Analysis of composition and dynamics of the plasma plume emitted by a 1 J pulsed plasma thruster fed with polytetrafluoroethylene and determination of thruster efficiency components

In recent years, the accessibility to space for small and medium enterprises as well as academia has increased greatly owing to the development of relatively inexpensive and versatile CubeSat technology^1–3—a class of satellites in which the spacecraft is made up of standardized cubic units where each unit (1 U) has side length of 10 cm and mass up to 1.3 kg. The relevant satellites may consist of 1–27 cubic units arranged in a mission-dependent configuration.⁴ These small spacecraft can carry out highly specialized tasks like Earth observation or in-orbit technology demonstration for a fraction of the price of >100 kg satellites.⁵ This has become possible mainly thanks to the miniaturization of essential components: power supplies, optics, attitude determination, and control systems. One piece that has been less susceptible to miniaturization is the thruster which suffers from large propellant tanks (chemical propulsion) as well as from efficiency drop at small scale and on-board power shortage (electric propulsion).⁶ However, despite these inherent difficulties, there are several companies that offer micropropulsion for CubeSats.^4,7–10

One of the electric propulsion technologies with significant space heritage, dating back to 1964^11,12 that is regarded to be well suited for the CubeSats is the pulsed plasma thruster (PPT), which may slowly accumulate energy and then release it in a quick discharge. By physics, PPT belongs to a larger group of magnetoplasmadynamic (MPD) accelerators¹³ like Marshall plasma gun¹⁴ or rail gun^15,16 (and is hence sometimes called instationary MPD or iMPD^17,18) in which the plasma sheet is speeded up due to interaction with magnetic field induced by its own discharge current. The most common implementation of PPT consists of a capacitor bank ended by discharge electrodes with propellant in between—typically polytetrafluoroethylene (PTFE, commonly known as Teflon), and an additional spark igniter with high-voltage transformer for discharge initialization.^11,19 The capacitors are charged to voltage usually in the range from 1 to 2 kV, storing the energy for the discharge. A high-voltage pulse from the transformer produces a low-energy spark that supplies initial electrons. These seed electrons induce the breakdown on the surface of the propellant, creating the main discharge in the ablated material. The thruster geometry is such that the electric field between the thruster's main electrodes (about 1 kV/cm) and the magnetic field induced by the flowing current (with peak on the order of 10 kA) produce Lorentz force which acts on the plasma, accelerating it out of the thruster, thus generating impulse propelling the satellite.¹¹ According to Mikellides et al.²⁰ in PPT with rectangular geometry 30%–35% of the momentum is carried also by gas-dynamically accelerated flux of un-ionized particles, which some electrothermal PPT variants optimize up to 75%–90%.²¹ 

Owing to the pulsed mode of operation, the firing rate of PPT can be adjusted to conform to the power available from CubeSat's small solar panels, resulting in power consumption as low as 1 W with virtually zero standby power.⁹ Moreover, due to the relative simplicity, the whole propulsive system (with control electronics and propellant) can be as small as 0.33U.²² The major drawback of miniaturized PPT, however, is its low energy efficiency (on the order of several percent), with poor ionization of the propellant and late-time ablation effects being the main limiting factors.¹¹ Although thanks to the solar panels the satellite can draw electrical energy from the Sun at no cost (except time), its inefficient transformation into kinetic energy of the ejected mass by the thruster results in excessive consumption of propellant due to longer firing periods necessary to achieve the desired change of the satellite's velocity. To find ways of improving the performance of PPT, better understanding of the ionization and acceleration processes is needed, which requires information about the composition of the plasma and its dynamics.

In the long history of PPT research,¹¹ electric probes (e.g., Faraday probe,^23–25 Langmuir probe^24–27) optical methods (e.g., high-speed cameras,^28–31 emission spectroscopy,^{23,27,29,31–33} laser interferometry^31,33,34) and other diagnostic tools (e.g., residual gas analyzers^24,35,36) have been extensively used to infer about the ion species, plasma density, angular spread of particles, or plasma bulk velocity. However, because of the multi-species, non-uniform, unsteady, flowing plasma of the PPT some information, like ionization fraction, relative abundance of ion species, or ion energy distributions, is more difficult to obtain^11,35 than in, e.g., Hall thruster for which these characteristics allow exposing specific factors of thruster inefficiency.³⁷ Although numerical and analytical models of PPT discharge exist,^{20,31,38–40} due to complexity of the problem, they must rely on a number of simplifications and assumptions (e.g., local thermal equilibrium and limited set of pre-defined ion species) which are experimentally justified only partially. For example, results of spectroscopic measurements inform about the presence of specific ion species in the plasma (which are introduced to numerical models) but do not easily yield quantitative information of their abundance⁴¹ nor dismiss the existence of other species emitting light outside the measured spectral range.⁴² 

