Experimental study of stability, quench propagation and detection methods on 15 kA sub-scale HTS fusion conductors in SULTAN

High-temperature superconductors (HTSs) enable exclusive operating conditions for fusion magnets, boosting their performance up to 20 T generated magnetic fields in the temperature range from 4 K to 20 K. One of the main technological issues of HTS conductors is focused on their protection in the case of thermal runaway (quench). In spite of the extremely high thermal stability of HTS materials, quenching is still possible due to local defects along the conductor length or insufficient cooling. In such cases, the high stability results in the slow propagation of a resistive zone. Thereby, a risky hot-spot temperature (>200 K) can be reached if applying conventional quench detection methods at a voltage threshold of 0.1–0.5 V, typical for fusion magnets. Aiming at an experimental study of the phenomenon, a series of sub-scale 15 kA 3.6 m long conductors based on stacks of tapes soldered in copper profiles are manufactured at the Swiss Plasma Center, including twisted rare earth barium copper oxide (ReBCO) and bismuth strontium calcium copper oxide (BISCCO) triplets, non-twisted and solder-filled ReBCO triplets, as well as indirectly cooled non-twisted ReBCO single strands. Applying either an increasing helium inlet temperature, overcurrent operation or energy deposited by embedded cartridge heaters, critical values of the electric field and temperature are evaluated for a given operating current (up to 15 kA) and background magnetic field (up to 10.9 T). Once quenching is actually triggered, the quench propagation is studied using distributed voltage taps and temperature sensors able to monitor the external temperature of the jacket and the internal temperature of the conductor (helium or copper). Thanks to the recent upgrade of the Supraleiter Test Anlage (SULTAN) test facility, quench propagation in the conductors is measured up to a total voltage of 2 V and a peak temperature of 320 K. Furthermore, advanced quench detection methods based on superconducting insulated wires and fiber optics are also instrumented and studied. A summary of the test samples, their instrumentation and corresponding test results are presented in this work.

High-temperature superconductors (HTSs) enable exclusive operating conditions for fusion magnets, boosting their performance up to 20 T generated magnetic fields in the temperature range from 4 K to 20 K. One of the main technological issues of HTS conductors is focused on their protection in the case of thermal runaway (quench). In spite of the extremely high thermal stability of HTS materials, quenching is still possible due to local defects along the conductor length or insufficient cooling. In such cases, the high stability results in the slow propagation of a resistive zone. Thereby, a risky hot-spot temperature (>200 K) can be reached if applying conventional quench detection methods at a voltage threshold of 0.1-0.5 V, typical for fusion magnets. Aiming at an experimental study of the phenomenon, a series of sub-scale 15 kA 3.6 m long conductors based on stacks of tapes soldered in copper profiles are manufactured at the Swiss Plasma Center, including twisted rare earth barium copper oxide (ReBCO) and bismuth strontium calcium copper oxide (BISCCO) triplets, non-twisted and solder-filled ReBCO triplets, as well as indirectly cooled non-twisted ReBCO single strands. Applying either an increasing helium inlet temperature, overcurrent operation or energy deposited by embedded cartridge heaters, critical values of the electric field and temperature are evaluated for a given operating current (up to 15 kA) and background magnetic field (up to 10.9 T). Once quenching is actually triggered, the quench propagation is studied using distributed voltage taps and temperature sensors able to monitor the external temperature of the jacket and the internal temperature of the conductor (helium or copper). Thanks to the recent upgrade of the Supraleiter Test Anlage (SULTAN) test facility, quench propagation in the conductors is measured up to a total voltage of 2 V and a peak temperature of 320 K. Furthermore, advanced quench detection methods based on superconducting insulated wires and fiber optics are also instrumented and studied. A summary of the test samples, their instrumentation and corresponding test results are presented in this work. * Author to whom any correspondence should be addressed.
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Introduction
Recent advances in the technology of high-temperature superconductors (HTS), such as an increased critical current density and higher production yield, have finally turned the possibility for HTS-based fusion magnets into a practical matter. From a variety of high-current HTS conductor designs proposed for fusion magnets, relevant demonstrations have already been performed on certain twisted stacked-tape concepts [1,2], while other twisted stacked-tape variants [3][4][5][6] as well as conductor on round core (CORC) conductors [7] are yet to be tested. Simplified concepts based on a straight stack of tapes are also considered for coil windings operated in stationary mode [8][9][10].
The need for HTS for fusion magnets is essentially motivated by the increase in the generated magnetic fields, which allows the overall performance of the fusion machines to be improved [11]. In the case of the European Demonstration power plant (EU-DEMO) magnet system, the innermost layers of the central solenoid (CS) made of HTS conductors can increase the baseline operation at 12 T in coils up to 19 T, thus strongly increasing the available magnetic flux [12]. As a result, by achieving a longer plasma burn time, the effective power of the demonstration reactor can be increased by 10%-20%.
The feasibility study of HTS conductors for DEMO CS is currentlyaimed at the optimal conductor layout resilient to strong cyclic electromagnetic loading (up to 1100 kN m −1 ), tolerant to potential crack formation in the steel jacket due to fatigue issues, and also featuring sufficiently low AC losses caused by the pulsed coil operation (up to ∼1 T s −1 ) [13]. Although it must ensure the nominal operation of the CS modules, potential failure modes, such as the loss of cooling or the presence of defects along the conductor length, may result in an uncontrolled thermal runaway ('quench'), despite the high stability of the HTS materials. Hence, quench detection and protection aspects also have to be addressed.
A variety of quench detection methods are being considered for HTS. Using voltage taps is the most common electrical method, providing robust and repairable instrumentation. However, in order to exclude the large inductive components present during the operation of fusion magnets, voltage taps need to be co-wound together with the main conductor [14], thus losing their reparability feature. Furthermore, compared to low-temperature superconductors (LTS), the much slower propagation of the resistive zone in HTS during a quench raises concerns about whether the co-wound voltage taps are sensitive enough for timely detection. Enhanced sensitivity of the co-wound voltage taps can be achieved by using superconducting wires ( [15][16][17][18]). By establishing a good thermal contact with the main conductor, the voltage response can be strongly increased due to the much higher off-state resistance of the superconducting quench detection (SQD) wires compared to the main conductor. In that regard, the SQD wires can be considered as exotic distributed temperature sensors, which can only indicate whether the operating temperature exceeds the corresponding critical temperature at a given magnetic field somewhere along the wire length. To further enhance the noise cancellation performance, the SQD wires can be integrated as a twisted pair, which is electrically insulated from the main conductor along the entire length.
