Experimental investigation of electron-impact reactions in the plasma discharge of a water-vapor Hall thruster

Electric propulsion (EP) is an essential technology for today space development. Among a variety of EP thrusters, Hall thrusters (HTs) play an important role in state-of-the-art space missions. Over the last decade, geostationary satellites equipped with HTs have dramatically increased.¹ In recent years, HTs have made a remarkable progress as primary propulsion systems for large satellite constellations.^2,3 Furthermore, HTs started to be utilized in deep-space exploration. In 2023, NASA launched a space probe toward the metallic asteroid Psyche, which is the first deep-space cruise propelled by HTs.⁴ 

Conventional HTs have used xenon as a propellant. Xenon has a large atomic mass, high ionization cross section, and chemical inertness. Those characteristics provide favorable thrust performance (up to 70% of thrust efficiency⁵) with operational stability. However, since the supply of xenon is getting unstable due to increasing demand and geopolitical uncertainties, the community is moving toward using more sustainable propellants, e.g., krypton and argon.^6–10 Moreover, the investigation of alternative propellants is expanding beyond the noble gases as more advanced applications are proposed. For example, the concept of air-breathing HT is promoting researches on nitrogen, oxygen, and their mixture-gas propellants.^11–14 Besides, since the application of HTs to small satellites is increasing, condensable propellants such as iodine and adamantane are attracting attention from the perspective of volume saving without high-pressure system.^15–17 In the context of future in situ resource utilization (ISRU), propellants that is procurable in space like carbon dioxide have been studied.¹⁸ As various alternative propellants are proposed,⁵ water is also one of the promising candidates. The major benefits of water are high availability, non-toxicity, and liquid-phase storability at atmospheric pressure. These characteristics contribute to tremendous cost reduction and have great affinity with the use on small satellites. In addition, because water is expected to widely exist in the solar system,^19,20 it is also attractive for ISRU. The application of water as a propellant has been proceeding in many types of propulsion system: electrolysis rocket motor,^21,22 hybrid rocket motor,²³ resistojet thruster,^24,25 and gridded ion thruster.^26–28 This suggests further growth of water-based thrusters as an element of unified multi-mode propulsion systems.²⁹ 

Development of HTs using water propellant is in progress. There are mainly two types of approaches being tested. One is a water-electrolysis Hall thruster, which uses oxygen produced by water electrolysis for the main discharge.³⁰ The unique feature of this system is using simultaneously produced hydrogen as a cathode working gas to avoid oxidation of the electron emitter. The other approach is directly using water vapor for the plasma discharge, referred to as a water-vapor Hall thruster. The entire system can be quite simpler in this way, being more suitable for small satellites. Shirasu et al. demonstrated the operation at 200 W-class discharge power and estimated the thrust performance from the plume characteristics.^31–33 Tejeda and Knoll operated a water-vapor Hall thruster and measured its thrust in the power range of 600–1600 W.³⁴ At the same time, a cathode compatible to water vapor is also under development.³⁵ 

Although the feasibility has already been demonstrated, there are still many unresolved aspects in the discharge plasma of water vapor. Regarding the ionization process, it contains not only direct ionization producing H $2$O $+$ but also dissociative ionization which generates positively charged fragments such as H $+$⁠. These dissociated ions can exist within the plume and have some influence on the thrust force; however, it has not been precisely investigated yet. The dissociated fragments possibly become negative ions through the electron attachment reactions, which induce unique phenomena reported in some devices.³⁶ The dissociative reactions also produce the neutral fragments in both ground and excited states that can be sources of ions in secondary processes. Some of the fragments have high reactivity and there are concerns about the effect on materials. Therefore, it is essential to understand the discharge processes including those reactions for the precise performance estimation and design improvement.

In this paper, we present the axial distribution of electron density and temperature in the discharge plasma of a water-vapor Hall thruster measured by a cylindrical Langmuir probe. Using the obtained results, the ion species fractions within the plasma plume were estimated and the influence on the thrust performance was evaluated. In addition, the collision frequencies of other electron-impact reactions are compared to figure out the dominant processes in the discharge plasma. Since the measured electron energy distribution functions (EEDFs) indicate the existence of high-energy electrons being anisotropic, the sensitivity to them is also investigated in every reaction analysis.

