New coil configurations with 2G-HTS and benefits for applications

The basic idea was to replace well established coil windings based on a multitude of turns of 2G-HTS tape (either planar circular or racetrack coils) by an assembly of slit disks (or plates) of 2G-HTS along the central axis. This is somehow similar to the stacking of copper plates in a Bitter magnet topology. However, using 2G-HTS disks with an architecture of stacked layers of at least substrate, buffer, HTS and cap layer required a more sophisticated stacking. In detail, the 2G-HTS-disks had to be positioned alternating in a HTS-up/HTS-down orientation—in short a DUDA had to be prepared. This approach ensures that the resistive current path outside the HTS layer is as short as possible and that the current does not have to cross the buffer or substrate layers of the tapes. Furthermore, to realize a continuous current path, the overlap-region of the (resistive) contacts will be roughly double the thickness of one disk. The insertion of appropriate insulation and filling elements ensure a smooth built-up of the assembly. Figure 1 shows the principle elements of the DUDA concept. The assembly process of the very 1st DUDA magnet is discussed in the next section.

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The commercial HTS tapes used for the DUDA assemblies are described in table 1.

To start with a very easy experimental setup, we used 2G-HTS tape by DNS. These tapes were not of highest electrical performance, but simply available in the largest width for first experiments. The DNS-tapes only had a silver cap-layer on top of the HTS-layer (no copper stabilization), a width $w = 40\,{\text{mm}}$ and a range of critical current per width of 24–30 A mm⁻¹ w. These samples were structured using a laser into 42 identical slit circular disks. For each disk, the silver cap-layer was covered with Kapton—except for sectors reserved for the contacts (figure 1(a)). Additional Kapton was attached to the substrate of the disk-down elements (figure 1(b)). The primary purpose of the Kapton was to compensate thickness differences in the stacking process; the electrical insulation was of secondary interest. The bottom electrode was covered with an indium disk to provide a good initial contact to the first disk-down element (figures 1(c) and (d)). The 2nd element of disk-up type was place on top and then turned to slide below the contact sector of the 1st element (figures 1(e) and (f)). To provide a smooth base for the next disk-down element, an additional disk of Kapton was placed on top of the assembly and a sector of indium was added on the uncovered silver cap-layer as part of the next contact (figures 1(g) and (h)). The next disk-down element was simply placed on top without the need to turn (figures 1(i)). An indium sector was added to the next disk-up element, which was added and turned to adjust the contact sectors on top of each other (figures 1(j) and (k)). According to this process, in total 42 elements were assembled and then the final top electrode (following an indium disk) was added. The central support part made of FRP for positioning a Hall probe was attached later. To ensure sufficient electrical conductivity across the resistive contacts, pressure was applied over all by clamping the assembly with bolts and FRP sockets (to keep the pressure even when cooling down). The completed assembly was connected with current leads and voltage taps. The voltage taps were placed on the copper plates; as a trial to apply pressure contacts to the disks by through-holes failed. Figure 2 shows a picture of the assembly with a cm-scale.

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In short, the assembly provides a stack of slit, insulated (Kapton), slightly non-planar (to achieve the required steps in the axial direction) disks resistively connected in series (contact sectors with indium).

Rectangular assemblies of modules based on the DUDA concept might be of interest in several configurations.

Figure 3 introduces the general architecture and defines some variables of the central gap. To start with a very easy experimental setup, we used 2G-HTS tapes by SuperPower and SuperOx (see table 1). In total, five of these sheets were stacked following the DUDA-approach (figure 3). In contrast to the circular DUDA, the tapes by SuperOx used for the rectangular assembly were electroplated with 20 µm layer copper. Figure 4 shows the assembly prepared for measurements in liquid nitrogen.

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The circular DUDA assembly (see section 2.2) was immersed into an open dewar filled with liquid nitrogen. The assembly was characterized by transient recording of voltage–current (V–I) and Hall-probe voltage while increasing the current stepwise from measurement to measurement and waiting for stationary conditions (the data corresponding to I = 0 → 10 A, I = 0 → 15 A and to I = 17.6 → 17.8 A is presented in figures 5–7, respectively). The rising ramp was limited by the time constant of the DUDA assembly (discussed in section 4.1); the voltage limit of the current supply (20 V) was clearly above the sample voltage. The recording time was in the 10 s.

