Interlaboratory validation of a hanging pendulum thrust balance for electric propulsion testing

The thrust produced by electric propulsion thrusters is notoriously difficult to measure in the laboratory. Typical electric thrusters weigh 200–600 times the thrust they generate.¹ For traditional off-the-shelf force measurement devices such as load cells and microbalances, the thruster weight is too great to tare, meaning that the thruster mass dominates over any thrust signal. To complicate things further, the thrusters must be tested within a vacuum environment. Therefore, the data acquisition must be performed remotely. The thrust balance can either be calibrated under atmospheric conditions, with the influence of the vacuum environment considered as a source of possible error, or calibrated in situ within the vacuum chamber using a remotely actuated mechanism or pulley.

Given the lack of off-the-shelf force measurement devices, which meet these particular requirements, most laboratories choose to develop their own thrust balances. The most common method of achieving this is with a pendulum thrust balance: The thruster is mounted horizontally to a moving platform so that the thrust vector is orthogonal to the gravity vector. Any generated thrust leads to the balance being perturbed from its equilibrium position. The displacement distance is measured with a high degree of precision. A calibration process is undertaken to characterize the measured displacement when a known force is applied to the balance. Once the thrust balance is calibrated, the force that a thruster generates can be determined accurately from the measured displacement. The conversion factor from displacement to force is called the sensitivity of the balance.

Pendulum thrust balances can further be divided into three subsets of configurations: hanging, inverted, and torsional pendulums. For a hanging pendulum, the moving platform is suspended below the flexures in such a way that both gravity and the flexure spring force act as the restoring force of the pendulum.^2–4 This style of balance exhibits less sensitivity when compared to other devices, yet hanging pendulum balances boast intrinsically higher stabilities due to gravity acting as the dominant restoring force. As the name suggests, inverted pendulum thrust balances position the thruster above the flexure. In this configuration, the flexure forces counteract the gravity forces, resulting in a less stable yet more sensitive thrust measurement.^1,5 Torsional pendulum thrust balances are constructed in such a way that the thrust generates a torque orthogonal to the gravity vector so that the flexure force presents the only restoring force. By decoupling the influence of gravity on the restoring force, the sensitivity of the torsional pendulum thrust balance can potentially be the highest among the three configurations, with the trade-off of added complexity and generally higher cost.^1,6,7

A hanging pendulum thrust balance has been developed to perform thrust measurements ranging from 1 mN to 1 N, using a series of interchangeable flexures of varying thickness. The thrust balance design is illustrated in Fig. 1. Four parallel linkages, each with two stainless steel flexures, ensure the central platform remains horizontal at all times. A novel self-compensating thermal management system has been developed in order to minimize the influence of thermal transients on the displacement measurements. Great care has been taken to ensure the thrust balance is immune to the electromagnetic interference (EMI) produced by electric thrusters. The thrust balance displacement is measured using a laser triangulation sensor that communicates with the data acquisition electronics through a digital interface. Digital signals are generally less susceptible to EMI, whereas analog measurements can be adversely affected by RF interference in the frequency range of 10 kHz and above resulting in a small DC offset of the voltage signal measured by the data acquisition electronics. A voice coil actuator (VCA) is used to calibrate the thrust balance, which itself is calibrated independently using a high precision commercial microbalance to ensure a traceability chain in measurement uncertainty to a trustworthy, independently certified source. It should be noted that the EMI produced by electric thrusters has been shown to interact with sensitive electromechanical components such as the coils and magnet within the VCA.⁸ Such interference has the ability to induce currents in these coils and produce erroneous parasitic forces. To mitigate this, we remove the VCA prior to testing and employ a second calibration system, based on a servomotor pulley system, so that the thrust balance can be calibrated in situ during the experiments in order to quantify drift in the calibration constant throughout the experimental campaign. Similar concerns about EMI effects have led us to forgo a traditional eddy damper, opting instead to operate the balance under-damped and removing the oscillations in post-processing.

The thrust balance has been developed by the Imperial Plasma Propulsion Laboratory (IPPL) in collaboration with the Electric Propulsion section of the European Space Agency (ESA). Two near-identical balances were constructed, with one of the balances staying in the IPPL in London and the second being integrated into the ESA Propulsion Laboratory (EPL) at the European Space Research and Technology Centre (ESTEC) in the Netherlands. The slight differences in the two designs flowed from differences in the vacuum facility dimensions in each laboratory but do not have a major effect on their functional characteristics. The mechanical design and operation are described in Sec. II. The data acquisition and processing are explained in Sec. III. We assess the uncertainty on the devices’ measurement in Sec. IV. An inter-laboratory validation campaign was performed to compare the two devices operating in their respective laboratories using the same quad confinement thruster and test procedure. These results are discussed in Sec. VI.