Figure 1 shows the system schematic of the water-vapor Hall thruster. The discharge channel had a mean diameter of 20 mm and a width of 6 mm. The total channel length was 11 mm, with 4 mm from the exit plane insulated by boron nitride. A electromagnet was located at the center pole and applied radial magnetic field near the channel exit. The radial magnetic flux density $B r$ and field lines near the channel are shown in Fig. 2. Water vapor was fed into the discharge channel through the anode. The mass flow rate of water vapor was controlled to 0.81 mg/s with an uncertainty of 7% by a originally designed controller. The structural detail and calibration of the supply system were described in Ref. 33. A LFN2000 electron source (Kaufman & Robinson) was used as the cathode, which was operated with xenon gas at the flow rate of 0.10 mg/s and the keeper voltage $V k$ of 20–25 V in this study. The negative terminals of the discharge voltage, cathode circuit, and electromagnet circuit were connected and electrically isolated from the chamber ground by a 1 M $Ω$ resistor. The cathode-to-ground voltage $V cg$⁠, the potential difference between the floating common and the chamber ground, was recorded. The thruster body and all other components were grounded. During the thruster firing, excessive temperature rise of the thruster was suppressed by a liquid-cooled board attached on the thruster base. The temperature at the anode bottom was monitored by a thermocouple, and all measurements were started after the temperature almost saturated, typically 600–650 K. The thruster was operated in a 1.0 m-diameter and 2.6 m-length vacuum chamber. The chamber was evacuated by a turbomolecular pump and a cryopump with 820 and 2400 L/s pumping speeds of N $2$⁠, respectively. The typical background pressure during the operation was $3× 10 − 2$ Pa with the vacuum gauge for nitrogen. A photograph of the plasma plume during the experiments is provided in Fig. 3.

The Langmuir probe measurements were conducted at the discharge voltage $V d$ of 200 and 250 V, where $V cg≃27$ V in both cases. The corresponding thrust performances were evaluated by far-field plume diagnostics using a Faraday probe and retarding potential analyzer (RPA), which were carried out in the same experimental campaign to the Langmuir probe measurements. The experimental setup and analysis method of plume diagnostics were almost same to the previous study.³³ The performance summary is presented in Sec. V D, considering the performance loss due to multi-species ions estimated from the results of the Langmuir probe measurements.

A cylindrical Langmuir probe consisting of a tungsten wire electrode with a radius $r p$ of 0.05 mm and a length $l p$ of 0.6 mm was used. The tungsten wire was covered by an alumina tube with an inner radius of 0.15 mm and an outer radius of 0.3 mm except for the tip portion. The total length of the probe was 170 mm, with a gradual increase in the radius of the supporting tube from 0.3 to 1.25 mm. The Langmuir probe was mounted on the fast-moving stage described in Sec. III B and inserted into the discharge plasma from the downstream side.

There are some general considerations regarding the probe orientation when measuring the Hall thruster discharge plasma. One is the existence of supersonic ion flow. Since the ions are accelerated by the strong electric field, they can flow into the probe over the limit of Bohm criteria, which increase the net ion current collected by the probe. A practical solution is to align the probe axis along the stream vector of the ion flow.³⁷ In this study, the Langmuir probe was inserted into the discharge plasma with the orientation shown in Fig. 2, in which the probe axis is approximately perpendicular to the field lines near the exit, i.e., along the direction of the electric field. The magnetic field imposes another requirement because strong electron gyromotion makes it complicated to interpret plasma parameters from the probe response. The magnitude of the magnetic field effect is usually evaluated by comparing the probe radius and electron Larmor radius $r L , e$⁠. The typical electron temperature is 10–30 eV, corresponding to $r L , e/ r p≃10$ with the maximum $B r$⁠. This satisfied the criteria proposed by Godyak and Demidov³⁸ for the use of conventional methods.

The thermal condition in the Hall thruster discharge plasma is quite severe for the Langmuir probe to stay in due to the high density and highly energetic plasma flow. To avoid excessive heating and ablation of the probe, a fast-moving linear stage driven by a shaft motor (S160D, Nippon Pulse Motor) was developed and used for the probe insertion, which was similar to the high-speed reciprocating probe systems in Refs. 39 and 40. The time-averaged $I$– $V$ characteristic at each measurement point was obtained by the following procedure. The probe-tip remained around 140 mm downstream from the channel exit while the bias voltage $V b$ was being swept with triangle wave by a bipolar power supply. The sweep frequency was fixed to 250 Hz, which was 2 orders of magnitude lower than the typical frequency of discharge current oscillation, to evaluate the time-averaged plasma characteristics. The probe was inserted toward the target point at the maximum speed of 1000 mm/s, paused for approximately 50 ms, and then returned back to the original position with the same speed of the insertion. The probe current $I p$ measured by a 10  $Ω$ resistor was recorded during the pausing time by a 10-bit oscilloscope. The probe insertion was repeated two or three times for each measurement point. Because the sweep frequency was relatively high, the measured current contained the capacitive current $I C=C( d V b/ dt)$ due to the stray capacitance $C$ in the entire circuit. This was compensated by the effective capacitance calculated from the $I$– $V$ characteristic without plasma that was measured in advance. After the compensation, $I p$ was averaged per $Δ V b$ (⁠ $=0.78$ V) discretized by the vertical resolution of the oscilloscope. The instantaneous maximum of $I p$ was about 70 mA even at the highest density region, which resulted in 0.7 V at the shunt resistor. Since this was lower than the typical uncertainty of the plasma potential in a Hall thruster plasma measurement,³⁷ the potential drop at the shunt resistor was neglected. Figure 4 shows the measurement process visually and an example of the time-averaged $I$– $V$ characteristic. A series of the process was conducted at 29 measurement points, every 0.5 mm from 4 mm inside to 10 mm outside relative to the channel exit. No significant damage or melting of the probe-tip was confirmed through the entire campaign.