An overview of the non-voltage detection techniques based on the magnetic, optical and acoustic phenomena can be found in [19]. Most of them have rather complex responses, caused, for example, by the integral sensing of Hall probes, pickup coils and acoustic sensors or the dependence on mechanical strain of optical fibers. Thorough interpretation of the detection signal is required in order to achieve sufficient sensitivity and to avoid false positives at the same time. Detecting a quench during a magnet charge or a fast transient operation, corresponding to the highest chance of quenching, is especially challenging using these techniques. Nonetheless, the active development of these techniques is ongoing, and promising results have been reported by various groups (for example, see [20][21][22][23]).
Large fusion magnets are commonly protected by extraction of the stored magnetic energy (E) using an external dump resistor. A negligible amount of energy is then released in the coil winding itself, but high operating currents (I) and high discharge voltages (V) are required to decrease the discharge time constant τ = 2E/ (IV). The protection criteria are set at peak temperature at the location of the hot-spot, which is typically 150 K in the conductor jacket and ∼250 K in the cable. In combination with the time constant order of 10-30 s, the criteria usually result in a relatively large amount of stabilizing copper, corresponding to a copper current density of ∼100 A mm −2 .
In contrast, compact fully HTS fusion magnets explore an 'opposite' protection approach using non-insulated coil windings, thus dumping the stored energy into the cold mass. To the authors' knowledge, the method was first proposed for LTS windings in [24], and it became a widespread approach once it was also applied for HTS windings [25]. This enables much higher operating current densities and negligible discharge voltages; however, such windings are only suitable for slow operation to prevent large parasitic currents between the turns. Complicated mechanical loadings during a quench and long cooling times to recover the nominal operation should also be addressed. In that regard, an 'intermediate' protection approach based on insulated windings protected by a partial internal energy dump provided by a co-wound heater can be considered as a trade-off. The high power required for sufficient heating of the winding can actually be obtained from the stored magnetic energy by implementing a high current switch in parallel with the co-wound heater and external dump resistor. In this case, the dump resistor can be rated for much lower discharge voltages compared to a conventional external energy dump.
Experimental investigations on the quench characteristics of cable-in-conduit conductors have mostly focused on the stability aspects of LTS and the qualification of the detection methods (see [26][27][28][29][30]). For instance, the quench experiment on long Length (QUELL) experiment in Supraleiter Test Anlage (SULTAN) was an extensive test campaign that allowed the dominant regimes of the normal zone propagation to be revealed, which were strongly affected by the cooling aspects. It also highlighted the advantages of the embedded cowound voltage taps and optical fiber detection methods over the hydraulic techniques based on the absolute pressure and mass flow rate of helium [31]. The hot-spot evolution has also been studied experimentally [32], indicating at the importance of a thermal coupling between the cable and jacket.
Quench considerations on HTS fusion conductors have mostly focused on the development of numerical models (see [33][34][35]). The case of graded EU DEMO CS was also analyzed recently in [36]. Although the predicted quench performance is often found to be acceptable, the analyses are inevitably prone to certain modeling assumptions such as lumped-element geometry, fixing the thermal coupling parameters, voltage-current transition metrics and quench detection characteristics. In order to perform relevant experiments on HTS fusion conductors, the SULTAN test facility was upgraded with a new test insert, allowing a direct drive operation up to 15 kA transport current and 10 V operating voltage [37], complementing its regular low-voltage operation up to 100 kA using a superconducting transformer. This provides the possibility to maintain the DC currents in the temperature range from 5 K to 300 K using forced-flow helium cooling. The first test results obtained on triplet conductors made of soldered rare earth barium copper oxide (ReBCO) stacks are discussed in [38]. As reported in [39], the obtained data allowed the benchmarking of 1D thermal-hydraulic and electrical models and the refining of the assessment of the quench performance for the EU DEMO CS.
Recently, two more 'quench experiments' were performed in SULTAN on sub-size 15 kA conductors made of bismuth strontium calcium copper oxide (BISCCO) and ReBCO tapes. Apart from voltage and temperature monitoring, the new conductors were also equipped with two types of promising quench detection sensors for fusion magnets. The first one was a modification of co-wound voltage taps using non-stabilized SQD wires embedded in the conductor jacket and operated at a relatively low transport current of ∼0.1 A. This aimed at the increased detection sensitivity compared to the conventional technique according to the results presented in [40]. The second was an optical interferometer containing two plain fibers (i.e. without gratings); one was on the conductor jacket, and the other was a reference arm, forming a closed optical circuit. The obtained interference pattern converted to an electrical signal served as a detection trigger [41]. Both methods use integral-type sensing, not suitable for identifying the location of the hot-spot and aiming only at a '0/1' response for quench detection.
A summary of the SULTAN quench experiments is provided in this work, starting with an overview of the measured HTS conductors and their instrumentation in the next section. The test results are presented by focusing first on the stability aspects, followed by the quench propagation dynamics and detection characteristics of the SQD wires and fiber optics. A simplified method to evaluate the total voltage and hot-spot temperature is formulated and applied in the consideration of insulated coil windings protected by an external energy dump.

Overview of the test samples
All the measured conductors are made of soldered stacks of HTS tapes. Following the previous full-scale HTS conductor development at SPC [42], the first four of them contain stacks between the two semi-circular copper profiles forming round strands of 8.5 mm diameter. Using the three strands, a triplet cable geometry is then constructed. Both the strands and triplets are twisted at a twist pitch of 400 mm and 1000 mm, except the 'No-twist' conductor, where the stack orientation is always perpendicular to the external magnetic field (i.e. the DC SULTAN magnetic field is along the c-axis of the tapes), as shown in table 1. The triplets are inserted into a stainless steel tube of 8.5 mm wall thickness and eventually crimped to close the insertion tolerance. For the 'Filled' conductor, the triplets are filled with Bi 57 Sn 42 Ag 1 solder inside a U-shaped groove of the rectangular steel jacket, and the steel lid is then welded on top of it. The strands of the BISCCO conductor have increased the slot dimensions from 3.4 × 2.4 mm 2 in the previous conductors up to 4.5 × 4.5 mm 2 in order to accommodate the wider and thicker BISCCO tapes.
