Winding angle optimization and testing of small-scale, non-planar, high-temperature superconducting stellarator coils

We designed and constructed two non-planar coils with high-temperature superconductors (HTS) based on shapes from the Wendelstein 7-X stellarator. Tape track orientation of the HTS was optimized to reduce the coil size as much as possible while staying within the strain limits of the gadolinium barium copper oxide (GdBCO) superconductor. This resulted in average coil radii of 0.23 m and 0.48 m at strain limits of up 0.45% to for the coil shapes that were chosen. The coils were produced by winding the GdBCO tapes onto 3D-printed plastic frames. We confirmed the integrity of the superconducting layer after winding by spatially resolved measurement of the critical current and by energizing the coils in liquid nitrogen. Coil 1 showed a resistance of 1.75μΩ and did not have any critical current degradation, while coil 5 had a resistance of 195μΩ and showed only one dropout, attributable to a handling error. We measured the magnetic field of the coil with a three-axis Hall probe system and found good agreement with predictions. This work demonstrates the manufacturing of small-scale, non-planar magnetic coils from commercially available HTS.


Introduction
Nuclear fusion reactors require strong magnetic fields for sufficient plasma confinement.Present experiments utilize low-temperature superconductors (LTS), primarily NbTi and 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.Nb 3 Sn, instead of copper for their coil systems.This avoids prohibitive current dissipation losses but limits the magnetic field strength and operating temperature [1][2][3].For fusion applications, high-temperature superconductors (HTS) could be used to create much stronger magnetic fields, to raise the operating temperature of the magnets from e.g. 4 K to 20 K, or some compromise between those two advantages.The most common materials for commercially available HTS are ReBCO (rare earth barium copper oxides) [4][5][6].Thin layers (∼4 µm) of these materials are usually coated onto a metal tape, which provides mechanical stability and protection.However, the brittle, ceramic functional layer will nevertheless crack under comparatively low strain.
Different concepts exist to manufacture cables out of individual tapes (e.g.[7][8][9]).The VIPER cable is the most prominent example of a ReBCO cable for fusion energy application [10].In it, four stacks of ReBCO tapes are helically wound around a copper core.Cables usually have relatively large-radius, isotropic bending limits, whereas individual tapes have strongly direction-dependent bending limits.An alternative approach to manufacturing cables involves winding tapes in a single stack with a rectangular cross-section around structural support in the desired coil shape.This technique can exploit the tapes' preferred bending direction to allow for much smaller bending radii compared to cables (≈2 cm vs. tens of cm), which may be used to reach smaller coil sizes or reduce the strain on the ReBCO conductor [11,12].The individual windings of the stack can also be soldered together, enabling current sharing between them, which increases robustness against quenches; this is called a non-insulated coil [13,14].
Considerable efforts have been made to construct planar ReBCO coils for tokamak experiments [15][16][17], which are the most developed fusion concept.ReBCO is considered in the design of the central solenoid for the European DEMO reactor [18].Recently, a team from CFS and MIT achieved 20 T in a 3 m diameter coil wound from a VIPER cable with an operating current of 40.5 kA [19].
Stellarators, like tokamaks, confine the plasma using magnetic fields, but they do not employ the large toroidal plasma current that tokamaks do.This offers the advantages of intrinsic steady-state operation and elimination of disruptive instabilities, but it requires breaking the axisymmetry of the external magnetic field and by extension, the magneticfield-generating coils.The resulting non-planar nature of stellarator coils poses an additional engineering challenge [11].Therefore, less work has so far gone into developing HTS stellarator magnets.A mock-up coil of the Helically Symmetric EXperiment (HSX) has been constructed and tested from the VIPER cable in recent work [12].
As a proof-of-concept demonstration of the techniques for and feasibility of producing stellarator coils out of winding angle-optimized HTS stacks, we chose two coil shapes from the Wendelstein 7-X stellarator (W7-X) and calculated how small we could scale them without breaking the tape.We then constructed these coils and energized them in liquid nitrogen to confirm the compatibility of the HTS tape with the desired winding path.The coils built in this project are smallscale technology demonstrators, not prototypes for a stellarator reactor.Operation at high magnetic field, under high magnetic forces and the development of a high current conductor concept are outside of the scope of this effort.
We present the results here, organized as follows: In section 2, we explain how we utilize numerical optimization to obtain a winding path for the 1st and 5th coil of a W7-X halfperiod [20] within the limits of torsional and bending strain on the tape at the smallest possible size.Section 3 details the construction and testing of coil 1.The success of the optimization is demonstrated by critical current measurements after winding and a current/voltage curve of the coil operating while submerged in liquid nitrogen.Section 4 shows the same for coil 5, which had to be built to a larger scale due to its increased nonplanarity.Critical current measurements are presented, alongside magnetic field measurements of the coil interior, taken with a custom-built 3-axis manipulator.Section 5 gives a summary and an outlook on future work.

