Characteristics of Aluminium-Stabilized HTS Detector Magnet Cable at 4 K and 5 T

A high-temperature superconducting (HTS) cable for future particle detector magnets has been developed using a 99.3% pure aluminium alloy as a stabilizer for the HTS. This HTS conductor features a stack of four ReBCO tapes (4 mm wide, SuperOx) soldered to a tin-coated copper-clad aluminium alloy cable profile using tin–lead solder at 188 °C. Here, we experimentally demonstrate that the cable withstands both thermal cycling between 4 K and room temperature and Lorentz forces induced by external magnetic field of 5 T when the HTS cable is driven by 4.5 kA. The HTS cable has no visual damage and no change in the critical current after being exposed multiple times to these extreme conditions. We show that since the phase transition of ReBCO is gradual, an aluminium alloy with low residual resistivity ratio (RRR) can be used as a stabilizer, which brings many advantages, such as a better availability compared to pure aluminium and a mechanically stronger cable.


Characteristics of Aluminium-Stabilized HTS
Detector Magnet Cable at 4 K and 5 T Anna K. Vaskuri , Joep L. Van den Eijnden , Benoit Curé , Alexey Dudarev , and Matthias Mentink Abstract-A high-temperature superconducting (HTS) cable for future particle detector magnets has been developed using a 99.3% pure aluminium alloy as a stabilizer for the HTS.This HTS conductor features a stack of four ReBCO tapes (4 mm wide, SuperOx) soldered to a tin-coated copper-clad aluminium alloy cable profile using tin-lead solder at 188 °C.Here, we experimentally demonstrate that the cable withstands both thermal cycling between 4 K and room temperature and Lorentz forces induced by external magnetic field of 5 T when the HTS cable is driven by 4.5 kA.The HTS cable has no visual damage and no change in the critical current after being exposed multiple times to these extreme conditions.We show that since the phase transition of ReBCO is gradual, an aluminium alloy with low residual resistivity ratio (RRR) can be used as a stabilizer, which brings many advantages, such as a better availability compared to pure aluminium and a mechanically stronger cable.Index Terms-Aluminium, cables and current leads, detector magnets, HTS magnets, HTS cables, stability, quench protection.

I. INTRODUCTION
T HE most cost effective way of reaching high magnetic fields in particle detectors is to use superconducting solenoid magnets with an operating current in the order of tens of kiloamperes [1], [2].During a magnet quench, superconductivity is lost and the stored energy is converted to heat.A superconducting magnet can be passively quench protected by adding a stabilizing normal metal with low electrical resistivity in parallel with the superconductor [3], [4], [5].The stabilizer mechanically supports the superconductor and temporarily carries the current during a quench keeping the local hotspot temperature reasonable, preferably under 100 K [6].
In some particle detector designs, such as the ATLAS Central Solenoid [2], the superconducting magnet is located between the electromagnetic and hadronic calorimeters, which sets a transparency requirement for the magnet as the particles to be identified need to travel through it before reaching the detectors.The key is to use a low-density material, which corresponds to high transparency to particle radiation [7], such as aluminium [1].Niobium-titanium (Nb-Ti) is the most used low-temperature superconductor (LTS) for detector magnets.Recent advancements and high yields in high-temperature superconducting (HTS) tapes partly driven by fusion [8], present unavailability of commercial aluminium-stabilized LTS cables [9], and global shortage of liquid helium [10], [11] have led CERN to start developing aluminium-stabilized HTS cables in the Experimental Physics Department R&D programme on Detector Magnets (WP8).Within this programme, the first critical current measurements at 77 K in self-field for the early version of the aluminium-stabilized HTS cable were published in 2023 [12].This HTS cable featured tin (Sn) and copper (Cu) coated pure aluminium as a stabilizer with a U-shape profile which had a cross-section of 10 mm × 4 mm, and 4.5 mm wide and 2 mm deep groove where the ReBCO (Rare-earth Barium Copper Oxide) tapes were soldered using bismuth-tin (Bi-Sn) solder.While this cable also performed well at 4.5 kA in self-field at 4 K, and there was no degradation when thermally cycling between 4 K and room temperature, the cable was damaged by the Lorentz force when operated at 5 T external magnetic field.The reason was a locally detached ReBCO tape due to the softness of pure aluminium and the brittle nature of bismuth-tin solder.Therefore, a more robust cable was developed, using tin-lead (Sn-Pb) solder and copper-clad aluminium alloy as a stabilizer, and reported upon in this paper.Within the CERN EP R&D programme, Deelen et al. [6] developed a conceptual design of an FCC-ee (The Lepton Future Circular Collider) particle detector magnet based on such an HTS cable.Other ongoing activities in the programme are the development of partially-insulated HTS coils based on 3D-printed Al10SiMg alloy [13], [14] to understand transient behavior of partially-insulated HTS magnets [15] which basis on the HTS cable soldering technology presented in this paper, and HTS flux pumps for powering superconducting magnets [16].
In this work, we have prepared an HTS cable sample with 99.3% pure aluminium as a stabilizer, described in Section II.In Section III, we present the critical currents measured for the HTS cable from 4 K to 77 K in self-field and at 4 K in external magnetic fields up to 5 T. Conclusions of the work are discussed in Section IV.

