Electrothermal quench modeling for the 100 kW SX3 thruster using superconducting coils

Electrothermal quench modeling for the 100 kW SX3 thruster using superconducting coils IEPC-2025-463 Presented at the 39th International Electric Propulsion Conference, Imperial College London, London, United Kingdom 14-19 September 2025 A.Dadhich * and E.Pardo  Institute of Electrical Engineering, Slovak Academy of Sciences, Bratislava, 84104, Slovakia G.Herdrich  , A.Behnke § , D.Wanke ¶ , A.Sperber  , and G.Becatti ** Institute of Space Systems, University of Stuttgart, Stuttgart, 70569, Germany Abstract: Applied-Field Magnetoplasmadynamic Thrusters (AF-MPDT) can generate very high thrust densities accompanied by comparably high specific impulse, due to the additional magnetic field and force applied by magnetic coils. On laboratory level, copper coils are used for generating these fields, but they have the drawback of large size and mass, and high-power requirements (for cooling and generating fields), which can limit their scalability and, in addition, their applicability for space flight is not adequately given. A good and practical alternative for copper is to use High Temperature Superconducting (HTS) coils in AF-MPDT, as they have high current densities at low power requirements, which can lead to very strong magnetic fields, and consequently higher thrust values. HTS coils are prone to electrothermal quench, where the temperature of the coils rises rapidly when the current in the coil rises above electrothermal quench current at part of the coil, or when unexpected damage occurs. This limits the total current in the coil, as well as the magnetic field and hence thrust. We have implemented our numerical models to design practical HTS coils for 100 kW SX3 thruster, to replace the copper coils in the SX3 system. Initial field mapping by HTS coils shows good agreement for applied field and thrust values measured by copper coils, and thus stronger fields of up to 1 T is simulated and thruster’s performance is discussed. Fail safe methods, like voltage limitation, for electrothermal quench is simulated for unexpected damage in HTS coils in SX3 thruster context, which shows considerable retained thrust values even after quenching of HTS magnets. * Post Doctoral Researcher, Department of Superconductivity, anang.dadhic[email protected]  Head, Department of Superconductivity, [email protected]  Head, Plasma Wind Tunnels and Electric Propulsion, Space Transportation, herdric[email protected] § Research Associate, Space Transportation, behnk[email protected] ¶ Research Associate, Space Transportation, wank[email protected].  Research Associate, Space Transportation, sperb[email protected] ** Research Associate, Space Transportation, b[email protected] The 39th International Electric Propulsion Conference, Imperial College London London, United Kingdom 14–19 September 2025 Copyright 2025 by the Electric Rocket Propulsion Society. All rights reserved. Page 1 Nomenclature ˙m= mass flow rate η= thruster efficiency KGD = empirical gas dynamic constant K∗ H= semi-empirical Hall constant Idis = discharge current through the plasma B0= applied magnetic flux density (on axis) Vdis = discharge voltage Pdis = discharge power Pkin = kinetic power Ic= critical current of superconductor Tc= critical temperature of superconductor ∆J= change in current density for HTS coil Bcen = Generated applied field at the center of HTS coil I. Introduction Modern day spacecraft generally use electric propulsion systems such as ion thrusters or Hall thrusters, which can generate up to 5 N thrust. A good alternative to these thrusters are magnetoplasmadynamic (MPD) thrusters, which have the potential of generating up to 30 N of thrust, with higher thrust density and specific impulse (Isp) than Hall thrusters.1One more advanced type of MPD thrusters, AF-MPDT traditionally employ copper coils to generate strong electromagnetic fields to push plasma out in order to generate high propulsive thrust (One example is the 100 kW SX3 thruster with an applied field of up to 0.4 T, developed at Institute of Space Systems (IRS), University of Stuttgart, which has a thrust force and specific impulse of around 2 N and 3670 s, respectively, at 60 percent thrust efficiency).2The disadvantage of using copper coils in these thrusters is their large size, and high power and cooling requirements, which is incapable for space missions as the goal is to have as low mass in space as possible, and to reduce the power requirements. Thus, we propose to use HTS