In-field strain and temperature measurements in a (RE)Ba2Cu3O7−x coil via Rayleigh-backscattering interrogated optical fibers

(RE)Ba2Cu3O7-x (REBCO) conductors have overcome technical challenges related to manufacturing quality, length homogeneity, scale-up of piece-length, and joints. There is one remaining technical challenge, however, which is common to all high temperature superconductors and lies in effective detection of failure to prevent material degradation. An innovative technique based on optical fibers interrogated by Rayleigh backscattering has been shown to have advantages over voltage taps at detecting incipient faults. Prior work has experimentally demonstrated the technique in several implementation scenarios, including direct integration of optical fibers into superconducting conductors and cables to create a class of ‘SMART’ conductors and cables that are able to monitor their own health. In this paper, the magnet monitoring technique based on Rayleigh backscattering interrogated optical fibers has been experimentally studied in a model coil subject to external magnetic field, where different fiber integration methods are used to increase selectivity of the fiber sensor to temperature. Results show that the spectral shift displays different features during strain and thermal transients. The implications of the results in terms of potential and limitations of each sensor as well as strain-temperature decoupling are discussed.

quench detection, superconducting magnets, high temperature superconductors (Some figures may appear in colour only in the online journal) * Author to whom any correspondence should be addressed.
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

Introduction
Due to the progress in manufacturing quality and uniformity along conductor length, high temperature superconductor (HTS) magnets are rapidly becoming a viable option for applications including particle accelerators, fusion reactors, nuclear magnetic resonance spectrometers, and power and defense devices [1][2][3][4]. Meeting the demands of these industrial applications requires a robust system protection methodology tailored to the unique challenges of HTS. The main failure mechanism for HTS devices, which can lead to complete loss of functionality and irreversible material damage, is an unrecoverable quench. A quench initiates with a localized loss of superconductivity, at which point current starts to flow into the normal material generating heat and propagating the normal zone. If this process is not arrested, it leads to complete thermal runaway and catastrophic failure [5]. Although qualitatively the process of transitioning to the normal state is analogous, a key difference of HTS from their low temperature counterparts is a low normal zone propagation velocity (NZPV).
Low temperature superconductors (LTSs) have a NZPV that is 2-3 orders of magnitude higher than that of HTS [6][7][8][9][10]. A small NZPV implies a highly localized hot-spot that must be detected before the local increase in temperature creates irreversible material degradation. Conventional quench detection consists of monitoring voltage via voltage taps on the coil winding. This is typically sufficient for LTS magnets. Because of the slower propagation, HTS present a narrow window of opportunity for highly localized normal zones to be detected before rapid protection measures must be employed. A novel quench detection approach based on Rayleighbackscattering interrogated optical fibers (RIOFs) has been shown to be a potential solution to the quench challenge for HTS [11].
The measurement principles of all optical fiber sensors are based on the dependence of light-matter interactions on the quantity to be measured. In the case of RIOF, the interaction is Rayleigh backscattering and the measurands are temperature and strain. The scattering centers that produce Raleigh backscattering are naturally occurring microstructural defects in the fiber material. This allows for the use of telecommunication grade optical fibers, without the need for any post-processing or specialty fibers [12][13][14]. The RIOF technique is based on the comparison of a reference scan that represents a snapshot of the interactions along the fiber length at reference conditions. If the scan is repeated after a change in temperature or strain, the deviation from the reference can be quantified via cross correlations to yield a 'spectral shift' signal as a function of position along the fiber. This can be done by virtually dividing the fiber into segments, thus defined the spatial resolution. The measurement can be repeated in time, using always the initial reference scan or any subsequent scan, yielding a realtime measurement. Although in this study the segment size is 2.6 mm (highest available with this commercial interrogator), the spatial resolution of RIOF can be as high as sub-mm, although this would require modifications to a commercial interrogator. The time resolution depends on the total interrogated length, the spatial resolution, and the computing power.
Some of the unique strengths of RIOF include immunity to electromagnetic noise, high sensitivity to thermal and mechanical perturbations, fast response time, and high spatial resolution (mm-range). Furthermore, it has been shown that thermal sensitivity and response time of RIOF at cryogenic temperatures can be improved via dedicated coatings [15] and that optical fibers can be compatible with harsh environments that are present in applications of HTS such as nuclear fusion and particle accelerators [16]. RIOF has been integrated into small coils via co-winding with HTS conductor [11,17], via direct integration into the REBCO conductor architecture, yielding a 'SMART' conductor that is able to monitor its state in realtime [18], as well as into cables such as the SMART Conductor On Round Core (CORC ® ) [19,20].
Both in LTS and HTS, in addition to a local rise in temperature that accompanies incipient quenches, superconducting coils also experience mechanical deformation. The deformation of superconducting wires can have different origins. It can be due to the cabling process and differential thermal contraction between winding components [21][22][23][24][25]. In this case, the strain is built-in during magnet manufacturing and cool-down and it is therefore static during nominal operation. When the strain is due to to Lorentz forces [26][27][28], however, it can be time-dependent, simply because the operating conditions are time dependent or because of any undesired electromagnetic transient.
Fundamental studies of the strain transfer from specimen to optical fiber have been carried out via analytical or numerical models [29,30], as well as a combination of an analytical model validated against dedicated experiments and numerical models [31]. Prior work involving optical fibers integrated in superconducting coils, however, was limited to reporting raw spectral shift signal that is a combination of temperature and strain changes of the optical fibers. Additionally, coils were not subject to any applied magnetic field. To overcome these limitations, and since prior studies on strain transfer were very fundamental in nature, the scope of this work is to experimentally study how different fiber integration methods in superconducting coils affect the fibers' ability to measure strain, temperature, or a combination thereof, and to work in a high background magnetic field. Thus, here we report experimental results on how different fiber integration methods affect the nature of the spectral shift signal, with particular attention to strain and temperature sensitivities. A small solenoid wound with REBCO conductor has been energized and de-energized while in presence of an external magnetic field as high as to 3 T, thereby subjecting the coil to deformation due to Lorentz forces. Control experiments have been carried out with different fiber integration methods in a tensile testing machine.

