Introduction

In the past decade nanosatellites (e.g. satellites with a mass of 1–20 kg) have become more prominent and account for an increasing portion of global satellite launches [1]. Developing proper propulsion solutions for nanosatellites is important to further utilize these platforms, enabling missions such as: 1) maintaining relative positioning of satellites in a constellation (station keeping); 2) injecting satellites into their designated orbits (orbit establishment); 3) aerodynamic drag compensation; and 4) end of life maneuvering (either deorbit or transfer to a safe orbit). Moreover, a propulsion system with several thrusters can also be used for attitude control [2]. Nevertheless, presently most nanosatellites either have no propulsion or only limited propulsion capability due to the limited number of available propulsion solutions and stringent requirements of nanosatellites.

The development of highly efficient and long-lasting Electric Propulsion (EP) systems for nanosatellites presents a new challenge due to the low available power (order of 1–10 W), volume and mass limitations. Therefore, new propulsion solution designs are needed. Specifically, the adaption of Hall Effect Thruster (HET) technology to nanosatellites is of considerable interest due to the potentially high thrust to power ratio (~ 60 mN/kW) compared to other forms of EP such as ion thrusters (~ 40 mN/kW), field emission electric propulsion (~ 20 mN/kW), vacuum arc thrusters (< 10 mN/kW) or electrospray (< 10 mN/kW) [3]. Presently, there are very few low power HETs that can operate at power levels below 100 W. A summary of laboratory and commercially available sub 100 W HETs is presented in Tables 1 and 2, respectively.

Table 1 Existing sub-100 W Laboratory Hall Thrusters
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Table 2 Existing sub-100 W Commercially Available Hall Thrusters
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In the 1980’, Prof. A. Kapulkin at the Dnepropetrovsk State University first suggested, and theoretically justified, a concept of a wall-less HET that was named Outside Electric Field Thruster (OEFT) [20,21,22,23]. One of the challenges in designing an efficient wall-less HET is the fact that the ionization and acceleration regions are almost inevitably pushed to the region of negative gradient magnetic field. That might cause low frequency instabilities that highly increase the axial electron current and reduce the efficiency of the thruster [24]. According to the dispersion relation obtained from the stability analysis and presented in [24], Eq. (3), in order to suppress the instabilities associated with the enhanced axial electron transport, the expression under the square root should be positive. A possible condition for stability is demanding the fulfillment of the inequality presented in Eq. (1).

$$\frac{d}{dz}\left(\frac{{B}_{0}}{{n}_{0}}\right)>0,$$
(1)

where \({B}_{0}\) is the magnetic field, \({n}_{0}\) is the neutral number density, and z is the axial coordinate. However, this condition is more challenging to achieve in a wall-less configuration. Another possibility for stable operation is to work in a set of conditions described in [21] as “Debye mode”, at which the Debye length of the ions is on the same order of magnitude as the acceleration layer length and the possible drawn ion current from the plasma is limited [21]. For achieving these conditions, a narrow channel and a high discharge voltage (≥ 1 kV) are used. Two OEFT prototypes were designed and tested experimentally – a single stage OEFT, with a single power supply and one enforced potential difference between the anode and the cathode, and a double stage OEFT with two power supplies – one to enforce a potential difference between the anode and the metal channel walls (< 100 V) and another power supply to enforce a potential difference between the metal walls and the cathode (accelerating voltage ~ 1000—2500 V). A schematic description of the double-stage OEFT is presented in Fig. 1.

Fig. 1
figure 1

schematic description of the double-stage OEFT (from [22])

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The prototypes were examined with various propellants, including xenon and cesium. The double stage OEFT showed better performance, but at the price of high erosion of the channel and a more complicated and heavy power processing unit. Typical measured values for the single stage OEFT with xenon are specified in Table 3. Measured performance for the double stage OEFT with xenon and cesium are summarized in Table 4. As demonstrated in Table 4, performance figures and efficiency with cesium were superior to the one obtained with xenon.