The main design driver for this thrust balance was that the device could be used to perform thrust measurements on a wide range of current and future thrusters. This ranged from low power electric thrusters of around 5 mN to chemical micro-thrusters with thrust up to 2 N. Extending the thrust range to lower thrusts than this would necessitate a considerable amount of vibration isolation and thus dramatically increase the cost and complexity. We decided on a hanging pendulum style balance for its simplicity and stability, given that a sufficient sensitivity could be achieved for our desired thrust range.

The moving platform of the thrust balance is hung from the support structure by four parallel linkages, with each linkage having a flexure at the top and bottom. This configuration was based on the design of Pottinger et al.,² which has shown great success with a range of thrusters.^2,9,10 The double pendulum configuration ensures that the platform and test article remains horizontal at all times and restricts all off-axis movement. The flexures are rectangular sections of stainless steel shim stock. By producing three sets of flexures of varying thicknesses, the thrust sensitivity can be increased across almost three orders of magnitude. We use flexures with thicknesses of 25.4 μm for thrust below 5 mN. For medium thrust up to 300 mN, we use flexures, which are 50.8 μm thick, and use a set of flexures of 101.6 μm thickness for a thrust above 300 mN. The test article is mounted at the end of the central platform using an interface plate. The laser displacement sensor (Micro-Epsilon model optoNCDT-1750) is fixed to the stationary base of the balance and measures the distance to a ceramic target attached to the moving platform. Any force along the thrust axis displaces the central platform. The displacement of the central platform changes the relative distance between the laser and the target, which is measured by the laser sensor.

There are slight mechanical differences in the design of the balance at IPPL and the one at EPL. The EPL balance is mounted on linear guide rails so that it can move within the hatches of both the Corona vacuum facility and the Small Plasma vacuum Facility (SPF). The length of the EPL thrust balance was also slightly different from the IPPL balance in order to accommodate the length constraints of the Corona and SPF hatches. The base of the IPPL balance is 620 mm, while the base of the EPL version is 570 mm long. The central platform of the EPL balance is also 50 mm shorter than that of the IPPL balance, which decreases the mass of the moving platform. Differences between the two balances have resulted in a discrepancy of the balance sensitivity of less than 3%. We consider this discrepancy to be negligible, considering that dismantling and rebuilding an identical experiment resulted in a change of 5% (see below). Such minor changes are expected and accounted for during the calibration procedure detailed below.

Not included in Fig. 1 are the fluidic and electric interfaces between the balance structure and the central platform. These connections provide power and propellant to the test article on the central moving platform from the top of the balance. This is done via wide arcs, which lie orthogonal to the thrust axis. These connections can be seen in Fig. 2. This is done to reduce any stiffness that they may add and to ensure any thermal expansion of the wires leads to forces orthogonal to the thrust axis.

A Micro-Epsilon optical laser triangulation sensor is used to measure the displacement of the central platform. Linear variable differential transformers (LVDTs) have traditionally been used to measure displacement in similar thrust balances.^5,11–13 However, LVDTs rely on the reading of an analog signal, which are potentially susceptible to EMI produced by the thruster. The laser sensor includes an internal analog to digital converter, allowing the user to communicate with the sensor digitally over an RS422 interface. The impact of the EMI generated by different electric propulsion devices on both laser triangulation sensors and LVDTs was investigated by Pottinger et al.⁸ While the two displacement sensors showed good agreement for cold gas thrusters, the analog LVDT signal was shown to be very sensitive to electric thruster EMI, producing highly erroneous thrust even with cable shielding. The authors showed that both hardware filtering and software filtering were unable to solve this issue for some thruster technologies.⁸ Our thrust balance uses the same laser triangulation sensor and digital interface recommended in this prior work. The thrust balances at IPPL and EPL were designed to use slightly different models of sensor: The EPL device uses an optoNCDT 1700-10, where the IPPL uses an optoNCDT 1750-10. The discrepancy was due to different procurement times of the two instruments and a corresponding change to the model number available from the Micro-Epsilon supplier. Both lasers operate over a 10 mm range at a frequency of 2.5 kHz. The sensors can operate at temperatures up to 50 °C, which is considerably higher than the base of the balance reaches, even when the instrument is heated (see Sec. II C). The digital readout of the lasers provides a resolution of greater than 0.6 μm and linearity of ±0.1% of the full scale output. The thickness of the flexures is selected such that the anticipated nominal thrust produces around 100 μm of platform displacement, for which the sensor provides ample resolution.