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Combining the individual measurements into a voltage–current dataset produced the curve in figure 8. From the resistive part in that curve, a resistance of 18.8 mΩ was estimated for the whole setup. The maximum current of 17.8 A corresponded to a calculated axial magnetic central field of $B \approx 40\,\;{\text{mT}}$; a uniform current density throughout the sheets was assumed for the calculation (given that the Hall probe is suitable for a maximum field of 5 T, this is a reasonable alignment at these field levels along with the simple assumption of uniform current density). Following that, to avoid heat production/temperature rise by slow current ramps, pulsed short time measurements (indices 18 and 19 in figure 8) were carried out for sample currents up to I = 150 A (producing ≈0.34 T and ≈400 W of ohmic heat) without a permanent degradation. This is underpinned by the measurement with index 20 reproducing the quasi-stationary U–I characteristic, but a detailed discussion of all transient experiments and effects is beyond the scope of this work.

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The electric measurements in liquid nitrogen on the rectangular assembly yielded an overall electric resistance of 465 nΩ and 10 µΩ, and critical currents of 29 A and 90 A for assemblies of wires by SuperPower and SuperOx, respectively. When removing one third of width of the tape, one would expect a remaining critical current of 2/3 of the uncut one. As this is not the case for the SuperPower tape used (see table 1), the weak performance of this assembly might result from critical current variations along the width of the tape (i.e. removing the best performing middle part will lead to a higher reduction of critical current). The SuperOx tape used seemed to be quite homogeneous over the width following the same argument.

Rectangular assemblies based on the DUDA concept are limited by the available 2G-HTS components. For an initial evaluation of if and how such rectangular DUDA may be of benefit and a subject for further experimental work, we assume $l = 1\,{\text{m}},\,w = h = 4\,{\text{mm}},\,{w_g} = 0.2\,{\text{mm}}$. Let ${I_{c,w}}\left( {30{\text{ K}},{ }3{\text{ T}}} \right) = 145{\text{ A}}\,{\text{m}}{{\text{m}}^{ - 1}}$ represent the critical current per mm-width at a temperature of 30 K and an external magnetic field of 3 T, which is in a typical range for an rotating machine. Furthermore, let $n = 40$ be the number of individual 2G-HTS plates adding-up to the height $h$. Given these values, we calculated the magnetic field profile (see figure 9).

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Having chosen a DUDA assembly of square cross sections with a higher p in the xz-plane (so $w = h$), several of these assemblies may be arranged to create a Halbach-array (see figure 10)—very similar to the arrangements by conventional rare-earth based permanent magnets. For the same parameters and combining five DUDA assemblies, the magnetic field on the 'top' side of the arrangement is increased and on the 'bottom' side decreased—see figures 10 and 11.

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Stacks following the DUDA concept are quite different from the conventional Bitter approach. In Bitter magnets, the complete current path is normal conducting and the resistivity of the contact areas might be comparable to that along the current path within the plates. The intra-plate resistivity yields a current profile $I\left( r \right) \propto 1/r$, which favours the largest currents near to the bore. The response behaviour of a Bitter magnet is determined mainly by the inductance and resistivity of the magnet.

In DUDA stacks, the contact resistances in between the disks sum up to the overall resistance, while at the same time producing local heat and raising the local temperature. The critical current of a superconducting disk is—especially at elevated temperatures—strongly depending on the local magnetic field and temperature, e.g. ${I_c}\left( {B,\,T} \right) \propto \left( {1 - \frac{T}{{{T_c}}}} \right)/B$. In contrast to Bitter magnets a DUDA stack shows some redistribution of current vs radius due to (a) increased temperature (more serious for small radii caused by the smaller contact area) and (b) higher magnetic field at small radii. An initial homogeneous current profile will re-distribute to a current profile with the maximum current at larger radii. The time scale of this redistribution is depending on contact resistances, heat removal, overall current and pinning properties of the HTS. This can be partly observed in the measurements: at low currents (e.g. 10 A), the current in the assembly follows the ramp quite simultaneously and there is no delay in the voltage built-up (figure 5). For higher currents, the voltage over the assembly shows a delay (figure 6). At currents near to the stable limit, not only the voltage, but the built-up of the magnetic field is also delayed (figure 7). More time dependent behaviour could be observed at higher current pulses (e.g. 150 A), but this is beyond the scope of a proof-of-principle discussion. In summary, when evaluating this simple DUDA, one has to consider that (a) the resistive contacts from disk to disk are not optimized at all, (b) the resistance of the contacts decreases with increasing radius due to increasing contact area, (c) there will be a heating from the contacts between the disks and (d) there will be a redistribution of current. To reduce these effects, one should optimize the contacts in shape, size and resistivity. The pulsed measurements indicate that the current performance of the circular DUDA is mostly limited by heating/ temperature increase and not by ${I_c}\left( {T = 77\,K} \right).$ This is supported by the observation on the rectangular DUDAs with SuperOx-tape showing the full expected current performance.