Straight samples
A set of three straight conductor samples were prepared to evaluate different fiber integration methods, ranging from a naked fiber attached to the conductor surface, to a fiber housed into a capillary tubing. Straight sections of about 15 cm in length of 4 mm wide YBCO coated conductor from SuperPower were used as substrate to incorporate the optical fiber. Three different samples were prepared, with different fiber integration methods. The first sample comprised a naked fiber directly placed on the conductor surface. Sample 2 had an optical fiber housed into a fused silica capillary tube, with the tube placed on the conductor surface, whereas the third sample featured the optical fiber inside a Hytrel ® tube. In all cases the optical fiber, or the tube that houses the optical fiber, was attached onto the conductor surface with Loctite Stycast epoxy 2850FT. Dimensions and material information of the two capillary tubing and the optical fiber are summarized in table 1. Photos of the three conductor sections can be seen in figure 1.
The fiber-conductor assembly was loaded in a tensile testing machine to undergo tensile stressing. The conductor section that was coupled to the fiber extends in between the grips, with the fiber by-passing the clamps, as shown in figure 1(b). The fiber was interrogated while the stress was applied, at progressively higher stress levels, with steps of about 5 MPa.

Solenoid
A solenoid was wound with Superpower's 4 mm YBCO tape and two optical fibers that were integrated using two different methods. The integration methods represented by straight samples 1 and 2 were adopted to integrate the optical fibers into the solenoid. A first set of experiments was carried out using the non-impregnated coil. The coil was subsequently impregnated with epoxy in preparation of the second set of experiments, using Loctite Stycast epoxy 2850 FT.
The same commercially available, telecommunication grade single-mode optical fibers were used to fabricate all samples, including straight conductor samples and solenoid. Both fibers adhered to the conductor surface such that they made uniform contact with the conductor as much as possible. However, no appreciable pre-tension was used to wind the optical fibers. Fiber-conductor integration is shown in figure 2 by means of schematic drawings as well as physical photos of the solenoid. The reason for impregnating the solenoid is to analyze how the epoxy matrix, by providing a solid strain and heat transfer medium, affects spectral shift profiles when compared to the non-impregnated case. Because the conductor and fibers were hand-wound without pre-tension, non-uniform fiber/conductor contact is expected within the solenoid.
A mushroom shaped cryostat was installed into a 200 mm room temperature bore superconducting magnet to provide sample refrigeration while exposing it to a background magnetic field. A probe serves as coil holder and provides current to the solenoid via flexible current leads. During testing, the coil lies inside the cryostat, submerged in liquid nitrogen and exposed to a known distribution of background magnetic field. A photo of this experimental setup is shown in figure 5(a).
In all experimental runs, the power supplies that were used to energize the coil were controlled remotely and all the experimental signals of interest were acquired by a dedicated LabVIEW application. The optical fiber data were measured using a commercially available ODiSI Interrogator by LUNA Innovations, which derives the spectral shift signal via Optical Frequency Domain Reflectometry. The background magnetic field was kept stationary by separate power supplies. For the purpose of these experiments, only one fiber was acquired during each experimental run. In addition to controlling the instruments and acquiring measurement signals, the experimental procedure was user-defined as an input in the LabVIEW application. Other user-defined experimental parameters include abort conditions (such as maximum spectral shift or voltages). The spectral shift acquired throughout all the in-field experiments was acquired with a 2.6 mm spatial resolution and a 30 ms measurement time. Note that no strain gauges were attached onto the conductor to carry out an independent strain measurement because of lack of space and because we do not envision using strain gauges, which are point sensors, in a superconducting magnet.