Thermal management is critical to all pendulum style thrust balances because the flexure stiffness is highly dependent on temperature.¹ Most thermal management systems aim to keep the balance cooled to a set low temperature. This is achieved by removing the heat produced by the thruster using active cooling such as water-cooling. Our balance, unlike the majority of designs, uses compensating heaters in a closed loop configuration to maintain an elevated temperature during testing. Before testing, we determine a set temperature for the balance, which must be above the temperature that the balance would achieve with the thruster firing in steady state. Before calibration and testing, the balance is brought up to the set temperature using a pair of 300 W mica heaters. One heater is attached to the moving platform, and the other is attached to the support structure. Ceramic thermal breaks, located between the stationary top surface of the balance and the legs, reduce thermal conduction to the base of the balance and the facility. The temperature of the balance is continually monitored at several locations using Resistance Temperature Detectors (RTDs). Once the set temperature has been reached, the balance software terminates the power to the heaters using solid state relays. Once the temperature falls below the set temperature, the heaters are again powered, operating as a bang–bang feedback control loop. When the thruster is turned on, this heating cycle continues and effectively compensates for the inability of the thruster to maintain the set temperature. While unconventional, our thermal management system ensures that the balance is calibrated and operated at a fixed temperature, without the added complexity and potential vibrations introduced by a water cooling loop. In practice, the thermal management system has been very effective at keeping the balance within 2.5 °C of the set temperature.

Two critical attributes of any measurement instrument are the traceability and stability of the instrument’s calibration. Traceability in this context means that a trusted calibration chain extends from the instrument to the relevant National Measurement Institute (NMI) standard reference. For thrust balances, this means producing a highly repeatable force that can be calibrated against a second traceable measurement system. By repeatedly monitoring the response of the balance to a consistent force, the stability of the calibration can be monitored. This is crucial in electric propulsion testing, as subtle changes in the experimental setup can result in significant deviations to the measured force, owing to the low levels of thrust produced by these devices. Our balance utilizes two independent calibration subsystems. One serves to ensure the traceability of our calibration to an NMI reference. The second monitors the stability of our calibration throughout the test campaign.

The thrust balance utilizes an AVM12-6.4 voice coil actuator manufactured by Akribis Systems to ensure the traceability of the calibration. The VCA consists of a coil section and a magnet section. By supplying a current to the coil section, a non-contact force acts to repel the magnet section. Bespoke alignment aids have been designed to guarantee the two sections are separated precisely and without contact in a repeatable manner. We use a Keysight B2902A precision sourcemeter to supply an ultra-low noise current to the VCA, which in turn generates a highly repeatable force. The sourcemeter has an uncertainty of ±1 pA, which results in a theoretical force resolution greater than 1 pN. This precise repeatability allows us to use the VCA as a link in our calibration chain. To accurately characterize the VCA, we rest the magnet section on the weighing pan of a microbalance that has been calibrated to an NMI reference. Next, we align the coil section of the VCA using our specially constructed VCA positioning system and tare the balance. The lack of contact between the two sections eliminates any offset due to friction. We now generate a wide range of current steps to the coil using the sourcemeter and record the force measured by the NMI-calibrated microbalance. This leaves us with a highly repeatable force vs supplied current relationship, which is traceable to the calibration certificate of the microbalance. The final step is to install the magnet section of the VCA to the moving platform of the thrust balance and again align the coil section using the bespoke VCA positioning system. We then use the same sourcemeter to generate the same forces and directly determine the sensitivity of the balance using an NMI-traceable force. An important consideration is to perform this step once the experiment is completely set up, and the balance has been brought up to operating temperature because the calibration constant (balance sensitivity) will change even with very minor changes to the experimental setup.