Table 3 Typical Experimental Results for Single Stage OEFT with xenon (from [20])
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Table 4 Experimental Results for Double Stage OEFT with xenon and cesium (from [22])
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In the OEFT, the ionization and ion acceleration regions are located outside of the thruster channel (hence the term ‘outside’), downstream from the exit plane. Thanks to the location of the ion acceleration region, ion collisions with the channel walls are almost eliminated and thruster lifetime is expected to extend. Later on, several wall-less designs were implemented and tested by other researchers. Mazouffre et. al. designed and tested a 200 W class wall-less HET called the Wall-Less Hall Thruster (WLHT) [25]. Although the WLHT showed steady operation in the region with negative magnetic field gradient, lower performance was observed with respect to the conventional version of this thruster, with lower beam energy and larger beam divergence. Some improvement in a 1.5 kW wall-less HET performance was achieved by adjusting the magnetic field topology and reducing the electron discharge current to the anode [26]. Karadag et. al. studied the External Discharge Plasma Thruster (XPT) and showed reasonable performance can be achieved with a wall-less \(E\times B\) device with power levels of 11 – 412 W [27, 28]. Simmonds and Raitses designed and tested the magneto-electrostatic trap (MET) thruster [29] for power levels \(\le 200\mathrm{ W}\). The authors showed generally lower performance compared to a classic design HET for the same power, mainly due to larger beam divergence.

Due to the growing interest in very low power \((\le 100\mathrm{ W})\) HETs for the use of small satellites, the research on the OEFT was continued at ASRI. The downscaling of HETs to low power involves an inevitable increase in the surface to volume ratio and plasma-wall losses, thus reducing thruster efficiency, increasing channel wall erosion rate and causing high thermal loads that damage the magnetic confinement of the electrons. Therefore, a low power wall-less HET might be a suitable candidate for a low power HET design. In this paper we present a first study of integral parameters of the ASRI xenon-powered, single stage OEFT. The new single-stage OEFT design includes several design changes that are meant to improve its performance with respect to its predecessor. The design changes are discussed in detail in the next section. Moreover, the aim of this research is to perform a more thorough study of the OEFT performance and understand the main physical processes behind the loss mechanisms for this thruster. That knowledge, in turn, will drive more design improvement in the future.

In Experimental apparatus section the experimental setup is described, including the new OEFT design, the vacuum system, the Retarding Potential Analyzer (RPA) measurement setup and the thrust measurement system. In Result and discussion section the experimental results are shown and discussed and in Conclusions section the conclusions are presented.

Experimental apparatus

The new OEFT design

The new OEFT design was developed for operation with metallic propellants (primarily alkali metals: Cs, Rb, K) in mind. The very low ionization potential of these propellants is expected to improve ionization efficiency, which was found to be very low for the single stage OEFT operated with xenon [20]. However, using solid propellants (at room temperature) requires a relatively complicated system for melting the solid propellant and delivering the very reactive gases to the anode. In particular, accurately controlling the low mass flow rate (in the order of a few SCCMs) has proven to be extremely challenging. Therefore, although far lower performance figures are expected, it was decided to focus first on xenon operation of the thruster, due to the simpler handling of the propellant. Xenon operation will be an important milestone for validating the ignition and overall operation of the thruster, the thermal and electrical insulations, refinement of the numerical modeling of the thruster using Particle-In-Cell simulations [30] and the coupling to the facility and the diagnostics tools. Moreover, despite the expected low efficiency and low specific impulse, operation of the single stage OEFT with xenon propellant can be relevant for some missions of nanosatellites due to its relative simplicity, reliability, small mass and size and the expected long lifetime.

The new OEFT design includes several unique features to allow its operation at low power levels and negative gradient magnetic field region. With small satellite weight, volume and power limitations in mind, the new generation design includes a single stage power supply. Moreover, the new design includes improved magnetic field topology, smaller gap between the magnetic poles and stronger magnetic fields to optimize the performance at very low power levels \((\le 20\mathrm{ W})\) and single-stage mode of operation. Previous small HET designs indicated high thermal load management problems, causing high temperatures and reduced magnetic field strength [6, 7]. Therefore, to maintain the magnetic properties of the magnetic poles at high temperatures, Hiperco-50A alloy was used for the electromagnet cores (Currie point at \(938\mathrm{^\circ{\rm C} }\)) [31].

The metal gas distributor and channel walls serve also as the anode, while the inner and outer magnetic poles are floating. The channel is 0.2 mm in width with a mean diameter of 15 mm. The sharp edges of the magnetic poles provide a strong localized magnetic field in order to prevent high electron current to the anode that may lead to low efficiency. A cross-sectional view of the OEFT is illustrated in Fig. 2. The evolution of the radial component of the magnetic field at the channel centerline with axial position for the electromagnet prototype at 9 A coil current is presented in Fig. 3.