A typical in-field experiment comprises the energization of the coil, while at 77 K in a background field, via a linear current increase, until a plateau is reached. The current is held constant for a certain period of time, until it is decreased with a certain decrease rate. In some cases, to highlight the different temporal behavior of strain and thermal transients, an abrupt current drop was used at the end of the current plateau. The current profile of a typical in-field experiment can be seen in figure 3. It is important to note that the transport current signal was measured independently from the power supplies, by measuring the voltage drop across a shunt resistor, and it thus represents the actual current flowing in the coil at any point in time.
During in-field coil experiments, the transport current is the source of the force that is applied to the conductor. Since background magnetic field and current density are perpendicular, a Lorentz force acting perpendicularly to the plane created by  the directions of the current flow and external field is generated. This is illustrated in figure 4. Note that the Lorentz force is distributed along the conductor and while the schematic illustration shows only a few vectors for the sake of simplicity.
Although it does not make a difference for the purpose of the results shown herein, it is worth mentioning that the background magnetic field was uniform throughout the coil volume in the experiments involving the impregnated coil, whereas it varied from 2-3 T along the coil axis in the experiments carried out with non-impregnated coil. The distribution of background field in the two cases is schematically illustrated in figure 5.

Experiments with straight samples
The results from tensile tests of straight fiber-conductor sections are shown as spectral shift as a function of applied tensile stress, for each sample. As can be seen in figure 6, sample 1 shows a linear spectral shift vs stress characteristic. This is consistent with a linear elastic behavior, with the spectral shift scaling with strain.
The characteristic response of all three samples can be seen in figure 6. Sample 2 shows a complete isolation of the optical fiber from the applied strain, since the spectral shift remains zero throughout the experiment, showing no dependence with the applied stress. Sample 3, which comprises the fused silica capillary tube, shows a partial strain isolation, with a spectral shift that weakly depends on the applied stress. Therefore, the two limiting cases are represented by the naked fiber directly embedded in epoxy, which provides a complete strain transfer, and by the fiber jacketed with the Hytrel sheath, which fully prevents strain transfer from the conductor to the fiber.

Experiments with solenoid
The results of an experiment with the impregnated coil at 77 K and 3 T of background magnetic field can be seen in figure 7. The naked fiber showed a spectral shift that closely resembles the transport current profile. This indicates that the naked fiber is highly sensitive to the strain generated by the Lorentz force. The same experimental procedure, carried out in the same conditions of temperature and background field, generates very different results when the jacketed optical fiber is used to measure the spectral shift. This can be seen in the right graph of figure 7. The spectral shift in this case does not scale with the transport current. Instead, it is approximately constant until about half way into the current plateau, where it shows a weak increase. Since the Lorentz force is constant during the plateau, the spectral shift increase indicates the onset of a thermal transient.
Although the spectral shift signal for the two fiber types at specific locations represent the behavior of a pure temperature signal (jacketed fiber) and a signal that comprises both temperature and strain components (naked fiber), which can be seen in figure 7, this behavior is not uniform along the fiber length within the coil. This can be seen in figure 9(b).
It is worth noting that the spectral shift measured during the experiments that yielded the results in figure 7 is negative for both fiber types. For the naked fiber results, this indicates that the fiber is experiencing a tensile strain, transferred from the conductor, due to the coil expanding. Because of the RIOF measurement principle, we also know that a temperature increase is seen by the fiber as a negative spectral shift. This explains why the spectral shift is negative for the jacketed fiber as well, being due to a temperature increase.