To obtain the missing information about composition and energy distribution of plasma plume in PPT, a group from University of Washington^43–46 suggested the use of retarding potential analyzer coupled with time-of-flight approach. However, due to the chosen methodology, the success of this series of studies was limited—ions were assumed a priori to have Maxwellian energy distributions and the resulting values of ion fractions were erratic. Similar setup with different measurement procedure was also presented by Barral et al.⁴⁷ for PPT fed with liquid propellant (PFPE—perfluoropolyether), who managed to identify individual ion species in the plume but did not acquire any quantitative information about their relative abundance or energy distributions.

In the present work, the retarding potential analyzer and time-of-flight combination was revisited with methodology extending this of Barral et al. and the aim of identifying the ion species in the beam, their relative abundance, and respective energy distributions which, to our knowledge, has never been achieved before for pulsed plasma thrusters. To correlate the far-field plume composition with ion content inside the thruster also, spectroscopic measurements were carried out in the plasma between the main discharge electrodes. Moreover, with the ultimate goal of carrying out efficiency analysis based on simplified phenomenological model similar to those in Hall thrusters,³⁷ the above-mentioned study was supplemented with Faraday cup measurements. The spatially resolved data obtained with this diagnostic, together with information about plasma composition and energy distribution, allowed us to determine main factors of thruster efficiency: mass utilization, energy utilization, and beam divergence.

The pulsed plasma thruster used in this study, shown in Fig. 1, was a laboratory model with rectangular geometry. It was equipped with 2.16 μF bank of ceramic capacitors charged to 1000 V which translated into stored energy of 1.08 J. The propellant block—PTFE, had approximately 10 × 10 mm² of surface area exposed to the discharge and was inserted between two pure copper, 20 mm long electrodes. The electrodes were tapered and each with 15° flare angle. The spark igniter was inserted through one of the main discharge electrodes which acted as a common cathode. As a laboratory model, this version of the thruster was not equipped with any propellant feeding mechanism and PTFE blocks needed to be manually replaced every 100 000 shots.

The thruster exhibited good repeatability of the discharge, evidenced in Fig. 2 by low variation of current and voltage waveforms. Owing to small energy and inductance (14.7 nH by design), a relatively short discharge duration of approximately 1.5 μs was achieved—similar to the 2 J PPTCUP²² and over 20 times smaller than 70 J SIMP-LEX.⁴⁸ In the presented configuration of the thruster, the discharge current (in the form of underdamped response of an RLC oscillator) tended to stop after the third half-period (with about 1% of the initial energy still in the capacitors).

The impulse bit produced by this thruster, averaged over 1050 separate measurements on a dedicated thrust balance, was 18.9(2.2) μNs at 1000 V, which translated into thruster efficiency of 3.16(72)%. Due to the construction of the thrust balance the effective firing frequency during these impulse bit measurements could not be higher than about 1/30 Hz. Consequently, performance variation with discharge frequency had not been studied for this thruster, and in this work, impulse bit and efficiency were assumed to be independent of frequency. The cumulative lifetime of the thruster (using in total 11 propellant blocks) was experimentally confirmed to exceed 10⁶ shots for nominal operating parameters (1000 V, 1 Hz). In this paper, one shot is defined as one full charge-discharge cycle of capacitor bank—its duration was driven primarily by charging time (about 400 ms in nominal conditions).

The thruster was mounted inside a 2.5 m³ vacuum chamber pumped down to about 5 × 10⁻⁵Pa. While the thruster was firing with frequency of 1 Hz, the pressure inside the chamber was periodically rising up to about 1 × 10⁻⁴Pa. The charge-exchange effects due to ambient pressure were deemed to have negligible impact on the measurements.^49,50

During this study, one Faraday cup (FC) and two retarding potential analyzers (RPA) were used. Faraday cup is a type of a collimated ion collector that is designed to minimize the impact of background ions and secondary electrons on the measured ion current. This allows performing accurate measurements to obtain spatial velocity distribution of the thruster plasma, plume divergence, and total ion current or charge emitted by a plasma device.⁵¹ The retarding potential analyzer (also known as a retarding field energy analyzer or a gridded energy analyzer) is an ion collector additionally equipped with a set of electron- and ion-repelling grids. The ion-repelling grid has regulated bias which allows collection of only those ions that have energy-per-charge ratio higher than that bias.⁵² By sweeping the discriminating voltage, this diagnostic tool serves to measure the cumulative distribution function of ion current (or charge in the case of pulsed devices) vs voltage.