materials in building AF-MPD thruster coils, as it reduces the size of the system, and increases the thrust values and the efficiency of such thrusters.3–6 HTS materials are a sub-type of superconductors, providing practically zero resistance, which allows for high current input, and thus very high magnetic fields can be generated by them when used as wires (current magnetic field record is up to 45.5 T).7–10 Additionally, HTS materials have high power density as well as high current density, which is optimal for having a high field magnet of small size. As a result, higher thrust and specific impulse, with lower power consumption and size can be achieved with AF-MPD thrusters using superconducting coils instead of traditional copper-based coils (This was experimentally investigated, e.g., at the Chinese Academy of Sciences on a 150 kW AF-MPD thruster, with applied field of 1 T, that generated 4 N thrust with Isp of 5714 s at 77 percent thrust efficiency).5Given their scalable feature, AF-MPDT are suitable for both small satellites (e.g. CubeSats) and future large size spacecraft.4 As AF-MPDT are globally at TRL 4-5, there is a huge scope in the improvement of the HTS coil and thruster designs, and related software development, where some research institutes have developed breadboard prototypes of these thrusters and tested them in laboratories.3, 4 The state-of-the-art temperature for all these experiments is between 50-77 K.12–17 These projects generally use commercial software (for example, COMSOL) or open source software (for example, FEMM) that can be slow or limited in nature, or their own methods, generally for modelling the multiphysics behaviour of these thruster coils, and many ignore important realistic features of superconductors like non-linear screening currents or damage possibilities in their simulations. The work in this paper uses specialized in-house software for superconductors in space context, which is substantially faster than the commercial software and many time-consuming case studies can be performed quickly.10, 18, 19 For instance, superconducting coils are prone to electro-thermal quench, when the current in the wire overcomes critical current, Ic, of the superconductor. This leads to rapid thermal runaway (quench), which reduces the current in the coil, and hence the applied magnetic field.10, 20 A damage can also occur during the construction of the coil, or during the launch due to extreme forces in upper atmosphere, which can affect Icof the coil.10, 18, 21 These factors can reduce the magnetic field The 39th International Electric Propulsion Conference, Imperial College London London, United Kingdom 14–19 September 2025 Copyright 2025 by the Electric Rocket Propulsion Society. All rights reserved. Page 2 Figure 1: SX3 thruster schematic with proposed HTS coils, adapted from Ref.11 (a) shows the HTS coil positioning in the place of copper coils, and (b) shows the cross section of HTS pancake coil system, with G10 material between the pancakes. generation capability of the coils within milliseconds, and hence lower the thrust generated from the system. The electrothermal quench, if not controlled, can also cause severe damage to the coils and spacecraft, and hence it is also important to design fail-safe systems. This paper is focused on presenting initial realistic design of the HTS coils for the 100 kW SX3 thruster Fig. (1), to replace the original copper coils on the thruster. Our original methods are applied to calculate HTS coils’ multiphysics behavior, and we also compare the magnetic field distribution by our HTS coil design with the existing copper coils that generate 400 mT. Then, a configuration of HTS coil system is presented to generate over 1 T of applied field, and related thruster performance is discussed. Lastly, a case scenario of coil damage, with voltage-limiting fail-safe technique, is simulated and discussed in terms of SX3 thruster. II. Modeling Method Institute of Electrical Engineering (IEE) has developed an in-house multiphysics software for the quench analysis of superconducting coils, that has been used in various European projects.10, 22 In the software, the electromagnetic calculations are done by our original and fast Minimum Electro-Magnetic Entropy Production (MEMEP) method, which is based on variational principles.18, 19, 23, 24 The method solves the fundamental electromagnetic equation E(J) = −∂A[J] ∂t −∂Aa ∂t − ∇ϕ, (1) where, Eis the electric field, Jis the current density, A[J] is the vector potential in Coulomb’s gauge generated