The two more studied conductors are a sub-sized version of the so-called ASTRA conductor (aligned stacks transposed in Roebel arrangement), which was proposed recently for application in the CS of the EU DEMO magnet [13]. The tape stack is oriented parallel to the external field, thus only one strand is used to achieve the target operation at 15 kA/10.9 T due to the higher critical currents. The strand is cooled indirectly through a contact with the top and bottom copper bars, delivering the cooling power from the tight cooling channel. Because of that, indium tapes are included in the contact and the conductor components are pre-compressed before the jacket welding in order to decrease the thermal resistance of the cooling path. With the exception of the BISCCO conductor, they are made of ReBCO tapes provided by shanghai superconductor technology (SST).
The conductors of about 3.6 m length are paired electrically in series and hydraulically in parallel to form a SULTAN sample. The voltage taps are distributed along the length at distances down to 100 mm in the region located in the high-field zone of SULTAN; see figure 1. The CERNOX temperature sensors are either placed on the conductor jacket or integrated within the cable space. The latter option is done using Swagelok fittings providing demountable and helium leak-tight instrumentation. In this case, the six sensors are facing the helium flow in each of the triplet conductors, whereas for the  ASTRA conductors the six of them (TH1-6) are touching the strand, the cooling channel and the copper bars. The conductors are cooled by a forced flow of helium through a dedicated space within the steel jacket, namely the voids between the strands for the Ref, No-twist and BIS-CCO conductors and the rectangular space between the solder domain and the top jacket plate for the Filled conductor. Both options correspond to a helium flow cross-section of ∼93 mm 2 . In the case of the ASTRA conductors, the rectangular cooling channel provides a ∼15 mm 2 section. The mass flow-rate of helium can be varied from ∼1 to 10 g s −1 at a pressure of 10 bar. Given that the SULTAN samples are tested in a vacuum environment, each conductor can be quenched individually, while avoiding a temperature rise in the neighboring conductor. Further details on the cooling circuit are given in [37].
The three types of SQD wires, which were found relevant for the following demonstration according to [40], are integrated in the grooves of the BISCCO and ASTRA conductors: MgB 2 monofilament wire in a stainless matrix of 0.3 mm diameter, MgB 2 60-filament wire in a Cu-Ni matrix of 0.5 mm diameter and Nb 3 Sn bronze-route wires of 0.8 mm diameter etched before the heat treatment. The performance of the wires in terms of their criticaltemperature as a function of the external magnetic field and the off-state resistance was preliminarily measured and reported in [40]. The 2 m long wires are inserted into a fiberglass sleeve and glued into the grooves using STYCAST; see figure 2. The epoxy glue and stainless jacket inhibit the thermal conduction to the SQD, thus decreasing the detection sensitivity compared to potential integration within the cable space. Nonetheless, it was chosen due to the simplicity of integration. As a relevant example, the co-wound voltage taps of International Thermonuclear experimental reactor (ITER) conductors are placed outside the steel jacket to simplify their integration, despite worsening their noise cancellation performance.
A bare optical fiber is also added in each groove. The F1 fiber was damaged during the first integration attempt upon removing a guiding scotch tape after epoxy curing because it was placed on top of the SQD wire and got stuck on the tape at the location of damage. Although the following fibers are placed beneath the SQD wires, the F2 fiber in the ASTRA conductor was also broken, presumably in the transition region between the narrow channel and the wider terminal section of the groove. The two fibers installed successfully ('F3' and 'F4') are in the grooves with the Nb 3 Sn SQD wires. Outside the groove, the fibers are protected by Teflon tubing. Each fiber is about 12 m long (including the 2 m long section of the conductor itself), which is routed inside SULTAN with the ends plugged into a feedthrough flange.
None of the SQD wires showed any issues after the integration, maintaining electrical insulation from the conductor, thus allowing their independent operation at a certain transport current. As discussed in the following section, the measured properties are also in agreement with the preliminary expectations based on the short sample measurements [40]. Thin insulated copper wires are soldered at the ends of the SQD wires; see the photographs in figure 2. One can also see the cross-section of the ASTRA conductor jacket showing the SQD wires and optical fibers, which was obtained after the test in SULTAN. A similar photo for the BISCCO conductor is not available because the conductor was not disassembled after the testing. The four-wire sensing method is used to measure the resistance of the SQD wires over the full length and also the 20 cm section in the high-field zone (HFZ).
Four cartridge heaters of about 3 mm (1/8 inch) diameter, 25 mm (1.0 inch) length and ∼20 Ω resistance are inserted into the steel jacket of the second ASTRA conductor. Two of them, 'H2' and 'H3', are near the center of the HFZ, and the other two, 'H1' and 'H4', are near the ends, at 200 mm distance from the center. In contrast toconductor heating by increasing the temperature of inlet helium, they allow the initiation of a quench in a more localized manner.

Experimental results and numerical assessment
So far, there have been five test campaigns focused on HTS quench experiments carried out in SULTAN, with the corresponding test conditions outlined in table 2. The first test on the sample made of the Ref conductor and an identical one made of non-soldered strands ended prematurely in the first quench run, when the latter conductor was burnt. This was caused by the manual current switch off being too late. As a result, an automatic sample protection system was implemented.
The two following tests on the HTS triplets allowed us to study the quench dynamics initiated by warming up the inlet helium using heaters wound around helium pipes. The sample made of the Filled and No-twist conductors was repeatedly quenched under 6 T, 15 kA and 11 T, 11 kA operating conditions, progressively reaching higher and higher hot-spot temperatures. The same was done on the sample containing the Ref conductor (the one used in the first test) and the BISCCO conductor at 4 T, 15 kA and 9 T, 10 kA.
The next test was performed on the ASTRA and BISCCO conductors. Following the extensive DC and AC characterization of the conductors, the ASTRA leg was also burnt on the fourth quench run. This time the reason was the poor termination design, where a short region of the strand was not stabilized by the copper bars. Although it was considered as a design feature that would provide the possibility for direct cooling (i.e. by preventing solder filling the cable space during the termination soldering), the initial assumption that the ∼1 cm long section was short enough to be effectively cooled by conduction was incorrect. No quench tests were performed on the BISCCO conductor during this campaign.