Fig. 2
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Cross-sectional view of the OEFT, electromagnet prototype

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Fig. 3
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Radial magnetic field with axial position along the channel centerline for the electromagnet prototype at 9 A coil current. The black dashed line marks the position of the exit plane

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Ideally, for low power operation one would tend to use permanent magnets rather than electromagnets for the magnetic circuit design in order to save power and avoid a high thermal load to the thruster. However, permanent magnets do not allow easy modification of the magnetic field strength during experiments at early development stages. Moreover, the thermal loads in small scale HETs might result in a reduction of the permanent magnet magnetic field. Therefore, two designs for the magnetic circuit were built and tested:

  • OEFT with a magnetic coil, capable of varying magnetic field

  • OEFT with a samarium-cobalt (SmCo) permanent magnet

Facility setup

The thruster was tested at ASRI medium size vacuum chamber. The chamber is a cylindrical enclosure, 1.2 m in diameter and 2.7 m long (~ \(3.05 {\mathrm{m}}^{3}\)internal volume), equipped with 3 Cryogenic pumps with a total maximum pumping speed of 12,500 l/s, backed by a single fore vacuum pump with a pumping speed of 58 l/s. Vacuum pressure is measured by IONIVAC pressure gauge (ITR 90, Leybold) with 15% accuracy. The ultimate chamber pressure is below \(8\times {10}^{-8}\) mbar (xenon corrected). During thruster operation, the measured chamber pressure is maintained below \(4\times {10}^{-6}\) mbar at mass flow rates of 2 sccm or less. The OEFT is fed solely by high purity xenon gas (99.999%) using a flow controller (M100B, MKS) with 0.1 sccm accuracy. A thermionic tungsten filament is used as the cathode/neutralizer, with nominal operating conditions of 7 A current and a 10 V voltage.

Thrust balance setup

The OEFT was mounted inside the vacuum chamber onto a FOTEC \(\mathrm{\mu N}\) thrust balance [32], as described in Fig. 4. This thrust balance is a horizontal deflection-based device, consisting of a 70 cm beam suspended by two spring bearings, and can measure thrust with two possible modes of operation:

  1. 1)

    Displacement mode – The deflection of the beam is measured with a high precision optical reflection-based transducer. The force is calculated by using the known rotational spring constant. Thrust up to 6 mN can be measured in this way.

  2. 2)

    Feedback mode – A closed loop PID control system is used to maintain the beam in a constant position. The opposing force to the thrust is generated by an electrostatic force actuator, with its force known with good accuracy from the applied voltage. Unlike the displacement mode, this method does not require accurate knowledge of the spring constant, which can change with loading conditions, temperature, and total displacement. Therefore, it is considered more accurate, especially for the expected low thrust values of the OEFT. Thrust up to \(500\mathrm{ \mu N}\) can be measured in this way with expected accuracy of 1.5% of the measurement \(\pm 1\mathrm{\mu N}\).

Fig. 4
figure 4

The OEFT mounted on the FOTEC \(\mathrm{\mu N}\) thrust balance

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The thrust balance also includes six liquid metal baths to allow electrical wires to be passed to the thruster without any friction affecting thrust measurements. An eddy current brake utilizing an adjustable permanent magnet is used to dampen long period oscillations of the system. The gas flow to the thruster is passed through an ultra-flexible gas tube that is connected above the pivot point to ensure minimal influence on the thrust measurement.

The cold gas contribution to the thrust was measured separately from the total thrust, in order to evaluate the ion beam contribution to the thrust. The anode efficiency is calculated from Eq. (2), [33]:

$${\upeta }_{\mathrm{a}}=\frac{{\mathrm{T}}^{2}}{{2\dot{m}}_{a}{P}_{d}},$$
(2)

where T is the thrust, \({\dot{\mathrm{m}}}_{\mathrm{a}}\) is the mass flow rate and \({\mathrm{P}}_{\mathrm{d}}\) is the discharge power. The mass utilization efficiency \({\eta }_{m}\) and the current utilization efficiency \({\upeta }_{\mathrm{b}}\) [33] are defined by Eqs. (3) and (4), respectively:

$${\upeta }_{\mathrm{m}}=\frac{{\mathrm{I}}_{\mathrm{b}}\cdot {M}_{i}}{e{\cdot \dot{m}}_{a}},$$
(3)
$${\upeta }_{\mathrm{b}}=\frac{{\mathrm{I}}_{\mathrm{b}}}{{\mathrm{I}}_{\mathrm{d}}},$$
(4)

where \({I}_{b}\) is the ion beam current, \({M}_{i}\) is the ion mass, e is the elementary charge and \({I}_{d}\) is the discharge current.