by the currents, Aais the applied vector potential in Coulomb’s gauge and ϕis the electrostatic potential. The equation (1) can be solved numerically by minimizing the following functional, at a certain time t, L[∆J] = ZΩC d3r1 2∆J·A[∆J] ∆t+ ∆J·∆Aa ∆t+U(J) + ∇ϕ·J(2) where, U(J) = ZJ 0 dJ0·E(J0) (3) The 39th International Electric Propulsion Conference, Imperial College London London, United Kingdom 14–19 September 2025 Copyright 2025 by the Electric Rocket Propulsion Society. All rights reserved. Page 3 is the dissipation factor. Here, E(J) comes from superconducting power law E(Jsc) = Ec|Jsc| Jc(B, T, α)nJsc |Jsc|,(4) where, Ecand nare the electric field criterion and power law exponent for superconductor, respectively. This is a relation between electric field, current density(Jsc), and critical current density (Jc(T)) in the superconductor. Here, it can be seen that this relation is non-linear, in contrast to normal conductors like copper (E=ρ·J), where ρis the material resistivity, and thus important to be considered in the simulations, as Jcis highly dependent on temperature (T), magnetic field (B), and field angle (α), which contributes to screening currents and high power losses. The thermal calculations are performed using explicit Finite Difference Method (FDM), which solves the general thermal diffusion equation in cylindrical symmetry10 Cv(T)∂T ∂t =1 r ∂ ∂r (r·kr(T)∂T ∂r ) + ∂ ∂z (kz(T)∂T ∂z ) + p(T),(5) where, Cv,k,p,rand zare specific thermal capacity at constant volume, thermal conductivity, heat dissipation, radial and axial coordinates of the magnet, respectively. Here, kand Cvare temperature dependent. Note that we consider different conductivities, krand kz, in radial and axial directions, respectively. The input for this equation is the power loss from equation 3, and this coupling is shown in Ref.10 For cooling implementation in this paper, constant convection parameter (h) is used at specified boundaries, and its implementation is shown in Ref.10 These methods are also benchmarked previously for pancake and racetrack coils with various mainstream methods and commercial software to prove its validity.20, 25 Additionally, axi-symmetric assumption is taken for pancake coils, and voltage limiting features are added as a fail-safe method to limit the current input in case of quench.26 Once we find the current density by minimizing the functional in equation (2), we obtain the magnetic field from the Biot-Savart law. This generated field (or ‘applied magnetic field’) is an input for thrust calculations for the SX3 thruster. The thrust is calculated by modified Tikhonov model by Herdrich et al27 F=KGD a0˙m+ 2K∗ HIdisB0R5/3 A+µ0I2 dis 4π3 4+ lnRA RC,(6) where, a0,RA,RC, and µ0are speed of sound, anode radius, cathode radius, and permeability of free space, respectively. Also, FGD =KGD a0˙mis the gas dynamic term, representing the thrust due to expansion of the plasma as a quasi-neutral gas, FAF = 2K∗ HIdisB0R5/3 Ais the applied-field term that represents the contribution of the externally applied magnetic field to thrust generation, and FSF =µ0I2 4π3 4+ ln RA RCis the self field term, which accounts for the thrust generated by the interaction of the discharge current with its own induced azimuthal magnetic field. The thrust efficiency, η, is kept constant as an input for this model, to calculate discharge power and voltage. Also, the coefficients K∗ Hand KGD are empirical parameters and have been fitted to measured data of SX3 for this study. The retrieved values from this fit are given in the next section. It should be noted here that the applied magnetic field is assumed quasi-static, so the thrust model’s predictions are accurate only for slowly varying or steady-state currents. For time-varying fields, such as in pulsed or modulated operation, or for electromagnetic quench, equation (6) neglects induced electric fields, eddy currents, and self-inductive effects, which can significantly alter the force. Incorporating these effects requires accounting for the instantaneous interaction between currents and fields or using time-averaged contributions from numerical simulations. Relying solely on the static-field approximation can therefore mis-estimate thrust, particularly at high frequencies, limiting the model’s predictive fidelity in dynamic regimes. However, for our current study, the thrust model is applied only at selected time points rather than at every step of the simulation. This approach is justified because the magnetic field varies slowly (or stays static in most