Design of a Power-Dense Aviation Motor With a Low-Loss Superconducting Slotted Armature

This article describes the design and analysis of a 2.5-MW, 5000-r/min electric motor with a slotted armature employing rare-earth barium copper oxide (REBCO) high-temperature superconductors (HTS). The alternating current and field in the armature induces ac losses in the superconductors, requiring cryogenic cooling. Therefore, the aim is to design a machine with sufficiently low losses to make this cooling realistic, which simultaneously outperforms the state-of-the-art. The reasoning behind the key design choices is presented before the model used for 2-D finite element analysis (FEA) is described. Then, HTS ac losses are studied with the T-A-formulation, examining the impact of various operating conditions. Aligning the HTS tapes with the field was found to successfully reduce ac losses, while filamentization was only successful for more than ten filaments. The final design had an active torque density of 50.9 N$\cdot$m/kg and an estimated efficiency of 99.8% when the HTS are operated at 40 K.


I. INTRODUCTION
M OST of the climate impact from the aviation sector is not caused by CO 2 , but contrails and NOx, produced by the high temperatures required in combustion engines [1].Electrically powered fans or propellers can avoid these emissions altogether, and the development of fully electric or fuel cell electric powertrains is required for a true zeroemission scenario.Nevertheless, it has proven a challenge to design electric components meeting the extreme weight and efficiency requirements posed by the aviation sector.
REBCO coated conductors can carry high currents and could potentially enable compact and lightweight electric machines even at direct-drive speeds.Also, their low losses give an extremely high efficiency, reducing the power and energy requirements and, thereby, the weight of other powertrain components.These properties have caused high-temperature superconductors (HTS) to be considered a key enabler for electric aviation [2].However, HTS experience AC losses when exposed to alternating currents and magnetic fields, and a complex cooling system with high cooling penalties is required to maintain cryogenic temperatures [3].Because of this, it is still unclear whether AC losses in an HTS armature compromise the machine benefits [4].For example, Haran et al. (2017) argues that losses in a superconducting armature must be significantly less than 0.1 % of the machine's rated power to be competitive with its alternatives [5].Even higher losses could be tolerated if using liquid hydrogen (LH 2 ) fuel as a cryogenic heat sink [6], but also this has a limited cooling capacity [7].
The recent development of the mixed T-A-formulation has enabled accurate AC loss estimations with low computation times [8], making it a powerful tool in the design of electric machines with large HTS stacks [9]- [12].Although aviation machines with HTS armatures have been explored in multiple previous papers [13]- [20], none have conducted a detailed finite element analysis (FEA) of AC losses in a power-dense full-scale aviation motor.In this paper, the T-A-formulation is therefore used to explore the potential of a 2.5 MW aviation motor with a slotted stator and HTS armature windings while assessing its feasibility with respect to cryogenic cooling requirements.This is done through a comprehensive AC loss analysis, studying special HTS design considerations, as well as the impact of multiple design modifications and loss mitigation methods.Lastly, the design is compared with the state-of-the-art (SotA) within power-dense conventional machines.
The paper starts with an overview of the machine design choices in Section II, followed by the FEA modeling approach and material properties in Section III.In Section IV, the HTS AC losses are studied for several operating conditions and loss reduction methods.In Section V, the key machine parameters are presented and are used together with results from the HTS analysis to evaluate the design relative to the state-of-theart while discussing the implications of the results.Finally, Section VI concludes this article and gives suggestions for future work.

II. ELECTRICAL MACHINE DESIGN
Before presenting the analysis part of this paper, the description of the machine design will be provided as a foundation, explaining the reasoning behind the key design choices, focusing on machine topology, HTS coil design, and the envisioned cooling method.

