Modeling and validation of nonlinear voltage-current characteristics of ITER PF joint sample tested in the SULTAN facility

The International Thermonuclear Experimental Reactor poloidal field (PF) coils are wound into double pancakes with NbTi cable-in-conduit conductors, which are connected by joints in shaking hands lap-type configuration. The coils are operating in pulsed mode with a maximum operating current of 55 kA and peak magnetic field of 6.4 T, utilizing electromagnetic load on the conductors and joints. A series of PF qualification joint samples modified in praying hands configuration is measured in the SULTAN facility. For some samples, a nonlinear voltage-current (VI) characteristic is observed during the assessment of joint resistance. The growth of joint resistance versus the B× I product is larger than what is expected from the magneto-resistant copper contribution. Two non-homogeneous contact resistance models are developed and combined to quantitatively evaluate the reason for the nonlinear VI behavior in combination with the relevant power dissipation and current redistribution in the joint. The simulations reveal that, for the particular pre-qualification PFJEU2 sample with resistance variation up to 3.5 nΩ, the most probable reason for the nonlinear VI characteristic is a widely spread defective connection between copper sole and shim. The electromagnetic force involves a separation effect on the mechanically and electrically weakly connected parts, resulting into a varying resistance depending on transport current and background field. The hypothesis and models are validated by an experiment on a similar sample PFJEU3 and a post-mortem examination of the PFJEU2 sample.


the ITER Organization.
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Introduction
The International Thermonuclear Experimental Reactor (ITER) magnet system contains six poloidal field (PF) coils. These coils are wound with NbTi cable-in-conduit conductors (CICCs). Firstly a double pancake (DP) is wound with two conductors in a two-in-hand winding scheme, then six to nine DPs are stacked together to form a complete PF coil. The conductors within and between the DPs, as well as the conductor terminals to the feeder system and to the jumper in case of bypassing a faulted DP are connected by twin-box lap-type joints. The PF coils are operating in pulsed mode with a maximum operating current of 55 kA and a peak magnetic field of 6.4 T (48 kA and 6.4 T for PF1/6, 55 kA and 4.8 T for PF2-4, 52 kA and 5.7 T for PF5). The windings are subjected to a radial force inwards and an axial force towards to coil mid-plane as the current increasing. The 100 PF joints in total are located at the outer surface of the coils to minimize the impact of the electromagnetic load and allow convenient assembly and maintenance [1].
A campaign of PF joints qualification measurements was carried out in the SULTAN facility (Swiss Plasma Centre) on six PF joints until August 2017, including DC, AC and stability properties. In terms of joint resistance, a nonlinear voltagecurrent (VI) characteristic is observed during the measurements of PFJEU2, PFJEU3 and PFJEU6 samples. Especially for the sample PFJEU2, which was the first trial sample built by a supplier well before the manufacturing procedure was stabilized, a resistance deviation up to 3.5 nΩ is observed for two different electromagnetic load conditions [2]. Similar behavior was also observed in the measurements of some toroidal field joints. A poor current redistribution in the joint with high strand-bundle to copper sole resistance was adopted as the probable reason [3,4].
The DC properties including the assessment of the joint resistance are simulated with the numerical model JackPot-ACDC, at the University of Twente. The JackPot code has the ability for quantitative analysis of CICCs at a strand level precision in both stationary and transient regimes [5][6][7][8][9][10]. A twin-box joint is built in the model as an object with three subobjects consisting of two cables and a copper sole. The cable is implemented following the trajectories of all the strands by the cabling subroutine, while the copper sole is treated as threedimensional electrical grid with the PEEC technique [11]. A network comprising all meshed elements of the sub-objects is constructed firstly, and accordingly the currents and voltages of the nodes are calculated in response to the transport current and magnetic fields (self-field and externally applied). This allows us to evaluate the individual contributions of cable, copper sole/shim and cable-sole interface to the evolution of the joint resistance. Except for the uncertainty in the heat transfer coefficients, there are no free parameters in the model so the electrical and thermal behavior are mainly depending on the joint configuration and the input contact resistances, the interstrand, inter-petal and strand to copper sole resistivity, which are derived from experiments.