cases) relative to the timescale of the coil’s response, so the system can be considered quasi-static at these snapshots. By evaluating the thrust at well-separated instances, the model captures the dominant effects without introducing significant errors from neglected dynamic contributions. Additionally, the thrust model assumes a linear behaviour between magnetic field and the applied field thrust term, and it is not known if this relation holds for very high magnetic fields where this effect may or may not saturate. The 39th International Electric Propulsion Conference, Imperial College London London, United Kingdom 14–19 September 2025 Copyright 2025 by the Electric Rocket Propulsion Society. All rights reserved. Page 4 Furthermore, the thrust model does not consider field geometry, which is an additional parameter in the coil design that cannot be addressed with this method, and hence thrust is calculated at the relevant reference points. III. Modeling parameters The coil design parameters are considered from SX3 thruster at IRS, which is currently fitted with a copper coil system as specified in Ref.28 For the initial goal of comparative field mapping with HTS coil to that of the copper coil, the inner radius and positioning of the HTS coil is kept the same as the copper coil, as shown in Fig. 1 (a). The length and number of turns for the HTS coils is kept within tolerable limits for the thruster, to not exceed copper coil length, for ease of replaceability. We have considered flat spiral or ‘pancake’ HTS coils for the model. For initial field mapping, we consider 4 pancakes in the system to generate around 400 mT at center, as similar as the copper coils in SX3. Later we increase the pancakes to 10 to generate over 1 T at the center. We use a current ramp of 1 A/s to reach 250 A steady state coil current. These summarized parameters are shown in Table 1. Table 1: Thruster and HTS coil design parameters Thruster parameters Values HTS Coil parameters Values Anode diameter, RA86 mm Inner radius 162.5 mm Cathode Diameter, RC12 mm Number of turns 120 turns Distance between anode-cathode tips 28 mm HTS tape/pancake width 12 mm KGD 2.624 G10 width 0.5 mm K∗ H0.683 Number of pancakes 4-10 Thrust efficiency 0.53-0.6 Resistivity between turns 10−6Ωm2 Argon temperatue 5 eV Coil current 250 A Mass flow rate 30-120 mg/s Operating temperature 50 K The HTS wire or ‘tape’ considered for the simulations is from Theva APC, and its Jc(B, T, α) dependence is shown in Ref.26, 29 It can be seen from there, that with increase in temperature and magnetic field, the critical current density reduces and hence the current carrying capacity wanes as well. The critical current is proportional to the width of the HTS tape, and thus a wider tape of 12 mm is considered for the calculations, which allows high critical current of up to 280 A. This allows us to pass up to 250 A coil current to generate strong magnetic fields, with less HTS tapes required for the coils. We also consider the operating temperature of 50 K, as critical current is higher at this temperature than at 77 K (liquid Nitrogen). In practice, 50 K can be achieved in space with current commercial low weight cryocoolers (mostly pulse tube configuration), and hence it is a feasible condition for HTS coil operation. The thermal boundary conditions for the calculations are considered adiabatic (no heat exchange at boundaries of the coil), to analyze the power losses and thermally weak spots of the coils. Later, we apply cooling (or power extraction) from top and bottom of the coil system (Fig. 1 (b)), by a weak constant convection parameter of 150 W/m.K. In future designs, the cooling may be done with conduction via thermal conductors, and initially a weak cooling convection parameter by coolants is justified for lab experiments. IV. Results and Discussion A. Initial field mapping The FEMM model by IRS predicts 400 mT at reference point (0,0) for 1880 A of coil current, using copper coils.28 IEE’s model predicts 430 mT at 250 A coil current at the same point (Fig. 1), using HTS coils, as also seen in Fig. 2 (a), which is less than 10 % difference (also can be seen in Table 2 predicted section). This minor difference is our target accepted value, as we aim to have smaller field differences at farther reference points, like at (140,180) and (0,180), because HTS coils are much smaller in length than the copper coils, and their field strength is not higher at farther reference points with shorter or less stronger coils that can achieve the same field values at (0,0). Fig. 2 (b) shows small power rise of 2.5 W during the ramping of the coil current, which later reduces to 0.05 W during the steady state of 250 A DC current. Table 2 summarizes The 39th International Electric Propulsion Conference, Imperial College London London, United Kingdom 14–19 September 2025 Copyright 2025 by the Electric Rocket Propulsion Society. All rights reserved. Page 5 (a) 0 0.5 1 1.5 2 2.5 3 0 10 20 30 40 50 60 70 80 60 80 100 120 140 160 180 200 220 240 260 0.06 W Coil Power [W] Coil Current [A] t [min] Coil power Coil current (b) Figure 2: (a) HTS coil applied field mapping at coil current of 250 A. (b) Steady state power loss of 0.05 W at 250 A. the measured and predicted performance at low mass flow rate (30 mg/s).13 The thrust values for these models are close to each other, and also with the measured values, and hence the initial field mapping is considered satisfactory at least at these field values, as the goal of this research is mainly to increase the magnetic field to above 1 T. From the design discussed in next section, we achieve 1.05 T applied field. The results confirm that while increasing the applied magnetic field to 1.05 T enhances thrust and specific impulse, the associated rise in discharge voltage (494 V) leads to a significant increase in power demand (98.7 kW), limiting the practicality in space. To address this limitation, a higher propellant flow rate is investigated. Alternatively the discharge current can be reduced to limit the discharge power, which might be beneficial for reducing the thruster erosion. Table 2: Measured and predicted performance at 200 A, 30 mg/s.13 Idis [A] ˙m[mg/s] B0[T] F[N] Isp [s] η Pdis [kW] Vdis [V] Measured 200 30 0.10 0.60 2039 0.33 18.4 92 200 30 0.20 0.90 3058 0.56 24.0 120 200 30 0.40 1.00 3398 0.60 28.0 140 Predicted (at 30 mg/s) 200 30 0.40 0.94 3197 0.60 24.5 123 200 30 0.43 0.98 3344 0.60 26.8 134 200 30 1.05 1.88 6381 0.60 98.7 494 B. Thruster and coil performance for high applied fields As HTS coils are able to generate very high magnetic fields, we aimed to generate at least 1 T applied field at the center of the HTS coils. This was achieved using the same inputs (120 turns per pancake, at 250 A) as in Table 1, and increasing the number of pancakes to 10. Thus, we achieved 1.05 T at the center of the coil, as can be seen in Fig. 3 (a) and (c). Fig. 3 (a) and (b) also show much higher field values at all reference points, as compared to Fig. 2, which even extends up to 1000 mm. Fig. 3 (c) shows that the field is generated constantly for over 80 minutes (around 5000 seconds) in steady-state, as generated heat power is extracted by cooling, for 250 A of applied coil current (Fig. 3 (d)). Fig. 3 (e) shows that the maximum power is generated during the ramping up of the current (around 9 W), with a good contribution from radial power (due to metal insulation between turns with resitivity of 10−6Ω.m2). However, during the The 39th International Electric Propulsion Conference, Imperial College London London, United Kingdom 14–19 September 2025 Copyright 2025 by the Electric Rocket Propulsion Society. All rights reserved. Page 6 (a) (b) 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 0 10 20 30 40 50 60 70 80 Bcen [T] t [min] (c) 0 50 100 150 200 250 0 10 20 30 40 50 60 70 80 Coil current [A] t [min] Iph Ir Itotal (d) 0 1 2 3 4 5 6 7 8 9 0 10 20 30 40 50 60 70 80 Coil Power [W] t [min] P total P radial (e) 50 50.1 50.2 50.3 50.4 50.5 50.6 50.7 50.8 50.9 0 10 20 30 40 50 60 70 80 Coil temperature [K] time [min] (f) Figure 3: HTS coil behaviour at coil current of 250 A, generating 1.05 T at coil center. The figures show (a) Applied field magnitude at different reference points, where (b) is zoom of (a) for farther points. (c) Applied field at coil center, (d) steady state currents: azimuthal (Iph), radial (Ir), and total current (Itotal), (e) power loss (P) of 0.3 W at steady state, and (f) rise in temperature during ramp up, is shown in other figures. The 39th International Electric Propulsion Conference, Imperial College London London, United Kingdom 14–19 September 2025 Copyright 2025 by the Electric Rocket Propulsion Society. All rights reserved. Page 7 steady state, the power loss is only around 0.3 W, which needs to be extracted for the DC operation of the coil. This results in a very small temperature rise of 0.1 K (Fig. 3 (f)), which can also be brought down if stronger cooling methods are employed later. Table 3 presents a parametric sweep of predicted performance at 1.05 T applied field and Idis = 282 