Operating the assembly at lower temperatures (e.g. 30 K, 20 K or 4 K) will also reduce the redistribution effects, because contact resistivities and the ${I_{\text{c}}}\left( {B,T} \right)$ dependence are reduced. When using state-of-the art 2G-HTS tapes with a higher performance (e.g. >60 A mm⁻¹ w instead of ⩽30 A mm⁻¹ w at temperatures of liquid nitrogen, or >300 A mm⁻¹ w at temperatures of 30 K) the expected magnetic field will be improved by at least a factor of 2–10 in the same geometry.

Having 2G-HTS sheets available in appropriate geometries and operating the assemblies at lower temperatures, magnets of 6–10 T are envisaged in the near future, when larger sheet numbers and dimensions are available. Presently KIT ITEP is erecting a pulsed-laser-deposition for the preparation of research tapes and sheets. There is the drawback of having contact resistances in between the sheets (which might be led out and cooled separately with higher power) and in general the magnetic field is mostly directed along the c-axis which leads to a reduced critical current—but this limits the operating current in nearly all windings. However, there are several advantages to counterbalance that:

• Homogeneous material in the radial direction. In tape-wound coils, due to the layered structure, there is always a sequence of substrate, HTS, copper and potentially other materials (e.g. silver, resin, insulation) leading to (shear) forces with increasing winding height and to potential degradation/delamination in the winding.
• The assembly is made up by several limited size modules, which might be tested in advance and should not ruin the material:scrap ratio of a supplier, which leads, in the long term, to a low cost situation.
• Heat removal (for nominal operation or considering quenches) from the inner radius to the outer radius is facilitated by in-plane heat conduction in the sheets, and thus expected to be superior to the heat removal in wound pancake coils.
• Lorentz-force/hoop stress is handled within the individual sheets not necessarily producing shear stress.

When considering miniaturized magnets, the (rectangular) DUDA concept enables the building of high-field benchtop magnets suitable for producing some Tesla—especially when arranging rectangular DUDA coils in a Halbach-array to strengthen the magnetic field in one half-space.

Rotating electric machines have been built using HTS in the field winding only (partially superconducting machines) [12] and in a very few cases in the armature winding as well (fully superconducting machines) [13, 14]. These machines benefit from the higher air-gap field by the HTS field winding (typically producing a field of ≈3 T) and the higher current density in the stator winding [15]. As long as the windings are based on wound-wire coils, there is a limit to miniaturization (resulting from the minimum bending radius) and thus in the possible number of poles and slots in a given cross section. Using the rectangular DUDA concept, these coils can be miniaturized to a width as low as e.g. 4 mm and easily extended to a length of 5000 mm—the latter one will reduce the impact of contact resistance on the overall performance considerably. Furthermore, placing the contacts at only one end of a rectangular DUDA allows easy heat removal at one side of the winding package. Such coils will allow extremely high numbers of poles and slots in rotors and stators.

Furthermore, deciding to use a Halbach-configuration of DUDA coils in the rotor (as is frequently the case with conventional rare-earth based permanent magnets) will lead to a higher air-gap magnetic field, a reduced rotor forging magnetic field and the reduction of harmonics. These approaches will be of special interest to motors and generators in wind power and in vehicles (e.g. electric aircrafts, ships and trucks).

The DUDA approach opens up pathways to miniaturize magnets by eliminating the restriction of minimum bending radii of wires. This will allow building of wiggler and undulator magnets with extremely small spatial wavelengths while providing strong magnetic fields [16, 17]. Given that the 2G-HTS sheets are available in appropriate sizes it will be possible to prepare strong dipole magnets for accelerators very similar to the 'feather' dipole magnet [18], but with fewer components. The DUDA concept is opening up new designs and topologies for accelerator magnets.

To further elaborate on the DUDA concept, the following challenges might be addressed:

• (a)  
  Improving inter-sheet contacts.
• (b)  
  Characterizing a DUDA stack at low temperatures and in background fields.
• (c)  
  Studying the potential of rectangular DUDA stacks for the windings in rotors and in stators of rotating machines.
• (d)  
  Experimentally accessing the potential and characteristics of a Halbach-array based on DUDA stacks (at temperatures of 20 K–30 K for rotating machines and for compact benchtop magnets).
• (e)  
  Building high-field short-wavelength undulators/wigglers following the DUDA concept.
• (f)  
  Assembling a deposition device for wide and homogeneous 2G-HTS sheets/tapes.
• (g)  
  Using wide sheets to explore DUDA-based dipole magnets.

We plan to address the challenges 1, 2, 3 and 6 in the short and mid-term.