Joint resistance test and simulation
During the manufacturing of the PF joints, the outer surface of the steel wraps, wound around the petals, are removed to get a better electrical contact between the cable and copper sole. In addition, AgSn solder is applied at the contacting interface to further improve the electrical, mechanical and thermal stabilization [12]. The prepared cable end is pressed into a bimetallic box machined from an explosive bonded stainless steel/copper plate to form a termination. A copper shim is inserted between two of these terminations to compensate for manufacturing and positioning misalignments. PbSn soldering is applied at the interfaces between the copper soles and shim, and then the pieces are hold together by two side plates welded to the joint boxes. A cross section of a PF joint including the solder applied between cable, sole and shim, is shown in figure 1 [13].
In the SULTAN facility, besides a maximum sample current of 100 kA, magnet fields are available from both DC and AC coils, orthogonal oriented to each other, as illustrated in figure 1. The DC high-field zone is ∼450 mm long and the AC field has an effective length of ∼390 mm. The samples are vertically inserted into the magnet bore and the terminals are connected to the current leads of a superconducting transformer [14]. The qualification joint samples are modified from shaking hands type (as on the PF coils) to praying hands type to fit the magnet. The configuration of a PF joint sample is shown in figure 2, and the schematic of the SULTAN magnetic fields applied on the joint sample is illustrated in figure 1. The resistance of the joint is measured at sample current I = 10, 20, 30, 40 and 55 kA in background DC fields of 0, 3 and 5 T. Two sets of voltage taps named 'Bottom' and 'Top' taps,are attached to the conductors at 40 and 490 mm distance away from the end of the jointbox, respectively, the average smoothed voltage signal V at the two positions are obtained correspondingly, and then the joint resistance is derived as R = V/I. For the PFJEU2 sample, after 1000 bipolar load cycles at 6 T/± 27.5 kA, the resistances measured at the 'Bottom' position, versus current and background field are shown in figure 3. The joint exhibits a strong nonlinear VI characteristic, the resistance increases by 3.5 nΩ as the B × I product increases from 10 kA and 0 T, to 55 kA and 5 T. Not only this resistance is too high compared to the design requirement of the PF joint resistance ⩽ 5 nΩ [2], but the variation is also not anticipated.
The tests performed in the SULTAN facility, are reproduced and analyzed with the JackPot model. The schematic of the praying-hands lap type PF joint is shown in figure 4, two cables are ideally circular if compared to the realistic oval shape as shown in figure 1. The copper sole and shim with different resistivities are represented with different colors, but the effect of the solder between them is neglected in the simulations. The geometry and resistivity parameters of the modeled PF joint are summarized in table 1, the mask [15] and patch resistivities are defined and explained in the later chapters. The transport current goes from the terminals of Cable A to Cable B, ramping up at t = 2 s, with a rate of 2 kA s −1 to a  maximum value of 10 kA, then the constant current lasts until t = 30 s, as seen in plot (a) of figure 5. The background field is oriented in the X direction. The power dissipation of the whole joint, as well as the three individual components, are calculated with respect to the constant transport current. For example, the power dissipations of joints with different strand to sole resistivities, ρ sj = 3 × 10 −6 and 3 × 10 −5 µΩm 2 , are derived and shown in plot (b) and (c) of figure 5. The joint resistance is obtained by dividing the produced power dissipation of the joint by the plateau current squared, R = P/I 2 . The joint resistances obtained from the simulations for all currentfield combinations and the SULTAN measurements are compared in figure 3. It shows that the variation of transport current and magnetic field should have relatively little influence on the joint resistance according to the model results. Even with the incorporated effect of the copper sole and strands' copper magneto-resistance, the computed joint resistance variation is still far smaller than the maximum 3.5 nΩ obtained from the measurements.

Non-homogeneous contact resistance model
According to the characterization and the power distribution as shown in figure 5, the joint resistance derived from the model is dominated by the component of power dissipated in the sole/shim, implying the importance of the resistivity of the copper sole and shim. For the PFJEU2, with a shim layer thickness of 7 mm and low resistivity 0.43 nΩm, the total resistance is reduced by 13%. Another important factor for the power dissipation is the resistivity of the interface between the strands and the copper sole, as demonstrated in figure 5 for two joints with different strands to sole resistivities (ρ sj ), 3 × 10 −6 and 3 × 10 −5 µΩm 2 . Compared to a normal conductor section containing larger voids between strands for helium flow and heat removal, the conductors in the joint section are further compacted and the void fraction is reduced from 34.1 to 24.5% and in addition to the voids occupied by the solder, the actual left void fraction is about 20.0 ± 0.4% [16]. It is expected that the strands in the cable are tightly compacted, which leads to relatively stable strand to strand resistivity and dissipation in DC conditions. This indicates that the observed nonlinear VI characteristic is most likely related to the contact resistivities between the copper sole and shim, or between the copper sole and cable surface, instead of the inter-strand resistances within both cables.
