A proof-of-concept Bitter-like HTS electromagnet fabricated from a silver-infiltrated (RE)BCO ceramic bulk

An idealised Bitter-like HTS bulk electromagnet was simulated using a 2D-axisymmetric FE model based on the H-formulation [18–20], and implemented in the commercial software COMSOL Multiphysics^®. Figure 2 shows the axisymmetric geometry used to model a 20 turn stack of 1 mm thick discs, with inner and outer radii of 3 mm and 17.5 mm respectively. This approach sets the integrated current in each disc layer to be equal to the injected current, I. The use of a 2D-axisymmetric geometry neglects the effect of interlayer joints, which will cause heating (suppressing $J_\textrm{c}$) and reduce the effective number of turns due to the overlap between layers in the joint region. Time-dependent solutions were obtained as I was ramped from zero at a rate of 10 A s⁻¹.

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The non-linear resistivity of the HTS material was captured using the E–J power law [21–23]

$$\begin{align} \textbf{E} = \frac{E_0}{J_\textrm{c}} \left| \frac{J}{J_\textrm{c}} \right| ^{n-1} \textbf{J}, \end{align} \tag{ 1 }$$

where $E_0 = 1\,\mu{\mathrm{V}}\,\mathrm{cm}^{-1}$ and J is the local current density. $J_\textrm{c}$ is the critical current density obtained from interpolations of experimental measurements, as described in the supplementary material [24–29].

Figure 3 shows computed values obtained from simulations of the idealised 20 turn Bitter-like HTS coil stack. Electrical field, E, and central magnetic field, $B_{z, \textrm{CF}}$, are plotted against current for a set of different operating temperatures between 30 K and 77 K. The critical current, $I_\textrm{c}$, of the coil was calculated to be 2.6 kA (average $J_\textrm{c} = 179$ A mm⁻²) at 77 K using a 1 $\mu{\mathrm{V}}\,\mathrm{cm}^{-1}$ criterion. This corresponds to a maximum central magnetic field of $B_{z, \textrm{CF}} = 2.3$ T. These values are strongly temperature dependent, such that at 30 K, $I_\textrm{c} = 30$ kA which corresponds to $B_{z, \textrm{CF}} = 26.7$ T. It should be noted that these modelling results are expected to yield overestimates of the maximum achievable field, as the model neglects both heating effects and the geometric effect of joints, which will lower $I_\textrm{c}$ and the corresponding $B_{z, \textrm{CF}}$. Nonetheless, the predicted central bore fields are substantial, especially when considering that the coil stack has a total volume of $\lt$20 cm³. Operation at low temperatures would require very large current leads, but these current-ratings are not unrealistic for a high-field facility. An alternative approach is to supply the current using an HTS flux pump [30–35].

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The FE model also illustrates the current-flow distribution within the HTS Bitter-like stack, which differs markedly from the normal-conducting (resistive) case. In resistive Bitter magnets, $V\ \substack{\propto\\ \sim}\ I$, and $B_{z, \mathrm{CF}} \propto I$ because the current distribution remains proportional to 1/r [36]. However, these linear relationships do not hold for the HTS Bitter-like coil-stack. The I–E curve of the HTS bulk magnet is shown in figure 3. This exhibits the expected non-linear conductivity of a type-II superconductor, which increases exponentially near $I_\mathrm{c}$. This is superimposed upon an approximately linear voltage response to the current ramp, which is apparent at lower currents.

The central field also deviates from a linear dependence upon I, with a lower value of $B_{z, \mathrm{CF}}$ calculated at higher currents than would be expected if linearly extrapolating the low current data. This is due to the changing current distribution within each layer as I is increased. Figure 3 shows the normalised circumferential current density, $J_\phi/J_\mathrm{c}$, at different operating currents. Initially transport current fills from the inner radius of the HTS discs, while secondary screening currents act to 'shield' flux from the remainder of the bulk. As the injected current increases, the region with $J_\phi {\approx} J_\mathrm{c}$ expands from the inner radius and the shielded regions shrink. The increasing radial distance of the current front from the centre of the bore causes the field to increase sub-linearly with current. At lower temperatures, $J_\mathrm{c}$ is higher and thus the region with $J_\phi \approx J_\mathrm{c}$ will remain closer to the inner radius. This results in a larger central field as the average current radius is now closer to the inner bore. The resulting temperature dependence of $B_{z, \mathrm{CF}}(I)$ is observed in figure 3.