A, where mass flow rate is varied systematically at constant efficiency as an input. The data shows that while lower flow rates yield high specific impulse, the thrust-to-power ratio remains modest. Also, discharge power and voltage remains quite high at low mass flow rates, which may not be mechanically good for the system. As the mass flow rate is increased, the specific impulse decreases, but the thrust and thrust-per-unit-power improve steadily, with values near 120 mg/s providing a practical balance between performance metrics. The cases above 120 mg/s are calculated purely from academic perspective, as they can generate high thrust values for high mass flow rates, but in reality these values may not be practical (for example, 300 mg/s), specially at 0.53 thrust efficiency. Table 3: Predicted performance at Idis = 282 A, B0= 1.05 T, η= 0.53, varying mass flow rate. ˙m[mg/s] Isp [s] Pkin [kW] Pdis [kW] Vdis [V] F[N] F[mN/kW] 60 4865 68.28 128.84 457 2.86 22.22 90 3643 57.45 108.39 384 3.22 29.67 120 3033 53.07 100.12 355 3.57 35.64 180 2422 50.76 95.78 340 4.27 44.63 240 2116 51.69 97.53 346 4.98 51.07 300 1933 53.91 101.71 361 5.69 55.91 Table 4 compares measured and predicted results at the higher flow rate of 120 mg/s at 1.05 T applied field. The agreement between prediction and experiment confirms that operation in this regime produces thrust levels exceeding 3.5 N. With HTS coils, applied field is higher at 1.05 T, as compared with measured copper coil system (0.4 T), while keeping similar thrust and Isp at lower discharge currents. This also validates the choice of higher mass flow rate under strong applied magnetic field as a viable operating condition for achieving higher absolute thrust without a disproportionate penalty in discharge power. Table 4: Measured and predicted performance at high power (120 mg/s). Idis [A] ˙m[mg/s] B0[T] F[N] Isp [s] η Pdis [kW] Vdis [V] Measured 770 120 0.10 2.27 1928 0.31 70.1 91 728 120 0.20 2.99 2540 0.37 100.5 138 624 120 0.40 3.59 3050 0.53 101.1 162 Predicted (at 120 mg/s) 282 120 1.05 3.57 3033 0.53 100.12 355 C. Quench control with voltage limitation An important case scenario is studied where a damage may occur in some turns of the HTS coils during operation or take-off (due to strong forces). This can generate strong power losses from the damaged turns, as the local critical current density can go down significantly, making these turns ‘normal’ from superconducting. In high field HTS magnets above 40 T, this can cause local thermal runaways, and the whole system can quench within milliseconds, with a risk of complete failure and burn, if not controlled. For space missions, this can be highly critical as well (as fields are still very high above 1 T) with no possible repair solutions, and proper automated quench detection systems should be in place to avoid such situations. Voltage limitation can be one of such fail-safe methods, where the power to the coils is cut down slowly by reducing the current to maintain voltage at certain value. Using this method, short amount of current can still be passed, generating enough applied field and thrust for ongoing missions, before quench protection to cut the coil current is applied in extreme damage cases. Fig. 4 shows results for SX3 thruster with HTS coils The 39th International Electric Propulsion Conference, Imperial College London London, United Kingdom 14–19 September 2025 Copyright 2025 by the Electric Rocket Propulsion Society. All rights reserved. Page 8 0 0.2 0.4 0.6 0.8 1 1.2 0 2 4 6 8 10 12 14 Bcen [T] t-tdeg [min] No Voltage Limiting-adiabatic Voltage Limiting-adiabatic Voltage Limiting-cooling-top-bottom Voltage Limiting-cooling-all-sides (a) 0 50 100 150 200 250 0 2 4 6 8 10 12 14 Azimuthal Coil current [A] t-tdeg [min] (b) (c) 50 100 150 200 250 300 0 2 4 6 8 10 12 14 Max. Coil temperature [K] t-tdeg [min] (d) (e) 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200 0 2 4 6 8 10 12 14 Isp [s] t-tdeg [min] (f) Figure 4: HTS coil quench behaviour due to damage in bottom pancake, from tdeg =1000s, and with and without voltage limitation for different thermal boundary conditions. The figures show (a) Applied field at coil center, (b) coil current, (c) power loss, (d) coil temperature, (e) Thrust forces at center: Fand FAF , and (f) specific impulse. All figures use same legend as (a). The 39th International Electric Propulsion Conference, Imperial College London London, United Kingdom 14–19 September 2025 Copyright 2025 by the Electric Rocket Propulsion Society. All rights reserved. Page 9