wire shows smaller J e for T > 34 K due to its critical temperature lowered by 2 K, see figure 2(b).Consequently, the ex situ wires' performances at increased temperatures would be much safer.
Figure 6(d) presents the comparison of critical currents for the two wires under study at 20 K as measured at ASG and IEE for different sample lengths and cooling conditions.Indeed, ASG measurements are performed on longer wire samples of 30 cm mounted on the Cu sample holder and directly cooled by a cryocooler system, which thermally stabilize the MgB 2 /Ni/Monel composite, thus allowing us to measure higher I c values at low magnetic fields of 1-1.8 T. Much shorter wire samples of only 7 cm length are instead measured at IEE and cooled by water ice medium, resulting in the reduction of thermal stability with respect to the ASG setup, limiting measurements of I c above 120 A. However, as one can see, quite good agreement is observed for I c (B, 20 K) measured by ASG and IEE.The different slope of I c (B) measured by ASG can be ascribed to the more apparent effect of self-field and also to the possible heating of the sample at high currents.Thus, the question arises whether the thermal stability of MgB 2 /Ni/Monel wires braided around the central Cu core will be sufficient at very low fields (0.2-0.5 T) and high currents (∼1000 A) expected for a powerful cable (marked by a dot-dashed square) in figure 6(d).The amplitude of the transport current in the cable should most probably be limited to around 0.75% of the critical one.

Tensile stress effect
Figure 7(a) shows the strain-stress (σ-ε) curves of wires W6-1.5 and W36-1.0 obtained at room temperature.Both wires are characterized by a small elastic part at ε ⩽ 0.05%, plastic one between 0.05% and 0.3%-0.4%,and the apparent flow of metallic materials above the plastic region.
Loading and unloading of W36-1.0 and W6-1.5 wire samples were performed at room temperature at up to various maximal stresses, see figure 7(b).The dashed lines with arrows show the unloading of wire samples to zero stress but not to zero strain, which remains due to some plastic deformation caused by applied tension.Critical currents of variably stressed wires were measured at 4.2 K. Figure 8(a) shows the critical current versus the maximal applied tensile stress, in which the apparent degradation appears above 180 MPa for    1). Figure 8(b) compares the normalized critical current of both wires, which shows some increase of I c before the radical degradation.The I c of wire W36-1.0 is increased by 7% at 200 MPa, it is around 3.9% at 179 MPa for W6-1.6.These small improvements can be explained by a partial compensation of the residual pressure stress acting on the MgB 2 filaments due to the more contact of metallic Ni/Monel sheath.

Torsion stress
Presented wires were also subjected to variable twisting (torsion stress) at room temperatures for which critical currents were measured at 4.2 K similar to the tensioned ones (chapter 3.4).Figure 9(a) shows the plot of critical currents and n-exponents versus the ratio of the twist pitch to the wire diameter (L t /d w ) for W36-1.0 measured at external field of 5 T.
As one can see, a small increase in the critical current is observed for 100 ⩾ L t /d w ⩽ 300 and at the beginning of Although I c improvement by 6.6% was measured for W36-1.0 at L t /d w = 100, no positive effect of partially compensated residual stress is observed for W6-1.5.Furthermore, W6-1.5 is more sensitive to torsion stress due to its filament architecture (figure 1).Usually, MgB 2 wires are twisted prior to the final annealing, and the critical current degradation is observed for L t /d w ⩽ 40 [16].The maximal increase of I c by 20% was measured for heat-treated 30 filament in situ wire at L t /d w = 90, (figure 9(b)), which can be attributed to the stronger GidCop sheath compared to Ni/Monel.Observed differences are explained by the reduction of residual stress in MgB 2 filaments by the applied torsion.It can be concluded that the safety torsion is expressed by L t /d w > 80 for wire W36-1.0 and above 150 for W6-1.5 wire.