The specific impulse was calculated according to Eq. (5):

$${\mathrm{I}}_{\mathrm{sp}}=\frac{\mathrm{T}}{{\dot{\mathrm{m}}}_{\mathrm{a}}{\mathrm{g}}_{0}}.$$
(5)

The error for the values calculated in Eqs. (2, 3, 4 and 5) was estimated by standard error propagation and the variance formula [34], while assuming independent variables.

The faraday bowl

A simple Faraday “bowl” biased to -60 V (with respect to the cathode) was used for some of the experiments to measure the total ion current. The bowl is 38 cm in diameter, and it was placed at a fixed position so the thruster exit plane is 35 mm away from the “exit plane” of the bowl, as described in Fig. 5. Changing the position of the bowl in the range of 20 mm – 40 mm did not change the measured ion beam current. The measured ion current showed negligible dependence on the bias voltage of the probe in the range of -100 V to -40 V. Moreover, the thrust was measured with/without the bowl, and the difference in thrust was within the thrust measurement uncertainty.

Fig. 5
figure 5

The ion current measurement with the Faraday hemisphere (“bowl”-shaped). Not to scale

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The estimated uncertainty in the measured total ion current is 10%, and it is based on recent measurements of secondary electron emission induced by Xe + ion bombardment of a stainless steel wall [35], showing a Xe + / electron ratio of ~ 0.05 for the typical energy levels of the ion beam observed in our experiment.

Retarding potential analyzer (RPA) setup

The ion current density in the far field plume region of the OEFT was examined by using a commercial retarding potential analyzer (Semion pDC, Impedans). The probe is comprised of 37 circular holes, each of 800 μm diameter. The RPA has three grids, each one is set to a different voltage, as described in Fig. 6.

Fig. 6
figure 6

The RPA concept of operation

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By sweeping the voltage in the \({\mathrm{G}}_{2}\) grid, the RPA allows filtering of ions with different energies. As it can be seen from Eq. (6), ions with energy to charge ratio lower than the \({\mathrm{G}}_{2}\) grid voltage will be reflected and will not reach the collector:

$$\frac{{\upepsilon }_{\mathrm{i}}}{\mathrm{Z}\cdot \mathrm{e}}<{\mathrm{U}}_{{\mathrm{G}}_{2}},$$
(6)

where \({\upepsilon }_{\mathrm{i}}\) is the ion energy, Z is the ion charge state and e is the elementary charge. It is important to clarify that the RPA cannot discern between singly or multiply charged ions. The measurements were performed in various angular positions and a fixed radius by placing the retarding potential analyzer (RPA) on a beam and using a stepper motor (573HBM20-1000 easy servo motor, Leadshine, 1.2 deg/step) as shown schematically in Fig. 7a and b.

Fig. 7
figure 7

a schematic description of the RPA exp. setup; b Photo of the RPA exp. setup

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A distance R of 79 mm between the OEFT exit plane and the RPA (radius of the arc) was chosen according to standard practices [36] and as a compromise between obtaining a strong signal to noise ratio while maintaining the assumption of far-field analysis and avoiding noise from the proximity of the filament cathode to the RPA. The leveling errors of the stepper motor as well as the RPA probe are estimated to be less than \(1^\circ\).

Once the I-V curve is obtained for each voltage sweep of the RPA, the corresponding Ion Energy Distribution Function (IEDF) is calculated from the derivative dI/dV [36]. After obtaining the IEDF, the mean energy of the ion beam \({E}_{mean}\) can be calculated according to Eq. (7):

$${\mathrm{E}}_{\mathrm{mean}}=\frac{{\int }_{0}^{{\mathrm{V}}_{\mathrm{max}}}\mathrm{ IEDF}\left(\mathrm{V}\right)\cdot \mathrm{VdV}}{{\int }_{0}^{{\mathrm{V}}_{\mathrm{max}}}\mathrm{ IEDF}\left(\mathrm{V}\right)\mathrm{dV}},$$
(7)

where \({V}_{max}\) is the maximum scanned voltage. Moreover, the ion current density can be measured for various angular positions by measuring the ion current without energy filtering. Assuming that the ion beam is symmetric, we can estimate the total ion beam current from Eq. (8) and using trapezoidal numerical integration.

