Physics of the high specific impulse alternative low power hybrid ion engine (alphie): Direct thrust measurements and plasma plume kinetics

In-space electric propulsion (EP) is a mature technology with commercial applications in orbit raising and station keeping maneuvers of large telecommunication satellites in geostationary orbit.^1–3 However, it is also a necessity for small satellites in Low Earth Orbit (LEO) that are currently being deployed to provide planetary internet coverage and other services, such as interactive television.

For these low altitudes, several interconnected satellites are necessary to provide service to specific areas of the Earth’s surface. Their orbits can undergo changes due to the small drag force produced by the atmosphere at these heights.^2,4

Therefore, the propulsive system of these LEO satellites needs to be continuously operated to compensate the orbital drag force and their inter-connectivity requires formation flying. Finally, thrust is also required for their controlled disposal at the end of its operational life. The in-space electric propulsion is the only technology available to provide the high specific impulses for these orbital maneuvers, required by the economic rationale of LEO satellite constellations.^3,4

Other issues that need to be addressed are the low weight budget (100–700 kg) and small size of these satellites and, in particular, the reduced electric power that may be available on board. The required thrusts are typically in the 0.1–10 mN range with electric power consumption below 500 W. Therefore, low power versions of well established technologies, such as Gridded Ion Engines (GIEs) or Hall Effect Thrusters (HETs), are being developed to meet these stringent requisites.^2,3

These plasma thrusters impart momentum to spacecrafts by ejecting a partially ionized gas stream, also denominated plasma plume. The ions exiting the thruster have a velocity distribution $fi(viz)$ of the ion speed components $viz$ parallel to its axis of symmetry. The dispersion of $viz$ around the mean value $⟨viz⟩=vex$ is characterized by the ion temperature $Ti$⁠. Thus, the thruster converts the feed electric power $W$ into kinetic energy power $dEk/dt=m˙ivex2/2<W$ of ions with mass $mi$ and $vex$ average drift velocity.^1–3 

Exceeding the performance of conventional chemical thrusters requires achieving high specific impulses $Isp=vex/go≳103s$⁠, where $go$ is the standard Earth’s acceleration. The required average drift speeds $vex≳10km/s$ are one order of magnitude higher than the typical plasma ion sound speed $vex≫cis=kB(Te+Ti)/mi$⁠, where $mi$ is the ion mass and $Te$ is the electron temperature. The plasma plume is a mesothermal flow where ions move with speeds that are intermediate between the electron thermal velocity and the plasma ion sound speed.^5,6

Plasma thrusters use different physical mechanisms to accelerate ions to these supersonic speeds. In conventional GIEs, it is the electrostatic field produced by a system of grids (denominated ion optics) connected to high voltages. As only ions are transported through the grids, the maximum current is space–charge limited. The positive charges are accelerated in HETs in the electric discharge established in a crossed electric and magnetic field. In this case, the ion current is not limited by the space charge effects, since acceleration takes place in a quasi-neutral plasma.^1–3 

In the recent Alternative Low Power Hybrid Ion Engine (alphie) introduced in Refs. 7–9, the electric charge acceleration mechanism is different from the conventional GIE scheme. It uses only one external cathode located in front of its two-grid system, similarly to HET configuration. The electron and ions counter-flow through the open spaces of its two flat parallel grids, contrary to the usual GIE scheme where only ions are transported through the ion optics system.

In the alphie, the electric charges are accelerated by the self-consistent electric field created by the currents of electrons and ions in addition to the electric potential applied to the grids. Therefore, as in HET thrusters, the exiting ion beam is not space–charge limited. This two species charge transport has been characterized in the laboratory^7,10 and also studied using particle-in-cell (PIC) numerical schemes.^11,12

In this paper, we discuss the one-dimensional ion velocity distribution functions (IVDFs) and the electron energy distribution function (EEDF) in the plasma plume of the alphie thruster in connection with the thrust delivered. As we shall see, in addition to the electric acceleration of ions, the propellant neutral gas is heated up to temperatures $T≃30eV$ by collisions with high-energy ionizing electrons. Both physical mechanisms contribute to the conversion of electric power $W$ into kinetic energy power $dEk/dt$ of heavy particles and then to the impulse delivered by the alphie thruster.