With regard to the two potential causes for the nonlinear VI characteristic, two non-homogeneous models are developed to demonstrate the mechanisms behind it. One is the nonhomogeneous contact resistance distribution between the sole and shim, focused on two different configurations with integral and discrete shim layers. The corresponding schematics are shown in plot (a) and (b) respectively in figure 6. The other is the non-homogeneous contact resistance distribution between the cable and sole interface, the schematic is shown in plot (c) of figure 6. In the schematics, the non-homogeneous resistance distribution is represented by the discrete sections with different resistivities, the blue color represents the sections with higher resistivity while the white sections are the regions with low resistivity. The non-homogeneity in resistance distribution could also be altered by the dimensions and quantities of the discrete sections.

Non-homogeneous contact resistance between copper sole and shim
The model concept is based on the assumption that the electrical connection between the copper sole and shim is changed under the influence of the electromagnetic force. For two conductors of the praying-hands type of joint, the transport currents are reversed while the background field direction is the same for both, thus the electromagentic forces applied on them are in opposite directions, producing a compressing or separating force. In such a case, the resistivity of the discontinuous interface instead of the sole and shim dominate the resistance deviation. In the model, a conservative simplification is made first by treating the separated copper sole and shim as a whole object with an equivalent copper resistivity ρ equ = 4.0 nΩm. This resistivity is derived from assuming the same power dissipation as generated in the sole and shim, both having different resistivities.
Based on this joint sole and shim with equivalent resistivity, the non-homogeneous contact resistance model is implemented by adjusting the resistivity and size of the sections with high resistivity, conform the blue regions represented in figure 6. The middle layer with equivalent or high resistivity is still referred to as shim for easy description. Two joint configurations with integral or discretized middle shim layer are considered here, corresponding to figures 6(a) and (b) respectively.
For the shim layer in between both sole parts, the discretization is formed by 11 meshed layers in height (Y) direction, the thickness of one layer is 35/11 = 3.2 mm. For the integral shim model as shown in figure 6(a), the whole shim layer has homogene high resistivity. For the discrete shim model two discrete configurations, one with seven and one with eleven high resistive sections are considered, the corresponding width is 450/(7 + 6) ≈ 35 mm and 450/(11 + 10) ≈ 21 mm respectively. In total three joint configurations are considered, integral shim, discrete shim with seven and one with eleven high resistive sections are simulated to evaluate the effect of the non-homogeneous sole to shim resistance on the current and power distribution.
Unlike the most probable situation in reality that the contact resistivity and areas of the discontinuous connections change gradually, in the model the resistivity of the individual shim sections is fixed. A factor k ρ is introduced to appoint the resistivity of the shim sections with respect to the normal regions with equivalent resistivity, ρ shim = k ρ ·ρ equ . For the two cases with integral shim and seven high resistive shim sections, simulatons are performed with 3 T background field and different transport currents, or 40 kA transport current but different background fields. The results are shown in figures 7 and 8 respectively, showing that a nice fit is derived for measured and simulated resistance data by adjusting the shim resistivity by means of the factor k ρ .