$${\mathrm{I}}_{\mathrm{beam}}=2\uppi {\mathrm{R}}^{2}{\int }_{-\uppi /2}^{0}\mathrm{J}\left(\uptheta \right)\mathrm{sin}\left(\uptheta \right)\cdot {\upkappa }_{\mathrm{D}}(\uptheta )/{\upkappa }_{\mathrm{A}}(\uptheta ),$$
(8)

where \(\mathrm{J}(\uptheta )\) is the ion current density, and \({\upkappa }_{\mathrm{A}},{\upkappa }_{\mathrm{D}}\) are geometrical factors to account for the systematic error in modeling the thruster as a point source [36]. Ions in HETs far field can be more accurately modeled by two-point sources [36]. Furthermore, the far-field divergence half-angle can be calculated from Eq. (9):

$$\uplambda ={\mathrm{cos}}^{-1}\left(\frac{{\mathrm{I}}_{\mathrm{axial}}}{{\mathrm{I}}_{\mathrm{beam}}}\right),$$
(9)

where the axial component of ion beam current \({\mathrm{I}}_{\mathrm{axial}}\) is defined in [36] for the two-point sources analysis. The thrust can be estimated from Eq. (10), assuming negligible multiply charged ions fraction [33]:

$$T\approx {\mathrm{cos}\left(\lambda \right)}^{ }{I}_{beam}\sqrt{\frac{2{M}_{i}{V}_{beam}}{e}},$$
(10)

where \({\mathrm{M}}_{\mathrm{i}}\) is the Xenon ion mass and \({\mathrm{V}}_{\mathrm{beam}}\) is the average beam voltage, estimated using Eq. (7). The thrust estimation using Eq. (10) is subjected to large errors, mainly due to poor estimation of the total ion beam current using the RPA measurements. The relatively weak signal in our case (due to very low ion currents) combined with the finite spatial resolution for numerically calculating the integral from Eq. (8) can result in large errors (~ 50%).

Results and discussion

Thrust measurements and performance figures

The OEFT was operated in ASRI vacuum chamber using a thermionic emission cathode filament for various scenarios of discharge voltage, mass flow rate, and magnetic field strength. An image of the OEFT during operation is presented in Fig. 8. The dark space between the exit plane and the cyan blue Xenon discharge, associated with the ionic XeII lines, indicates that a peak density value of the plasma might be obtained outside the channel, rather than a monotonic decrease in the plasma density downstream from the exit plane. Preliminary Optical Emission Spectroscopy (OES) measurements with high spatial resolution (~ 0.1 mm) indicated that the peak value of the XeII line of 541.9 nm is obtained ~ 1.7 mm away from the exit plane, thus supporting this claim. The OES preliminary results are presented in Fig. 9.

Fig. 8
figure 8

The OEFT in operation (the filament cathode is not shown)

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Fig. 9
figure 9

Preliminary OES results – The 541.9 nm line relative intensity along the axial position. The black dashed line marks the position of the exit plane

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Several selected thruster operation points (the highest anode efficiency working point for each mass flow rate) are listed in Table 5. Thrust and current measurements were obtained after the thruster has reached a thermal equilibrium (after ~ 20 min of operation). Although no time-resolved measurements of the anode current were taken, the thruster showed reduced stability at high mass flow rates and high discharge voltage values, as was observed in [4] for example. Hence, the discharge voltage values of the working points were changed with mass flow rate to ensure stable operation of the thruster. It is important to clarify that the values of the ion beam current for the performance analysis was taken from the Faraday bowl measurements, as the authors believe it is subjected to smaller errors compared to the RPA measurements.

Table 5 Thruster performance at selected operation points
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A drop in performance (reduced ion current) with time was observed in both electromagnet and the permanent magnet configurations, suggesting that the thermal load might be reducing the magnetic properties of magnets and/or the magnetic poles. However, the performance of the electromagnet prototype showed a far more significant deterioration with time, sometimes even resulting in a complete shutdown of the thruster. Moreover, thrust and anode efficiency slightly increased with increasing the coil current for the electromagnet prototype, suggesting that a stronger magnetic field is favorable. Overall, the electromagnet prototype showed inferior performance compared to the permanent magnet version for the same mass flow rate and voltage. This is demonstrated in Table 5 by the performance figures for the two prototypes for the nominal case of \({\dot{\mathrm{m}}}_{\mathrm{a}}=1\)[sccm] and Vd = 1 [kV]. Therefore, it was decided to focus on the permanent magnet prototype for most of the measurements. Naturally, a proper comparison between the two prototypes will involve using the same magnetic field (measured in atmospheric conditions) for the two prototypes. However, the magnetic field of the electromagnet prototype was limited by the maximum possible current than can be passed through the coil without damaging the thruster in vacuum operation.