By revising the termination design of the ASTRA sub-size conductor, it was rebuilt aiming only at the 'indirect' cooling (i.e. helium flow only in the tight cooling channel). The sample was finally tested in a wide range of operating conditions (9-15 kA, 0-10.9 T) applying 'pulse' helium heating on both   legs. In addition, quenches initiated by embedded heaters and overcurrent operation were also performed on the ASTRA leg. The measured DC performance of the conductors at 10.9 T background magnetic field is compared in figure 3. The critical current obtained with the 1 µV cm −1 criterion is within a few percent of the expected values for the ASTRA conductor, about 5% lower for the BISCCO, Filled and No-twist, and up to ∼25% lower for the Ref and ASTRA2 conductors. The reasons for the reduction are being investigated; however, not preventing the quench measurements, for which the variation of the performances is actually useful to obtain a broader view on the quench dynamics. Note the wide range of n-values of V-I transitions, from ∼8 up to ∼40. Its impact on the conductor thermal stability is further considered below.
In order to interpret the observed behavior of the conductors during the quench measurements, the following heat balance equation is considered: which applies to a certain cross-section S of the conductor with the uniform temperature distribution and accounts for the dependence on the time t and longitudinal coordinate x. The contributions of copper, steel, superconductor and helium flow on the main thermo-electrical properties can be outlined as follows: • The heat capacity term CS (in J m −1 K −1 ) is a sum (CS) i for the involved materials. Considering their full amount, it is strongly dominated by steel (>70% contribution). The impact of helium becomes negligible above 10 K due to the strongly decreasing density with temperature. • The electrical resistance per unit length R 1 (I, T) = ρ (I, T) /S (in Ω m −1 ) as a function of the operating current I and temperature T for a given magnetic field has three distinctive modes: the one defined by the superconductor for I and T near the superconductor critical surface, the currentsharing regime between the superconductor and normal metals typically up to ∼40 K, and the normal-type operation at higher temperatures driven by copper. The currentsharing is assessed by solving an equality of the electric fields along the superconductor and normal metals, neglecting the transverse currents. In this calculation, the n-value is considered as a constant value in the range from 10 to 40. The impact of steel on the specific resistance of the conductors in the normal state is within 5%. The critical current density as a function of the magnetic field and temperature, required to calculate the resistivity of the superconductor, is taken according to the scaling laws reported in [1] for ReBCO and [43] for BISCCO tapes. • The thermal conductivity term kS (in W m K −1 ), a sum of (kS) i , is dominated by copper. Note that the material properties (C, ρ, k) as a function of temperature (and also magnetic field in the case of ρ and k of copper) are evaluated based on the Cryosoft material database [44]. • The cooling term q He P (in W m −1 ) features the wetted conductor perimeter P = πD h and the cooling flux of the forced flow helium q He , which can be expressed as q He = Nu · k He (T − T He ) /D h for the Nusselt number Nu = 0.026Re 0.8 Pr 0.4 (T He /T) 0.716 [45], the Reynolds number Re = 4ṁ/πD h µ and the Prandtl number Pr = µc He /k. The hydraulic diameter D h is of the order of a few mm for the test conductors, and the mass flow-rateṁ is a free parameter set in the experiment in the range from 1 to 10 g s −1 . This assessment requires the use of the helium thermal conductivity k He , viscocity µ and heat capacity c He as a function of its pressure p and temperature T He , which can be found tabulated in [46]. A certain value of T He will be assumed in order to avoid the complete hydraulic analysis of the turbulent helium flow. Note the strong impact ofṁ on the cooling power, increasing it from ∼40 W m −1 at 1 g s −1 up to ∼200 W m −1 at 10 g s −1 for p = 10 bar, T_He=5 K and T = 10 K.

Stability
Although the stability study was not among the main objectives of the quench experiments, the deposited energy is often increased gradually in the measurements until thermal runaway is finally observed in the conductors. This allows us to identify the critical operating parameters, such as the temperature and electric field, for a stable operation at a given operating current, magnetic field and helium flow. For example, a comparison of the observed performance of the No-twist conductor operated at 15 kA, 6 T and 1.5 g s −1 flow is presented in figure 4 for the two heating pulses. The first pulse is about 14 s long at 86 W heating power, thus releasing in total 1.2 kJ energy. Once heated helium reaches the conductor volume, an increase in the temperature and voltage and a decrease in the mass flow-rate is observed. However, the conductor recovers from the disturbance, reaching a maximum temperature of about 16 K and 1.9 mV voltage. The corresponding voltage contributions from the four 10 cm long sections increase downstream of the conductor at 13%, 21%, 30% and 36%. In contrast, when applying the heat pulse for 16 s, the initial temperature and voltage response are nearly identical, but this eventually leads to conductor quenching. The operating current is then switched off when the peak temperature increases up to 100 K, almost 70 s after the beginning of the pulse.
Similar values of the quench voltage, though less accurate, are observed in the other triplet conductors. The Filled conductor recovers after reaching ∼3 mV, but quenches once ∼4 mV is developed. These two values are ∼2 mV and ∼3 mV for the Ref conductor, and ∼0.5 mV and ∼0.6 mV for the BIS-CCO conductor.
The recovery behavior is analyzed in terms of the 'coldend' recovery, also known as the 'equal-area' theorem [47]. This method provides a solution for equation (1) in the case of a stationary operation (i.e. ∂T/∂t = 0), which can be expressed as follows: where T 0 and T q are the initial and quench temperatures. The equation terms are presented as a function of temperature for the ReBCO triplet conductors operated at 15 kA, 6 T and 1 g s −1 cooling in figure 5.
The two assumptions are considered in the calculation for the helium temperature: T He = 5 K independent of the conductor temperature (dashed line), and imposing a 5 K limit on the difference between them (solid line). Under these assumptions, the solutions of equation (2) in terms of T_q are respectively 20.9 K and 18.7 K; see the circles in figure 5. At these points, the Joule heating is about 2-3 times higher than the cooling power.
The minimum propagating zone (MPZ) can be estimated from equation (1) assuming that ∂T/∂t = 0, simplifying the heat conduction term as kS (T q − T 0 ) /MPZ 2 and also accounting for the cooling term, thus MPZ = √ kS (T q − T 0 ) / (I 2 R 1 − q He P). It yields MPZ ≈ 15 cm for the case considered above and the quench voltage V q = MPZ · IR 1 (I, T q ) = 1.8 mV. Note the relatively low value of adiabatic quench energy (i.e. the enthalpy difference for the operation at T 0 and T q of the conductor section of the MPZ length), which is only about 30 J compared to the energy required to trigger the quench (∼kJ). This highlights that the impact of cooling on the conductor stability is decisive.