The FC (made in-house) had a collimating aperture of 10 mm in diameter and carbon collecting cavity with depth of about 4 cm. The collector bias was set to −20 V which was well below the −10 V at which the collected ion current became saturated, what was checked in separate tests. The two RPAs were commercial button probes from Impedans Ltd. embedded in stainless steel holders (with an external diameter of 5 cm) kept at floating potential during the measurements. Each probe at the entrance had 37 orifices 800 μm in diameter and 3 grids with 20 μm holes. Due to large ion flux from the thruster, the dedicated electronics had to be changed to laboratory power supplies with higher current rating for keeping constant bias at each grid. The electron suppressing grid was biased to −40 V and the collector to −20 V. Signals from all probes were measured on shunt resistors connected to Picoscope 4824A PC oscilloscope (20 MHz bandwidth, 12 bit vertical resolution, and 12.5 ns time resolution). For RPA, a 50 Ω shunt resistor was used, but for FC, due to large surface area of the collector, a smaller 3.3 Ω shunt was needed. The discharge current or voltage could not be measured directly in the same setup, so reliable triggering of the acquisition and zero-referencing of all signals was ensured by a magnetic (B-dot) probe located near the thruster, which provided a signal mostly proportional to the time derivative of discharge current.

The setup is shown in Fig. 3. FC and one RPA were mounted on the boom of a rotary stage which allowed to perform angular measurements. For FC, these were carried out from −85° to +90° (with 0° defined as the thruster axis) with a non-constant step: from −50° to +50° by 2° and 5° elsewhere. The −90° was unavailable due to the collision with the scaffolding supporting the manipulator. RPA measurements, being more time-consuming, were limited to range from −60° to +60° with 30° angular step. Because of the chamber diameter, the distance of the probes from the thruster was set to about 30 cm. The second RPA was stationary and was mounted on axis at a distance of about 1.4 m to obtain better charge separation. The magnetic probe was located about 5 cm above the thruster to not interfere with the plasma plume.

Additionally, spectroscopic measurements were carried out in auxiliary vacuum vessel (0.035 m³) in which the background pressure was kept below 2 × 10⁻⁴Pa. Ibsen Freedom UV-NIR FSA-380 spectrometer with Hamamatsu S11156 CCD linear image sensor was used which allowed measurements in the range from 190 to 1100 nm. However, the BK7 glass window in the chamber limited the effective range to above approximately 300 nm. Ocean Optics HG-1 Mercury-Argon lamp was used as calibration light source for wavelength readout correction. The measurements were performed approximately 1.5, 6.5, and 11.5 mm from the propellant surface, in the middle between two discharge electrodes, with optical path perpendicular to the thruster firing axis (Fig. 4).

To account for azimuthal asymmetry of the PPT, the angular measurements were done in two perpendicular planes. In one case, the measurement plane intersected with the discharge electrodes which obstructed the view at large angles—this orientation in the rest of the paper will henceforth be called “obstructed.” In the other case, the thruster was mounted such that the electrodes were aligned in the vertical direction and so the horizontally moving probes at all angles had a clear view on the propellant surface—this plane is termed “unobstructed.” These orientations are illustrated in Fig. 5.

As is shown in Fig. 6, after prolonged thruster operation, non-uniform evaporation of the PTFE block resulted in distorted surface of the propellant which became increasingly more asymmetric, concave, and receded with respect to its original position between the discharge electrodes (there was no pushing mechanism implemented in this version of the thruster). Although, assuming uniformity of PTFE, impact of this effect on the composition of the plasma was unlikely, it was possible to have an influence on the angular profile of the beam. Consequently, in the case of FC, the measurements were done twice—when the PTFE block was new (i.e., its face surface was flat), and after approximately 100 000 shots when a significant distortion had already formed. These two cases will be referred to as “fresh” and “worn,” respectively. The measurements with RPA were carried out immediately after the FC measurements with fresh propellant block.