Winding angle optimization of the coil track
The coil shapes start out simply specified by a discretized 'filament representation'.That is, they are defined in threedimensional Euclidean space by a set of points γ k (where k is the index), that together form a closed curve; adjacent points are connected by straight lines.From that, we calculate the Frenet frame, a triplet of the three mutually orthogonal unit vectors {T k , N k , B k } for each point along the curve.This is a moving (right-handed) coordinate system.We start by defining the tangent unit vector T k at point γ k , based on the subsequent and previous points : This definition uses the central difference, i.e. a type of discrete derivative, as shown in figure 1.We also define the forward-difference tangent unit vector If a smooth curve is twice differentiable, then its second derivative is orthogonal to the tangent, pointing toward the center of a circle with the local radius of curvature at any given point on the curve.Correspondingly, we calculate the normal vector to the discrete curve from the change of the tangent unit vector relative to the subsequent and previous points: We use the Gram-Schmidt method to assure numerical orthogonality to T k , defining and from this, we define the normal unit vector Finally, we define the binormal unit vector as mutually orthogonal to the tangent and the normal vectors, i.e.
We associate the 2D tape with the surface spanned by B k and −B k , scaled by the tape width, for each point γ k along the coil filament, as shown in figure 2. We now have a discrete representation of the tape and its orientation, based on the Frenet frame, from which we can calculate metrics for strain.The three types of deformation (and corresponding strain on the tape) that we will consider are normal curvature, torsion, and binormal curvature.The normal curvature of the tape at the  point γ k can be defined from the filament points as the inverse radius of the osculating circle passing through the γ k+1 , γ k and γ k−1 [21]: where φ k is the angle between t k and t k−1 , i.e. φ k = cos −1 (t k • t k−1 ), as drawn in figure 1.
The twist of the tape at point γ k , as illustrated in figure 3(b), is characterized by the torsion, which is defined as the change of the binormal vector in the direction of the normal vector: where a right-handed (left-handed) twist has positive (negative) torsion, and B ′ k is calculated using both the previous and subsequent points, scaled by the respective point separation: Since B k ⊥ N k by definition (equation ( 5)), equation ( 7) can also be written The Frenet frame tends to result in very high torsion at certain locations along the curve; winding the tape in such a way would damage the HTS.The peak torsion can be reduced by introducing and numerically optimizing a winding angle adjustment θ k for each point on the curve.This changes the rotation of the binormal and normal unit vectors around their respective tangent vectors (i.e.modifications to the Frenet frame that had been calculated from the filament points' coordinates alone): This process simultaneously, however, increases the magnitude of , the change of the binormal vector parallel to the tangent vector.This generates binormal (or 'hard-way') bending of the tape, which is illustrated in figure 3(c).We compute the magnitude of the binormal curvature κk at point γ k by projecting the previous and subsequent points (γ k−1 and γ k+1 ) onto the T k B k plane, then computing the curvature defined by the osculating circle: where φk is the angle between the forward-difference tangent vectors of the projected points t k and t k−1 .In a modified Frenet frame (equation ( 10)) the normal curvature in equation ( 6) needs to be redefined to use points projected into the T k N kplane, analogously to the projection performed to calculate the binormal curvature (equation ( 11)).However, we will not treat the normal curvature further, as we will omit it from the winding angle optimization, due to the low critical normal bending radius of the HTS tape [11,22].As described above, the Frenet frame leads to a tape with zero binormal curvature but very high torsion at certain locations; however, the finite (albeit large) critical radius of binormal curvature for HTS tape, discussed in detail below, allows for an optimization of the winding angle to reduce the maximum torsion the tape experiences, while not exceeding the The subsequent point γ k+1 is not included, because its winding angle will be adjusted next; the optimization of the track was directional, treating one point after another, going around the coil path.We found it helped convergence if the direction was reversed every ∼1.25 rounds.For the coil shapes we chose (shown in figure 4), each specified with 96 points on the curve, ∼200 rounds were sufficient for proper convergence, and the optimization took less than 1 min on a 2.4 GHz Intel Core i9-9880H.Only the innermost winding is treated by the optimization; all subsequent windings have lower strain due to their larger radii.
Optimizing the winding path of W7-X coils 1 and 5 in the way described above tended to produce solutions with the characteristic of a Moebius strip, in that the surface is non-orientable, and only after two turns does one return to the same point with the same orientation.This is undesirable because it would require winding the tape on both sides of the support structure, complicating the engineering unnecessarily.To change the winding path such that it is not a Moebius strip, we have to add or remove a twist of 180 • over the length of the tape.Distributing a rotation of 180 • over all points of the curve was done manually for our two coils.Moebius solutions are avoided in future versions of this optimization.
The final scaling factor of the coils depends on the material limits.In this work, we used TPL2301 tape manufactured by THEVA; it contains a ceramic HTS layer of GdBaCuO.An illustration of the tape with all its layers is depicted in figure 5 The torsion limits are obtained from personal communication with THEVA and based on experimental data.There is currently no data specifically about the binormal strain tolerance of the tape, but we can relate the critical binormal curvature radius κcrit to the critical strain ϵ crit via 1/κ crit = d/2ϵ crit for a tape of width d.We chose a riskier critical strain of 0.45% for coil 1; as this coil was optimized for 3 mm tape, this allowed a critical binormal curvature of 0.33 m −1 .We chose a conservative critical strain of 0.3% for coil 5; as this coil was optimized for 4 mm tape (though it was ultimately built with 3 mm tape, due to availability), this allowed critical binormal curvature of 0.66 m −1 .
These limits of torsion and bending were used as upper bounds for the optimization of the winding angle for smallscale HTS versions of coil shapes from the W7-X stellarator.If the optimization yielded a winding path within the strain limits of the tape, the coil was further scaled down.This was repeated until we found the smallest possible size to build the coils without breaking the superconductor.The results of this optimization can be seen in figure 6.The optimization reduced the peak torsion (both positive and negative) in a trade-off with the binormal curvature, and the coils were scaled to lie just within the material limits.For coil 1 this yielded a test coil that is 11% of the original W7-X size; coil 5 could be scaled down only to 25% due to the coil path's stronger deviations from planarity (figure 4) and being intended for wider tape.These coil sizes are comparable to those obtained in Paz-Soldan's prior work, in which a similar optimization of the tape orientation was performed for a variety of different existing stellarator coils [11].