The quench temperature is also obtained for the second ASTRA conductor. It decreases from about 35 K at 9 T to 29 K at 10.9 T for the operation at 9 kA, 1 g s −1 and from 24 K at 9 T to 22 K at 10.9 T for the operation at 12 kA, 2 g s −1 . The results are shown in figure 6 as a function of the operating current together with the predicted curves based on the 'coldend' recovery method for the operation at 10.9 T and various cooling rates.
The n-value, which characterizes the steepness of the voltage-current transition, is set at 15 in the calculation. It corresponds to the value obtained in the second ASTRA conductor, although a much higher value of about 45 was observed in the first one (see figure 3). Note that the n-value has a strong impact on T q , decreasing it from ∼24 K at n = 10 down to ∼10 K at n = 45 for the operation at 15 kA, 11 T, 2 g s −1 .
The calculated MPZ and quench voltage are similar to those obtained in the triplet conductors, falling in the range of 10-20 cm and 1-10 mV, depending on the operating conditions. The measured quench voltage is in the same range, except for the two measurements performed at 9 kA and using the two heaters H2 and H3, resulting in voltage recovery after reaching 11.2 mV at 9 T and 12.5 mV at 6 T.
Considering the specific resistance of the ASTRA conductor, the quenching conditions are reached in the range of 1 to 10 µΩ m −1 , near the end of the current sharing operating mode. This can be seen in figure 7, where the performance of the conductor in that range becomes nearly identical to the one corresponding only to copper and steel, excluding the superconductor. The beginning of the current sharing mode, which can be defined at the voltage threshold of 1 µV cm −1 , is also indicated by the current-sharing temperature T cs , which corresponds to the specific resistance order of 10 −2 µΩ m −1 , i.e. 2-3 orders of magnitude lower than the range where the quenching conditions can be reached.

Quench propagation
Once the conductors are actually quenched, the operating current is kept constant until their thermal runaways reach certain limits in terms of the measured voltage or peak temperature. After that, the operating current is switched off almost instantaneously, and they start recovering to the nominal operating conditions.
An example of the electric field evolution along the BIS-CCO and ASTRA conductors is shown in figure 8. For the BISCCO conductor operated at 12 kA and 10.9 T, the quench initiates at the beginning of the HFZ of about 0.4 m length caused by the 30 s heating pulse at 160 W applied to the helium inlet flow; see the left plot. Relatively fast and uniform propagation over the entire HFZ and also partially outside of it is observed. In contrast, quenching the ASTRA conductor at 12 kA, 10.9 T by a 10 s pulse at 170 W on the helium flow (the central plot), the runaway starts at the end of the HFZ and then propagates slower mostly in the downstream direction of the helium flow. The right plot corresponds to the overcurrent operation of the ASTRA conductor at 15 kA, 10.9 T, leading to quench initiation at the start of the HFZ, but then quickly propagating downstream over the entire HFZ.
Using the embedded heaters on the second ASTRA conductor, the quench dynamics are presented in figure 9 for the operation at 9 kA and 6 T. All of the three studied cases, using Heater 1 at the beginning of the HFZ (−0.2 m wrt to the HFZ The maximum electric field in the performed measurements is typically around 10 mV cm −1 . Considering the specific resistance of the ASTRA conductor as a function of temperature (see figure 7), the peak temperature can be estimated at about 200 K (∼70 µΩ m −1 ) and up to 300 K (∼110 µΩ m −1 ) for the operation at 15 kA and 9 kA, respectively. The temperature measured along the conductor follows the electric field distribution, although lower values are typically observed on the sensors compared to the estimate from the electric field, with the difference up to 50 K in some cases. However, some of the measured temperatures are actually higher than the estimated ones. Hence, it should be noted that a direct comparison is not justified because the estimate is based on the voltage obtained from a relatively long section (at least 10 cm long) and the temperature can vary significantly along such length.
An illustration of the electric field and temperature distributions is provided in figure 10 for the triplet conductors at the moment of reaching 0.5 V total voltage, except for the Filled conductor where this voltage was not achieved, thus 0.4 V is set instead. The temperature estimates (dashed lines) are obtained from the electric field, similar to that discussed for the ASTRA conductor above, and shown only above 40 K, i.e. in the range where the impact of the HTS on the electric field can be neglected. The measured temperatures (solid lines) are those from the sensors located in the helium flow. They typically show higher temperatures compared to the sensors on the steel jacket, especially at the location of hot-spots. The difference is relatively low for the Filled and ASTRA conductors, deviating by up to ∼10 K and ∼30 K, respectively. However, it increases to up to ∼50 K for the Ref and No-twist conductors, and even ∼90 K for the BISCCO conductor.
Comparing the pulse and continuous heating applied to the Ref conductor, a downstream shift of the voltage and temperature profiles can be noted. Although the measured peak temperature is around 100 K in both cases, the voltage profile is sharper and narrower in the latter case, with the peak slightly outside the HFZ, at the ∼0.25 m coordinate. This is related to the relatively weak dependence of the ReBCO critical current on the magnetic fields, and thereby the HFZ defined as the 4% SULTAN field homogeneity does not provide a strong confinement on the quench propagation.
Similar profiles are obtained in the No-twist and Filled conductors for the pulse heating. A larger discrepancy between the measured and estimated temperatures is observed in the triplet conductors, at up to about 100 K for the Ref and No-twist conductors, and 55 K for the Filled one. This corresponds to the enhanced thermal coupling between the steel jacket and cable in the Filled conductor. Its overall impact on the quench performance is further discussed in the next section, alsoaccounting for the additional relevant observations reported below.
The BISCCO conductor, which should be identical to the Ref conductor in terms of the thermal coupling, demonstrates a temperature mismatch of up to 70 K between the estimated and measured values. However, it varies among the quench runs performed under the same operating conditions (4 T, 15 kA, 1.5 g s −1 ), with the maximum difference decreased down to 30 K for some of them.  The location of the maximum electric field and temperature does not change during the thermal runaway in most of the performed measurements on all the conductors. As an example of the few exceptions observed, see again the voltage evolution in the overcurrent operation of the ASTRA conductor (the right plot in figure 8).