The operation of the thruster was pulsed, so all the measurements were necessarily carried out over multiple firings which raised the issue of the repeatability. Because the variation of the discharges (and so of the probe signals) was not negligible, in order to limit the influence of shot-to-shot variation on the quality of data, the collected signals were averaged. In other words, any infrequent events were effectively discarded in favor of the better quality of the persistent features of the discharge. For both FC and RPA, the tests indicated that average over 25 signals already produced satisfactorily stable mean signals, as evidenced in Fig. 7. Eventually, because of the relatively fast repetition rate of 1 Hz, two times this value was chosen, and so all the probe data were averaged over 50 discharges.

In spectroscopic measurements, the signal was averaged over five thruster firings, which was sufficient to remove most of the noise. The minimum allowable acquisition time of 2.2 μs was set with trigger at 200 ns before the main discharge. With such settings, the entirety of the discharge (1.5 μs) was encompassed.

From this preliminary analysis, it can be seen that error was largest in the case of non-monotonic shape of the plume, where the lack of measurements at intermediate azimuthal positions resulted in omission of important features of the beam. In all other cases, the discrepancy was much smaller and dependent on the finer details of the plume. Without the knowledge of the true azimuthal dependence, the relative uncertainty stemming from the assumed simplification was conservatively chosen as 5% (in addition to other systematic and random errors).

The measurements with the retarding potential analyzer were carried out for retarding voltage swept up to the value at which there was no further visible reduction in the collected ion current (only noise remaining)—typically from 0 to 250 V. At large angles, the upper limit was reduced because of faster decline of the signal that was due to the expected lower energies of the ions in those regions. In most cases, the voltage step between consecutive measurements was 5 V (two times smaller than in Barral et al.⁴⁷) Only in the case of the distant RPA located on axis, the voltage step between 0 and 25 V was 2.5 V in order to improve accuracy for low-energy ions.

As a reference to Faraday cup measurements, side-view long-exposure photographs were taken, which are shown in Fig. 10. The divergence of the beam was visibly larger in the plane unobstructed by the discharge electrodes. This is also clearly seen in angular profiles of ion charge density derived from FC measurements, presented in Fig. 11. The difference became even more pronounced after 100 000 shots: the obstructed beam narrowed and the unobstructed profile widened further, which might have been related to the receding surface of the propellant as the PTFE was consumed. In all cases, a small, up to 4° offset from the thruster axis was identified in the angular profiles, which was slightly above the estimated 2° assembly inaccuracy.

The Gaussian function used to fit the data matched with the profile in the unobstructed plane and in the core of the obstructed plane. However, a significant discrepancy appeared for the angular positions located in the shadow of the discharge electrodes, where the ion charge density was much higher than expected. In the case of plasma thrusters with continuous operation (like Hall thruster), the increased signal at high angles is associated with low-energy background ions from charge-exchange process. In this case, however, this scenario is unlikely. As was explained in the description of the vacuum facility, the ambient pressure oscillated between 5 × 10⁻⁵ and 1 × 10⁻⁴Pa at which the charge-exchange effects are not significant.^49,50 Even though there might have been much higher local pressures of neutrals close to the thruster, the gas-dynamic expansion of neutrals is much slower than the electro-dynamic acceleration of ions,²⁰ which is clearly visible in images from high-speed cameras.^18,29,30 It means that most of the plasma would have already been far away by the time the neutrals reached the end of the thruster where they would need to obtain the charge in the charge-exchange process. Moreover, apart from the effects in or near the thruster itself, the design of Faraday cups specifically reduces the influence of background ions.⁵¹ 

One can also note from time evolution of ion current density, shown in Fig. 12, that the ions collected at these shadowed locations exhibited slightly heightened velocities—illustrated in obstructed cases by an inflection of “50% $ρ i$” contour lines (the time in which half of the total charge arrives to the collector). Also, the ion current density at these angles was highest for ion velocity range between 10 and 20 km/s. This provides further evidence that background ions from charge-exchange could not have been responsible for the observed effect.

Instead, more likely the additional ions in the obstructed regions might have been the result of plasma expanding from the unobstructed regions. This may explain the similar slope of the profiles in both planes at high angles. Also, some erosion observed on the dark side of the discharge electrodes suggests that the lightweight electrons may be deflected there by the electrostatic potential around the electrodes, again facilitating off-axis, ambipolar acceleration of ions. This last effect should be investigated by near-field Langmuir probe measurements. Another possibility assumes the presence of additional, in-plume acceleration mechanism which would contribute to the off-axis charge densities. The time-resolved data from FC do not preclude any of these hypotheses.