Commercially available 35 mm diameter GdBCO-Ag bulks prepared by buffer-assisted TSMG [37] were procured from CAN Superconductors. These were bored using a 6 mm diameter diamond drill bit. A slit parallel to the c-axis was cut radially from the outer to inner diameter, using a diamond wire saw. Further cuts were then made parallel to the a–b plane to produce a set of ∼1 mm thick slit annular discs. After cutting, the disc surfaces were polished using P2500 SiC paper.

Electrical joints were formed between adjacent discs via solid-state diffusion of silver foil into the (RE)BCO discs. This method was chosen as it has been demonstrated that the addition of Ag does not degrade (RE)BCO systems [38, 39]. Segments of 12 µm thick silver foil were shaped to cover one-eighth of the annular discs. The stack was then assembled by placing an Ag-foil segment on the top face of a GdBCO-Ag disc adjacent to the slit, and then placing a second slit disc on top of the first such that the foil was positioned azimuthally between the two slits (as shown in figure 1(a)). This process was repeated to make a six-layer coil stack. To promote current transfer at the coil terminals, an unslit (RE)BCO disc was added to both ends of the coil. This was joined to the outermost slit layer via a full annular silver layer, which had the effect of shorting the two outermost turns resulting in a four-turn coil. Resistive silver diffusion joints were formed by annealing the assembled coil for 3 h in air above 800^∘C. The coil was then annealed in oxygen for 6 h at 450^∘C to transform the tetragonal GdBa₂Cu₃O$_{7-\delta}$ structure to the superconducting orthorhombic structure. Scanning electron microscope images were taken along a cross-section of an annealed sample, to confirm that intimate joints had been formed. Figures 4(a) and (b) correspond to images taken at areas where the foil was present and absent respectively. The foil is present as an ≈10 µm thick line in figure 4(a), while a clear void is present in figure 4(b).

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Figure 4(c) shows an assembled coil after annealing. The surface of the coil stack was then coated by evaporating under vacuum a ∼15 µm thick layer of Ag and then Cu onto both sides of the sample (see figure 4(d)). This coating was added so that soldered connections could be made to the stack without damage from flux or indium diffusion.

After voltage taps and Cu current terminals were soldered to the coil, the entire assembly was mounted on a G10 strongback. The top terminal was connected to a Cu intermediary with Cu braid, which was in turn bolted to Cu current leads connecting to an Agilent 6680A-J04 dc current supply (1 kA, over-voltage protection limit set to 1 V). The bottom terminal was connected in a similar manner to complete the circuit. Voltages were read from the taps using a Keysight 34 420A nanovoltmeter. A calibrated HG106C Hall-effect sensor was placed in the bore of the coil stack, mounted on a rod connected to a micrometer screw that enabled z-axis translation. The Hall sensor was supplied with 1 mA of current and read using a HP 34 401A digital multimeter. A diagram of the coil testing rig is presented in figure 4(e).

3.2.1. Current sweeps.

The coil testing rig described in section 3.1 was placed in an open dewar filled with liquid nitrogen. An initial current of 50 A was applied to the four-turn prototype coil, and the Hall-effect probe was scanned through the bore and positioned at the field maximum. The current was then removed.

A series of current-sweep loops were then performed to investigate coil hysteresis. The coil voltage and $B_{z, \textrm{CF}}$ were measured while the current was ramped to a maximum value, $I_\textrm{max}$, swept back to zero, and then the measurement repeated with the polarity of the current supply reversed. Measurements were made for $I_\textrm{max} = 50$, 100, 250, 500, 750 and 1000 A. Measured data for the 1 kA loop are presented in figure 5. The data for all hysteresis loops are presented in the supplementary material.

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Both pairs of voltage taps showed good agreement with no noticeable difference for increasing or decreasing current, which implies good thermal stability. For $|I| \lesssim 700$ A the coil voltage was linear, with a constant coil resistance of $R_\textrm{coil} \approx 3\,\mu \Omega$ attributed to the series-connected silver diffusion joints in the stack.