Given the relatively high temperature range at which the conductors actually quench (∼20-40 K), the time evolution of the maximum temperature T max can be assessed by neglecting the heat conduction and cooling terms in equation (1) and noting that the specific resistance R 1 becomes independent of the operating current (see figure 7). As a result, T max can be calculated from the following equation: where the quench temperature T q is used as the initial temperature and q is commonly referred to as the quench integral. T q is set at 40 K in the following discussion. In order to justify the considered assumptions, the impact of the current-sharing Figure 11. Peak temperature as a function of the quench integral for the ASTRA conductor using adiabatic assumptions.
mode on the T max (q) dependence is studied in figure 11. Note that the time is set to zero at T = 40 K, therefore q < 0 at lower temperatures. The curves obtained from equation (3) (see the dashed lines) are compared to those from equation (1), by neglecting the last two terms and considering T cs as the initial temperature, thus R 1 (I, T) depending also on the operating current. As expected, the impact of the current-sharing is negligible for temperatures above 40 K (i.e. q > 0), thus the superconductor can be neglected in that range of temperatures in the electrical and thermal considerations. At lower temperatures (i.e. q < 0), the performance is determined by the superconductor through the current-sharing term represented by R 1 (I, T), resulting in a strong non-linear behavior. The value of the quench integral required to increase the conductor temperature from T cs up to 40 K decreases with the operating current despite the lower values of T cs (i.e. higher margin to 40 K), from about 10 10 A 2 s at 6 kA (∼13 K margin) down to 0.5 × 10 10 A 2 s at 15 kA (∼35 K margin).
The obtained curves are essentially linear in a semilogarithmic scale for T max > T q . This allows us to parameterize them as follows: where the parameter p is a characteristic value of the quench integral q, which leads to T max = 2.71T q ≈ 110 K. By extracting q from equation (4) and combining it with equation (3), the following explicit expression can be derived for arbitrary temperatures T 1 and T 2 : p ≈ It is proportional to CS, meaning a strong impact by the steel jacket as outlined in the beginning of the section. The actual values are extracted implicitly by fitting the T max (q) curves for the considered conductors based on their material composition (see table 1). It was verified that p indeed depends linearly on the steel cross-section as suggested by the explicit expression. As a result, it can be expressed as p = p 0 + f · (p 1 − p 0 ), where p 0 and p 1 are the values calculated for the full and null Table 3. The values of p considering zero (f = 0) and full (f = 1) cross-section of steel for the studied conductors.
Conductor cross-section of steel and the factor f is its relative fraction considered in the calculation. The values of p 0 and p 1 are reported in table 3.
The factor f provides a quantitative measure of the thermal coupling between the cable and steel jacket, expressing the 'perfect' coupling as f = 1 and the absence of it as f = 0.
The actual values can be assessed from the measured T max (q) curves, which are summarized for the various operating conditions in figure 12. The measured curves correspond to the highest temperature observed from the collection of instrumented sensors.
A rather weak impact of the different operating currents, external magnetic fields and methods of quench triggering (i.e. pulse and continuous helium heating, embedded heaters and overcurrent) is observed on the T max (q) curves, which confirms the validity of the considered adiabatic assumptions. A weak thermal coupling, expressed as f ≈ 0.25, can be concluded for the Ref, No-twist and BISCCO conductors, which is due to localized contacts between the cable and steel domains. An improved effective heat capacity, corresponding to f ≈ 0.5, is observed in the Filled conductor, caused by the large contact area provided by the solder. The highest effective heat capacity, f ≈ 0.6, is for the ASTRA conductors following the large contact area and the pre-compressed conductor structure. However, note that the peak temperatures measured on the ASTRA conductors actually rise faster than those of the Filled conductor because the absolute cross-section of steel is ∼50% lower.
The measured distributions of the electric field are used to evaluate the quench propagation velocity (QPV) using a threshold of 1 mV cm −1 . It corresponds to a specific resistance of 5-10 µΩ m −1 and an estimated temperature of ∼50 K (see figure 7), thus ReBCO is still in a superconducting state (critical temperature ∼70 K at 11 T), although its current capacity becomes negligible compared to the large copper stabilizer, whereas BISCCO is already in the normal state (critical temperature ∼30 K at 11 T). By obtaining the time moments of reaching the threshold among the distributed voltage taps, the QPV can be estimated as the ratio of the difference between the centers of the neighboring sections and the difference between the corresponding moments. In that regard, the QPV can be attributed to the location of each individual voltage tap, which can be considered virtually as a stopwatch point for the traveling resistive zone. However, four locations cannot be used in this method, namely the two taps enclosing the first section, where the threshold was reached, due to uncertainty of the hot-spot initial location, and the two at the conductor ends. Focusing on the HFZ containing five voltage taps spaced by a The QPV can also be assessed numerically. Accounting for the broad current-sharing mode in the conductors, the following expression is considered [48]: where T 0 is the initial operating temperature and T t the transition temperature. The applicability of this formula for HTS is further justified in [49]. As T t is defined for the propagating resistive zone, it is expected to be slightly higher than the quench temperature T q , which corresponds to a stationary, non-propagating situation. Note that QPV ∼ 1/CS, meaning that increasing the thermal coupling with steel (f → 1) slows down the quench propagation, while the hot-spot build-up also becomes slower as the parameter p increases. The values of the factor f obtained from the measurements (see figure 12) are used in the following calculation. The values of QPV obtained from the experiments and T t that result in a QPV of the same range, but derived from equation (5), are summarized in table 4. The data indicate a gradual increase of the QPV and decrease in T t by increasing the operating current. The values of the QPV are typically in the range from 10 to 100 mm s −1 , except those for the ASTRA conductors operated at 15 kA, which is due to the very high n-value of the first conductor and the overcurrent operation of the second one, both leading to a strong decrease in T t down to ∼10 K. The Ref and No-twist conductors demonstrate a similar performance. Compared to the BISCCO conductor, they are of increased stability and slower quench propagation, whereas the opposite can be stated if compared to the Filled conductor. This corresponds to the lower critical temperature of the BISCCO tapes and the increased effective heat capacity of the Filled conductor by solder filling. The total voltage developed along the conductor can be assessed in a simplified manner given that the QPV is obtained for the conductor operation, at which the impact of the superconductor becomes negligible on the electrical properties, i.e. corresponding to an operating temperature of ∼50 K. As the specific resistance R 1 becomes a linear function of temperature (see figure 7), integration of the electric field E = I op R 1 along the length can be estimated as the peak electric field multiplied by the size of the resistive zone, i.e.
where T max is the maximum temperature defined by equation (4), and t denotes time, which is set at zero when T max = T q . The impact of the thermal coupling with steel on the total voltage is twofold, because T max follows an exponential rise upon t/CS, and the size of the resistive zone is proportional to t/CS. Therefore, increasing the thermal coupling would only lead to a longer time to reach a certain value of the total voltage, but the corresponding value of T max at that voltage would remain almost unchanged.