Section II briefly describes the principles and basic operation of the alphie thruster. Next, in Sec. III, the ion and electron velocity spectra obtained in the laboratory along the axis of symmetry of the plasma plume are introduced. The direct measurements of thrust delivered in Sec. IV confirm the throttle capability of the alphie thruster that gives specific impulses between 13 900 and 20 000 s for argon propellant gas. After the discussion of experimental results in Sec. V, we end with some concluding remarks.

Figure 1 shows schematically the longitudinal cross section of the small (15 cm in length and 10 cm in diameter) alphie plasma thruster and its electrical connections. Details of its operation and performances are available in Refs. 7, 10, and 13.

Vertical dashed lines in the diagram of Fig. 1 represent the extraction and cover grids that are separated 2.5 mm. These two grids are made of two flat parallel stainless steel disks 1 mm thick with 665 aligned holes of 1 mm in diameter uniformly distributed within a circle of 20 mm of radius. Similarly to HET thrusters, the only cathode is located in front of the cover grid and provides electrons for both ionization of the propellant gas and ion beam neutralization.

In the present study, the cathode was a thin tungsten wire heated up to thermionic electron emission by the $ICH$ DC. It was arranged along a diameter of the cover grid and separated 4.0 mm from its outer surface. Therefore, the alphie plasma thruster is the sole origin of the ion groups observed in the IVDFs in our experiments. However, the thruster can also be operated with other electron sources employed in electric propulsion systems, such as hollow cathodes.

A significant amount of thermionic electrons are driven by the acceleration potential $VAC=400−750V$ established between the ground and the metallic ionization chamber of Fig. 1. The cover grid is negatively biased with respect to ground and repels electrons from the cathode when its cover grid voltage $VCG$ is not null. In this case, the inflow of ionizing electrons toward the ionization chamber is reduced and can be interrupted if $VCG$ is high enough.⁷ 

These electrons are accelerated through the aligned holes of the two-grid system and become confined within the ionization chamber of Fig. 1 along the magnetic field lines produced inside by a set of permanent magnets. The propellant neutral gas (Argon and Xenon) introduced into this chamber at the constant rate $Q=dm/dt$ is ionized by these high energy electrons.

The ions move toward the extraction grid held fixed at the negative extraction potential $VEG=100−200V$⁠. Electrons are repelled and are finally captured at the walls of the ionization chamber. The unmagnetized ions are first extracted and then exit the cover grid accelerated by the electric field established between the grids. Finally, the positive charges neutralized by electrons from the cathode as shown in the scheme of Fig. 1.

Delivered impulse is essentially controlled by the propellant gas mass flow rate $Q$ and the acceleration voltage $VAC$⁠. In normal operation, the extraction potential is fixed to $VEG=150V$ and the cover grid potential is usually set to null to maximize the ion production and therefore the thruster performance.⁷ 

Since the ion production is interrupted by increasing the voltage $VCG$⁠,⁷ the thrust is also delivered without the need to shut off the entire electrical system (hollow cathode, power supplies, etc.). The electrical configuration of Fig. 1 allows two equal alphie thrusters to share the same voltage $VAC$ but different $VCG$ power supplies. Since this cover grid voltage can reduce or interrupt the thrust of each one separately, this two-thrusters set can provide a torque in addition to the thrust along the axial direction.

In the alphie design, only one cathode provides electrons for both ionization of propellant gas and ion beam neutralization, as in the HET scheme. Contrary to conventional GIE designs, no additional cathode is required inside the ionization chamber. Therefore, the alphie can be classified as a hybrid concept since it combines elements of GIE and HET thrusters. However, it differs from conventional gridded ion engines because both electrons and ions flow through its two-grid system.