Construction and tests of coil 1
To validate the optimization scheme, the THEVA GdBaCuO HTS tape was wound onto a 3D-printed frame with the calculated winding angles, tested for damage, and operated in liquid nitrogen.
The data points of the optimized winding path serve as the anchor around which the 3D-printed, plastic support structure in figure 7(a) is designed.The superconducting tape lies in a U-shaped profile; the cross-sectional area of the frame is about 25 mm × 15 mm.The finished frame was split into 30 segments to allow for easier printing.One of these segments containing the support for the current leads is depicted in figure 7(b).Each segment contains two holes on each end for connection via 50 mm long nylon threaded rods.Further details on the construction of the coils are given in appendix A. Five turns of 3 mm HTS tape were wound around the coil frame and subsequently unwound again, after which the spatially resolved critical current was measured with a TAPESTAR XL™ device.(The TAPESTAR XL™ device measures the critical current I c along a tape by submerging a part of it in liquid nitrogen and measuring the local response to an applied magnetic field [23].)The resulting measurement, as shown in figure 8, shows no degradation of the critical current.Thus, it can be concluded that the strain put onto the tape by the deformation into the shape of the optimized coil did not exceed the critical strain and did not create measurable defects in the crystal structure.This confirms the successful winding of ReBCO tape into a non-planar shape after careful optimization of its winding path.
Seven new turns of tape were would around the coil frame, and current leads were soldered onto the ends, as pictured in figure 7(d).Voltage taps were placed to measure the total resistance, including the current leads.The coil was submerged in liquid nitrogen, and the current in the coil was ramped up to 100 A, which corresponds to approximately 60% of the critical current.This resulted in a total coil current of 700 A. The coil showed flawless superconducting operation.A four-point measurement of coil 1 is presented in figure 9; linear regression to it yields a resistance of R = 1.75 µΩ, which is consistent with expectations for the current leads alone.