Basing on the time of arrival to the collector, the velocity of ions on axis up to 100 km/s were observed, which is comparable to the velocities of leading-edge ions reported by Ling et al. using electric probes,²⁵ but much higher than the propagation velocity of visible radiation front estimated from high-speed cameras^29,31,55 and other optical methods,⁵⁶ which are typically below 50 km/s. The reason for such discrepancy stems from the fact that, as will be seen in the RPA results, the fastest ions are multiply charged and emit light in the ultraviolet part of the spectrum.⁴² Hence, they are undetectable for most optical measurements which investigate only the visible range of the spectrum. However, most of the charge is carried by particles that emit light in visible range. So, the median velocity (line “50% $ρ i$”) reached about 35 km/s on axis, which is consistent with the optical measurements mentioned above. Similar conclusions were drawn by Gatsonis et al.,³⁵ supported by previous measurements of Thomassen and Vondra.²³ 

When the propellant block was worn out, the on-axis velocities stayed approximately the same, but at larger angles the mean velocity of the plasma decreased in obstructed plane and increased in unobstructed plane. This was probably related to the receding propellant surface and hint at yet another parameter with which the thruster performance can be optimized.

The data from Faraday cup were used to calculate beam divergence $cos θ$ and total ion charge $Q i$ emitted from the thruster [Eqs. (5) and (9)]. These are presented in Table II together with the contributions from each measurement plane [Eqs. (3), (4), (7), and (8)]. Please note that about 5%–7% uncertainties shown in brackets (estimated using standard method of error propagation) were driven mainly by systematic errors related to the chosen integration method and experimental setup (e.g., distance to the probe or angular position of the probe) which were constant between all measurement sessions. Meanwhile, relative uncertainty from random errors was in all cases below 0.1%. Potential error sources related to the probe itself (e.g., emission of low-energy secondary electrons or backscattering of incident particles) were neglected due to the design of the Faraday cup which efficiency should be close to 1 for this cavity length (4 cm) and expected energies of incident ions (<1 keV).⁵¹ 

The plasma plume ejected in unobstructed plane carried 2–3 times more charge than in the plane with discharge electrodes. With an assumption that all charges traveled with the same momentum, independently of the plane of probing, it follows that the total beam divergence was mainly driven by the unobstructed plane and so in time the value of total $cos θ$ decreased by 3.4%. However, at the same time, the total ion charge increased by 25.2%. Together, it would translate into 20.9% increase in impulse bit. The measurements done on dedicated thrust balance at those times (for fresh and worn PTFE block) confirmed the increase in impulse bit, but only by 9.1%, meaning that more sophisticated model needs to be used that would take into account non-constant mass bit and energy-per-charge as well as different ion content and more complex distribution of momentum.

Using the method described in Sec. III, the data collected with the retarding potential analyzer were used to assess the ion composition of the plasma beam. In Fig. 13, a $(V,t)$ map of ion charge calculated from the measurements of the distant RPA is shown, revealing the presence of six distinct hyperbolas. This map was overlaid with curves of the species expected in PTFE [polytetrafluoroethylene, (C₂F₄)_n]—carbon, fluorine, and molecular ions, with the addition of copper (from discharge electrodes), each one characterized by its own mass-to-charge ratio $m i k / q i k$ shown in Table III. It was found that the experimental traces match with the fluorine ions up to sixth ionization state. At the same time, however, there was no trace corresponding to carbon (although $m i k / q i k$ of F³⁺ and C²⁺ are similar, the absence of any trace of C⁺ in the data made the presence of C²⁺ unlikely). Weak trace of C⁺ was eventually detected closer to the thruster by the RPA mounted on a boom—this is shown in Fig. 14. The strong signal from fluorine ions (again up to F⁶⁺) and the chosen voltage step masked possible traces from higher carbon ions, so the presence of C²⁺ was uncertain. At that distance from the thruster, also Cu⁺ and Cu²⁺ ions were identified. Similar traces were found also at other angles, albeit with lower signal-to-noise ratio and without copper ions at the largest angles—they are provided in the supplementary material for the interested reader.

In the case of close RPA on axis (Fig. 14), there was a visible deviation of the theoretical hyperbolas with respect to the experimental curves at lower voltages. This was probably caused by a mismatch between the RPA geometry and the local plasma parameters. That close to the thruster and with low retarding voltage, the plasma density might have been high enough to result in Debye sheath shrinking well below the hole diameter of the RPA grids, so the proper electric field inside the probe could not be established. Off-axis measurements in lower density plasma taken with the same RPA showed no such deformations (see figures in the supplementary material).