Effect of bending
Figure 10 shows how the critical currents of W6-1.5, W36-1.3, and W36-1.0 are affected by bending to variable diameters at room temperature.Although the I c degradation of W36-1.0 is observed for diameters below 175 mm and 200 mm for W36-1.0 and W36-1.3,respectively, small I c decrease is measured for W6-1.5 bent to 300 mm (figure 10(a)).
The strain on the outermost brittle filaments has been obtained by the ratio of the outer filaments from the neutral axis to the radius of bending.The filament distances of the compared wires were estimated from figure 1, and the corresponding critical bending strains of outer filaments are: ε bf = 0.387% for W36-1.0 and W36-1.3, and ε bf < 0.30% for W6-1.5 (figure 10(b)).It is evident that the wire W6-1.5 is more sensitive to the bending strain due to its size and architecture with only six MgB 2 filaments arranged in one ring.

Conclusions
Short samples of ex situ made MgB 2 /Ni/Monel wires produced by ASG have been subjected to electrical and mechanical characterizations.
It was found that the I-V curves of wires with different filament numbers and diameters are affected by the sample length, and also by the cooling conditions.Due to the low conductivity of Ni and Monel sheaths, the thermal stability of these wires is limited, and the measurement of high critical current at low magnetic field is not possible above 150 A. High critical currents (100-1000 A) can be measured for more longer samples (∼30 cm) attached to a massive Cu sample holder cooled by a cryocooler.It is shown that the stability can be improved by Cu electroplating, which also protects the wire damage after quenching.
However, ex situ made ASG wires have higher critical temperatures than the in situ ones, as well as, higher current densities in low external fields and temperatures close to the critical one, which make them more advantageous for safer cable operation.
The tension applied at room temperature has shown the maximal applicable stress below 180-200 MPa.The limit in torsion stress is expressed by the ratio of the twist pitch to the wire diameter L t /d w , and it has to be above 100 for 1 mm wire and above 150 for 1.53 mm wire.
The critical bending is affected by the wire diameter, and also by the filament number.Safety bending was observed above 175 mm for 36 filament wires of 1 mm diameter, and above 300 mm for the 6 filament wires of 1.53 mm diameter.The mentioned limits allow the optimization of the cabling process for the safe manufacture of future cable design.

Data availability statement
The data that support the findings of this study are available upon reasonable request from the authors.

Figure 3 .
Figure 3. I-V curves of W36-1.0 measured up to quench currents between 3 T and 8 T at liquid He temperature (a), I-V of W36-1.0 at 2 T and temperatures 20-30 K (b).

Figure 4 .
Figure 4.The effect of added Cu layers on I-V characteristics of W6-1.5 and W36-1.0(a) and comparison of Iq/Ic ratios versus Ic for wires with Cu layer and also with Cu stabilized 6-54 filament in-situ SamDong wires with [20] (b).

Figure 6 .
Figure 6.In-field critical currents measured between 10 K and 37.5 K for W6-1.5 (a) and for W36-1.0 (b), self-field engineering current densities of W6-1.5, W36-1.3 and W36-1.0 compared with 18 filament in situ wire [20] (c) and the critical currents at 20 K measured for different sample lengths (70 and 300 mm) and cooling mode by ASG and the Institute of Electrical Engineering (IEE) (d).

Figure 7 .
Figure 7. Stress-strain curves of wires W36-1.0 and W6-1.5 obtained at room temperature (a) and selected loading and unloading applied for these wires to variable stresses (b).

Figure 8 .
Figure 8. Critical currents measured for wires W36-1.0 and W6-1.5 subjected to variable tensile stresses at room temperature (a) and normalized Ic of both wires (b).

Figure 9 .
Figure 9. Critical currents of and n-exponents of twisted W36-1.0 wire measured at 5 T (a) and the comparison of normalized critical currents for W6-1.6,W36-1.0 and 30 filament in situ wire twisted after heat treatment [16] (b).

Figure 10 .
Figure 10.Critical currents of compared wires bent to variable diameters at room temperature (a) and normalized critical currents of W36-1.0,W36-1.3 and W6-1.5 versus the outer filaments strain (b).