A. HTS Cable Profile
The HTS conductor developed features a 99.3% pure aluminium (Al) alloy as a stabilizer which is copper-cladded using the hydrostatic extrusion method by Hydrostatic Extrusions Ltd.In the hydrostatic extrusion method, a copper cladding is bonded to the aluminium core by a surrounding high pressure fluid.The temperature-dependent electrical resistivities of Al 1100 series [17] and 99.99% pure Cu [18] are depicted in Fig. 1.Al 1100 series contains 1% of impurities that slightly higher content than in this cable, so their electrical resistivities can be considered approximately similar.This cable has a 0.1% proof stress of 163 MPa stated by the manufacturer and it costs ∼19 €/kg.These are advantageous factors over pure aluminium, which has extremely high electrical conductivity at cryogenic temperatures, RRR ≈ 500, but a yield strength of 30 MPa, cost of > 500 €/kg, and limited availability [6].
The cable profile was tin-coated to prevent oxidation of the ∼300 µm copper-cladding during soldering.The stabilizer has a cross-section of 20 mm × 10 mm with a 4.5 mm wide and 1 mm deep groove on the wide surface of the stabilizer where a stack of four ReBCO tapes were soldered.For the conductor it would take 45 s to reach the "safe" hotspot temperature of 100 K if all superconductivity would be instantly lost and all the current would flow through the stabilizing normal metal.This time is estimated by where the initial temperature T 1 = 4 K, safe hotspot temperature T 2 = 100 K, mass per unit length m l = 0.53 kg , and operating current I = 4500 A. In practice, the time to reach 100 K is longer due to the gradual phase transition and high critical current margin of ReBCO.Time reaching the 100 K hotspot temperature in a cable is a balance between current density, heat capacity, and electrical conductivity of the stabilizer.Therefore, comparing each of these factors individually will not lead to a fair comparison.Cross-sectional area for the HTS conductor is 200 mm 2 , whereas it is 500 mm 2 for the LTS cable of the ATLAS central solenoid [2] and 1390 mm 2 for the LTS cable of the CMS solenoid [21].HTS CORC (Conductor on Round Core) cables with various diameters from a few millimeters to a few tens of millimeters were developed in [22], [23].
The ReBCO tapes (4 mm wide, manufactured by SuperOx, see Table 1 in [12]) require support by the stabilizer as their shear delamination strength is measured to be 3 MPa-7 MPa [24].The yield strength of tin-lead is greater than 40 MPa [25] which means that the delamination of ReBCO tapes is the most probable cause of cable failure.

B. Soldering of the ReBCO Tapes
Prior soldering the cable profile was bent according to Fig. 2 so that it fits inside a 200 mm diameter bore of the 5 T Nb-Ti solenoid of a cryostat setup used for characterizing the cable.The cable section with 85 mm inner bending radius has a length of 170 mm and six voltage taps are placed with a pitch of 30 mm along this part of the cable.The two sharper bends in the cable profile have a radius of 40 mm.Any sharp bending of the ReBCO cable should be avoided since bending of the already soldered cable leads to an irreversible degradation the critical current of the HTS cable.
Four ReBCO tapes by SuperOx were soldered in the groove with tin-lead solder in an oven at 188 °C for 6 hours, after which the oven was switched off and the cable slowly cooled down to room temperature.The method of soldering of ReBCO tapes is discussed in [12].The ReBCO tapes were placed in a staircased pattern so that each ReBCO tape end has a direct contact area of 10 mm × 4 mm to the stabilizing metal to enhance current distribution to the tapes by reducing the effect of the resistances of the 38 µm Hastelloy substrate layers.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.We non-destructively inspected the quality of tin-lead solder contact between ReBCO tapes and the stabilizer by a 3D computed tomography [26].Fig. 3 shows the HTS cable's crosssection at three locations.The soldering quality is generally good, similar as in Fig. 3(a), but voids as large as 1 mm in width are present in Fig. 3(b) and (c).Videos of the HTS cable's cross-section across the full cable length, showing the soldering quality between the ReBCO tapes and the stabilizer, are included as the supplementary material of this paper.