At the steady state, the thruster current $IE≫IEG$ measures the flow of two particle species through the open spaces of the two-grid system. Positively and negatively charged particles are accelerated along opposite directions by the self-consistent electric field produced by the charge separation due to the electric potentials applied to the grids and the currents of electrons and ions.¹¹ 

The transport of ions and electrons through the two-grid system and the self-consistent electric field has been studied using PIC numerical simulations.^11,12 It constitutes a distinctive feature of the alphie concept compared to the conventional GIE scheme, where only positive ions move through the open spaces of the grids.¹ 

The steady IVDFs along the alphie plasma plume have been studied in the laboratory using a four-grids retarded field energy analyzer (RFEA), which provides the one-dimensional ion velocity spectrum along its $Z$ symmetry axis.^7,10,14 The details of the RFEA employed in our experiments are discussed in the  Appendix. Additionally, Langmuir (LP) and emissive (EP) probes are used to obtain the stationary electron energy distribution function (EEDF) and the plasma potential profile.^15,16

The alphie plasma thruster was installed on the side of a stainless steel vacuum tank 80 cm of length and 40 cm in diameter aligned with its axis of symmetry. The plasma diagnostics (RFEA, EP, and LP) were placed on a platform that can be moved in rectangular motions in all three directions $(X,Y,Z)$⁠, driven by three independent computer controlled stepper motors.

The probes face the thruster and can be displaced 300 mm from its exit section along the $Z$ axis of symmetry and 150 mm along the transverse $X$ and $Y$ directions. However, the minimum axial distance in the experiments was 50 mm, since prolonged exposure to infrared radiation emitted by the hot cathode wire can damage the probes. Details of the mechanical arrangement and plasma facility are also available in Refs. 7 and 10.

Figure 2 shows the waterfall superposition of ion velocity distribution functions $fi(viz)$ along 50–350 mm of the axis of symmetry of the plasma plume under two different operational conditions. These ion velocity spectra were obtained from the stationary RFEA current–voltage (IV) characteristic curves^7,10,14 as discussed in the  Appendix.

In Fig. 2, the constant mass flow rate of Argon injected into the alphie thruster was $Q=0.2SCCM$ (standard cubic centimeters by minute) and the neutral gas pressure in the vacuum tank was $pa=4.0×10−5mbar$⁠.

The total cross section for Argon ions with neutral atoms is the sum $σia=σel+σcx$ of the typical values of the elastic $σel≃2×10−15cm2$ and charge-exchange $σel≃3×10−15cm2$ collision cross sections.¹⁷ The mean free path for the above gas pressure was $λia∼2.6×103cm$⁠.

Electrons also have similar values $σea=σel+σtr$ sum of the elastic $σel≃5×10−16cm2$ and momentum transfer $σtr≃5×10−16cm2$ collision cross sections that give $λea∼1.8×103cm$⁠.

Both $λia$ and $λea$ average estimated mean free paths are much longer than the characteristic size (80 cm) of our vacuum tank, as well as those for all Argon gas pressures in the present study.

Therefore, the IVDFs in Fig. 2 are those of a collisionless plasma expansion along the axial direction. However, the peak heights of these velocity spectra decrease as the plasma stream expands, reflecting the reduction in the plasma density along the $Z$ axis.

For a low acceleration voltage of $VAC=350V$⁠, the thruster current is $IE=140mA$ and the velocity spectra of Fig. 2(a) show only one peak with a maximum speed around 23 km/s. When $VAC$ increases to 500 V, the heights of the IVDFs are higher and split into two different populations as in Fig. 2(b). The thruster current increases to $IE=200mA$ in this case since the ionization of propellant neutral gas increments.

The slow ion population in Fig. 2(b) is less sensitive to the acceleration potential $VAC$ than the group of fast ions. This last voltage acts as a throttle parameter since when $VAC$ is increased (or decreased), the maximum of the fast ion group shifts at higher (lower) velocities.^7,10

The two groups of ions in Fig. 2(b) move downstream of the plasma plume along the axial plasma potential profile $Vsp(z)$ of Fig. 3(a), obtained with the emissive probe by means of the inflection point method.¹⁵ The velocities corresponding to the maxima of the slow $vms≃15km/s$ and fast $vmf≃43km/s$ ion groups are represented in Fig. 3(b) against the axial $Z$ coordinate. Since the plasma expansion is collisionless, these values remain essentially unchanged in the plasma expansion process.

The IVDFs are measured in arbitrary units but can be compared with each other and Fig. 3(c) shows the heights $Ph(z)$ of the ion velocity spectra of Fig. 2(b) along the $Z$ axis. The peak height of the slow ion population decreases as $Ph(z)∼z−2$ with the axial distance $z$ faster than those of the high velocity ion group $Ph(z)∼z−1.47$ having a smaller exponent.