A. Investigated Machine Design
An overview of the machine design is shown in Fig. 1, with parameters given in Table I.The machine has 24 slots and 8 poles and a distributed winding layout with a coil span of 3 slots.This layout has four symmetrical sectors, where each can be coupled to its separate converter module.This technique is described as functional modularity and allows each module to be operated separately from the others, introducing redundancy in the drive design [21].In the case of a fault in one module, it can be switched off, allowing the machine to continue operation at a reduced output.Furthermore, the parallel coupling of four converters helps keep the voltage at a manageable level.
A high current loading in the armature winding is required to ensure a high power density.However, the high armature current introduces a non-negligible slot leakage flux, meaning that the slots are not entirely successful in protecting the superconductors from alternating magnetic fields [22].Nevertheless, with respect to HTS losses, the authors think a slotted armature is preferable compared to a slotless one.As shown in this paper, a careful design of the slot shape can keep the slot field amplitude relatively low and also almost unidirectional, making it easy to align the HTS tapes with the field, largely avoiding eddy currents from the perpendicular field component.Since the field will be mostly in the tangential direction, the HTS must be placed almost flat in the slot, ruling out the typical racetrack coil since it has out-of-plane bent HTS, which would be perpendicular to the field.In-plane bending of HTS is both difficult and could lead to irreversible damage, and a saddle-like coil could be necessary.A saddlelike type of coil is well suited for the chosen winding layout.Lastly, Lorentz forces are less of a problem in a slotted design since they will point into the slot.
A four-segment permanent magnet Halbach array without back-iron has been chosen for the rotor magnetization.This is a mature solution offering a near sinusoidal flux distribution and a high power density [23], and could also be designed for low losses through axial magnet segmentation [24].Fur- thermore, the design study of Corduan et al. (2020) suggested that in a fully superconducting machine, the preferable air gap flux density is below 0.9 T, well within the range of NdFeB magnets [14].While the thermal stability of NdFeB-magnets is worse than that of SmCo, a machine with an HTS armature will have a negligible stator-to-rotor heat leak, making it easier to maintain a low temperature.Also, with grain boundary diffusion (GBD), the coercivity of these magnets can be increased, reducing the risk of irreversible demagnetization.HTS field windings are also a good alternative with significant potential [25], but its specifics were not examined since the paper's main focus is the HTS armature.

B. HTS Coil Design
To reduce insulation requirements, the phase voltage was restricted to a maximum of 500 V, meaning that the number of turns must be limited.Consequently, to get the desired power output, each turn must carry a high current, and multiple superconductors must be coupled in parallel.With a substantial slot leakage flux, the parallel conductors must be transposed to avoid large circulating currents within the stack.Alternatively, all strands could be insulated with a thin layer of polyimide/Kapton and be parallel coupled at the very ends.However, this would not only insulate the conductors electrically but also thermally, making cooling more difficult.In addition, it would require more slot space.
Because of the high aspect ratio of the HTS tapes, there are limited ways in which transposition can be done effectively.For this purpose, the Roebel cable has been shown to be manufacturable for HTS through a punching technique [26], [27].This configuration transposes the conductors along the axial direction of the electric machine, illustrated in Fig. 2. As shown in the same figure, this work considers the two-dimensional (2-D) cross-section of the Roebel cable in the middle of a transposition both on the top and bottom of the cable.This cross-section should give slightly higher losses than one where all conductors are side-by-side [28].Due to the transposition, the current is assumed to be evenly distributed between the strands.
The Roebel cable geometry was based on the work by Otten (2019) [30], with tightly packed 1.9 mm wide strands without inter-strand insulation.Otten's ten-strand cable had a transposition length of 116 mm.In this paper, 18 parallel   Shanghai SC LFHT [29] strands are assumed, and the active length of 240 mm is considered sufficient to fit one full transposition.The superconductor height is set to 80 µm, and a 0.5 mm vertical distance between each turn is reserved for electric insulation and mechanical clearance.Fig. 3 shows the resulting coil and slot layout, with parameters given in Tables I and II.