Construction and tests of coil 5
Coil 5, scaled down to 25%, was built similarly to coil 1. Thirty PLA segments were connected using nylon threaded rods.The frame was wound with five turns of 3 mm tape,  and a TAPESTAR XL™ measurement of that tape was performed after unwinding, the result of which is shown in figure 10.This TAPESTAR XL™ again verified the optimization of the torsional bending since tape did not show significant systematic degradation of the critical current.The unwinding processes introduce of isolated dropouts-one of them to 0 mishandling and could be by an improved winding procedure.Due to its larger dimensions and larger non-planarity, coil 5 was significantly more difficult to wind than coil 1.In particular, a concave part of the winding path around the most non-planar section of the coil required several additional T-pieces to be  Critical current measurements of tape that had been wound around the optimized coil 5 frame.Two turns of 4 mm wide, unlaminated superconducting tape slit with a rolling knife (blue) exhibited quite few defects, as micro-cracks from the slitting process opened under strain.Five turns of 3 mm tape slit with a laser (orange) show nearly no degradation of the critical current, with the exception of a couple of isolated dropouts that can be attributed to handling errors.
properly wound.Moreover, the winding path carries out one full rotation over the course of one winding.This complicates the manual handling of the spool from which the tape rolls off and would be a significant challenge for a winding machine.
Additionally, a second winding test was performed for coil 5 using 4 mm wide tape, for which this coil had originally been optimized.However, the available tape in this width was merely silver coated, possessed no additional copper layer for stabilization, and had been slit (from 12 mm tape) using a rolling knife.It was wound twice around the support structure, then unwound; the results of the subsequent TAPESTAR XL™ measurement can be seen in figure 10.These show a clear degradation of the critical current with many dropouts to I C = 0.This shows the much better mechanical stability of laser-slit tape; tape slit with a rolling knife has cracks in the microstructure of the HTS crystal that open under strain that would be tolerable for an undamaged tape [24,25].
To enable full testing of coil 5 in cryogenic conditions, a large, robust liquid nitrogen tub was constructed with double  The increased resistance compared to coil 1 is likely due to a few point defects attributable to handling errors.Superconducting operation was shown up to 100 A which is ≈60% of the critical current.
3 mm thick walls of A2 stainless steel.The tub had a rectangular footprint of approximately 1.5 m by 1.2 m and a height of 0.75 m.A schematic and a picture of the fully assembled test stand are depicted in figure 11.The coil frame was wound with 15 turns of 3 mm tape, then submerged in liquid nitrogen and energized with up to 100 A.
The resulting resistance measurement (figure 12) shows two orders of magnitude higher resistance than coil 1 (figure 9): 195 µΩ vs. 1.75 µΩ.The increased resistance can be attributed to a few point defects on the superconductor and a subsequent redistribution into the copper lamination.For 150 µm thick lamination, with a resistivity of 1.5 • 10 −9 Ωm, and if the contact resistance between the HTS and lamination layer is neglected, we calculate the length of the normal conducting section to be 39 mm.This is on the order of the length of a few point defects, which could have been introduced by handling errors.
For volumetric magnetic field measurements, a trio of hall probes (B.2) was mounted onto a custom-built three-axis manipulator.Details on this setup are given in appendix B. In figure 13, the resulting field strength contours within the measurement volume are compared to values calculated from the ideal coil shape and the applied current using the Biot-Savart law.Generally, a good match can be observed in the absolute values of the field strength and shape of the contours, although some differences exist.These are consistent with the deformations of the coil observed while it was being submerged, due to the plastic support structure not remaining fully rigid.
In the linear profile plotted in figure 14, the good match between calculation and measurement is seen again.The field in the interior of the coil is very well represented; the slight undulations in the middle are likely due to tilts of the individual hall elements with respect to the Cartesian directions.Figure 15 shows a section of the time trace of the recorded magnetic field values, comparing the measurement to the calculation.Starting from 700 s, the relative error increases.This is due to the current leads producing additional field components, which are not modeled for the calculation.The current leads carry 1/15 ≈ 6.6% of the total current.Their error field is on the order of the deviations observed in figure 15.The total relative measurement error given by where N is the number of recorded measurements, yields a value of 5.8%.