The ion temperatures of the slow $Tis$ and fast $Tif$ ion groups were determined from the ion energy distribution functions of Fig. 2(b) using the half width at half maximum (HWHM) approximation.^7,10 Both temperatures are represented in Fig. 3(d) and remain essentially constant $Tif≃62eV$ and $Tis≃35eV$ along the axial coordinate.

Because the temperatures from Fig. 3(d) and the peak velocities of the IVDFs in Fig. 3(b) remain essentially constant along the region studied, we can conclude that the collisional energy losses are negligible along the plasma plume expansion. These experimental results agree with the long mean free paths previously estimated for ion collisions.

As discussed in the  Appendix, the RFEA characteristic curve $Ic(VID)$ allows to discriminate the contributions of the slow and fast ions in the current collected at its end collector plate. This makes it possible to analyze the distribution of the current of fast ions with velocities parallel to the $Z$ axis over a transversal cross section of the plasma plume.

Figure 4 shows the spatial profiles of the fast ion current over two cross sections of the plasma plume. The big dots in these figures indicate the actual measurements of the fast ion current and the mesh is calculated by a numerical approximation. The acceleration voltages were $VAC=550V$⁠, the thruster currents $IE=200mA$⁠, and $Q=0.4SCCM$ in both cases.

Figure 4(a) for $z=150mm$ shows the sharp peak that exceeding $100μA$ located between $−$20 $≤X≤40$ and $−$20 $≤Y≤20$⁠. It is roughly centered within a circle defined by the projection of the open spaces of the alphie two-grid system and suggests that the fast ion group has moderate divergence angles.

Finally, in the transverse profile at $z=250mm$ in Fig. 4(b), the peaks vanish and the cross sectional distribution of fast ion current becomes smoother with values 75% below the maximum of Fig. 4(a). The current of fast ions with velocity parallel to the plasma plume axial of symmetry decreases in the plasma plume expansion process.

The current–voltage curves or the Langmuir probe along the $Z$ axis are shown in Fig. 5(a) and the corresponding EEDFs are in Fig. 5(b). The 4.44 mm in diameter spherical LP was placed facing the exit section of the alphie thruster and IV curves of $106$ data were acquired at a rate of 100 Hz using the fast sweep data acquisition system of Ref. 16. These curves were numerically approximated as those of RFEA for ions^7,10 and, using the values of the plasma potential profile of Fig. 3(a), the EEDFs in arbitrary units were obtained using the Druvystein method.¹⁵ 

The EEDFs in Fig. 5(b) along $z=50−250mm$ are the superposition of two non-Maxwellian electron groups with different average energies that merge approximately 250 mm away from the exit section of the alphie plasma thruster. In Fig. 5(b), the maximum of the high-energy electron group reduces its energy and the EEDF becomes very wide for $z∼175−250mm$⁠. Finally, for $z≳250mm$⁠, both populations merge to form a single electron group.

This process is shown in Fig. 6(a) where is represented the decreasing energy corresponding to the maximum of the fast electron group (open circles) along the $Z$ axis. On the contrary, those of the low-energy electron population (open diamonds) remain essentially constant. For $z≳250mm$⁠, both groups merge into a single electron population with one maximum whose velocity (solid triangles) still decreases along the plasma plume.

Figure 6(b) represents the temperatures of the fast, slow, and merged electron groups along the $Z$ coordinate. Temperatures were evaluated from the EDDFs using the HWHM approximation. The dispersion in the values for the low energy group reflects the effect of the large energy spread and reduced amplitude of this distribution when both groups merge.

These estimates of $Te$ between 7 and 2.5 eV give ion sound velocities in the range of 6.1–7.1 and 10–11 km/s, respectively, for the slow and fast ion groups of Fig. 2. Therefore, most ions leaving the alphie thruster have supersonic axial velocities, specifically, the ions of the fast group that moves along the $Z$ axis with speeds within the 35–50 km/s range.

The thrust delivered by the alphie plasma thruster for Argon propellant gas was measured using a thrust stand with a sensitivity of $δFs=0.3mN$⁠, which is the minimum impulse that can be realized over the noise level.¹⁸ For measurements in the 0–15 mN thrust range, its typical absolute errors are of $ΔF=±0.3mN$⁠. The details of thrust stand and data reduction are available in Ref. 19.