To the best of authors' knowledge, the presence of such highly ionized species in the plume of PPT has never been reported before. Because the composition of the PPT plasma is mainly derived from optical measurements in visible range, fluorine ions were seen only up to F³⁺.^{23,32,33,54,56} Beiting et al.⁵⁷ who utilized several low spectral resolution EUV (extreme ultraviolet) detectors to indirectly infer about the ion species, speculated that the obtained signals were driven mainly by C³⁺. In the work of Barral et al.⁴⁷ who used the same time-of-flight/RPA combination on PFPE-fuelled PPT, at least 4+ ions seemed to be present, but due to the poor quality of the data, it was not possible to conclusively identify them as carbon or fluorine.

Such high ionization states of fluorine that were detected here require much more energy than the creation of C⁺ ions which were barely visible in the plume (e.g., in total 473.69 eV to create F⁶⁺ vs 11.26 eV for C⁺).⁴² Similar scarcity of carbon was found at all investigated probe positions. However, the spectroscopic measurements between the main discharge electrodes (presented in Fig. 15) mostly indicated the presence of carbon ions (up to C³⁺) and only the first ion of fluorine (NIST database was used as reference for spectral line identification⁴²).

These seemingly contradictory results can be explained if one makes an ad hoc assumption that mostly fluorine ions were accelerated electromagnetically in the plasma and carbon ions were not. In this way, the abundant presence of carbon in long-exposure optical spectra would stem from long residence time of these ions inside the thruster, whereas the fast fluorine ions would quickly leave the acquisition area (except the slowest F⁺ ions) emitting too little light to be registered above the noise level of the spectrometer. Also, the relatively quicker disappearance of strong C II lines at larger distances suggests very low, gas-dynamic-like velocity of this species (e.g., position of 11.5 mm and acquisition time of 2 μs corresponds to mean velocity of about 5.8 km/s). Meanwhile, the RPA would register only the electromagnetically accelerated species with mean velocities over 10 km/s (due to poor quality of the data below about 7 V) which, according to our assumption, would be mostly fluorine. It is unknown why carbon ions should behave differently in that regard from fluorine ions, although some hints of that were also given by Keidar et al.^58,59 who postulated that due to their larger mobility some of the carbon ions flow back from the plasma, which perhaps could also explain the observed RPA and spectroscopic data.

These results are also consistent with the observations reported by Kawahara et al.²⁸ who collected on aluminum plates the mass ejected by their PPT of similar energy and analyzed it under EDX (energy-dispersive x-ray) spectrometer. At all angles, the contamination was almost entirely composed of carbon, with small amounts of fluorine as well as zinc and copper from the brass electrodes. Also, it is well known that after prolonged operation the discharge electrodes in PPT tend to get covered with black deposit (so-called charring effect) which is mostly carbon and was also observed in our thruster. Such deposits could accumulate only from low-energy and possibly neutral part of the ejected mass, indicating that carbon is much less likely to be ionized and/or is ejected with very small velocity. Indeed, the appearance of trace amounts of C⁺ (and possibly C²⁺) ions together with Cu⁺ and Cu²⁺ only in the near RPA measurements may suggest that some carbon ions did not stem directly from the propellant, but instead were created from the deposits left on the discharge electrodes. In any case, it seems that fast, low-inductance discharge in the PPT did not provide conditions to establish local thermal equilibrium in the plasma, and instead the high energy attained by the electrons at the beginning of the discharge was delivered mainly to fluorine, ionizing it to a high degree and accelerating before carbon. It is an open question whether similar results would be obtained for thrusters of higher energy and slower discharge.

The traces shown in Fig. 13 that were measured by the distant RPA probe, having the best resolution and no deformations, were subsequently used to infer about the velocity (Fig. 16) and energy (Fig. 17) distributions of individual species as per the procedure outlined in Sec. III. The raw distributions were filtered using Savitzky–Golay approach (despite the non-constant step) which yielded visually acceptable smoothing of the data.

According to authors’ knowledge, these are the first such ion distributions measured for pulsed plasma thruster^11,27,60 so no comparison can be made with the existing literature. Velocity distribution deviated from the Maxwell distribution that is typically assumed in numerical models or analyses of probe data.^26,35,46,60 Instead, a narrow peak at low velocity/voltage and a second broad peak at higher velocity/voltage could be discerned, as if from two distinct acceleration processes. It is possible that these two peaks were indicative of plasma creation and acceleration in the first and second half-period of the discharge—a so-called “restrike” phenomenon that was observed in many thrusters.^29,30,53 F⁺ distributions were dominated by the first, low-energy peak, contrary to the F²⁺ or F³⁺ species, suggesting that the highly ionized species originated mainly from the first phase of the discharge and the single ions from the second phase.