C. Cryogenic Cooling System
While not the main focus of this paper, the cryogenic cooling system will have a significant impact on the machine layout and the resulting power density.Therefore, a few design considerations are discussed in this subsection.
To provide cryogenic cooling, mainly two options are envisioned: cryocoolers and/or dual use of LH 2 as fuel and coolant [31].As shown in this paper, an HTS armature will have cold losses in the kW range.A cryocooler consumes a substantial amount of power to remove heat at cryogenic temperatures (cooling penalty).Using optimistic cryocooler performance estimations from Felder et al. [32], removing 1 kW of losses at 40 K would result in a cryocooler requiring 21.6 kW of input power and weighing 64.8 kg.Hence, using a cryocooler to provide the main cooling power does not seem like a viable option for this machine.On the other hand, an LH 2 cooling loop running through the whole superconducting propulsion system has an extraordinary potential [6].Such a system was studied by Hartmann et al. (2022), showing that the cryogenic cooling capacity of LH 2 is more than enough to cool kW-scale losses at cryogenic temperatures [7].Nevertheless, the authors are not aware of a detailed design of such a cryocooling circuit.
Several cooling concepts for superconducting armatures have been proposed in the literature.Broadly speaking, they can be grouped into designs with either a cryogenic or a warm stator core.A cryogenic stator core can be achieved by cooling channels in the slots and/or yoke.Cooling channels in the yoke enable a simpler cooling system, and a cold steel would require no thermal insulation in the slot.The primary downside with this solution is that in addition to the coil losses, the steel losses would also need to be dissipated into the coolant.The alternative is to keep the stator steel warm by thermally insulating the HTS coils from the steel core.This can be achieved by a vacuum gap [14], a cryostat [33], or thermal insulation.In this paper, the last option is assumed since it is easier to realize for a slotted stator.
A first-order calculation shows that if a material similar to closed-cell polyurethane, considered for LH 2 tanks [34], can be used for slot insulation, the heat leakage into the slot is manageable.A sketch of this concept is shown in Fig. 4. With a thermal conductivity of 0.01 W/mK, 3 mm of insulation results in a heat leak of 16 W per slot for a 250 K difference between slot and stator iron.This is less than the HTS AC loss per slot, as will be discussed later.The downsides of this concept become clear from Fig. 4 as well.The thick insulation layer will lead to a low slot fill factor, partially cancelling the benefit of a high current density gained by using superconductors in the stator.The electrical insulation and impregnation of the coils could also pose a challenge related to keeping the HTS cooled since it will act as a thermal barrier [35].When using many different materials within the slot, thermal contraction must also be considered.For now, the slot layout is assumed to be feasible, but further research is required to investigate whether this is the case.

III. FINITE ELEMENT MODELING
In this work, 2-D FEA is conducted with COMSOL Multiphysics to analyze the machine performance and the HTS AC losses.This section describes the modeling approach along with the implemented material properties.

A. FEA Machine Model
Symmetry allowed the FEA machine model to be reduced to a sector with one pole, three slots, and antiperiodic boundary conditions.As illustrated in Fig. 5, two models were used.A basic model with only the A-formulation and lossless coils was used for the initial design and to analyze the machine's performance.A separate model was made to analyze the HTS AC losses, where the T-A-formulation was implemented on the superconductors in one slot only (i.e., phase B+) since losses in the other slots are equal but phase-shifted due to symmetry.Both models have a pure q-axis current to obtain maximum torque per ampere (MTPA) and optimal utilization of the armature current.

B. Steel and Magnet Material Properties
The BH-curve of Vacoflux 50 was applied for the electrical steel in all analyses.Its material properties were imported from the COMSOL library.Vacoflux 50 saturates at a magnetic flux of approximately 2.3 T, allowing for minimal steel volume for a given magnetic loading.Characteristic data obtained from 0.2 mm thick Vacoflux 50 was used to obtain loss coefficients in the steel loss estimation.For the permanent magnets (PMs), COMSOL data of the NdFeB BMN-46EH (GBD) was implemented.At 20 • C, this material has a remanent flux density of about 1.38 T.

C. HTS Material Properties
The superconductor resistivity, ρ HT S , was modelled through the E-J power-law with field-dependent critical current density J c , and power-law index n: where E c =1 µV/cm is the defined critical electric field, B ext is the external magnetic field, and J is the current density.To model the field dependency of the critical current and the power-law index, anisotropic Kim-like models [36],

T Normalized critical current density [-]
Fig. 6.HTS curve fits at 40 K for normalized critical current density (left) and power-law index, n (right), based on measured data from the Robinson database [38].The color coding is equal for both.A 90-degree field is parallel with the tapes.[37] were fit on data from the Robinson database [38] for the Shanghai Superconductor low-field, high-temperature 2G HTS [29].The resulting curve fits at 40 K are plotted in Fig. 6 together with the input data.Due to the curve shape of n's field dependency, it was slightly difficult to make an accurate curve fit for it.Still, n does not impact the losses nearly as much as the critical current density, and a constant n-value is often assumed.Therefore, the curve fit is considered adequate for this analysis.
At 40 K, the self-field critical current for this superconduc-tor is about 2543 A/cm, while the self-field power-law index is approximately 27.2.For the analysis of AC loss temperature dependency, similar curve fits were made for 25 K, 30 K, 50 K, and 60 K.