In Fig. 7 are represented the impulses delivered by the alphie plasma thruster as a function of the mass flow rate $Q$ at four $VAC$ acceleration potentials. Lines in the figure are numerical fits of experimental data for each acceleration voltage to facilitate its visualization.

In these experiments, the neutral gas pressures inside the vacuum tank were between $1.5−8×10−5mbar$ and the thruster currents of $IE=90−198mA$ for the 0.2–0.6 SCCM Argon mass flow rates. The thrusts delivered by the alphie thruster were in the range between 0.8 and 3.5 mN as shown in Fig. 7.

For the lower acceleration potentials $VAC=500V$ (open circles, dotted line) and $VAC=550V$ (open diamonds, dash-dotted line), thrusts are similar and their values are within their respective error bars. For $VAC=600V$ (open squares, dashed line), the thrusts are higher for $Q=0.5−0.6SCCM$⁠, whereas at $VAC=650V$ (open triangles, dash-dot-dot line) the relation between thrust and mass flow is approximately linear.

Figure 7 also shows the throttle capability of the acceleration potential $VAC$ at fixed $Q$ that ranges from 0.8 to 1.1 mN at $Q=0.2SCCM$ up to 2.1–3.5 mN for $Q=0.6SCCM$⁠.

The experimental data in Sec. III reveal the complex steady structure created by the expansion of the plasma stream from the alphie plasma thruster. The electron densities far from the plasma plume were evaluated at points for $z>250mm$⁠, where the EEDFs can be considered as approximately Maxwellians. For the electron temperatures of Fig. 6(b), the electron densities obtained from the electron saturation currents of the LP probe were in the $ne∼(0.1−8.0)×108cm−3$ range.²⁰ These give reference values for the Debye lengths of $λD∼6.0−0.64mm$⁠.

The propellant neutral gas is injected into the discharge chamber of the thruster, where ions are produced by electron impact ionization as discussed in Sec. II. These ionizing electrons, confined along the magnetic field lines, have typical energies of 400–750 eV controlled by the $VAC$ acceleration voltage.¹¹ Both ions and neutral atoms exit toward the vacuum tank through the open spaces of the two-grid system. When are confronted with the current of electrons from the cathode, resonant and non-resonant charge exchange collisions transform a fraction of the accelerated ions into fast neutral atoms.

The slow ion population originated by charge exchange collisions in Fig. 2 is produced within the orifices of the two-grid system and/or in the 4 mm wide gap between the cover grid and the neutralizing cathode. However, the measurements of Sec. III are for $z≥50mm$ and describe the collisionless expansion process of the plasma plume.

The IVDFs in Fig. 2 result from both the electric acceleration of ions and those produced by charge exchange collisions. Similar ion velocity spectra have been observed in plasma plumes of GIE and HET thrusters.^21,22 In Fig. 2(b), the maximum of the IVDF of the slow ion population has a velocity of $vms≃15km/s$ lower than that of the group of fast ions $vmf≃43km/s$⁠, the last is consistent with the applied $VAC$ potential.

The neutral atoms are unaffected by the electric field and enter into the vacuum tank by effusion through the holes of the two-grid system. Since all directions are equally likely, the directions of the atom exit velocities are distributed with hemispherical symmetry. They do not deviate from their original path as their collisional mean free paths are much longer than the dimensions of the plasma plume region. Therefore, the number of neutral atoms along any radial direction $r$ must be proportional to $r−2$ in this hemispherical expansion.

When a fast ion experiences a charge exchange collision with a neutral atom, the latter transforms in a slow ion, but both particles retain their initial energy and velocity. Therefore, the spatial profile of the slow ions has along the $Z$ axis is similar to those of neutral atoms. This is observed in Fig. 3(b) where the best fit of IVDF peak heights is proportional to $z−2$⁠.

Since the fast ion group is more focused than neutrals, the exponent of the corresponding fit $z−1.47$ has a lower value. Although the RFEA only measures ion current with velocities parallel to its $Z$ axis, Figs. 4(a) and 4(b) would confirm that fast ions are distributed over a smaller solid angle than slow ions produced by charge exchange collisions. On the contrary, slow ions and neutral atoms have a uniform distribution over hemispherical surfaces centered in the exit section of the thruster.