The second derivative was calculated using the Savitzky–Golay filter, which has an advantage in the energy resolution among some numerical techniques.⁴⁵ The quadratic function was selected and the window of 45 points (⁠ $=±17$ V) was used for the smoothing and differentiation, though the window size was adjusted for the both ends not to protrude the $V b$ range. The standard deviation of the probe current $Δ I p$ was used to estimate the uncertainty as $d 2( I p±Δ I p)/ d V b 2$⁠. The total uncertainty of the EEPFs was calculated including that of the probe area $Δ A p/ A p≃0.16$ and propagated for the error analysis of the density and temperature. The plasma potential was found as the zero crossing point of the second derivative.

Blue curves in Fig. 5 show the measured EEPFs obtained by Eq. (1) in the region of $−3≤z≤4$ mm. We can see a bump structure in the EEPFs around the channel exit, suggesting the existence of two electron populations. The second population has a large kinetic energy $ε k$⁠, characterized by its peak, and a relatively low temperature, characterized by the inverse of its slope. Such a high-energy population has also been observed with a conventional xenon Hall thruster, and it was discussed to be caused by the cathode-derived electrons.⁴³ In this study, the kinetic energy was determined by the peak fitting in $−1≤z≤4$ mm, where the second peak was clearly found. In Fig. 6, the kinetic energy is plotted with the plasma potential on the spatial map of the EEPFs. On the plume side, the kinetic energy is around 30 eV. Since the cathode body is negatively biased to about 60 V with respect to the plasma potential (⁠ $= V p+ V cg− V k$⁠), the incident electrons are accelerated with this potential difference. Besides, ionization also occurs during this process, decreasing the kinetic energy of the high-energy population. In this context, 30 eV is reasonable for the electrons originating from the cathode. In the ion-acceleration region, the kinetic energy increases toward the anode side along with the plasma potential, which suggests acceleration from the plume region. Given that perspective, these electrons could exhibit anisotropy because they are accelerated by a directional electric field. As mentioned above, the Druyvesteyn formula is derived from an isotropic assumption. Therefore, the kinetic energy and temperature of the high-energy population discussed here may need to be modified depending on the anisotropicity, which requires more detailed measurements.

Water-molecule density is the other important factor because the electron-impact reactions are largely governed by collisions with H $2$O. The propellant flow diffuses outward from the channel exit, resulting in a spatial distribution of water-molecule density along the thrust axis. The water-molecule density was calculated by axial-symmetric direct simulation Monte Carlo (DSMC). The calculation domain was defined from the gas injection surface to 20 mm downstream of the channel exit in the axial direction, from the center axis to a distance of twice the channel mean radius in the radial direction. The channel shape was simplified to a coaxial cylinder and the propellant was injected from both edges of the injection surface emulating the real configuration. The velocity of injected particles was given assuming a shifted Maxwellian velocity distribution function with the speed of sound at 650 K and the net-flux at the injection surface was adjusted to be same mass flow rate as the experiment. The temperature of all wall surfaces was also set to 650 K and particles colliding with them were diffusively reflected. Elastic collisions between particles were treated using the hard-sphere model. Figure 7 shows the steady-state solution of the spatial distribution of the water-molecule density. In fact, the propellant flux decreases with ionization because the total mass flux is conserved. As shown in Sec. V D, the mass utilization efficiency is less than 20%, which means at least 80% of the mass flux remains as neutrals. Taking this into account, the ionization has small influence on the H $2$O distribution compared to the effect by spatial diffusion.