In order to catch the increasing tendency of the SULTAN measured data, an increasing k ρ is required for both shim models. As the current increases from 10 to 55 kA at 3 T background field, the k ρ needs to be increased from 25 to 85 for the model with seven discrete shim sections. For the integral shim model the change from 5.4 to 7.0 is relatively small. When the areas of the discrete shim sections are increased, the resistivity is then decreasing and approaching to the shim resistivity of the integral model. A similar tendency is observed as the background field increases from 0 to 5 T and keeps the 40 kA transport current, the k ρ changes from 17 to 85 for the model with seven discrete shim sections, and 4.6-7.3 for the integral shim model.  1.25 × 10 −5 Inter-petal resistivity ρ ip (µΩm 2 ) 5.0 × 10 −5 Strand to sole resistivity ρ sj (µΩm 2 ) 3.0 × 10 −6 Mask resistivity ρ mask (µΩm 2 ) 50 Patch resistivity ρ patch (µΩm 2 ) 50 The joint resistance is directly derrived from the power dissipation and thus largely depending on the contribution of the copper sole. For the three defined shim configurations, the integral shim, the discrete shim with seven and eleven high resistive sections, the power distribution across the copper sole length is shown in figure 9 for 40 kA transport current and 3 T background field. A pronounced non-homogeneous distribution is observed for both discrete shim cases and the power is distributed in a few regions along the joint axis. The number of high power regions seems positively correlated but not equal to the quantity of the high resistive shim sections. There are three and five high power regions in the joints with respect to seven and eleven high resistive shim sections.
Considering that the power dissipation is directly related to the current distribution, the current distribution in the sole of the three joint configurations in DC condition, together with the AC condition for comparison, are shown in figure 10. For AC applied field, the joints are subjected to a magnetic field in the Y direction with a ramp rate 1 T s −1 for 0.5 s. The present current range is set to ±1 A to emphasize the distribution itself and ignore the relatively small difference between the magnitudes. The blue color represents the negative current flowing from the far to the near end (figure perspective), the red color represents the opposite current. For DC conditions, the current distribution in the joint is partly affected by the non-homogeneous shim configuration. For AC conditions, the energy distribution in the sole is determined by the resistivity and quantity of the shim sections.
Besides the current distribution, the current density distribution in the copper sole for the three shim configurations are shown in figure 11, when viewed from the position of Cable B. The arrows point in current flowing direction and the color shade represents the density. For Joint 1 with integral shim, the copper resistance and the current are almost uniformly distributed along the joint axis. However, still some local current loops induced at both ends of the sole are observed, due to the masks blocking the electrical connections between the sole and one end of the petals having double contacts with the sole [15,17]. For Joint 2 and 3, with 11 and seven discrete shim sections respectively, the highest current density flows through a few specific regions, indicated by the dark green color. The current density is not evenly passing all low resistive shim sections, meaning that the current distribution is not only dominated by the resistance distribution in the sole. This can be explained by the current distribution in the cables. For Joint 3, with seven high resistive shim sections for example, the current density in the sole with respect to the petal current distribution in Cable A, is illustrated in figure 12. In order to emphasize the petal current distribution, two plots viewed from the same angle are compared. The upper plot shows the physical arrangement of the six petals of Cable A, which are labeled from 1 to 6, the lower plot shows the corresponding current distribution. For both plots, the current distributions in the copper sole are identical and the high current   regions are named as a, b, c. The magnitude of the strand currents is below 20 A in the jointbox region. For negative transport current from the cable right end, there are positive currents (red color) produced in some strand sections that are in direct contact with the copper sole, especially in the regions with low power dissipation. On first sight it seems there is no resemblance between the shim configuration and the current distribution. The corresponding shim configuration is shown  at the bottom of figure 12, using the blue and white color to represent the high and low resistive shim sections respectively. Looking at region a and b for instance, the distributions of the shim sections are actually opposite, while the current densities appear alike.
According to the observation in figure 11, the current transfer mainly occurs in the center of the sole. As a result, the current is mainly carried by one petal, depending on the specific cable rotation with respect to the cable-sole interface. For Joint 3, the currents in petal 1 and 6, petal 2 and 3, and petal 4 and 5 contribute most in regions a, b and c respectively.

Non-homogeneous contact resistance between strand and copper sole
Another possible reason for the nonlinear VI characteristic is a varying contact resistance distribution between strands and copper sole, which is demonstrated with a non-homogeneous contact resistance model. Two levels of contact resistivities and associated locations, as shown in figure 6(c), are defined as regions (blue color) with higher resistivity, referred to as 'patches'. The size of the patches and the corresponding spatial distribution are determined by two factors M and N, the overall patch ratio is P ratio = N/M. Similar to the non-homogeneous sole to shim contact resistance model, only two resistivity levels are considered, the patch resistivity ρ patch which equals to the mask resistivity (ρ mask ) [15,17], and the resistivity of the remaining regions maintaining the strand to sole resistivity (ρ sj ). A summary of the resistivity parameters is listed in table 1.