D. HTS Finite Element Modeling
The T-A formulation of Maxwell's equations was used for modeling the superconductors.This is a computationally efficient modeling method developed specifically for REBCO tapes [8].With this approach, the current vector potential, T, is applied to infinitely thin one-dimensional (1-D) lines representing the HTS tapes, while the magnetic vector potential, A, is solved everywhere.The T-A formulation's applicability to HTS machine modeling has been previously validated in several articles [9], [12], [39].
A uniform mesh distribution of 50 elements was used for the T-formulated superconductors, and the discretization was set to linear for T and quadratic for A. Both the current and the magnet remanent flux density was ramped up from zero to obtain initial convergence.Since all HTS analysis was done on a 2D cross-section of the active part of the machine, end winding losses were not considered.The Roebel strands were simulated as perfectly uncoupled, and eddy currents in the non-SC layers were neglected.The simulations were run on Dell Poweredge C6420 computing nodes on NTNU's IDUN cluster [40], resulting in a computation time of about 8 hours for the base design.
The superconductor loss density (p HT S ) in W/m 3 was found through the dot product of the electric field E and current density J in each tape: The losses per axial length (P HT S ) in W/m were found by integrating this over each HTS tape and multiplying with the thickness of the REBCO layer, δ, set to 1 µm: To find the time-averaged losses, eq. ( 3) was integrated over the third half-period to avoid including transient behaviour.The average losses in the slot of phase B+ were multiplied by the active length (l a ) and the number of slots (N s ) to find the average HTS losses in the entire machine ( QHT S ) in W:

IV. HTS LOSS ANALYSIS
This section analyses AC losses in the superconductors.First, a base design is studied, which has the parameters presented thus far.Then, losses at different conditions are studied before alterations are made to the design itself, investigating the impact on AC losses of: varying the current loading through the number of strands per turn, aligning the HTS with the slot leakage flux, dividing the HTS into multiple filaments.Lastly, it is studied how an HTS critical current improvement would impact the AC losses in this case.

A. Base Design Analysis
The base design is here defined as the machine and coil geometry given in Table I at full load, 5000 rpm and a temperature of 40 K in the superconductors.For this case, the instantaneous losses were found for all three slots in the model as shown in Fig. 7.As initially mentioned, the losses in each phase are symmetric and phase-shifted.Therefore, only the slot with phase B+ is investigated from this point.
A high alternating magnetic field over the HTS should be avoided since it has such a large impact on the AC losses.According to Ampere's law, the slot leakage flux is proportional to the current within the slot, and inversely proportional to the slot width [41], meaning that the peak SC current coincides with the peak field, as seen in Fig. 8.The maximum perpendicular and parallel field across the SCs is 0.60 T and 1.27 T respectively.The flux increases towards the slot top, and the turns closest to the air gap experience the highest magnetic field.Further, the flux is slightly inclined in the rotation direction due to the q-axis current.
In Fig. 9, the normalized current density, J/J c (B), is plotted for the time instant at which peak losses occur.Here, the net current is positive (red), and the negative current (blue) indicates shielding currents opposing the external perpendicular field.A relatively large portion of the conductors is shown to be inactive, i.e., without any current flowing in either direction.In the same figure, the loss density at peak losses is plotted along with the time-averaged loss density.The current and loss dissipation are both highest at the outer ends of the Roebel cable, with an asymmetry giving higher losses on the bottom side, coinciding with the asymmetry in the magnetic field (see Fig. 8).The total losses per turn are plotted against time in Fig. 10 for half an electrical period, where it can be observed that the outermost turns have the highest losses due to the higher external field.