The measured data on the ASTRA conductor are compared to the results of the assessment using the values of QPV taken from table 4 and the factor f = 0.6; see figure 13. The calculation typically overestimates the measured voltage. This is clearly seen for the operation at 9 kA for voltages above 0.2 V. This discrepancy should be primarily caused by the QPV, which is assumed to be constant in the assessment, whereas it decreases substantially in the SULTAN measurements once the propagating front exits the HFZ of ∼0.5 m length (see related discussion in [39]). Note that the measured voltage at higher currents has an offset at zero time corresponding to the contribution from the resistive zone that reached the peak temperature of ∼40 K, which is not included in equation (6).
According to equation (6), a linear dependence of the total voltage upon the maximum temperature is expected for temperatures above 40 K. This correlation is also observed from the measurements; see figure 14. The operating current has a strong impact on the measured curves, resulting in a counterintuitive trend of the maximum temperature decrease with the increasing current for a given value of the total voltage. However, it can be understood from the terms comprising equation (6), which actually indicates at the maximum temperature being inversely proportional to the quench integral, i.e. T max ∼ V/ ( . In contrast, the impact of the magnetic field is relatively weak, affecting the maximum temperature of the BISCCO conductor within 10% deviation. Nonetheless, similar to the operating current, increasing the magnetic field reduces the maximum temperature at a certain voltage.

Detection methods
Apart from the experience gained on the integration and operation of the optical fibers installed on the ASTRA and BISCCO conductors, no useful information concerning their actual detection performance has ever been obtained. Issues related to the detection sensitivity were actually expected due to the negligible thermal contraction of fibers at temperatures below 50 K as well as the high attenuation of the signal in the performed measurements, which is not yet fully understood. Considering the successful demonstration of the nearly identical optical method based on the optical fibers integrated in the cable space without firm fixation, which is reported in [31], a certain detection response was nonetheless expected. Unfortunately, no evident correlation has been observed by analyzing the raw oscillating signal from the photodetector. For example, for those test runs where the minimum and maximum levels of the signal are maintained almost unchanged, counting the number of fringes per second is not correlated with the thermal runaway of the conductors. In multiple runs, the levels are actually drifting, preventing reliable data treatment. Decoupling the fibers mechanically from the test conductors might be suggested for future tests in order to obtain a reliable response.
The SQD wires were first characterized during the cooldown and warm-up, and also during the DC measurements performed on the ASTRA and BISCCO conductors. The critical temperature (T c ) of the four wires as a function of the SULTAN DC background field (see table 5) is in line with the preliminary results obtained on the corresponding short wire samples, which are reported in [40]. Due to the undoped composition of the MgB 2 wires, their critical temperature decreases rapidly with the magnetic field. At 10.9 T, it is even below the minimum operating temperature in the experiment of about 6.5 K, thus a proper operation is not possible under such conditions.
The resistance of the wires per unit length is measured from ∼5 K up to ∼300 K at zero magnetic field; see figure 15.  At temperatures exceeding T c by up to ∼40 K, the normal state resistance is nearly constant at about 3.6 Ω m −1 for the MgB 2 /SS wire and 0.07 Ω m −1 for the Nb 3 Sn etched wires, whereas it increases gradually for the MgB 2 /CuNi wire up to 1.1 Ω m −1 at 270 K. The relatively low resistance of the Nb 3 Sn wires could be compensated for by increasing the operating current to achieve a stronger absolute response; however, it was kept fixed at 0.1 A in the experiment. Alternatively, thinner or even non-stabilized monofilament Nb 3 Sn wires can also be used to increase the resistance. For example, up to 60 Ω m −1 is estimated for the external tin 0.13 mm wire used in the SUL-TAN conductor [50], and a wire size reduction down to 30 µm diameter was recently reported for bronze route wires [51]. Given the weak dependence of the normal state resistance of the wires upon the temperature, the measured resistance is normalized by the specific resistance near T c . In the case of relatively low peak temperatures (up to ∼T c + 40 K), such normalization corresponds to the length of the conductor resistive zone, which exceeds T c of the wire. For example, the normalized signals are compared for the ASTRA conductor operated at 11 kA, 0 T, as shown in figure 16.
At zero time, the peak temperature measured by T8 is about 17 K and the Nb 3 Sn wire starts to react, reaching the 2 m equivalent length in 18 s, i.e. matching the actual total length of the instrumentation (see figure 1). Afterward, the increase rate sharply drops, suggesting that the entire wire length is in the normal state. A similar reaction rate is observed on the MgB 2 /SS wire, which starts at 36 K measured by T8 and takes around 7 s to saturate the 20 cm section in the HFZ and 30 s to complete the transition over 2 m. The takeoff temperatures obtained from T8 nearly match the T c of the wires, which allows us to conclude that there is sufficient thermal coupling between the SQD wires and the conductor. One can estimate the QPV as ∼100 mm s −1 at ∼20 K from the Nb 3 Sn wire and ∼29-67 mm s −1 at ∼40 K from the MgB 2 wire. In contrast, the total voltage increases relatively slowly for ∼110 s, until the peak temperature reaches ∼60 K, but starts to rise much faster afterward. Note that one cannot attribute whether the SQD response is still due to the quench trigger or already due to the quench propagation. However, this should not anyhow violate the idea of quench detection, i.e. detection of the exceeding temperature can never be a false positive event (assuming T c (B) is appropriately selected).
The in-field performances at 10.9 T of the Nb 3 Sn SQD wire are shown in figure 17 for the ASTRA conductor quenched by the helium heating and using the embedded heaters. The wire reaction starts at ∼12 K measured by T8 and it saturates within ∼15 s. The transition is slightly faster for the helium heating due to the more uniform distribution of the deposited energy. In both cases, acceleration of the transition can be seen after developing ∼1 m long resistive zone.