For the case of 3 T background field and transport current increasing from 10 to 55 kA, a comparison between the SULTAN measured joint resistance and the simulated resistance of joints with different patch ratios is shown in figure 13. The patch ratios of 36, 40, 44 and 50% are obtained by setting N = 4, M = 11, 10, 9 and 8 respectively. The comparison shows that in order to match the increasing tendency of the measured joint resistances, the patch ratio is required to  increase from 40 to 50%. This means that almost half of the interface between cable and copper sole is in low conductive contact.
Since the calculation of the joint resistance directly depends on the power dissipation, the impact of the patch configuration on the power dissipation is evaluated. Two joints, with and without patches are compared, the patch ratio P ratio = 50% (M = 8, N = 4). The distribution of the power in the five components, two cables, two cable-sole interfaces and copper sole, is shown in figure 14. Although the non-homogeneous connection is at the interfaces between the cables and sole, the largest effect is still in the copper sole with a non-homogeneous power distribution along the joint axis. The effect is analogous to the periodic distribution of the joint with non-homogeneous sole to shim resistance, as shown in figure 9. In the latter case, the number of power  peaks is determined by the combination of shim configuration and cable rotation together. While in the case of the non-homogeneous strand to sole resistance model, it is solely determined by the patch configuration, with seven power peaks corresponding to the seven patch sections. The power dissipation in the cable-sole interface also interlaces with that in the patch distribution, which is illustrated in the enlarged view in figure 14.
The petal current distribution in Cable A of these two joint cases are compared in figure 15. For the joint without patches, the petal currents transfer into the copper sole smoothly and in a sequence following the petal rotation pattern. While the implementation of the patches prevents such a continuous current distribution, the current plateaus indicate the barrier effect resulting from the patches. However, even though with a patch ratio of 50%, there is still an effective current redistribution in the cable.
A 3D view of the current density distribution of the joint with patches is shown in figure 16, the cable and the copper sole are shown separately to obtain an inside  view of the cable to sole interface. The strands in red and blue colors represent the currents flowing in opposite directions indicating that many current loops are induced nearby the patch locations. This is also partly the reason for the periodic current distribution pattern of the cable-sole interfaces observed in figure 14. For the current distribution in the copper sole, the arrows represent the current direction and the shade of color indicates the density. The majority of transport current is passing through only a few regions, which are directly determined by the patch configurations.
In addition, the current is distributed laterally between the mainstream passages, illustrating the phenomenon observed in figure 10 that the positive and negative current occurs alternately. Since a quench is not directly detected in the JackPot model, the impact of the patches on the current redistribution and stability is evaluated by means of examining the current margin of the strands. The current margin is defined as I margin = Min(I c −|I s |) [18], a negative current margin means the strand current exceeds the critical current. In addition, the number of strands with negative current margin is also detected.
In the case of a maximum operating current of 55 kA and 5 T background field, the evolution of the joint resistance and the current redistribution is evaluated by gradually increasing the patch ratio. The patch factor M is set to 15 and as a result there are only three main outlets for the transport current in the cable, the factor N = 10, 11, 12, 13 and 14 are corresponding to ratios of 67, 73, 80, 87 and 93% respectively. For the joints with these five patch ratios, the evolution of the current margin in time is shown in figure 17. The time scale here corresponds to the transport current, after a period of 2 s the current increases from zero to 55 kA with a ramp rate of 2 kA s −1 , then it remains constant for 30 s. As the patch ratio increases, an earlier current saturation of the strands is observed. For the case of 93% patch ratio, the current saturation occurs at the time instant of about 20 s corresponding to a transport current of 35 kA. Current saturation is observed for all patch ratios except for the smallest patch ratio of 67%. A further examination shows that the number of strands, which get saturated, is 0, 3, 2, 8, and 17 in Cable A and 0, 2, 4, 14 and 19 in Cable B, respectively, for increasing patch ratios. The results reveal that the increasing patch ratios degrade the stability of the joint, a conservative estimation is that a patch ratio up to about 70% may still be tolerated.

Analysis and validation
The models reveal that the non-homogeneous contact resistance between either the copper sole and shim, or the strands and sole, both affect the current redistribution and the power dissipation. However, for any specific configuration, the joint resistance seems independent on the varying input current or background field, if neglecting the effect of the magnetoresistance of the copper sole. Furthermore, the magnetoresistance contribution is much smaller than the resistance variation observed in SULTAN measurements.
