1. Introduction
High AC loss occurring in superconducting armature windings could present a significant problem hindering the development of competitive fully superconducting rotating machines. Magnesium diboride (MgB2) wires are a promising candidate for the realization of fully superconducting rotating machines in aircraft applications [1], [2], [3], as they have the potential for low AC loss properties due to their multifilamentary structure. Owing to insufficient experimental and numerical AC loss research on MgB2 wires, estimating AC loss in multifilamentary MgB2 wires thus becomes an urgent task for aircraft applications. As the first step, the dependence of critical current and associated power-law index (n-values) on magnetic fields and operating temperatures of MgB2 wires, Ic (B, T) and n (B, T), needs to be measured, because they will be used as basic input parameters for AC loss simulation.
Over a 20-year period, substantial work has been done on transport critical current and magnetic critical current measurements of mono- and multifilamentary MgB2 wires. These were conducted over a wide range of temperatures and fields [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15]. Transport measurements typically use a standard four-probe direct current method to measure electric field - current (E-I) characteristics while magnetic critical current measurements typically use a magnetometer to infer Ic from magnetization hysteresis loops. The majority of MgB2 wires measured to date were produced using magnetic sheaths (iron/nickel/monel) that increase AC loss and are therefore not preferred in aviation applications [13]. Additionally, transport critical current at low magnetic fields, which are important for AC loss simulation, were often lacking due to heating problems [6], [7], [8], [9], [10], [11], [12]. Therefore, critical current measurements of MgB2 wires with a non-magnetic sheath over a wide range of temperatures and fields are needed, particularly around temperatures of 20 K close to the boiling point of liquid hydrogen which is a suitable cryogen for cooling superconducting MgB2 windings [16].
Hyper Tech Research Inc has developed new range of MgB2 wires with multifilamentary structure, non-magnetic sheaths and small twist pitches, targeting low AC losses for superconducting stators to enable all-superconducting motors and generators for aircraft. In this paper, we measure the transport critical current of three non-magnetic multifilamentary MgB2 wires (MgB2/Nb/CuNi/CuZn), manufactured by Hyper Tech Research Inc, USA. The three MgB2 wires measured here have different sizes: one wire with a 0.70 mm diameter and 25 mm twist pitch, and two wires with a 0.48 mm diameter each and 10 mm and 30 mm twist pitch respectively. Critical current and n-value versus magnetic fields and temperatures were obtained in fields from 0 T to 5.5 T and temperatures ranging from 15 K to 35 K, presenting sufficient data to be useful for AC loss simulation. Based on the detailed analysis of transport measurements, we established an empirical expression of the magnetic field-dependence on critical current density for all fields and temperatures.
2. Experimental method
2.1. MgB2 wires
Transport critical current measurements were performed on three round MgB2 wires. All of the wires consist of 54 filaments of MgB2 superconductor prepared by a continuous tube forming and filling (CTFF) process [10]. Each filament is surrounded by a Nb barrier and CuNi inner sheath and CuZn outer sheath (MgB2/Nb/CuNi/CuZn). Related specifications of three samples were listed in Table 1, Fig. 1 shows the cross-sections of HS1 wire of 0.48 mm diameter and HL1 wire of 0.70 mm diameter. The HS2 wire has a similar cross section to HS1.
Table 1. Three MgB2 wires specifications. |
| HS1 | HS2 | HL1 | |
|---|---|---|---|
| Filaments | 54 | 54 | 54 |
| Average diameter of one filament (μm) | 25 | 25 | 35 |
| Barrier | Nb | Nb | Nb |
| Mono sheath | Cu30Ni | Cu30Ni | Cu10Ni |
| Multi sheath | Cu30Zn | Cu30Zn | Cu30Zn |
| Central fill | Cu30Ni | Cu30Ni | Cu10Ni |
| Powder ratio (%) | 14.9 | 14.9 | 13.8 |
| Diameter (mm) | 0.48 | 0.48 | 0.70 |
| Twist pitch (mm) | 10 | 30 | 25 |
Fig. 1. SEM image of 54-filament HS1 wire and HL1 wire. |
2.2. Ic measurements
The transport critical current measurements were carried out in a SuperCurrent Ic Measurement System that can provide magnetic fields, B, of up to 8 T and transport current I up to 1200 A in a cryostat cooled by flowing helium gas [17]. To obtain and control the required temperatures, the gas temperature was controlled and a heater was also directly attached to the sample holder. Measurements were thus performed in a variable-temperature range between 15-35 K. The DC transport current here was controlled in a ramp-and-hold sequence with 0.2 A steps and 40 ms step time for all measurements. The rapid sequence limits Joule heating in the sample mount. The critical currents here were determined via E-I curves.