Ideally, the VCA would remain installed during testing so that the same force can be repeated to ensure the balance calibration remains stable. This is, however, not possible due to potential EMI produced by the electric thruster. Such interference can induce currents within the VCA coil and generate a force on the magnetic section indistinguishable from an actual thrust. For this reason, the VCA is removed from the thrust balance before pumping down the facility, and a second calibration system is used to monitor the stability of the thrust balance calibration throughout the experimental campaign.

The primary role of the in situ calibration system is to monitor the stability of the calibration constant at intervals throughout the test campaign. The subsystem consists of a servo motor fixed to the leg of the balance, a thread, and a known test mass. The test mass is suspended via a thread from the moving central platform. The thread also runs horizontally from the mass to the servo motor via a guide hole in the servo holder. This is shown schematically in Fig. 3.

Rotating the servo arm pulls the horizontal string through the guide hole and changes the angle of the thread between the test mass and the moving platform. This creates a force along the thrust axis between the moving central platform and the rigid leg. A test mass of 2 g allows us to generate forces up to 2 mN for servo angles α = 0°–60°. This force range can be tailored by substituting for a larger or smaller test mass.

The in situ calibration system can be commanded remotely and is not affected by EMI generated by an electric thruster, meaning that it does not need to be removed, unlike the VCA calibration system. The servo motor is commanded to sweep through a range of angles, generating a range of forces with the response of the balance being recorded. The first calibration is done directly after the VCA calibration has been established in order to correlate both calibration methods. We call this the “baseline calibration” as it overlaps with the traceable VCA calibration. The VCA can now be removed, and the chamber can be pumped down. The in situ calibration system can now be commanded to run “spot checks” in which the same commands are sent as during the baseline calibration. By comparing the response of a spot check to the baseline, we are able to monitor the stability of the calibration and verify the balance response has not changed since the NMI-traceable calibration. We perform these spot checks before and after any measurements are taken.

In summary, the traceability of the measurement is ensured through the VCA calibration approach, whereas the drift of the calibration constant throughout the experimental campaign is monitored using the pulley system calibration approach. By correlating both methods simultaneously during the baseline, we ensure that the two systems are in agreement.

Thrust is determined by comparing the measured displacement when the thruster is firing vs when it is turned off. The thruster is brought to a steady operating point and held there for several minutes until both the balance and the thruster settle. The laser sensor data acquisition is then initiated, followed by the thruster power and mass flow rate being shut down. A representative sample of the raw displacement data is shown in Fig. 4. Note that the absolute value of the displacement is not important, only the relative difference between the thruster in the on and off state. In post-processing, two linear fits are performed on the data: one for 30 s before the step and the other for 30 s after the step. These are shown as dotted and dashed lines in Fig. 4. The fitted trends are averaged over the large natural frequency oscillations and span sufficient periods to identify the equilibrium position of the balance in both thruster on and thruster off states. The step size is the relative difference between the two fits at the time of the step. Any zero-drift that may have occurred is accounted for by measuring the zero value directly after the thruster is stopped. The change in displacement between the thruster on and off states is then converted to a thrust using the sensitivity parameter that was established during the VCA calibration procedure.

The natural frequency of the balance was experimentally found to be between 1 Hz and 1.5 Hz depending on the mass of the thruster and harnessing. We sample the data at 500 Hz. Unlike many similar balances, we have chosen not to include an Eddy damper to combat natural frequency oscillations. The strong magnetic components in Eddy dampers have the potential to interfere with the highly sensitive magnetic field generated by our VCA calibration system and could also potentially interact with the electromagnetic environment of electric thrusters during their operation. Such interference would jeopardize the traceability of our calibration. Therefore, our balance behaves like an under-damped harmonic oscillator, as is evident in Fig. 4. When in vacuum, vibrations from the laboratory excite the oscillations at the natural frequency to the point that the amplitude can easily exceed that of the thrust signal by an order of magnitude. In order to investigate the extent to which these large oscillations near 1 Hz may override important low frequency features, we filter the raw thrust data using a fifth-order low-pass Butterworth filter with a cutoff frequency of 0.5 Hz. Low-pass filters such as this have been used to smooth out raw data on similar balances.¹⁴ This Butterworth filter is applied to the raw data in Fig. 4, with the results shown on the same plot as the thick line. This filter restricts high frequency, low amplitude oscillations, similar to an Eddy damper, but is accomplished during post-processing. We assess the impact of this filter by performing the same post-processing procedure on both the raw data and the Butterworth filtered data of a full set of VCA calibration forces ranging from 0.7 mN to 330 mN. We then compare the final step sizes for the same raw data to determine the impact that the filter has on the post-processing procedure. The mean difference between the step size of the two datasets is 0.32% of the measurement, with the maximum difference being 1.35%, which is negligible compared to other sources of uncertainty, which are described in Sec. IV. These results show that vibrations above 0.5 Hz have an almost undetectable impact on the final displacement measurement. By extension, the large natural frequency oscillations between 1 Hz and 1.5 Hz are hereby also shown to have a very little impact on the step measurement. We consider this an adequate justification for leaving the thrust balance under-damped.