Summary and outlook
In this paper, we have demonstrated the numerical optimization of the winding track of two stellarator coil shapes-coil 1 and coil 5 from W7-X-within the strain limits of copperlaminated, laser-slit HTS tape.The winding angles onto the given filament points were modified from the Frenet frame to reduce torsion while keeping binormal curvature within acceptable limits.The optimization indicated minimal scale sizes of 11% for coil 1 and 25% for coil 5. We successfully built and operated these small-scale coils at 77 K to verify the integrity of the superconducting tape, thereby confirming the methodology.
The spatially resolved measurements of the critical current of copper-laminated, laser-slit tape after being wound and unwound showed no degradation of the critical current (except for one dropout attributable to a handling error).Tape slit with a rolling knife was unable to handle the strains of the stellarator coil winding, due to microcracks from the slitting opening up.This emphasizes the advantages of the laser slitting technique for parting HTS tape into thinner tapes.
Both coils operated stably (without quenching) at 100 A of current when submerged in liquid nitrogen.For coil 1, we measured an internal resistance of 1.75 µΩ, which is the resistance from the current lead solderings.Coil 5 had a resistance of 195 µΩ, which is likely attributable to a few dropouts (e.g.due to a handling error).Three-dimensional measurements of the magnetic field were successfully conducted and produced results in quantitative agreement with calculations based on the Biot-Savart law.The differences are attributable to the deformations of the plastic support structure when submerged in liquid nitrogen and to error fields from the current leads.The coils built and tested in this work are not prototypes for largescale reactor coils.Magnets for a stellarator relevant for fusion would require several tens of kA of current and would operate at 20 K temperature or lower.Stresses on the conductor from j × B forces and reduction of the critical current due to a coil's own magnetic field are issues not addressed in this project.Reactor coils would also require long-length cables with their more sophisticated winding scheme, not only single conductors being wound around the frame.
The authors' work on HTS stellarator coil optimization will continue with the development of the EPOS stellarator [26], a tabletop-sized experiment for confining an electron-positron plasma.Due to its small scale, strain optimization of the coils will be essential.A metric for the strain will be implemented into the coil design optimization function; this will optimize the winding path alongside the coil shape, further developing the method described in this paper.The planned magnetic field strength for EPOS of 2 T is comparable to larger present-day machines; the corresponding consideration of j × B forces will also help to pave the way for future larger fusion machines.
As pointed out previously [11], non-planar coils (e.g.helical shapes, saddle coils, etc) also have applications in other areas of science/technology, such as particle accelerators.The techniques for optimizing non-planar HTS magnets that we have demonstrated here for stellarator coil shapes could be easily applied to other non-planar geometries.

Data availability statement
The data cannot be made publicly available upon publication because they are not available in a format that is sufficiently accessible or reusable by other researchers.The data that support the findings of this study are available upon reasonable request from the authors.was modeled and sliced as for conventional 3D printing.This gFile was then loaded by the Arduino Mega with a customized version of the widely used Marlin firmware [27].It controlled the NEMA17 stepper motors with a step size of 1.8 • resulting in a linear movement of 10-20 mm/turn.A custom g-Code was implemented to enable periodic position reporting by this Arduino to another one responsible for collecting the data.Upon receiving a position, this Arduino measured the three magnetic field components (three channels) from the hall probes using the multiplexer and wrote the dataset to the SD card, indicating successful measurement with an LED.The switching of channels limited the measurement frequency to around 3 Hz from a hardware standpoint.The entire control and data acquisition setup used for the magnetic field measurements can be seen in figure B.1.The hall probes (Lake Shore HGT-2101) were bare components requiring custom wiring, as off-the-shelf boards with magnetic field sensors including operation amplifiers (e.g.MPU-9250) could not withstand the liquid nitrogen environment.The hall elements on the probe head can be seen in figure B.2.The current sources were set to output 5 mA to the hall probes for the magnetic field measurement.The trio of hall probes was calibrated with a 100 mT permanent magnet while submerged in liquid nitrogen.Offsets were applied to the voltage signal of the hall probes to adjust the value at zero field.

Figure 1 .
Figure 1.Illustration of the unit tangent vectors t k and t k−1 calculated from forward differencing and the unit tangent obtained with central differencing T k .Additionally, the osculating circle intersecting γ k and the adjacent points is shown in blue.