A temperature rise under high current tests can occur at the current contacts where the current must be transferred through the resistive sheath. The heat generated can trigger a quench effect initiated at the ends of the sample but propagating into the measurement zone between voltage taps [6], [15]. This is a widely reported problem, especially for gas-cooled measurements. To reduce the heating issue, we devised a sample mounting method, as shown in Fig. 2(a). The round MgB2 wire was soldered into two copper lugs with a 0.80 mm diameter hole for minimizing the possibility of temperature rise arising from current transfer. Then a piece of flat stainless steel (SS) was soldered to the copper lugs as well as the round MgB2 wire, to improve the mechanical strength. A piece of copper (Cu) was attached to the MgB2 wire for temperature sensor contact. In all Ic tests, 60 mm long samples of each MgB2 wire were used for measurement, as shown in Fig. 2(b). Two pairs of voltage taps were soldered to the sample in the middle with 5 mm distance. Fig. 2(c) gives the prepared sample mounted on the sample holder. With this sample mounting method, the heating issue was significantly reduced, but could not be eliminated completely considering the dimensions of the sample holder. Reliable measurements of Ic were therefore limited to around 350 A for the small wires and 150 A to 200 A for the large wire. Similar limits were reproduced after testing multiple samples of each wire. The lower current limitation for the large wire may be due to its thicker sheath.
Fig. 2. Sample mounting of transport measurement of MgB2 wires, (a) schematic of sample preparation, (b) sample preparation (inverted), (c) prepared sample mounted on sample holder. |
3. Results and discussion
3.1. Ic(B, T) and n(B, T) of three samples
Fig. 3(a)-(c) show the transport Ic(B, T) results of the three MgB2 wires at temperatures from 15 K to 35 K. For the HS1 wire with a 10 mm twist pitch, presented in Fig. 3(a), Ic could be up to 318 A at 15 K and 0 T. No Ic degradation was observed even following the highest-current tests, and this sample had consistent Ic value at all temperatures in all repeated measurements. For the HS2 wire with 30 mm twist pitch, the data was almost complete with only the critical current at 15 K and less than 0.1 T missing due to the sudden temperature rises of more than 1 K during current ramping. Such temperature rises recurred at 15 K after remounting the sample or measuring a new sample. For the large sample HL1, more limited critical current data was obtained with significant temperature rises occurring under high current conditions. The maximum critical current successfully measured was 184 A at 20 K and 1.1 T, shown in Fig. 3(c). In Fig. 3(c), Ic data from Hyper Tech at 20 K was also included, excellent agreement has been obtained compared with our measurements.
Fig. 3. Ic(B, T) of three MgB2 wires, (a) HS1 (diameter 0.48 mm and twist pitch 10 mm), (b) HS2 (diameter 0.48 mm and twist pitch 30 mm), (c) HL1 (diameter 0.70 mm and twist pitch 25 mm) with experimental data from Hyper Tech at 20 K. |
Fig. 4. E-I characteristics of HS1 wire measured up to 8 μV/cm at 20 K and different magnetic fields. |
The n-value is a critical input parameter for detailed AC loss simulations but often neglected. It is included here since this index varies significantly with temperature and magnetic field. Fig. 5(a)−(c) present the fitted n(B, T) of the three MgB2 wires at temperatures from 15 K to 35 K.
Fig. 5. n(B, T) of three MgB2 wires, (a) HS1 (diameter 0.48 mm and twist pitch 10 mm), (b) HS2 (diameter 0.48 mm and twist pitch 30 mm), (c) HS1 (diameter 0.70 mm and twist pitch 25 mm). |
As shown in Fig. 5(a) and (b), both smaller wires gave low n-values with most being lower than 20. These low n- values were reproducible over several samples for the two small wires. For the large sample HL1, the n-values increased to much higher levels with monotonic increase in decreasing fields and temperatures. The maximum n-value could be up to around 100, as presented in Fig. 5(c).
We therefore attribute the lower n-values of samples HS1 and HS2 to their smaller filaments.
3.2. Jc(B, T) and Je(B, T) of three samples
Fig. 6(a)-(c) shows the material critical current density Jc of the three MgB2 wires, calculated using the cross-sectional area of the MgB2 filaments only. Fig. 6(d)-(f) displays the engineering critical current density Je, calculated using the total cross-sectional area of the wire (the diameter is 0.48 mm and 0.7 mm in this work). Both are included for their relevance to practical applications. For the two small wires, the engineering critical current densities Je were up to 109 A/m2. The critical current density, Jc, values could be up to 1.12 × 1010 A/m2 at 15 K in self-field.