B. Impact of Torque Loading
An aviation motor operates at full load at take-off and during a shorter portion of the climb phase.At cruise, the load for a regional aircraft will typically be around 60 %, while it is even lower for the descent and landing [42].The output power is governed by speed and torque through the equation: In this analysis, the speed was kept constant at 5000 rpm while the torque was reduced through the applied current.Fig. 11 shows the resulting AC losses normalized with respect to full-load losses, as well as the magnetic field and normalized current density in turn 8 at peak losses.The figure shows that reducing the torque loading to 85 % cuts the losses in half, while we see only 13.7 % losses at 60 % load.Hence, the combination of a reduced transport current and consequently a lower magnetic field is shown to give a substantial AC loss reduction for the slotted armature, meaning that AC losses can be significantly lowered for a large part of the flight.Also, it is evident that designs with even lower AC losses are possible if allowing lower torque densities.

C. Speed and Temperature Dependency of AC losses
Total HTS AC losses, QHT S , divided by the output power, P mech , are shown in Fig. 12 for selected temperatures and rotation speeds.From this, the relation QHT S /P mech is found to be almost constant within the speed range, since both the ouput power and the hysteresis losses in the HTS REBCO layer are proportional with the electrical frequency.From the same plot, the HTS operating temperature is shown to have a significant impact on the losses.However, eddy currents in the non-SC layers, proportional to f 2 and increasing when reducing the temperature [43], were not included in the model.

D. Effect of Number of Strands in Roebel Cable
In Fig. 9, a relatively large portion of the superconductors was found to carry close to zero current.To investigate whether the superconductors could be utilized better, the number of parallel strands per turn in the Roebel cable was varied.In the analysis, the turn center was kept at a constant location by increasing the distance between turns.The rest of the geometric entities were kept constant while applying a constant current per turn.This way, superconductors were exposed to a comparable external field in each case, while effectively varying the normalized current (I/I c ).This led to the normalized current density shown in Fig. 13, and the corresponding total AC loss increase (compared to 18 strands) in Table III.
Reducing the number of strands per turn can reduce the coil height slightly, and as such the required slot height, slightly reducing the machine weight.However, since much of the slot space, in this case, is reserved for cooling and thermal insulation, this has a small impact on the power density.When

E. Impact of HTS Field Alignment
Because of the high aspect ratio (width/height) of the superconductors, an alternating magnetic field perpendicular to the tape surface will induce eddy currents.Aligning the tapes with the external field has been shown to effectively reduce the losses [44].Initially, the superconductors were parallel with the slot bottom, while the field was found to be slightly inclined in the rotation direction (see Fig. 8).To align the HTS with the field while keeping the coil in place, each Roebel cable turn was tilted counterclockwise relative to the turn centre as shown in Fig. 14.In each coilside, all turns were tilted by an equal amount.
In Fig 15, we see that the optimal configuration would be to tilt the two coilsides with 10 and 12 degrees respectively.Doing this would give an AC loss of 788 W for the entire machine, about half of the losses in the base design.The maximum perpendicular flux over the SCs is now reduced to 0.47 T. A plot of the magnetic field and normalized current density is given in Fig. 16 for this case.From this figure, it can be observed that the current is almost unidirectional, meaning that shielding currents have been reduced compared to the base design.However, it should be noted that this loss reduction is specific both with regards to the rotation direction and the q-axis current.