Although no uncertainty budget can be given at this time, possible sources of error are discussed below. The presented distributions were calculated from the values lying on the theoretical hyperbolas, but the experimental curves exhibited additional broadening typical for RPA measurements, stemming from unequal distribution of potential at the grids and collisions inside the probe⁶¹ (it should not be confused with the natural broadening of the curves at lower voltages which was related to the voltage step and slope of the curve). As a consequence, the particles detected outside of the theoretical hyperbolas, although originating from the same population, were not included in the calculations. Depending on whether this effect was constant, voltage-dependent or proportional to the current, the resulting distributions might or might not have been somewhat skewed or biased. This aspect needs further investigation, possibly aided with probe simulations. Also, the shape of theoretical hyperbolas themselves was influenced by uncertainty of thruster-probe distance $L$ and ion creation and acceleration time $t 0$⁠. Another source of error stems from the fact that probe retarding potential was not corrected with local, time-dependent plasma potential. However, because of the great distance from the thruster (almost 1.5 m) and large retarding potentials involved, this last error source was assumed to have negligible effect on the measurements.

Integrating these distributions, the relative abundance of fluorine species and the energy fraction carried by them could be obtained, shown in Fig. 18, as well as mean velocity and mean energy per charge, presented in Table IV. Without formal uncertainty budget yet, the uncertainties were instead estimated using bootstrap method (100 repetitions) with resampling of RPA current signals and expansion factor 3 for the calculated standard deviations. F²⁺ was the most frequent species, with over 40% contribution, and F⁺ ions constituted 30%—only slightly more than all the ions with 3+ charge or above. However, F⁺ ions were behind only about 14% of the beam kinetic energy while F³⁺ up to F⁶⁺ in total carried 44%—over 3 times the energy of F⁺, highlighting the importance of higher charge-state particles which are often neglected in numerical models and efficiency analyses of PPT. The mean velocity of the most dominant species, F²⁺, was consistent with the median on-axis velocity measured with Faraday cup (about 35 km/s). Despite qualitatively different distributions, the mean energy per charge was the same for ions from F⁺ to F⁴⁺—about 67 V, and the same for ions F⁵⁺ and F⁶⁺—about 40 V.

Basing on the relative abundance of ions measured on axis, the mean ion charge $q i$ in the plasma was calculated as 2.154(35) times elementary charge $e$ and mean ion mass $m i$ was that of fluorine, so 3.15 × 10⁻²⁶ kg. Moreover, knowing that the mass bit $m bit$ during these studies was 5.499(44) μg per shot, and having total ion charge $Q i$ from Faraday cup measurements, the mass utilization $η m$ defined as ratio of ionized to total mass bit expelled from the thruster in each shot [Eq. (18)] could be estimated. Thus, taking into account $Q i$ for fresh and worn propellant, the mass utilization ranged from 9.81(55)% to 12.27(69)%. Without the knowledge of the plasma composition, so assuming only F⁺ and C⁺ ions in the same proportions as corresponding atoms in PTFE, the mass utilization would be about 1.9 times higher.

The above-mentioned values are difficult to compare with literature, because mass utilization may depend on the geometry and energy of the device. Also, in every below-cited work, only singly charged fluorine and carbon ions were assumed. Older works estimated the ionization [as defined in Eq. (18)] to be in the range from 10% (1.85 J discharge)^23,54 to 20% (25 J).³⁴ More recent investigation conducted by Scharlemann and York⁶² with pressure probe for energy of 30 J deduced it to be 25%. Schönherr et al.³¹ indirectly assessed propellant utilization for various discharge voltages using refined slug model coupled with plasma velocity measurements on 68 J-class thruster and concluded that between 40% and 60% of the mass was ionized in their case. Recent numerical analysis by Huang et al.⁶³ using multi-sheets model predicted 34% mass utilization for the case similar to our thruster (2 μF, 1000 V, electrode width 10 mm, electrode gap 30 mm), which overestimated our results about 3 times (1.6 times if difference in plasma composition was excluded).