The build-up of the SQD detection signal in the BISCCO conductor is more sophisticated; see figure 18. There is a fast increase up to the ∼1 m long resistive zone within 5 s, followed by a slower propagation for ∼20 s at 9 T and ∼30 s at  6 T up to a ∼1.5 m length, after which it accelerates again. However, once the peak temperature increases above ∼50 K, slightly before ∼1.5 m length is reached, the used normalization of the SQD signal can no longer be interpreted simply in terms of the resistive zone length, because certain regions along the wire, which experience elevated temperatures, start increasing their specific contributions to the total signal. Sufficient increase of the total voltage by at least 0.1 V is typically observed at the peak temperature of ∼50-70 K. Regarding the SQD wires, an increase in the resistive zone until ∼1 m length, corresponding to a peak temperature of ∼20-30 K, can be considered sufficient for triggering the quench protection. It results in a reduction of the quench detection time by 10-20 s.

Outlook on the coil windings
In contrast to the quench measurements in SULTAN, where the operating current is switched off instantaneously, the operating current follows an exponential decrease at a certain time I 0 e −t/τ ) 2 dt = I 2 0 τ /2. In large EU DEMO magnets, τ ≈ 10 s for the CS modules and ≈ 30 s for the toroidal field coils. Due to the relatively slow decrease in the operating current, the additional increase in the hot-spot temperature is assessed below, considering for convenience the 15 kA Ref conductor discussed above. Even though the operating currents of the DEMO conductors are substantially higher than 15 kA, they also require a proportionally larger cross-section of the components, thereby not essentially changing the outcome of the analysis.
Considering the total voltage developed along the conductor as the detection signal, the detection time t 0 is defined as V (t 0 ) = V th , where V is calculated according to equation (6) and V th is the detection threshold. As a result, the hotspot temperature is obtained as T hot -spot = T max ( I 2 0 t 0 + I 2 0 τ /2 ) using equation (4) and neglecting the quench validation time (typically ∼1 s), which is applied to avoid false positives. The maximum temperature at the detection time, T max ( , is almost independent of the thermal coupling between the cable and steel represented by the factor f, as indicated previously in the discussion of equation (6). However, T hot -spot strongly decreases with the increasing f because it only results in an increase in the conductor thermal capacity; see figure 19.
The hot-spot temperature design criterion is typically set at 150 K on the steel jacket and ∼250 K on the cable. In that regard, the conventional quench detection and protection systems applied at τ ≈ 10 s result in acceptable values of T hot -spot , except for the very low values of f (<0.2) and high values of V th (>0.1 V). At τ ≈ 30 s, the detection threshold of 0.1 V becomes unacceptable for conductors with a low thermal coupling, f < 0.4, whereas the entire range of f fails to fulfill the temperature requirement at 0.5 V detection. Note that the highest value of f observed so far in the measurements is ∼0.7 (according to figure 12). In that regard, decreasing the detection time or increasing the amount of stabilization is required to avoid overheating. The first option is preferred as it does not affect the nominal magnet performance.
Considering the SQD wires to decrease the detection time, both T c and the normal state resistance should be sufficiently high. Given that the voltage developed along the conductor at 0.1 V detection threshold is of the order of 0.1 V m −1 at a peak temperature of ∼50-70 K, the normal state electric field of the wires of ∼1 V m −1 should be pursued. This is a reasonable value considering the thin wires (<0.5 mm diameter) at 0.1-1 A operating current. For conductors having a relatively low n-value of the voltage-current transition (∼15), a quench temperature in the range from 30 K to 40 K would be required to achieve a T c in the same range to avoid potential false positives for the quench detection.
In that regard, proper operation of the SQD wires has not yet been demonstrated in the quench experiments, as the MgB 2 wires, having sufficiently high off-state resistance, are of low T c at high magnetic fields and the Nb 3 Sn etched wires are of low off-state resistance, having T c ∼ 10 K at high fields. The latter option, with the increased resistance by the wire size reduction, might still be applicable for HTS conductors with a high n-value, which substantially reduces the quench temperature down to ∼10 K (as observed in the first ASTRA conductor). Otherwise, achieving a T c of ∼30-40 K at high magnetic fields, up to 18 T for DEMO CS, is expected from MgB 2 -doped wires or, more likely, iron-based superconductors (see also [40]).

Conclusion
A series of sub-scale 15 kA 3.6 m long conductors based on a stack of tapes soldered in copper profiles were measured at the SULTAN test facility at SPC, aiming to establish the stability and quench characteristics. These include the ReBCO and BISCCO triplet conductors as well as sub-size ASTRA conductors, containing a single indirectly cooled strand operated in parallel magnetic field. The cross-sections of the material components used in the sub-scale samples are proportional to the designed full-size conductors, such that the current densities are the same.
A very stable operation featuring a quench temperature T q typically in the range from 30 K to 40 K is observed, which requires a large amount of energy to initiate quench propagation. Lower values of T q , down to ∼10 K, are found in conductors with a high n-value (∼45) or when operated in the overcurrent mode due to the presence of defects along the conductor length. The well-known 'equal area' stability method is also proven to be adequate to analyze the measured behavior of the HTS conductors cooled by a forced flow of helium. The estimated and measured values of the quench voltage are in the range from 1 mV to 10 mV.
In the actual thermal runaways of the conductors, the developing voltage and temperature profiles basically follow an adiabatic release of the Joule heating, unlike the LTS conductors, whose performance is strongly affected by cooling effects during the quench propagation. Corresponding expressions for the peak temperature and total voltage are proposed and validated by the test results. As a result, enhancing the thermal coupling between the cable and steel jacket is found to be crucial to avoid overheating, despite the fact that it decreases the QPV.
In order to address the slow quench propagation, developing at the rate of ∼10-100 mm s −1 in the experiment, fast quench detection can be achieved by using SQD wires, as demonstrated in the measurements using MgB 2 and Nb 3 Sn wires. Even though the SQD wires were integrated in the steel jacket of the ASTRA and BISCCO conductors, sufficient thermal coupling was observed in the measurements. Depending on the actual quench temperature, the optimal detection performance can be provided either by non-stabilized ironbased wires addressing the T q range of 30-40 K at high magnetic fields or Nb 3 Sn thin wires for T q ∼ 10 K. The electric field developed along the SQD wire in the normal zone has to be ∼1 V m −1 to ensure the superior performance of this detection method. The optimized performance and issues related to high-voltage insulation at the extraction regions of the instrumentation are yet to be addressed. Even though the intended demonstration of quench detection based on optical interferometry did not succeed, further investigations of this method should be attempted.
HTS conductors for fusion with high n-values (>30) may also be appealing in order to increase the propagation velocity due to the reduced stability. This is in contrast to fusion conductors made of LTS, for which decreasing the n-value is often proposed to enhance their stability.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).