Figures 10, 11, 12, 13 and 14 depict the variation of the permanent magnet thruster performance with discharge voltage and power, for different mass flow rate values. In Fig. 10 the measured thrust is presented. The ratio between the total thrust to the cold thrust was ~ 2–5, meaning that although most of the thrust comes from the accelerated ion beam, a non-negligible contribution originates from the gas dynamic expansion. As can be seen from the graph, the common trend is that the thrust is increasing with power and voltage for a fixed mass flow rate, as usually observed in HETs. However, a few data points don’t follow that trend. Further investigation is required to determine the origin of this behavior. Higher thrust is achieved for higher mass flow rates due to the higher contribution of the cold gas thrust and the higher ion beam current. Figure 11 presents the calculated specific impulse according to Eq. (5). The specific impulse is generally increasing with voltage and power for a fixed mass flow rate. The increase is attributed to the combined effect of higher voltage, higher mass utilization efficiency and higher gas temperature. The large error estimation is due to a large uncertainty in the mass flow rate, especially for low mass flow rate values.

Fig. 10
figure 10

Measured thrust as a function of voltage (left) and power (right)

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Fig. 11
figure 11

Specific impulse as a function of voltage (left) and power (right)

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Fig. 12
figure 12

Anode efficiency as a function of voltage (left) and power (right)

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Fig. 13
figure 13

Mass utilization efficiency as a function of voltage (left) and power (right)

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Fig. 14
figure 14

Current utilization efficiency as a function of voltage (left) and power (right)

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In Fig. 12 the anode efficiency, as calculated according to Eq. (2), is presented. The anode efficiency drops with voltage for every mass flow rate. That can be explained by a significant increase in the discharge current combined with a slight (if any) increase in thrust for any voltage increase. That also explains the drop of anode efficiency with power. The seemingly “high” performance values for the 1.4 sccm case originate from the low power and the high fraction of cold gas thrust contribution to the overall thrust.

In order to better identify the main loss mechanism that causes the overall low anode efficiency, the mass utilization efficiency and current utilization efficiency were calculated according to Eqs. (3) and (4), and are presented in Figs. 13 and 14, respectively.

Preliminary simulation results of the neutral dynamics using a PIC simulation [30] indicate that at 1.7 mm downstream of the thruster's exit plane, the neutral density is roughly one order of magnitude lower than the value observed inside the channel. Therefore, the authors suspect that the overall low values for the mass utilization efficiency are due to the ionization of the gas outside the channel, where the gas density is significantly lower. Consequently, most of the gas “escapes” without being ionized.

As it can be seen from Fig. 13, for most cases, increasing the voltage results in a slight increase in the mass utilization efficiency, for each given mass flow rate. This is probably due to higher energy electrons at higher discharge voltages, causing enhanced ionization. For the case of \({\dot{m}}_{a}=1.6\) sccm, the thruster mode of operation changed significantly, with the plume visually extending significantly beyond the exit plane and the discharge current increasing dramatically. Thus, we conclude that the ionization in this mode takes place in a broad region. Although the ion beam current is increased significantly in this mode, the electron current is increased even more dramatically, resulting in overall lower anode efficiency in this mode of operation, as observed in Fig. 13. The dependence of the mass utilization efficiency in the discharge power graph indicates that \({\eta }_{m}\) is increasing with power until some saturation is reached. The authors suspect that at high enough power levels a local depletion of the gas occurs in the ionization region outside the channel. As for the 1.6 sccm case—since the ionization in this mode is suspected to occur in a large volume, more of the gas can be ionized and we observe a larger mass utilization efficiency value.

From Fig. 14 one can see that higher current utilization efficiencies were observed for lower mass flow rates. This could be attributed to the enhanced classical electron transport for higher gas densities, impeding the electron confinement in the channel and enabling more electrons to reach the anode without taking part in any ionization events.

Moreover, for each mass flow rate a higher voltage leads to reduced current utilization efficiency \({\eta }_{b}\), meaning more electrons are going through the circuit without ionization. The authors are not sure what the physical process behind this behavior is. Bohm-like diffusion of electrons across the magnetic field, often associated with the anomalous transport in HETs [37], is increased with electron temperature. Consequently, it is increased with discharge voltage [38] and might explain this behavior. The expression for the Bohm-like diffusion is given in Eq. (11).

$${D}_{B}=\frac{1}{16}\frac{{k}_{B}{T}_{e}}{eB},$$
(11)

where \({k}_{B}\) is the Boltzmann constant and B is the magnetic field strength. The overall decrease of the current utilization efficiency with power reflects the observed behavior when the voltage is increased: the discharge current is significantly increased (and consequently the power) compared to the relatively small increase in the ion beam current.