Figure 2 .
Figure 2. Discrete representation of the ReBCO tape, based on the Frenet frame (red vector triplets), at point γ k .The HTS tape is associated with the surface spanned by dB k and −dB k .d is the width of the tape.

Figure 3 .
Figure 3. Illustration showing different ways the tape can be bent.(a) Normal bending at point γ k , plus projection of the adjacent points onto the B k T k -plane, which is used for calculating binormal curvature.(b) Torsion at point γ k , as evidenced by the rotation of the binormal vector between the previous and subsequent points.(c) Binormal curvature at point γ k , along with a segment of the osculating circle through the projection of the adjacent points onto the B k T k -plane.

Figure 4 .
Figure 4.The shapes of W7-X coils 1 and 5 are shown from two different perspectives, at their optimized sizes of 11%, and 25% of the original, respectively.These correspond to average radii of 0.23 m and 0.48 m.

Figure 5 .
Figure 5. Illustration of the TPL2301 tape used in this project.It includes a copper surround (≈10 µm) and a copper lamination (≈100 µm) for additional electrical and mechanical stabilization.

Figure 6 .
Figure 6.Effect of winding angle optimization on binormal curvature (red) and torsion (blue), for coil 1 (top) and coil 5 (bottom), scaled to 11% and 25%, respectively.The peak torsion is decreased at the cost of increased binormal curvature.

Figure 7 .
Figure 7. (a) Overview of the 3D-printed frame for coil 1.The ReBCO tape stack is colored copper, and the surrounding support material is gray.(b) A detailed CAD of the 3D-printed module where current leads are attached.(c) A close-up view of the assembled coil 1.This shows the U profile in which the tape is wound, as well as the T-pieces for its fixation.The T-pieces and segments are interconnected using nylon screws and threaded rods, respectively.(d) Current leads on coil 1.The voltage taps are soldered onto the silver droplets, marked with red arrows.The power supply was attached to the copper cylinders.(e) Coil 1 constructed with seven turns of 3 mm wide, laser-slit HTS tape.

Figure 8 .
Figure 8. Spatially resolved critical current measurement of superconducting tape, after being wound in the shape of coil 1.The tape shows no degradation of the critical current.

Figure 9 .
Figure 9. Four-point measurement of coil 1.A current of 100 A (≈60% of the critical current) is fed into the coil via the current leads.The voltage is measured between the leads and the slope of the curve can be used to determine the resistance of the current leads to be R = 1.75 µΩ.

Figure 10 .
Figure10.Critical current measurements of tape that had been wound around the optimized coil 5 frame.Two turns of 4 mm wide, unlaminated superconducting tape slit with a rolling knife (blue) exhibited quite few defects, as micro-cracks from the slitting process opened under strain.Five turns of 3 mm tape slit with a laser (orange) show nearly no degradation of the critical current, with the exception of a couple of isolated dropouts that can be attributed to handling errors.

Figure 11 .
Figure 11.Left: CAD schematic of the test stand for coil 5. Right: the fully assembled test stand.The coil was mounted on a steel plate and placed in the liquid nitrogen tub.The three-axis hall sensor was mounted on a 3D manipulator to take magnetic field measurements over a large volume inside the coil.

Figure 12 .
Figure 12.Resistive measurement for coil 5 following the same procedure as in figure 9.The resistance of the coil is R = 195 µΩ.The increased resistance compared to coil 1 is likely due to a few point defects attributable to handling errors.Superconducting operation was shown up to 100 A which is ≈60% of the critical current.

Figure 13 .
Figure 13.Three views of 3D contours of the measured magnetic field strength (left) and the values calculated from the coil filament and the applied current (right).The absolute values agree well, and the conductor shape is visible from the regions with comparably high fields.

Figure 14 .
Figure 14.Profile slice through the measured and calculated magnetic field.The deviations are bigger at the edges of the domain, which are closest to the coil, but are generally smaller than everywhere.

Figure 15 .
Figure 15.Comparison of the measured and calculated magnitude of the magnetic field values over the entire measurement process.The total relative measurement error is 5.8%.The peaks, corresponding to the field closest to the coil and current leads are less well reproduced.

Figure B. 1 .
Figure B.1.Schematic of the data flow within the measurement apparatus.Off-the-shelf and open-source components were used wherever possible.

Figure B. 2 .
Figure B.2.The head of the probe arm is equipped with a 3-axis hall probe.The three individual hall sensors (marked with red circles) are glued onto a 3D-printed mount.