Effect of current intensity and polarity.
The ability of the spectral shift measured by a naked fiber to distinguish compressive from tensile strain is demonstrated via a dedicated set of experiments with opposite current polarities and the 2-3 T field distribution shown in figure 5. The results of this study are shown in figure 8, where the non-impregnated coil is subject to the typical experimental procedure with a parametrically higher current plateau level. Only the naked fiber is used for this study, since the study requires strain sensitivity.  The spectral shift signals shown here are measured at 0.1515 meters along the fiber length, which is where the spectral shift was the strongest across multiple tests. It is worth mentioning that this is a typical parametric study, where the current plateau level is the parameter: each curve is the result of a different experimental run, where the transport current is ramped to a certain plateau level and then decreased.
A reference scan is taken at the beginning of each experiment, when the coil is de-energized, approximately in steady state at 77 K and constant background field. The spectral shift then starts to increase or decrease based on the stress applied to the coil by the Lorentz force. This parametric study shows that the spectral shift of a naked fiber scales with the source of stress, i.e. the transport current (since the background field is constant) both during a single experiment, and across experiments that have different plateau levels. It also shows as the sign of the spectral shift depends on the nature of the deformation, becoming negative for deformations that create tensile strain on the fiber, and positive for those that create compression.

Statistical analysis.
The analysis that follows below is used to extract consolidated information from the non-uniform spectral shift spatial distributions. The mean of spectral shift distributions over the fiber position within the solenoid at a time near halfway through the current plateau have been calculated for experiments carried out at different conditions. Figure 9 is used to show the process that leads to mean and standard deviation values from the full data set consisting of a spectral shift map in position and time for each experiment. The data shown in figure 9 are from an experiment with impregnated coil and naked fiber. The same calculations are carried out and compared across fiber types, experimental conditions, and current polarity, in terms of mean and standard deviation of the spectral shift signature across the length of the fiber that spans throughout the coil.
The mean and standard deviation data obtained from spatial distributions of spectral shift, as explained above, are shown in figure 10 for the impregnated coil, and in figure 11 for the non-impregnated coil. Switching of current polarity has been used to create cases where the fiber is in compression vs tension, by reversing the direction of the Lorentz force. For the impregnated coil this study has been carried out for both naked and jacketed fibers. For both fiber types, the compression cases show lower spectral shift means compared to the values from experiments where the coil was in expansion (which puts the fiber in tension). This is due to the fact that the conductor is constrained by the mandrel when the coil is subject to compression, whereas the conductor does not have physical constrains when the Lorentz force causes coil expansion (in this case the conductor tries to move away from the mandrel, only constrained by its own stiffness). This same effect can also be seen from the polarity study summarized by the plots in figure 8: for the same current level, the spectral shift of the compression case is roughly half of that in tension. From the plateau current dependence, it can be seen that the mean increases with increasing current plateau in the tensile cases, whereas it is approximately independent of the current in the compression cases. Additionally, comparing the naked fiber to the jacketed fiber, it can be seen that means are always smaller in the jacketed fiber, for any current level and both  compressive and tensile cases. This demonstrates as the naked fiber is picks up higher signals than the jacketed one at equal conditions, simply because it is sensitive to both temperature and strain, and because its thermal sensitivity is slightly higher than that of the jacketed fiber.
The same conclusions can be drawn from the results obtained with the non-impregnated coil and naked fiber, which can be seen in figure 11. In particular, mean and standard deviation of the tensile cases show an approximately linear trend with increasing current, which is the same behavior seen in the impregnated coil. Note that, unlike tensile cases, the means of compressive cases do not show a clear dependence with the plateau current.
An analysis of the standard deviation results of both impregnated and non-impregnated coils and both fiber types, shows that the increase in spectral shift measured by the naked fiber is non-uniform. This is indicated by the increase in standard deviation as the current and spectral shift values increase, suggesting a less uniform distribution. This effect does not seem to be significant for the jacketed fiber, as can be seen in figure 10(d), because this fiber prevents most of the strain transfer from conductor to fiber, leaving the fiber only sensitive  to temperature increase. The reasons for the non-uniformity of the strain seen by the fiber can be due to a non-uniform fiberconductor contact due to a combination of negligible fiber and conductor pre-tension and non-uniform thickness of the epoxy matrix.