RPA measurements

The ion beam in the plume was examined by using the RPA probe described in Experimental apparatus, Retarding potential analyzer (RPA) setup section. The selected voltage values for the RPA grids, with respect to chamber ground, are specified in Table 6.

Table 6 RPA grid voltage values
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Voltage sweeps with varying \({\mathrm{G}}_{2}\) voltage were performed. The I-V curve was obtained for the electromagnet prototype and the following nominal case: 1 kV discharge voltage, 1 sccm mass flow rate and 9 A coil current. The angular position was \(\uptheta =0^\circ\) (along the axis of symmetry). The results are shown in Fig. 15 (a). The corresponding IEDF is calculated from the derivative \(\mathrm{dI}/\mathrm{dV}\) and presented in Fig. 15 (b). The voltage was corrected for cathode potential.

Fig. 15
figure 15

a The I-V curve of the RPA measurement for the nominal case: 1 kV discharge voltage, 1 sccm mass flow rate and 9A coil current; b The corresponding IEDF

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The measurements indicate a relatively broad ion energy beam behavior, with average ion energy of \({\mathrm{E}}_{\mathrm{mean}}=385\mathrm{ eV}\), as calculated from Eq. (7). This value is far lower than the discharge voltage value of 1000 V, which implies low voltage utilization efficiency for this thruster, as observed in [4]. The measurement was repeated for various angles. The results shown in Fig. 16 indicate that at angles further away from the axis \((\uptheta =0^\circ )\), the IEDF is flattened, suggesting a larger population of lower energy ions. This behavior is also common in classic HETs RPA measurement and was concluded as the effect of charge exchange process between the high angle ions and the nearby neutrals [39].

Fig. 16
figure 16

IEDF for various probe angular positions

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Voltage sweeps were performed for various angular positions. In order to avoid a strong influence of the cathode on the measurement due to the proximity of the cathode to the RPA probe, the sweeps were performed in the range of \(-90^\circ \le\uptheta \le 10^\circ\). The obtained results for the ion current density are presented in Fig. 17. The dashed line for \(\uptheta \ge 10^\circ\) is the concatenated results from the \(-90^\circ \le\uptheta \le -10^\circ\) region, assuming axisymmetric plume. The slight discontinuity at \(\uptheta =10^\circ\) suggests a minor positioning error and/or a slight asymmetry in the ion beam that can be caused by the cathode.

Fig. 17
figure 17

RPA measurement of the ion current density in the far field for the nominal case

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The ion beam current was calculated using Eq. (8). The obtained value for the nominal case (1 kV, 1 sccm and 9 A for the electromagnet prototype) is \(1\mathrm{ mA}\), compared to the \(1.7\mathrm{ mA}\) obtained using the simple Faraday bowl. The discrepancy can be explained by the inherent error in the numerical integration and/or errors in the measured current density. Moreover, possible secondary electron emission from the bowl might result in a slightly over-estimated value for the Faraday bowl measurement.

The far-field divergence half-angle was calculated from Eq. (9) A value of \(25^\circ\) was found according to Brown’s definition [36]. Using the alternative definition of the divergence angle – the angle at which 95% of the total ion current is contained, yields a value of \(57.7^\circ\). Overall, the measured divergence angle is low compared to other wall-less devices [26, 28, 29]. Moreover, a thrust estimation of 29 μN was found from Eq. (9). There is a non-negligible difference between that value and the value obtained from the ion beam contribution to the thrust measured directly by the thrust balance for the same scenario (value of \(15 \mu N\)). The discrepancy can be explained by the large uncertainty associated with using Eq. (10) for thrust estimation, as discussed in Retarding potential analyzer (RPA) setup section.

Stability analysis

In order to examine the stability criterion described in Eq. (1), the expression for the derivative was calculated similarly to the analysis for the XPT thruster [28]. The results are presented in Fig. 18. \({\mathrm{B}}_{0}\left(\mathrm{z}\right)\) was measured for the electromagnet prototype at 9A coil current, while \({\mathrm{n}}_{0}\left(\mathrm{z}\right)\) was calculated based on particle in cell Particle-In-Cell (PIC) simulation [30] results.