Further using the data from both beam diagnostics, other efficiency factors—energy utilization and beam divergence efficiency, were calculated according to Eqs. (20) and (21). Finally, the total thruster efficiency was retrieved [Eq. (19)]. All efficiency factors and total efficiency are summarized in Table V. All uncertainties were calculated using an error propagation method.

The final value of thruster efficiency from beam diagnostics was close to the corresponding efficiency calculated from impulse bit measurements. Although for worn PTFE block, the two values were the same (in the range of measurement uncertainties), in fact, the beam-derived thruster efficiency for fresh propellant should be deemed more reliable, because the RPA measurements were conducted immediately after the first FC measurements (approximately 3400 shots), so near the beginning of life for PTFE block. In that case, the difference between the thruster efficiency calculated with both methods could have stemmed from the used approximations (e.g., angularly uniform ion distributions) and/or from the gas-dynamic input into the measured impulse bit. If only the latter were true, then the gas-dynamically accelerated neutral particles would be responsible for approximately 12% of the impulse generated by the thruster.

The measurements carried out in this work for a 1 J pulsed plasma thruster with a retarding potential analyzer combined with the time-of-flight approach allowed us to identify the presence of highly ionized fluorine (up to F⁶⁺) and showed a scarcity of carbon ions in the plume. Moreover, the data made it possible to directly derive velocity and energy distributions which were non-Maxwellian and showed that F⁺ ions, constituting about 30% of the plasma ions, carried only 14% of energy. These findings may question numerical models of PPT, which assume the presence of Maxwellian C⁺ and F⁺ ions in the plasma in PTFE-like proportions.

The time-resolved data from Faraday cup showed velocities of both fast plasma front (up to 100 km/s) and the plasma bulk (35 km/s on axis) to be in agreement with literature. The measurements carried out in two perpendicular planes demonstrated significant axial asymmetry which needs to be taken into account in rectangular PPT geometries. Moreover, integrated FC signals coupled with results from RPA probe allowed us to determine different efficiency components (energy utilization, divergence efficiency, and mass utilization) which, taken together, could be used to assess the magnitude of gas-dynamic contribution into impulse bit generated by the thruster. Calculated mean ion charge (approximately 2 times elementary charge $e$⁠) and observed dominant ion mass (fluorine) highlighted the possibility of significant overestimation of propellant utilization if only singly charged carbon and fluorine ions are assumed.

Further work should focus on the study of dependence of obtained results on operation and design parameters like discharge voltage, discharge energy, propellant geometry, etc. Also, a dedicated retarding potential analyzer should be designed to better suit the PPT plasma which would improve its performance closer to the thruster, allowing to measure velocity/energy distributions of other low-signal plasma constituents (carbon and copper ions) and to study spatial evolution of distributions. To further improve data resolution, the measurements with RPA should be carried out with smaller voltage steps.

See the supplementary material for a complete set of measurements performed close to the thruster with retarding potential analyzer mounted on the rotating boom. The data presented therein was collected at angles −60°, −30°, 0°, 30°, and 60° in two perpendicular planes—in total ten measurement points. Each shown ( V , t ) map of ion charge is supplied with theoretical hyperbolas of fluorine, carbon, and copper ions for reference.

The presented study was carried out as part of the project “Pulsed plasma thruster for nano and micro satellites” funded by the National Centre for Research and Development (Grant Agreement No. POIR.01.01.01-00-0857/19). The authors would like to acknowledge the industrial partner Liftero Sp. z o.o. (formerly Progresja Space Sp. z o.o.; especially Przemysław Drożdż, Marcin Chuchla, and Grzegorz Bywalec) for their great contribution in designing and manufacturing of the thruster components, as well as the company Semicon Sp. z o.o. (specifically Piotr Ciszewski and Grzegorz Pasek) for their help with reflow soldering of the capacitor bank. The authors would also like to thank IFPiLM colleagues: Arsenii Riazantsev and Olgierd Cichorek for their support in preparation of the experimental setup, Paweł Gąsior and Adam Kwaśnik for lending and setting up the spectrometer, and Zbigniew Peradzyński for discussions.

The authors have no conflicts to disclose.

Maciej Jakubczak: Conceptualization (equal); Formal analysis (lead); Investigation (equal); Methodology (lead); Supervision (equal); Visualization (lead); Writing – original draft (lead); Writing – review & editing (lead). Agnieszka Jardin: Investigation (equal); Writing – review & editing (supporting). Jacek Kurzyna: Conceptualization (equal); Investigation (supporting); Supervision (equal); Writing – review & editing (supporting).

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