Fig. 6. Transport critical current densities versus transverse applied fields at temperatures between 15 K and 35 K. Left column, Jc for (a) HS1, (b) HS2 and (c) HL1. Right column, Je for (d) HS1,(e) HS2 and (f) HL1. The experimental data points are represented by symbols and the fitted empirical Jc(B, T) expression are represented by dashed lines. |
Considering the limited Ic data at lower fields for the HL1 sample and the need for data for AC loss simulations, we have developed an analytical expression to facilitate extrapolation into this range. The magnetic-field dependence of critical current density (including Jc and Je) can be described phenomenologically by
$J_{c}(B, T)=J_{c 0}(T) \exp \left(-k B^{2}+c B\right)$
where Jc0(T) is the temperature-dependent critical current density at zero field. The dashed lines in Fig. 6(a)-(f) represent the fitted curves of critical current densities of three MgB2 wires. From the established expression of Jc(B, T) above, critical current densities obtained through measurements can be properly predicted by the fitted equation. The missing data at low fields of HL1 wire can also be extrapolated via Equation (1), with Ic up to 924 A at 15 K and 0 T where the engineering current density Je is 2.4 × 109 A/m2 and the critical current density Jc is predicted to be 1.6 × 1010 A/m2.
Fig. 7 compares the engineering critical current density of the three samples at temperatures between 15 K and 35 K. For two small wires HS1 and HS2, the Je of both wires agree well under high fields but then diverge slightly under low fields. Especially at 15 K, the Je values of HS2 were approximately 25 % higher than HS1 when the applied field was less than 2.5 T. This may be due to the tighter twist pitch of HS1 increasing strain in filaments. For the large wire HL1, the Je under low temperatures was very similar to the two small wires, but at 28 - 35 K was significantly larger than both small wires.
Fig. 7. Critical engineering current density versus transverse magnetic fields of three samples at temperatures between 15 K and 35 K. |
3.3. Hysteresis of Ic(B, T)
Fig. 8 shows the critical current versus magnetic field of the HS1 wire measured with both decreasing and increasing magnetic field at four temperatures. The Ic(B, T) curves in decreasing and increasing field are indistinguishable within our experimental uncertainty. This is due to the non-magnetic sheaths and is of great significance for reducing AC loss because the additional losses from magnetic sheaths can be eliminated. A similar absence of hysteresis was also recorded in HS2 and HL1 samples.
Fig. 8. Critical current versus transverse magnetic fields of HS1 wire with increasing and decreasing external magnetic fields at four temperatures, demonstrating the absence of Ic hysteresis. The solid line is for decreasing field and markers are for increasing field. |
4. Conclusions
As a preliminary study of MgB2 wires for fully superconducting rotating machines in aviation applications, we have performed transport Ic measurements on three MgB2 wires with non-magnetic (MgB2/Nb/CuNi/CuZn) sheaths over a wide range of temperatures (15 - 35 K) and fields (0 - 5.5 T). All wires were manufactured by Hyper Tech Research Inc. USA, specifically targeting low AC loss all-superconducting motors and generators for aircraft. In these three wires we investigated variations in diameter and twist pitch.
For two small wires with a 0.48 mm diameter each, HS2 wire (30 mm twist pitch) wire has higher Ic than HS1 wire (10 mm twist pitch), because the tighter twist pitch of HS1 increases the strain in filaments. The HL1 wire with 0.70 mm diameter and 25 mm twist pitch has higher Ic commensurate with its greater cross-section.
The transport critical current of HS1 wire could be fully tested without temperature rise at all temperatures down to 15 K, while for HS2 with slightly higher Ic only 15 K, very low field, data is missing due to sudden temperature rises. Similarly, the Ic(B, T) data of HL1 wire is also limited at low fields, due to heating issues at high current values. The n-value of HL1 could be up to around 100, even in a moderately high magnetic field of 1.5 T at 15 K. This contrasts with two small wires, which both have lower n-values, mostly less than 20. We attribute the smaller n-values of HS1 and HS2 to their smaller filaments.
Considering the necessity of critical current density being an input parameter for further AC loss simulation, a suitable empirical expression has been established. This describes the measured critical current densities versus magnetic fields, particularly providing the extrapolations to lower fields of the HL1 wire.
All wires had negligible difference in in-field transport Ic when exposed to increasing or decreasing magnetic fields. The non-hysteretic property is critical for lowering AC loss because the additional losses from magnetic sheaths can be eliminated. We expect these measured data, together with the empirical expression for the critical current density, can be useful for future AC loss simulation, and also useful for choosing operational regimes of MgB2 wires in aviation operation.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
This work was partly supported by CSC (Chinese Scholarship Council) and was partly supported by the New Zealand Ministry of Business, Innovation and Employment under the Advanced Energy Technology Platform program. This program is the “High power electric motors for large scale transport contract number RTVU2004”. This work was also supported by the Royal Society of New Zealand Catalyst: Seeding New Zealand - Japan Joint Research Project Programme contract number E4153. We also acknowledge Sarah Spencer for providing the SEM images of three samples.