Fig. 18
figure 18

\(d({B}_{0}/{n}_{0})/dz\) calculated for the nominal case and 9A coil current

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The stability region extends up to ~ 0.4 mm away from the exit plane, and can be compared to the expected mean free path \({\lambda }_{i}\), as estimated from Eq. (12).

$${\lambda }_{i}=\frac{{V}_{nz}}{{n}_{e}<{\sigma }_{i}{v}_{e}>},$$
(12)

where \({V}_{nz}\) is the neutrals axial velocity, \({n}_{e}\) is the electron number density, \({\sigma }_{i}\) is the ionization cross section for xenon, \({v}_{e}\) is the electron velocity magnitude (temperature dependent) and \(<{\sigma }_{i}{v}_{e}>\) suggests averaging over the electron velocity distribution function.

From a conservative estimation of \({T}_{e}\sim 15 eV\) (from OES), neutral temperature of \(400 K\) and \({n}_{e}={1\bullet 10}^{18}[{m}^{-3}]\) the obtained mean free path is \({\lambda }_{i}\sim 0.84 mm\), which is more than twice the size of the stability region. This result demonstrates the need for working in the “Debye mode” for stable OEFT operation, unlike the XPT thruster, where the ionization mean free path (and consequently the ionization region) was well within the stability region.

Conclusions

In this paper, an experimental study of the OEFT was presented. Operation of the OEFT using xenon propellant was demonstrated with thrust levels of 20–160 μN, specific impulse values of 50–102 s and anode efficiencies of 0.5%-2.8% at power levels of 1–14 W. Both permanent magnet and electromagnet configurations were studied. The degrading effect with time on the performance of the OEFT in both the electromagnet and the permanent magnet configurations is attributed to the thermal load of the OEFT. The performance of the permanent magnet prototype was superior to that of the electromagnet prototype for the same anode power levels. Overall, in its current design and xenon propellant, the OEFT showed poor performance, mainly due to low mass utilization efficiency. The measured performance figures of the new single stage OEFT with xenon were similar to the one obtained in [20], and no significant improvement was achieved by the new design. However, the thorough performance study did reveal a few interesting aspects in terms of the OEFT loss mechanism. Some evidence was found that the ionization region is at some distance from the exit plane, where the gas density is low, thus resulting in low mass utilization efficiency. In alkali metals, with lower ionization potentials (and consequently lower ionization mean free paths), \({\eta }_{m}\) is expected to improve dramatically. RPA measurements conducted in the thruster far-field plume indicated a far-field divergence angle of \(57.7^\circ\) (95% ion flux) at nominal operation with electromagnet, a relatively low value compared to other wall-less HETs. However, the voltage utilization efficiency was surprisingly poor compared to classic HETs, with 38% for a discharge voltage of 1 kV and a mass flow rate of 1 sccm xenon. Examining the OEFT after several hundred hours of operation showed insignificant erosion, thus suggesting a long lifetime, as expected. The data collected from the experiments will be used for refinement of the OEFT PIC simulations.

Nomenclature

\(B\) magnetic field strength

\({B}_{r}\) radial component of the magnetic field

\(\mathrm{e}\) elementary charge; \(1.6022\times {10}^{-19} C\)

\({E}_{mean}\) mean ion energy from RPA measurement

\({\mathrm{I}}_{\mathrm{axial}}\) axial ion beam current

Ibeam integrated ion beam current

Id discharge current

\(IEDF\) ion energy distribution function

\({k}_{B}\) Boltzmann constant

\({\dot{m}}_{a}\) gas mass flow rate

Mi ion mass

ne electron number density

R radial measurement distance for RPA measurements

RPA Retarding Potential Analyzer

PIC Particle In Cell

\({\mathrm{P}}_{\mathrm{d}}\) discharge power

Te electron temperature

T thrust

\({\mathrm{V}}_{0}\) RPA ground grid voltage

\({\mathrm{V}}_{1}\) RPA electron repelling grid voltage

\({\mathrm{V}}_{2}\) RPA sweeping grid voltage

\({\mathrm{V}}_{\mathrm{beam}}\) thruster beam voltage

\({\mathrm{V}}_{\mathrm{collector}}\) RPA collector voltage

Vd discharge voltage

\(\mathrm{Z}\) ion charge state

\(\lambda\) far-field divergence half-angle

\({\kappa }_{A}\) correction for ion angle of incidence

\({\kappa }_{D}\) correction for probe distance to thruster

\(\theta\) RPA angle

\({\upepsilon }_{\mathrm{i}}\) ion energy

\({\upeta }_{\mathrm{a}}\) anode efficiency