F. Impact of Filamentization
Filamentization is another way to reduce HTS eddy currents from alternating perpendicular fields.By cutting the tape into multiple narrow filaments, its aspect ratio can be reduced.In theory, the magnetizing losses can be reduced by a factor equal to the number of filaments [45].The filaments are separated by grooves, typically between 20-100 µm, to have a sufficiently large matrix resistivity to avoid high coupling currents [27].
In this section, it is investigated whether filamentization is a loss reduction technique well suited for this design.In the analysis, each strand is separated into multiple filaments which are modeled as perfectly uncoupled, meaning that an equal current is imposed on each one and that coupling currents are not modeled.The groove width was set to 50 µm, and the reduction in tape width due to grooves is taken into account for the critical current.A gradient mesh (see [11]) with 35, 25, 20, 15, 15, 12, and 10 elements was used for the 2, 4, 6, 8, 10, 15, and 20 filaments, respectively.
Varying the number of filaments per strand resulted in the losses given in Table IV.Here, the losses increased for 10 filaments or less, even when coupling losses between filaments are not considered.Fig. 17 shows that the timeaveraged loss density in the original case was very high only at the very ends of the tapes, while the losses are more evenly distributed within the multifilamentary tapes with a much lower peak loss density.Similar observations can be made for the normalized current density in Fig. 18.An explanation for this might be that the magnetic field induces shielding currents in the SCs.When investigating the magnetic field in Fig. 19, we find that the shielding seems to be more effective for the non-filamentary case, protecting a larger SC-volume from the perpendicular field at the cost of a higher peak current on the tape edges.For 4 filaments, the shielding effect is still there, albeit not as effective as the original case.For 20 filaments, the shielding effect is much weaker, seeing how the flux lines are almost unaffected by the HTS.The proximity effect is likely playing a part here, and might be stronger for few filaments due to a larger current capacity within each filament.
The analysis suggests that many filaments are needed in order to have a worthwhile impact on the AC losses.While the loss reduction potential of 20 filaments looks very promising, several downsides must be kept in mind.Producing too narrow filaments in long conductors is risky since this increases the likelihood of defects in different filaments, potentially blocking the current path [45].Furthermore, the filamentization process reduces the critical current beyond the loss of HTS-material, due to material inhomogeneity and possible damage from laser ablation [46].Also, it degrades mechanical strength [47], and coupling losses between filaments can be substantial, especially at higher frequencies [45].

G. Impact of Critical Current Improvement
Recently, REBCO HTS has undergone rapid development and entered the stage of early commercialization, where multiple actors can supply long lengths with a relatively high critical current.We might see HTS with even higher critical current density in the years to come, through improving artificial pinning or increasing the thickness of the REBCO layer [48].For example, the commercially available HTS used in this analysis had a self-field critical current of 648 A/cm at 77 K, while works such as Kim et.al. (2014) achieved over 1500 A/cm for a short sample [49].Therefore, a short investigation was made on how further improvements would help reduce losses in the given design.This was done by using the same field dependence curves as in Fig. 6 while increasing the self-field critical current by a given factor, k.When increasing the critical current, a larger portion of the current accumulates at the very edges of the tapes.To capture this, a gradient mesh (see [11]) with 50, 50, 70, and 90 elements was used for k = 1.5, 2, 3, and 4, respectively.The results are given in Table V, where doubling the critical current is shown to almost halve the losses.III Full load with optimal tilt (see section V.E).
IV Assuming PM losses of ca.2.5 kW

V. DESIGN EVALUATION AND DISCUSSION
In this section, an overview of the machine's performance is presented before a discussion part containing a brief comparison with the state of the art for conventional machines as well as some of the study limitations.

A. Machine Performance Overview
Table VI presents an overview of parameters related to the machine performance.With the exception of HTS losses, the results were found with an overview model with lossless coils given in Fig. 5. From these results, it can be seen that the cryogenic cooling requirement was estimated to be 1188 W, or 0.0475 % of the output power, for full-load operation at 40 K.While this is likely an underestimate, as will be further discussed, it shows that this machine has significant potential as a highly efficient alternative to conventional machines with a low enough cooling requirement to encourage further development and research on the unsolved aspects of the design.The torque density might be high enough to warrant direct drive operation, but a detailed analysis of the cooling system is required to get a good estimate of the weight of passive components.
The magnetic flux density for t=0 s is shown in Fig. 20.At this time instant, the flux in the middle slot is at its maximum.The steel is saturated both in the teeth and yoke.As previously discussed, it can be observed that the flux has a slight asymmetry because of the q-axis current, particularly in the tooth shoes which are over-saturated.A time-domain formulation of Bertotti's loss equation given in [50] was used  to estimate the steel losses, of which the hysteresis, excess and eddy current loss components amounted to 772 W, 255 W and 470 W respectively.In the PMs, the minimum flux in the magnetization direction was found to go down to -0.05 T in the innermost part of the outwards-facing magnet.Hence, the magnets must be kept below ca.150 • C to avoid demagnetization [51], [52].This could be improved by having a rotor back-iron, but optimizing the rotor design has been considered out of scope for this paper.In [24], Golovanov et al. showed that that axial segmentation is very effective at reducing PM eddy current losses.Therefore, without closer examination, these losses are assumed to be in the range of a few kW, which should be manageable to cool and also not impact the efficiency greatly.