Thus, to explain the non-linear VI characteristics within the proposed models, one should assume that the nonhomogenous contact resistance is a function of the current as can be seen in figures 7, 8 and 13. The most likely explanation is that the electromagnetic force acting on the joint boxes is the cause of the changing contact status. Indeed, the transport current I and background field B as demonstrated in figure 18, result in the electromagnetic force F = B × I acting on the two cables in opposite direction. The produced separation effect with respect to the joint boxes interface, is positively dependent on the applied B and I, and probably affects the conductive contact between the cable, sole or shim parts. This hypothesis is confirmed by the effect of the load cycles on the joint. It can be seen from figure 19 that after the 1000 bipolar cycles at 6 T/± 27.5 kA, the joint resistance measured at 40 kA is irreversibly increased by 15%-18% at 0 and 5 T, and by 35% at 3 T.
During the measurements of the pre-qualification PFJEU3 joint sample [19] built by another supplier, a similar nonlinear VI characteristic was observed although the resistance variation is smaller compared to the PFJEU2 sample and the maximum joint resistance remained within the accepted value of 5 nOhm after load cycles. Considering the direction of the electromagnetic force would be changed if changing one direction of the transport current or magnetic field, −F = − B × I, the joint resistances were measured with opposite transport currents so as to obtain opposite electromagnetic force. The results with different transport current and magnetic field combinations are shown in figure 20. An opposite resistance evolution is observed, which corresponds to the separation and compression effect respectively, and validates the effect of the electromagnetic force on the nonlinear VI characteristic.
As seen in figure 1, the AgSn solder and PbSn solder are used in the cable-sole and sole-shim interfaces respectively. A post-mortem examination of the sample PFJEU2 was performed at CERN, to check the soldering conditions [13,20,21]. The thickness of the AgSn layer is approximately between 200 and 450 µm, obtained from the microscope Scanning Electron Microscope (SEM) images with 60 times original magnification, the solder is in good connecting conditions. While for the PbSn solder, a defective soldering condition is observed with 100 times magnification, and a further energydispersive x-ray spectroscopy analysis is performed on the SEM images to detect the probable discontinuity along the interface, a clear gap is observed between the copper shim and PbSn solder, as shown in figure 21. The separation on this unfavorable solder connection under changing electromagnetic force is the most likely reason for the nonlinear VI characteristic. This observation is in line with the prediction obtained from the non-homogeneous contact resistance  models-a widely spread defective connections between the sole and shim.
The postmortem examination performed on the PFJEU3 sample did not reveal any defects at the soldered interface between the boxes and shim, and the cable void fraction in the middle part of the joint was as low as in the PFJEU2 sample. However, the void fraction appeared to be larger in the portion of the conductors towards the box ends due to larger twist pitch, which could be responsible for the sensitivity of the joint resistance to the EM load. It should be noted, that after the trials with the PFJEU2 and PFJEU3 samples and consequent improvement of the technological process, the next qualification and production samples did not reveal any sensitivity to the EM load [22].

Conclusion
The measurements of the ITER pre-qualification PF joint samples (PFJEU2 and PFJEU3) were performed in the SUL-TAN facility and unexpected nonlinear voltage-current characteristics were observed during the DC tests. The resistance variation reaches 3.5 nΩ as the transport current and background field increase. The simulations based on the JackPot model show that the joint resistance should be nearly independent from transport current and background field, only a small effect from the magneto-resistance of copper sole and shim is anticipated. The model was updated to emphasize the possible electrical features related to the interfaces between the components of cable, sole and shim. The simulations reveal that the strong nonlinear voltage-current characteristic is most likely a defective connection between copper sole and shim, affected by the electromagnetic force. The weakly connected parts generate a separating or compressing force under a varying electromagnetic force from transport current or background magnetic field, causing a varying resistance correspondingly. Further, on a detailed analysis of the local power dissipation and current distribution in the joint and its strands is presented, allowing a quantitative assessment of the joint stability in AC operating conditions. The model outcome is validated by an experiment on a similar sample PFJEU3 and a post-mortem examination of the PFJEU2 sample.

Data availability statement
The data generated and/or analysed during the current study are not publicly available for legal/ethical reasons but are available from the corresponding author on reasonable request.