Figure 8 shows the axial distribution of electron density and temperature obtained from the EEDFs by the two methods described in Sec. III C. The electron density shows quantitatively similar trend between the two methods. This is mainly caused by a trade-off of these methods. As shown by the blue lines in Fig. 8, the lowest part of the EEPFs is depleted, which typically occurs due to the finite resistance of the probe circuit or magnetic field effect.³⁸ The distortion diminishs the actual physical structure of the EEPFs, causing the density from Eq. (2) to underestimate the low-energy populations. In contrast, the density found by the fitting method compensates the depleted regime with a Maxwellian distribution. The similarity between the two methods indicates that the uncertainty on the density due to the high-energy electrons is no greater than that caused by the distortions of the EEPFs. On the other hand, the electron temperature shows a significant difference depending on the analysis methods. Because of the feature of each method mentioned above, the temperature defined by Eq. (3) is weighted toward higher energy, while the temperature obtained by the fitting is weighted toward low energy. Therefore, the actual electron temperature is expected to be between them. According to the previous probe studies on conventional xenon Hall thrusters, the electron temperature typically becomes around 10% of the discharge voltage at the peak point.^43,46,47 In the case of the water-vapor Hall thruster, it appeares to reach slightly higher (⁠ $∼30$ eV at 200 V and $∼40$ eV at 250 V), but does not significantly exceed the typical values of them. The axial profiles approximated by single Gaussian functions are used in the following analysis.

Table III shows the results of efficiency analysis. Every efficiency is calculated using the angular distribution of the beam current and ion energy distribution function downstream on the center axis obtained by the far-field plume diagnostics and the current fraction estimated in the previous section. The effect of ion fragments is evaluated both without and with consideration of the secondary ionization, corresponding to Figs. 12(a) and 12(b). The performance loss by dissociative ions has a minor effect compared to the other loss factors. The change of current fraction by the secondary processes is also not sensitive to the performance estimation because of the small mass difference between H $2$O $+$ and OH $+$⁠. Nevertheless, the influence of multi-species ions is more significant than that by multiple-charged ions in xenon Hall thrusters, whose efficiency is typically more than 95%.^54,55 This is almost due to the production of H $+$⁠, which has a large mass difference to $H 2 O +$⁠.

Figure 10 indicates that inelastic collisions occur more frequently than elastic collisions near the channel exit, and the primary reaction is not ionization but electronic excitation. Some of the excited molecules can contribute to the ion production by cumulative ionization, which is not considered in the above analysis. Besides, dissociation to neutral fragments outweighs ionization reactions, leading to secondary ionization processes discussed above. Predominance of electronic excitation and dissociation is also unfavorable in terms of electron-energy consumption because it means that higher energy is effectively consumed per one ionization event. While inelastic collisions have small influence on the energy balance in xenon Hall thrusters,⁵⁹ their contribution may increase in the case of water-vapor Hall thrusters. On the other hand, the energy loss to the wall is also expected to be large in this thruster case because of the narrow width of the discharge channel. The difference in the energy-loss process is also affect the EEDF formation. Further study is needed to reveal the importance of inelastic collisions in the total energy balance and determine the electron energy distribution. In the near-anode region, elastic momentum transfer dominates as the electron temperature decreases. Rotational and vibrational excitation also occur more actively. Nevertheless, because their collision frequencies are lower than that of elastic momentum transfer and their energy thresholds are less than 1 eV,^49–51 the energy consumption by these processes may not be significant.

We predict the mass utilization efficiency using Eq. (28) and compare it with the two ultimate cases to investigate the contribution of each processes. Two pairs of $n e$ and $T e$ are used based on the measurement results, which are obtained by averaging $n e , EEPF$ and $T e , EEPF$ over the region of $z≤2$ mm for 200 and 250 V, respectively. The average neutral velocity from DSMC is used for the calculation of the mean free paths. Figure 13 shows the predicted mass utilization efficiency as a function of the ionization length. Assuming a short ionization length, the influence of dissociation and secondary ionization is small, which is relevant to this thruster case. When the length is extended, dissociation to neutral fragments reduces the total amount of H $2$O available for ionization. Nevertheless, owing to relatively high ionization rate of OH, the mass utilization efficiency is recovered by the secondary ionization processes and does not deviate much from the prediction without dissociation. Therefore, dissociation to neutral fragments is not a significant concern from the perspective of mass consumption. In Fig. 13, the monotonic increase in the mass utilization efficiency is deduced assuming constant electron temperature; however, a greater contribution of the secondary ionization leads to lower electron temperature, causing a decrease in the mass utilization efficiency. According to the previous studies,^51,53 the energy yield of OH production from H $2$O and yield of OH $+$ production from OH are 6.5 and 13.1 eV, respectively; thus, the effective ionization energy of this secondary process is around 20 eV, $∼1.5$ times larger than the energy yield of H $2$O $+$ (12.6 eV).⁵⁰ The most beneficial ionization length will be determined by the balance between the gain in ion fluxes from the secondary ionization and the corresponding loss in electron energy. Increasing the discharge voltage is another possible way to improve the mass utilization efficiency, as demonstrated in this study. Even with this approach, the secondary processes remain significant as more propellant is consumed. When the increase in the effective ionization energy outweighs the electron-energy gain by Joule heating, the electron temperature will no longer rise, limiting further improvements in the mass utilization efficiency.