B. Trade-Offs Compared to SotA and Other Design Choices
Conventional electrical machines can also reach high power densities through high-speed design.For example, Golovanov et al. did an optimization study of a design with a Halbach array rotor and slotted stator with copper windings [23].In this work, this was considered the state-of-the-art for electric aviation machines, and in Table VII its key performance parameters are compared with the ones for this paper's machine.
When only considering active parts, Golovanov's machine has a superior power density since it is designed for a higher rotational speed.If comparing the speed-independent torque density instead, the superconducting machine is over twice as torque-dense, only considering the active parts.However, when comparing the two designs, there are many nuances to consider.For example, considering only the active parts is a large simplification.Nevertheless, the immaturity of superconducting machines makes it more difficult to make an accurate estimate for passive components such as the cooling loop.Also, high-speed designs lead to increased friction and windage losses, in addition to the need for a gearbox if the machine is used as a propulsive motor, further increasing system losses and weight.Moreover, a higher efficiency could also cut weight through a lower power and energy demand for the entire drivetrain.
In this slotted design with warm steel, much of the slot space is reserved for thermal insulation, resulting in a coil area (68 mm 2 ) of only a fifth of the useful slot area (340 mm 2 ), which leads to a relatively low current density in the useful slot of this design (28.1 A/mm 2 ), not significantly higher than Golovanov's conventional design (ca.20 A/mm 2 ).Other topologies or design choices, such as a slotless stator or a cryogenic steel, could improve the power density but would almost certainly increase the required cooling.For now, the true challenge and constraint is to limit the AC losses sufficiently to be able to keep the HTS coils at cryogenic temperature.The same reasoning also applies to the current loading.It can be argued that I peak /I c,s.f.= 11.1 % is low, not fully utilizing the superconductor material.However, as shown in Section IV-D, maintaining the same current while reducing the number of parallel coupled HTS tapes increases losses significantly while having a minimal impact on PTW since most of the slot space is occupied by the thermal insulation.

C. Study Limitations
The AC loss estimate is most likely too low since it only considered the REBCO layer in the active part of the machine, neglecting eddy losses in non-SC layers and coupling losses.Further, cold losses, as well as heat leaks in the end-winding and current leads, have not been included in this analysis, and the total cryogenic cooling requirement will be significantly higher.On the other hand, it was shown that the torque loading has a large impact on the AC losses of the HTS coil (see Fig. 11), and in other flight phases than take-off, the losses can be significantly lowered.Nonetheless, the magnitude of the losses indicates that a cryocooler is unsuitable for this application due to its cooling penalty and weight, and an LH 2 cooling system is most likely needed to make an HTS armature an attractive alternative to conventional machines.The AC loss estimation from this paper can be used further to investigate designs for such a cooling system and scrutinize the slot layout outlined here.
While striating the HTS into a large number of filaments was shown to have a large loss reduction potential, aligning the HTS with the field seemed a simpler, and less risky measure.However, this leads to a complicated end winding shape, which could be difficult to manufacture.It should also be noted that when the external field is more perpendicular to the tape, filamentization is a more effective loss reduction measure, as shown in [11].