Our uncertainty budget calculation was based on the guidelines recommended in the work of Polk et al.¹ During the VCA calibration process, we measure the displacement x_i that each calibration force F_i produces. The least squares approach is used to determine b_cal and S_cal such that the expected displacement $xi^$ can be calculated from

where S_cal is the estimate of the sensitivity of the balance in m/N and b_cal is the intercept to overcome the small but finite force needed to account for friction in the system. The force produced by the VCA is highly linear and has been measured to the highest precision possible with our microbalance: ∼±0.2 mN for individual measurements. For the derivation that follows, we assume that the force produced by the VCA is exact. For the n calibration steps we took, we can estimate the variance of the random disturbances of the balance $sx2$ using Eq. (25) from the work of Polk et al.,¹ 

We assume that this estimate is close to the actual value: $σx2≃sx2$⁠. Taking the square root of the variance, we are provided with the standard deviation of the random disturbances of the balance to a known input s_x. This value is more tangible when converted into a force. We do this using the sensitivity to gain the estimate of standard deviation of the thrust measurement s_F, which again we assume is close to the actual value $σFt$⁠,

The size of this standard deviation is one of the most important metrics for assessing the resolution of the balance. We can also estimate the standard deviation of the sensitivity itself s_Scal,

where $F¯$ is the average force used in the calibration. We again assume that the actual value of the standard deviation of the sensitivity σ_Scal is similar to our estimated value: σ_Scal ≃ s_cal.

The overall uncertainty of the thrust measurement is the aggregate of the displacement measurement uncertainty and the uncertainty of the thrust balance sensitivity parameter. For a measured displacement x, the thrust measurement F_t has an uncertainty given by

The resulting quantitative values for the uncertainty of the IPPL and EPL balances are reported in Table I. Additional potential sources of uncertainty stemming from the experimental setup exist, such as the electrostatic interactions of the feedline and the pressurization of the gas feedlines. These factors were evaluated experimentally and are described below.

Each of the two balances was tested in its respective laboratory in November 2019. Both tests used the same test article, procedure, and thruster operating points. The test article was a 200 W class Quad Confinement Thruster (QCT) named the QCT Phoenix, which was operated on 5 sccm–15 sccm of research grade xenon at discharge powers between 50 W and 115 W. The thruster plume was neutralized using a filament plasma bridge neutralizer, which was run on 5 sccm of xenon for all tests. Bronkhorst massflow controllers were used to regulate the thruster and cathode flow.

Both the thruster and cathode were mounted on the interface plate of the thrust balance, with arcs orthogonal to the thrust axis being used to connect electronics and fluidics from the moving platform to the top of the balance, as shown in Fig. 5. These arcs are fixed so that any vibration or thermal expansion is most likely to occur perpendicular to the thrust axes. The balances were fitted with a set of flexures of 50.8 μm (0.002 in.) thick. The flexure thickness was selected on the basis of preliminary testing showing that this thickness provided adequate resolution and range for the anticipated thrust values (1 mN–10 mN).

Originally conceived within the Surrey Space Center, the QCT is a low power electromagnetic device designed for small satellites.^15,16 The QCT’s most attractive properties, namely, its ability to function at low anode voltages and the fact that it can vector thrust without the use of mechanical gimbals, garnered a substantial amount of commercial interest over the course of its development. This ultimately culminated in the launch of the first QCT flight model on board SSTL’s NovaSAR-1 satellite. Despite this success, the further commercial exploitation of the QCT has been limited by its poor thrust efficiency. Experimental testing of the QCT has indicated a maximum thrust efficiency of ∼6% under all of the conditions surveyed, which is a notably lower performance than Hall effect thrusters (HETs) and gridded ion engines at the same power level.^15,17 Laser Induced Florescence (LIF) measurements taken in the plume of the thruster to investigate the cause of this shortcoming pointed to a potential link between the efficiency and the electromagnetic topology.¹⁸ More recent work within IPPL has suggested a possible alteration to the magnetic field topology, which aims to reduce the beam divergence and move the ion acceleration front nearer to the region of peak ionization, with the hope of improving the thrust efficiency.¹⁹ A prototype of this new device, termed the QCT Phoenix, was designed and built within the IPPL in 2019 and serves as the test article within this study.