Comparison of naked and jacketed fibers.
A closer look at the time evolution of the spectral shift measured by the naked fiber (sensitive to both temperature and strain) during experiments with opposite current polarities can also reveal the nature of the transient that is generating the signal. Figure 12 includes the spectral shift versus time plots for compression and tension cases with impregnated coil, generated by opposite current polarities and an equal background magnetic field of 3 T. Both signatures closely follow the current with a distinct difference during the plateau. Since the conductor is in current sharing during the plateau, this causes a rise in temperature that is measured by the fiber as negative spectral shift. In the tensile case, where the spectral shift was originally negative in magnitude because of the accumulated strain, the heating effect combines to the strain creating a further increase in spectral shift during the plateau. On the other hand, the compressed fiber responds with a dip in spectral shift because the initial spectral shift due to accumulated strain is positive. When the negative spectral shift is created due to a temperature increase, the combination leads to a slightly decreasing overall signal.
Further insights can be obtained by analyzing how the spectral shift signal decays after the current is turned off, as measured by the naked and jacketed fiber types. For this purpose, a dedicated set of experiments has been carried out, with analogous experimental procedure, where the transport current is abruptly dropped at the end of the plateau, instead of performing a slower linear decrease. Results of these experiments, carried out with the impregnated coil, can be seen in figure 13, where measurements by naked and jacketed fibers are compared. Both fibers operated at the same conditions of current polarity (causing coil expansion, thus subjecting the fiber to tension), background magnetic field (3 T) and identical temporal current profiles.
The spectral shift measured by the jacketed fiber at two locations as a function of time is shown in figure 13 along with the transport current. Note the abrupt drop in transport current at the end of the plateau, shown as the continuous black line. In this jacketed case, the spectral shift is a smooth function of time that peaks at the end of the plateau, and smoothly decreases after the current is turned off. This behavior is a clear signature of a pure thermal transient. The spectral shift measured by the naked fiber at the same conditions results very different from the jacketed case. These transients measured by the naked fiber are also plotted in figure 13 against the same spectral shift and time axes for comparison. An abrupt decrease of spectral shift occurs upon current drop, approximately within one 20 ms time cycle. This abrupt drop in signal is associated with a change in strain state, which occurs virtually immediately after the Lorentz force is reduced to zero, due to the mechanical nature of the transient and a linear elastic behavior. It is important to note that the naked fiber is sensitive to both strain and temperature, and therefore, at least locally, signs of a thermal transient can be seen in combination with the signal due to strain. This can be clearly understood by comparing the Figure 13. Temporal profiles of spectral shift measured by jacketed fiber and naked fiber, along with temporal evolution of transport current. two plots at 1.28 and 1.08 m, which are part of figure 13. Note that the 1.09 m location shows an almost purely strain transient, because of an approximately flat spectral shift during the current plateau, and a vertical drop of the signal to approximately zero GHz. The behavior of position 1.28 m shows a combination of strain and temperature, given the increase of spectral shift during the current plateau (which can only be due to a temperature increase since the Lorentz force is constant), and a two-steps decay, comprised of an abrupt drop (strain component) followed by a slower, smooth decay (temperature component). Lastly, it is worth mentioning that, as discussed previously, this exact temporal behavior is not identical along fiber positions due to non-uniformity of conductor-fiber thermo-mechanical coupling. The positions shown in figure 13 are those experiencing higher spectral shifts.
As demonstrated by the results discussed above, the strain signal scales with the current profile. This observation allows the decoupling of strain and temperature components from the spectral shift measured by a naked fiber. The spectral shift of a naked fiber, as indicated by the results in figures 12 and 13, can be the combination of strain and temperature. This is clearly the case for the spectral shift signal measured by the naked fiber in the signal shown in figure 14, where the current polarity was such that the Lorentz force causes the coil to expand. In these conditions, spectral shift due to strain will be negative since the coil is expanding, putting the fiber in tension, while temperature increases also cause a negative spectral shift. Observing the results in figure 14, where the plotted spectral shift signal is a moving average of the measured values with a period of 10, it can be seen that the spectral shift scales with the transport current until the beginning of the current plateau. During the current plateau, the spectral shift slowly deviates from the transport current profile. As previously discussed, this deviation that occurs during a constant Lorentz force is accounted for by a temperature increase. Therefore, if the transport current profile is scaled to match the intensity of the spectral shift at the top of the linear current ramp, this quantity approximately equals the strain component of the spectral shift. This function is shown in figure 14 as a dashed black line. The temperature component of the spectral shift is obtained by subtracting the strain component from the raw spectral shift signal. Note that the temperature component grows smoothly during the current plateau and it peaks exactly at the end of it, when the transport current starts to decrease. This is consistent with the temporal evolution of a temperature transient.