VI. CONCLUSION AND FURTHER WORK
In this paper, a power-dense electric aviation motor with a slotted HTS armature and Halbach array rotor was designed and analyzed.Its figures-of-merit demonstrate a high technical potential with an efficiency of 99.8 %, an active torque density of 50.9 Nm/kg, and an estimated cryogenic cooling requirement at 40 K of about 0.05 % of the output power.
A comprehensive AC loss analysis of the HTS coil configuration was conducted.This showed that the bulk of the AC losses is highest in the outermost turns, where the slot leakage flux is highest.The losses are highly dependent on the torque loading of the machine since increasing the transport current also contributes to higher slot leakage flux.Consequently, in other flight phases than take-off, the AC losses can be very low.The speed and temperature dependency of the HTS REBCO layer's AC losses was shown, and the impact of the current loading was investigated by varying the number of strands per Roebel cable turn.
High precision alignment of the HTS tapes with respect to the slot leakage flux was shown to be an effective loss reduction measure, roughly halving the losses with a 10-degree tilt difference.On the other hand, it seems that filamentization is no silver bullet for AC loss reduction.While a large number of filaments indicated an efficient loss reduction, fewer than 10 filaments was shown to actually increase losses, showing that extra care should be taken when considering multifilamentary tapes in cases where the field is not directly perpendicular to the HTS tapes.When doubling the critical current of the HTS tape, the AC losses were nearly halved, illustrating the potential for further HTS material advancements.
Still, other key aspects of the design remain unexamined.A more thorough analysis of the cryogenic cooling requirement is recommended since AC losses related to coupling, end windings, and eddy currents in the non-SC layers were not considered.The heat leak should also be examined more closely, not only in the slots but also in the end windings and current leads.A detailed design of the cryogenic cooling loop is also necessary to make further conclusions on the feasibility of the HTS armature winding.

Fig. 1 .
Fig. 1.Overview of the machine design, where the armature is divided into four separate sectors, each connected to its own converter module.The arrows in the Halbach array rotor magnets indicate their magnetization direction.

Fig. 2 .
Fig. 2. Illustration of one turn of REBCO Roebel cable with the modelled two-dimensional (2-D) section.Only the REBCO layer is modelled in the HTS loss analysis in the form of an infinitely thin strip.

Fig. 3 .
Fig. 3. Sketch of slot layout with parameters for the HTS coil and slot geometry.The turns are numbered for discussion of the results.

Fig. 5 .
Fig.5.Machine models used in the analysis.All results except HTS losses were obtained from the left model where the coils have been modelled as lossless.In the right model, all is equal except for applying the T-formulation on infinitely thin strips in one slot.

Fig. 7 .
Fig. 7. Applied current and AC losses for one electrical period in a single slot for each phase found through 2-D FEA modeling of the HTS coil.

Fig. 8 .Fig. 9 .Fig. 10 .
Fig. 8. Magnetic field in the slot with phase B+ at selected time instants, showing how slot flux co-varies with current.

Fig. 11 .Fig. 12 .
Fig. 11.Left: Time-averaged HTS losses at 40 K, 5000 rpm, normalized with respect to losses at full load (1574 W).Right: Magnetic field and normalized current density in turn 8 at 60% and 100% of full load torque at t=3.3 ms.60 K 50 K 40 K 30 K 25 K

Fig. 13 .
Fig. 13.Normalized current density in turn 8 at 3.3 ms when varying the number of strands in Roebel cable.

Fig. 14 .Fig. 15 .Fig. 16 .
Fig.14.Illustration of counterclockwise HTS tilt.The base design, where the HTS are parallel with the slot bottom is considered as the reference (0 deg).Each turn is rotated separately with respect to its geometric centre.

Fig. 17
Fig. 17.HTS time-averaged loss density in turns 8-14 for the base design, 4 filaments and 20 filaments.The range was set manually in all cases to have a comparable color legend.The maximum value in each case is indicated in the respective legends.

Fig. 19 .
Fig. 17.HTS time-averaged loss density in turns 8-14 for the base design, 4 filaments and 20 filaments.The range was set manually in all cases to have a comparable color legend.The maximum value in each case is indicated in the respective legends.Bottom half of turn 8, t = 3.0857 ms

Fig. 18 .
Fig. 18.Normalized current density in turns 8-14 at 3.0857 ms for the base design, 4 filaments and 20 filaments.The range was set manually in all cases to have a comparable color legend.The maximum and minimum value in each case is indicated in the respective legends.

TABLE III HTS
LOSSES WHEN VARYING THE NUMBER OF STRANDS IN ROEBEL CABLE, WITH 18 STRANDS AS REFERENCE Strands I peak /I c,s.f.(%) P HTS (W/m) Increase (%) taking the AC losses in TableIIIinto account, it becomes clear that a relatively low current loading is beneficial for this design, and the number of strands per turn should not be reduced.

TABLE V HTS
LOSSES WHEN INCREASING THE CRITICAL CURRENT kI peak /I c,s.f.(%) P HTS (W/m) Reduction (%)