This work investigated the electron-impact reactions in the discharge plasma of a water-vapor Hall thruster based on the experimentally obtained EEDFs by Langmuir probe measurements. A cylindrical Langmuir probe was inserted along the thrust axis using a fast-moving system to prevent the thermal damage and the time-averaged $I$– $V$ characteristics were acquired at 29 measurement points from 4 mm inside to 10 mm outside on the channel center. The EEDFs were obtained by the second derivative of the time-averaged $I$– $V$ characteristics. Since the measured EEDFs indicated two electron populations and the high-energy part was suspected to be anisotropic, we evaluated the electron density and temperature in two ways: One is by the integration of the measured EEDF and the other is by fitting of a Maxwellian EEDF to the low-energy part of the measured EEDF. The density distribution showed a similar trend in both ways, whereas the temperature distribution by the integration method $T e , EEPF$ and the fitting method $T e , Mxw$ showed a discrepancy; the actual temperature was considered to be found between them. While the electron temperature seemed to be slightly higher, the axial profile of the discharge plasma was similar to that of conventional xenon Hall thrusters.

The ion current density for each species produced by electron-impact ionization was estimated as an axial integration of the one-dimensional steady-state continuity equation. The ion production rates were calculated using the electron density and temperature obtained by the Langmuir probe measurements and the water-molecule density computed by DSMC simulation. As a result, H $2$O $+$⁠, OH $+$⁠, and H $+$ were expected to be contained as the main products. The current fractions were estimated about 67%, 18%, and 12% if only the primary ionization was considered, and about 49%, 32%, and 15% if the subsequent secondary ionization from the neutral fragments was considered. This ratio was not sensitive to whether we used $T e , EEPF$ or $T e , Mxw$⁠, nor to the discharge voltage. We calculated the efficiency loss due to the mass difference based on the estimated current fraction, which resulted in an additional 20%–25% loss of the anode efficiency estimated by the plume diagnostics.

The effects of reactions other than ionization were also examined. Although water-vapor plasma produced negative ions through electron-attachment reactions, the collision frequencies of them were estimated to be so small that the existence of negative ions could be negligible. It was anticipated that inelastic collisions increased near the channel exit; however, electronic excitation and dissociation to neutral fragments were more likely to occur than ionization reactions, leading to higher effective energy cost per ionization. Energy losses in rotational and vibrational excitation were expected to be minor because these reactions were not dominant and did not consume significant electron energy per collision.

We finally discussed possible approaches to improve the mass utilization efficiency, such as extending the ionization length or increasing the discharge voltage, based on the investigated ionization mechanisms. From the analytical expressions, it was predicted that the contribution of secondary ionization from the neutral fragments increased as the mass utilization efficiency improved. Therefore, the effectiveness of these approaches was expected to be determined by the balance between the gain in ion production from the subsequent ionization processes and the corresponding increase in effective ionization energy.

This work was supported by the Takahashi Industrial and Economic Research Foundation, MEXT Coordination Funds for Promoting AeroSpace Utilization (Grant No. JPJ000959), and JSPS KAKENHI (Grant No. 22KJ1149). The authors acknowledge fruitful discussions about the interpretation of the measurement results and the reactions of water-vapor plasma with K. Hara, Y. Yamashita, and L. Vialetto.

The authors have no conflicts to disclose.

K. Shirasu: Conceptualization (equal); Data curation (lead); Formal analysis (lead); Funding acquisition (equal); Investigation (lead); Methodology (equal); Project administration (equal); Writing – original draft (lead); Writing – review & editing (equal). H. Koizumi: Conceptualization (equal); Funding acquisition (lead); Investigation (equal); Methodology (equal); Project administration (equal); Supervision (lead); Writing – review & editing (equal). H. Sekine: Funding acquisition (equal); Methodology (equal); Supervision (equal); Writing – review & editing (equal). K. Komurasaki: Supervision (equal); Writing – review & editing (equal).

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