Implications of the results and future work
It is worth mentioning that in all experiments that generated the results reported herein, the reference condition used for real-time computation of the spectral shift is a steady state condition with the coil at 77 K, stationary background field, and zero transport current. Because of its definition, the spectral shift is determined as the result of a comparison between a reference state and a measurement state. The measurement state is what varies over time, and is acquired periodically with a certain measurement rate. The reference state, however, can be updated at any moment in time during the acquisition. This means that if a naked fiber is integrated into a coil and a new reference is taken with the coil at operating current, for example during the plateau of one of our experiments, then the subsequent spectral shift measurements will not include the strain that was built up during energization, leaving temperature increases and potential perturbations the only possible cause for deviation of the spectral shift from a near-zero baseline.
The use of a jacketed fiber has resulted in almost complete prevention of strain transfer from conductor to fiber. This is a useful approach for those cases where the integration of multiple fibers is viable because it allows for real time separation of strain and temperature components. The main downside of using a jacketed fiber is in the increased diameter and the consequent lower thermal sensitivity due to an increased thermal resistance between conductor and fiber. The addition of the jacket, however, makes the fiber more robust against potential damage induced by integration, winding processes, as well as easier to handle. Therefore, the use of both naked and jacketed fibers should be preferred when possible, as it provides the greatest amount of information. The use of the naked fiber can be especially desirable for cases where variations in the strain state is of interest. This could include experimental feedback for design of new magnet geometries where the strain is simply due to bending of conductors into the target geometry, as well as real-time monitoring of magnet operation where the strain is generated by Lorentz forces. For all cases where an accurate strain distribution is desired, uniform contact of the naked fiber with the conductor is necessary. Lastly, in order to ensure stability and durability of the optical fiber sensors, and in turn maintain measurement accuracy, mismatch of material properties should be minimized since it induces uncoordinated deformation that can lead to interfacial debonding, especially in time-dependent operation. An excellent analysis of this problem, which includes potential solutions, is available in the literature [32]. A dedicated study on sensor durability and debonding, however, would be valuable.

Conclusions
The implementation of different fiber integration techniques has been tested in a control experiment where a conductorfiber assembly is strained in a tensile test machine, as well as in a small YBCO solenoid energized under background magnetic field. Results of the tensile control experiments show that the integration of a naked fiber provides total strain transfer between fiber and conductor, while the integration of a jacketed fiber shows a total strain isolation of the fiber from the deformation applied to the conductor. Experiments with a small solenoid show that a jacketed fiber can be used to eliminate strain-temperature cross sensitivity and obtain a spectral shift signal that is purely dependent on temperature. Additionally, swapping current polarity has been used to apply compressive or tensile strain on the conductor due to swapping direction of the Lorentz forces. The naked optical fiber was capable of distinguishing between compressive and tensile strain, with a spectral shift signal that is positive when the fiber is compressed and negative when it is subject to tension. Lastly, clear features of the spectral shift indicating thermal or mechanical transients (or a combination thereof) have been found, and the decoupling of strain and temperature components has been demonstrated.

Data availability statement
The data cannot be made publicly available upon publication because no suitable repository exists for hosting data in this field of study. The data that support the findings of this study are available upon reasonable request from the authors.