The QCT Phoenix functions on similar principles to a HET. The most important commonality between the two thruster types is that the plasma discharge is created by the overlap of an axial electric field and a radial magnetic field. The axial electric field is generated between an anode located at the base of the discharge channel and an external neutralizing cathode positioned downstream of the thruster exit plane. In the QCT Phoenix, the radial magnetic field is created by a set of eight vertical electromagnets placed on the centerline of the discharge channel walls. The resulting quad cusp magnetic field topology, as can be seen in Fig. 6, is a key characteristic of the QCT thrusters. It yields an open ExB drift, differing strongly from the closed drift seen in classic HETs. As a result, primary electrons supplied by the external cathode are drawn along the vertical plane to the channel center where they have a clear path to the anode. The low impedance path between the cathode and anode is the likely reason for the experimentally observed low anode voltages. In the horizontal plane, the ExB drift pushes and confines electrons in two quadrants, corresponding to the left and right hand sides of the lower diagram in Fig. 6. It is expected that ionization of the propellant injected at the base of the channel will occur primarily in these zones; this is corroborated by visual inspection of the plume revealing two bright quadrants of the discharge channel in the horizontal plane. The reduced axial electron current in these zones causes a potential gradient to develop. Thus, ion acceleration is enabled and the resulting ion beam is neutralized by electrons from the cathode.

A cut-away view of the QCT Phoenix can be found in Fig. 7. It shows the characteristic square faced discharge channel. The sides of the channel are 35 mm long and has a depth of 68 mm. The anode of the QCT Phoenix is made of copper and features a square cross-section with a 29 mm side length. The anode also serves to baffle the propellant injected at the rear of the chamber via a 1/8 in. stainless steel tube. A ceramic electrical break in the feedline ensures the propellant reservoir is not electrified. The supporting thruster structure is built in 6082 aluminum and the magnetic components in electrical steel. Electrical steel was selected as a good alternative to soft iron as it is both less expensive and readily available. The wiring of the electromagnets is an enamel coated copper wire. The resulting magnetic field strength varies within the channel, as can be seen in Fig. 6. It features a magnetic null region at the center of the channel and peaks at the magnetic cusps along the channel walls.

The Imperial College London test was conducted in the Boltzmann vacuum facility of the IPPL in South Kensington London, at the beginning of November 2019. The facility has a 1.5 m diameter by 2 m long main chamber with a 0.75 m diameter by 1.5 m long load-lock hatch. The facility is pumped by a primary scroll pump and two Leybold turbomolecular pumps each with a pumping speed of 2200 l/s and a Leybold cryopanel at 15 000 l/s xenon.

The ESA test campaign was performed in the Corona vacuum facility, within the EPL at ESTEC in the Netherlands at the end of November 2019. The main chamber of this facility is 4 m long, with a diameter of 2 m, and a hatch of diameter 1 m and length 1 m. The Corona facility has two primary pumps, two turbomolecular pumps, and up to six cryopumps. The maximum pumping speed of this facility has been measured at 45 307 l/s when fully operational. For this test, one turbomolecular pump, one cryopump, and four cryopanels were used.

The response of both balances to the VCA calibration force is shown in Fig. 8. A linear fit is applied to the data, with the gradient being the balance sensitivity S_cal, as described in Eq. (1). Four calibration forces (n = 4) were used ranging from 0.687 mN to 5.690 mN to cover the thrust range of the QCT Phoenix. These forces were used to perform the error calculations detailed in Sec. IV. The intermediate results of the uncertainty calculations are all included in Table I, with the results of Eq. (5) dictating the size of error bars in the remainder of the paper.