C. HTS Cable Assembly
The critical current of ReBCO tapes is highly anisotropic: the critical current is the lowest when the external magnetic field is aligned perpendicular to the wide surface of a tape and highest when the field lines are co-planar with the tape, and this is also the best way to wind an HTS solenoid.When winding the magnet, the safest way is to bend the cable so that the HTS tapes are facing inwards, and select the current polarity so that the Lorentz force presses the tapes against the stabilizing metal.Therefore, we bent the cable accordingly and measured it in two configurations: Fig. 4(a) with the external field oriented parallel to the wide surface of the tapes and Fig. 4(b) oriented perpendicular, respectively.Fig. 4(c) shows a cryostat insert of the liquid helium setup used in this work.The cryostat includes the Nb-Ti solenoid magnet with a bore diameter of 200 mm and length of 400 mm for providing an external magnetic field between 0-5 T. The HTS cable is assembled to the copperstabilized superconducting busbars at the center inside the magnet.
In the parallel configuration the magnetic flux direction was selected that the Lorentz force pressed the ReBCO tapes against the stabilizing metal of the cable.The force can be significant, for example, with 4.5 kA current and 5 T external field, the Lorentz force is 3.8 kN which is equivalent to 390 kg.For the perpendicular field orientation shown in Fig. 4(b), G10 fiberglass-epoxy support plates were fixed to the superconducting busbars to prevent the bending of the HTS cable during the measurements.In the perpendicular field orientation, the Lorentz force vector is co-planar with the wide surface of the ReBCO tapes' cross-section, commonly referred to as shear stress.

III. CRITICAL CURRENT MEASUREMENTS
The liquid helium cryostat setup in Fig. 4(c) was used for the critical current measurements of the HTS cable sample.We measured the current through the HTS cable sample from a voltage drop across a room-temperature shunt resistor with R s ± 2σ R s = (20 ± 0.06) µΩ consisting of two calibrated resistors rated with 100 mV at 2.5 kA connected in parallel to the positive side of the power supply.
In the measurements, the current was ramped up with a rate of 15 A/s, after which the current was kept constant for 30 s, and then the current was ramped down with a rate of −15 A/s.A scanning voltmeter (DAQ6510) was used to record the voltage across each individual section (1-2, 2-3 etc.), across all the sections (1-6), and across the HTS cable including the joints to the superconducting busbars.In addition, simultaneously the cable temperature was monitored by a bridge temperature sensor [27] with a 2σ uncertainty in the calibrated sensitivity of ±2.3 K, which allowed the critical current measurements at known temperatures elevated above 4 K.

A. Current-to-Electric Field Measurements at 4-77 K in Self-Field
Current-to-electric field measurements in self-field as a function of temperature in Fig. 5 were performed in the horizontal Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.Fig. 5. Critical current of the HTS cable in self-field at various temperatures with 2σ uncertainties (blue circles).A second order polynomial (dashed curve) depicts a trendline.The predicted critical current of the HTS cable in self field (solid curve) was simulated using the dataset in [28].Resistance per unit length of the cable's stabilizing metal is plotted as a dotted curve.Fig. 6.Current-to-electric field characteristics across five cable sections at the beginning (a) and after the tests at 4 K and 5 T (b).I c of sections 1-2 and 5-6 is lower due to the current transfer near terminals.configuration (see Fig. 4(a)) to minimize the temperature gradients across the HTS cable sample when operated in helium vapor between 4-77 K. Due to the combination of a short cable sample which has low normal state resistance per unit length, with the corresponding current transfer length in the order of centimeters at 77 K [12], two distinct current redistribution regions are present in the current-to-electric field plots in Fig. 6.The first region, where the current redistributes from the stabilizer to the nearest ReBCO tape, has an Ohmic footprint of ∼ 30 nΩ/m, which was fitted as a line at currents well below the transition edge and subtracted from the current-to-electric field curves.In the second region, I c of the first tape is reached and the current redistributes among the rest of the ReBCO tapes.Due to these effects, the measured I c determined using E c = 100 µV/m threshold for superconductivity would be significantly lower than the I c predicted for a long cable sample where the self-field of the cable is expected to be the only factor reducing the I c .Therefore, we use the following fitting of the electric field to obtain I c values in Fig. 5: where E c = 100 µV/m and n = 20.Free fitting parameters: I x is the start of the current redistribution (region 2), R x is the corresponding ohmic footprint due to the current redistribution, and I c is the critical current of the cable.The cable resistance per unit length (Ω • m −1 ) in Fig. 5 was calculated as: using the cross-sectional areas (A Al , A Cu ) of Al and Cu and the temperature-dependent resistivities (ρ Al (T ), ρ Cu (T )) in Fig. 1.