The $B_{z, \textrm{CF}}$ data in figure 5 shows the field hysteresis loop obtained from this coil stack. Current was initially swept in the negative polarity. There is an initial 54 mT offset due to trapped flux from the previous measurement (concluded 10 min prior) in which $I_\textrm{max} = 750$ A. This results in a short 'flat section' in the plotted data, until the injected current overwhelms the trapped flux. Once this has occurred the field magnitude increases approximately linearly to $B_{z, \textrm{CF}} = -283$ mT. When the current is swept back to zero a clear hysteresis is observed, with $|B_{z, \mathrm{CF}}|$ greater on the return loop due to flux-trapping within the HTS discs. There was a ≈30 s time delay while the polarities of the current supplies were switched at I = 0 A, during which $|B_{z, \textrm{CF}}|$ decayed from 120 mT to 87 mT. After this, the $B_{z, \mathrm{CF}}$ behaviour in the positive current loop behaved entirely similarly to the negative loop, reaching a maximum of +270 mT at +1 kA, with 112 mT of hysteretic trapped field observed when I returned to zero.

3.2.2. Field stability.

The temporal field stability of the four-turn prototype coil was investigated by ramping the current to 1 kA and holding there for 15 min while continuously measuring V and $B_{z, \textrm{CF}}$. This data is shown in figure 6. (Note that this sweep starts with $B_{z, \textrm{CF}}$ offset of 82 mT due to trapped flux from the positive polarity 1 kA hysteresis measurement made 45 min prior).

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The voltage was observed to be stable throughout the 15 min hold at 1 kA, indicating that the coil was thermally stable despite the ≈3 W of internal heating due to the resistive interlayer joints. However, the central field was observed to drift slightly over this period, increasing from 270 mT to 284 mT, an increase of 5.6%. This is attributed to current relaxation towards the inner radius of each disc layer.

At the end of the 15 min hold, the Hall-effect probe was again scanned through the bore, before removing the applied current. This confirmed that the field maximum remained in the same z-position at 1 kA as was initially observed at 50 A. The data for the 1 kA field profile are presented in the supplementary material.

3.2.3. Maximum current capacity: test-to-destruction.

The coil-stack was warmed to room temperature before re-cooling in liquid nitrogen. A current of 500 A was then used to position the Hall sensor in the field maximum, leaving a trapped field of 44 mT. There was no distinguishable change in coil behaviour following the thermal cycle.

In order to ascertain the maximum current carrying capacity of the coil, a current ramp until failure was performed. This required injected currents above 1 kA, so a second Agilent 6680a current supply was added in parallel to the first.

Data from this experiment is shown in figure 7. One current supply was ramped to 250 A over 50 s and then held there for ≈50 s. During this hold period the voltage was stable, but the central field was observed to slightly increase in a similar manner to that observed for the 1 kA hold. Control was switched to the second supply which was then ramped to further increase the applied current in 25 A increments.

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As before, the coil voltage increased linearly with I until I ≈ 700 A, with total joint resistance of 3.3 $\mu \Omega$. At higher applied currents the expected non-linear I–V behaviour emerged. The central field also behaved as before. Initially, $B_{z, \textrm{CF}}$ remained relatively flat until applied current fully displaced the circulating currents responsible for the trapped field. This occurred at ≈550 A. Between 550 and 875 A, $B_{z, \textrm{CF}}$ increased approximately linearly with applied current. However, for I > 875 A, this linear approximation no longer held, with $B_{z, \textrm{CF}}$ exhibiting a lower value than would be expected if linearly extrapolating the 550 to 875 A data. This is consistent with the behaviour observed in the FE model, described in section 2.2.

A maximum central field of $B_{z, \textrm{CF}} = 382$ mT was reached when I = 1.2 kA, before a failure event occurred at 1.225 kA. At 1.2 kA, the total dissipated heating power in the coil, IV, was 6.1 W. At 1.225 kA, the voltage rose rapidly to the current supply limit of 1 V, while the current dropped to 140 A. This corresponded to an increase in the coil resistance to 7.1 mΩ. After failure, the central magnetic field dropped to zero indicating no trapped flux remained post-failure. This implied that none of the (RE)BCO discs remained superconducting at this point, which was likely due to heating of the entire stack to a temperature above $T_\mathrm{c}$. Current was applied at 140 A for a further 3 min after the failure event before the current supply was disabled. This current was most likely conducted through the silver matrix and must have been flowing in an axial direction as no central field was measured.

After warming to room temperature, a post-mortem coil disassembly was carried out. This revealed that the $4\textrm{th}$ HTS bulk disc in the stack had broken at a facet line adjacent to the Ag-diffusion joint between the $3\textrm{rd}$ and $4\textrm{th}$ HTS discs. This breakage meant that post-failure, current transfer between the $3\textrm{rd}$ and $4\textrm{th}$ HTS discs would have been through surface contact only, hence the substantial increase in total coil resistance.