The resulting sensitivities are S_cal = 1.462 ± 0.071 μm/mN for the IPPL tests and S_cal = 1.535 ± 0.106 μm/mN for the EPL tests corresponding to the gradients of the two trends in Fig. 8. Note that both trends are linear yet with slightly different intercepts and gradients. This is expected given that each setup has a slightly different mass and configuration. The standardized residuals shown at the top of Fig. 8 are given by $Rs=(x^i−xi)/sx$ and allow us to assess the quality of the fit. As a rule of thumb, standardized residuals distributed uniformly between −2 and 2 are considered indicative of a good fit. The linearity of the balance in this configuration was tested over a greater thrust range than expected for the QCT characterization in order to assess the full capabilities of the measurement instrument. Good linearity of the balance in this configuration was observed up to 100 mN, as shown in  Appendix A.

The estimate of the standard deviation of the thrust measurement ultimately provides the resolution of the balance. For this test, these values are s_F = 0.1870 mN for the IPPL and s_F = 0.2673 mN for the EPL data. This resolution degrades when we extend the thrust range up to 100 mN to s_F = 2.269 mN for the IPPL and s_F = 3.080 mN for the EPL data.

Potential errors resulting from the electrostatic interaction of the thruster supply lines on the thrust balance measurements were investigated experimentally. These tests were performed within the IPPL but were not repeated at EPL. The gas supply to the thruster and cathode was closed throughout these tests, so the physical thrust produced should be zero. The maximum possible voltages were applied to both the keeper and the anode, being 650 V and 100 V, respectively. The thrust measurement procedure followed the same protocol as for the actual thrust measurements, and it was found that the maximum measured force was 0.014 ± 0.19 mN. This is small enough when compared to other sources of uncertainty that it can be disregarded.

Gas flow effects were investigated to quantify the influence of pressurizing the propellant feedlines on the measured thrust. These tests were performed in the IPPL in vacuum conditions, with the thruster unpowered. Since gas is flowing to the anode and cathode, a cold gas thrust is expected. The observed thrust was 0.18 ± 0.19 mN and 0.40 ± 0.19 mN for the 5 sccm cathode flow and 15 SCCM anode flow, respectively. These are consistent with cold gas thrust operating on xenon without a nozzle: 39 ± 39 s and 28 ± 13 s of specific impulse (I_sp) for the cathode and anode, respectively. Any great disagreement from the expected cold gas I_sp being observed would suggest a source of experimental error due to the physical pressure of the lines applying a force to the moving part of the thrust balance.

The stability of the calibration is monitored by running spot checks with the in situ calibration subsystem throughout the test and comparing the response to the baseline measurement. This baseline is attained in ambient conditions with a heated balance directly after the VCA calibration is performed, and therefore, it acts to link the traceability from one calibration system to the other. The spot checks on two days of testing at the IPPL are compared to the baseline measurement in Fig. 9. The results at the EPL were similar and have thus been omitted. We see very similar trends across the three datasets, with the exception of one outlier at 10° during the baseline measurement. We conclude that the calibration drift is minimal over the three tests, indicating that the balance was not altered significantly over the duration of the campaign. The baseline, which was performed in ambient conditions, is in good agreement with both the spot checks, which were performed in a vacuum. This confirms that the calibration traceability is not compromised by the evacuation of the chamber.

Included in Fig. 9 is the expected force as calculated from the geometry of the in situ calibration subsystem. This calculation was based on the seven measured variables, α, R, a, b, h, H, and m, shown in Fig. 3. The errors in measuring these variables will compound to add uncertainty to the calculated force. To quantify this uncertainty, we have performed a Monte Carlo simulation of the subsystem to accurately propagate the error for all measured dimensions. The measured values and conservative error estimates are provided in Table I. For each run, the value of α, R, a, b, h, H, and m was picked from a normal distribution about the measured value, with the error being one standard deviation. We performed 100 000 simulations at 1000 different servo positions. The gray shaded area in Fig. 9 represents the band in which the median 95% of these simulations fell. We see the majority of the measured data fall below the theoretical force, yet within the 95% median band. Experimental error in measuring the seven variables, which describe the system, likely accounts for the systematic under-prediction of the force compared to the calculated value. The important finding is that the experimentally observed trend line lies within the error bound predicted by the Monte Carlo analysis when considering the relative uncertainty of each measured parameter. Even with the small systematic discrepancy between the measured values and the theoretical force seen in Fig. 9, we stress the significance of this result: The measured forces were derived from the displacement as determined by the laser and converted into a force based on the sensitivity calculated using the VCA subsystem. The calculated forces, on the other hand, were derived purely from the geometry of the setup. Any large disagreement between measured values and calculated values would indicate systematic errors. The mean difference between the calculated and the measured value is 0.1878 mN, with a standard deviation of 0.2329 mN. The good agreement we see in Fig. 9 is a direct indication of the accuracy of the balance and consistency of the two separate calibration approaches.