B. Current-to-Electric Field Measurements in Parallel External Fields of 0-5 T at 4 K
The HTS cable orientation in Fig. 4(a) was used for measuring the current-to-electric field curves in external magnetic fields between 0-5 T parallel to the ReBCO tapes' wide surface at 4 K.As shown in the critical current datasets describing individual ReBCO tape characteristics by different manufacturers [28], the external magnetic field lines co-planar with the surface of the ReBCO tape do not reduce its critical current, which also holds for the HTS cable.The superconducting transition edge was not reached when operating the HTS cable at 4 K in 5 T parallel field.

C. Current-to-Electric Field Measurements in Perpendicular
External Fields of 0-5 T at 4 K We used the HTS cable orientation in Fig. 4(b) to measure the current-to-electric field curves in perpendicular external magnetic fields between 0-5 T at 4 K.As seen in the results plotted in Fig. 7, the critical current reduces at higher perpendicular external fields.This trend is similar to the critical currents for individual ReBCO tapes measured in external magnetic fields perpendicular to the tape's wide surface [28].
In the external magnetic field, the predicted I c matches the experiment (see Fig. 8), indicating that the I c reduction due to high field is the dominating factor for current redistribution since Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.Fig. 8. Critical current of the HTS cable at 4 K in various external magnetic fields with 2σ uncertainties obtained using E c = 100 µV/m threshold for superconductivity.The predicted critical current of the HTS cable at 4 K (solid curve) was simulated using the dataset in [28].
Based on cycling between 0 and 5 T, we do not observe critical current degradation or visual damage in the cable as demonstrated in Fig. 6.This is an encouraging result since the maximum shear stress experienced by ReBCO tapes in the cable at 4.5 kA and 5 T is 5.6 MPa which is near the delamination limit measured for individual copper-coated ReBCO tapes (3 MPa-7 MPa [24]).As a virtue of the aluminium stabilization, the HTS cable could be stably operated at an electric field a factor eight above the threshold of 100 µV/m.

IV. CONCLUSION
This paper describes an HTS cable stabilized using an aluminium alloy with 99.3% purity level, rather than pure aluminium conventionally used in LTS cables in particle detector magnets.The HTS cable survives thermal cycling between 4 K and room temperature and the Lorentz force induced by 4.5 kA operating current and 5 T external magnetic field in both parallel and perpendicular magnetic field alignments.There is no visible damage in the HTS cable and no change in the critical current after being exposed six times to 5 T external field.
Due to the limitations in the magnet and cryostat geometry available, the cable sample tested was short.Therefore, we determined the I c of the cable by fitting the power law to the current-to-electric field curves with an additional term accounting for the linear current redistribution region.The trendline of the measured I c in the self-field is lower but follows the predicted curve and the critical currents measured in the external fields match the predictions obtained using E c = 100 µV/m threshold for superconductivity due to the suppression of the current redistribution region.
Thanks to the gradual phase transition of ReBCO together with current redistribution to the aluminium stabilizer via lowresistivity tin-lead solder, this HTS cable is inherently stable and difficult to quench.This is an encouraging step towards a particle detector magnet based on an aluminium-stabilized HTS cable.
In case of a quench, an HTS detector magnet design based on Al 1100 as a stabilizer has a few orders of magnitude higher normal state electrical resistivity at cryogenic temperatures compared to pure aluminium and will thus build up higher voltages.For this conductor type, there is a risk of a high voltage discharge [6], requiring a special thick, high quality insulation between the coil windings.CERN Experimental Physics Department R&D programme on Detector Magnets continues further studying such detector magnet technology.

Fig. 2 .
Fig. 2. Tin-coated copper-clad aluminium stabilizer with 4.5 mm wide and 1 mm deep groove.Six voltage taps (1-6) are placed with a pitch of 30 mm along the cable profile.Four precoated ReBCO tapes are soldered to the stabilizer after bending of the cable.

Fig. 3 .
Fig. 3. Computed tomography maps of HTS cable's cross-section at three locations (a)-(c) along the cable.

Fig. 4 .
Fig. 4. Horizontal configuration where HTS wide surface is magnetic field (a) and vertical configuration with perpendicular magnetic field (b).The liquid helium cryostat insert with the 5 T Nb-Ti magnet (c).

Fig. 7 .
Fig.7.Current-to-electric field curves measured for the HTS cable at 4 K in various external magnetic fields.The power law fitted to each measurement to determine the critical current are plotted as solid curves.