The thrust and I_sp of the IPPL test of QCT Phoenix measurements are shown in Fig. 10. The thrust and specific impulse were found to increase linearly with power for all flow rates surveyed. The highest specific impulse was achieved with a combination of the lowest propellant flow rate and the highest discharge power. While higher levels of thrust were obtained at higher flow rate conditions, the drop in specific impulse was significant.

We define the anode thrust efficiency η_T as

where T is the thrust, $mȧ$ is the anode mass flow rate, and P_a is the anode power. The resulting anode thrust efficiency of the QCT Phoenix is shown in Fig. 11. The measured thrust efficiencies of the QCT Phoenix are comparable to the previous QCT-200 model of the thruster, as can be seen in the work of Knoll et al.²⁰ The anode thrust efficiency of the QCT Phoenix decreases significantly as the mass flow rate increases. This is a feature that is yet to be explained, but has been observed in previous QCT type thrusters in this power range.²⁰ Unfortunately, this suggests that the novel magnetic topology of the QCT Phoenix was unsuccessful at increasing the anode efficiency.

While the performance measurements of the QCT Phoenix proved to be somewhat disappointing, the functionality of the thrust balance for measuring electric propulsion devices was nevertheless confirmed. Smooth linear trends were recovered as a function of operating power, and it was evident that the underlying trend line was within the previously quantified uncertainty for the individually measured data points.

A pair of nearly identical hanging pendulum thrust balances have been constructed and validated for electric propulsion testing. A voice coil actuator determines the sensitivity and allows the calibration to be traced to an NMI standard reference. The stability of the calibration was monitored using a servo motor pulley system. Thermal stability was maintained by a feedback loop, which monitors the temperature of the balance and provides further heat when necessary.

One balance was tested in the Boltzmann vacuum facility in the Imperial Plasma Propulsion Laboratory. The second balance was installed and tested in the Corona vacuum facility in the ESA Propulsion Laboratory. The balances differ slightly in size of the moving platform but behaved almost identically. Both balances have demonstrated a highly linear response in the thrust range of between 1 mN and 100 mN with a resolution better than 3.1 mN for the complete range, which was increased to a resolution of better than 0.27 mN when the thrust range was reduced to 5 mN. Both balances have shown high calibration stability over several days of testing.

The correct functioning of the thrust balance with an electric propulsion system was demonstrated with a test article called the QCT Phoenix. The thruster showed a thrust of 0.71 ± 0.19 mN to 2.21 ± 0.22 mN for powers of 50 W–130 W and the mass flow rate ranging from 5 sccm to 15 sccm of xenon. This resulted in an I_sp range of 65 ± 13 s to 274 ± 41 s and an anode thrust efficiency of 0.61 ± 0.25% to 1.54 ± 0.46%, both of which are comparable to previous QCT type thrusters.

The development and construction of these instruments along with the research described in this paper were carried out by Imperial College London with the support of the European Space Agency and the ESA Propulsion Laboratory in the frame of Contract No. 5001026101: mNewton Thrust Balance for the EPL.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

The sensitivity calculation and error analysis, shown in Fig. 8 and Sec. IV, were performed using only the n = 4 lowest calibration forces to best fit the range of thrust produced by the QCT Phoenix. To demonstrate the full range of the balance in this configuration, we have also included the sensitivity of the balance with all n = 11 calibration forces in Fig. 12. We see the balance behaves linearly from 0.1 mN to 100 mN, with only two standardized residuals falling outside of the desired range of −2 to 2. Using the entire range of calibration forces, we generate a sensitivity of S_cal = 1.715 μm/mN for the IPPL data and S_cal = 1.394 μm/mN for the EPL data. Over this range, the estimate of the standard deviation of the thrust measurement is s_F = 2.269 mN for the IPPL and s_F = 3.080 mN for the EPL data. Note that the apparent divergence seen between the two fits at the bottom of the plot is due to differing signs of the intercept b_cal.

Table I includes all intermediate values and errors used to calculate the uncertainties in the above thrust measurements.