Figure 2(a) shows that, when the value of the acceleration potential is low, the two ion populations observed in Fig. 2(b) cannot be differentiated. Ions produced by charge exchange collisions and those accelerated by the electric field merge into a single group. For values $VAC<450V$⁠, it was not observed two distinct ion groups in the IVDFs. When the acceleration potential increases, the average velocity of fast ions rises and also the ionization rate of the propellant gas due to the higher energy of the ionizing electrons. Therefore, ion production and its acceleration are coupled processes in the alphie thruster and the acceleration potential $VAC$ acts as a throttle parameter since it controls the average velocity of the fast ion group.

Figures 3(b) and 3(d) show that the velocities (⁠$vms$⁠, $vmf$⁠) corresponding to the IVDFs maxima and the temperatures (⁠$Tis$⁠, $Tif$⁠) of both two ion groups remain essentially constant in the plasma expansion process. Since the ion motion is collisionless, the average value $⟨viz⟩$ for each group of ions remains constant. Also, the distribution of axial ion velocities $viz$ in the IVDFs around their averages.

The values of the temperatures $Tis≃30eV$ and $Tif≃62eV$ in Fig. 3(d) for both ion groups are high due to the neutral gas heating process that takes place inside the ionization chamber of the alphie thruster.

The electrons from the external cathode that enter the ionization chamber have energies controlled by $VAC$ in the 400–750 eV range and are confined therein along the magnetic field lines. The cross sections for elastic, momentum transfer, and ionization collisions for Argon have similar values¹⁷ of $(0.7−2.0)×10−15cm2$ for electron energies over 100 eV. Consequently, two processes take place simultaneously; the electron impact ionization and the collisional energy transfer to the neutral atoms. Although the propellant gas is injected at room temperature, collisions with high energy electrons considerably raise the average kinetic energy of atoms.

This energy exchange explains the extended velocity spectra and the high values of the ion temperatures (⁠$Tis$⁠, $Tif$⁠) in Figs. 2 and 3(d). The increase in the acceleration potential produces a double effect; it rises the average velocity of the ions and also the amount of energy transferred to the neutral atoms by collisions.

The dynamics of electrons along the axial direction of the plasma plume is more complex than that of ions. Along the axis of symmetry of the plasma plume, it is observed that the EEDFs are the superposition of two different electron populations. The existence of multiple electron groups with different energies in the plasma plume expansion has been reported in previous studies with Helicon plasma sources^23,24 and also in PIC numerical simulations.^5,6

Light electrons are more affected by changes in plasma potential in the axial direction. The maximum of $Vsp(z)$ in Fig. 3(a) between $z=80−100mm$ would be at the origin of the fast electron population. A local increase in the ion density develops in this region, which raises the plasma potential, accelerating electrons that form an important group of high average energy.

In Figs. 5(b) and 6(a), it is observed that between $z=150mm$ and $z=350mm$ both electron groups merge into a single population. Their temperatures change along the axial coordinate and the energy corresponding to the maximum of the fast electron group decreases. This thermalization process is not due to collisional energy losses, since for the working pressures the mean free paths for the ion-neutral and electron-neutral collisions are longer than the plasma expansion region studied.

The motion of heavy ions would be responsible for the monotonic fall of the plasma potential from $z=150mm$⁠. It reduces the average speed of fast electrons to drive the thermalization process of the two populations. Since the energetic electron group is larger, it absorbs the low energy population, resulting in a single, high temperature electron group far from the thruster.

The measured thrusts in Fig. 7 are the result of two physical mechanisms combined. First, the acceleration of ions in the self-consistent electric field. Second, the collisional energy transfer from ionizing electrons to the neutral gas, which reaches temperatures of the order of tens of electron volts. The effusion of this hot neutral gas through the orifices of the two-grid system also contributes to the impulse delivered by alphie thruster.

The specific impulses $Isp=F/(m˙go)$ obtained from thrusts in Fig. 7 are between $13900$ and $20000s$⁠. These values are higher than the ratio $vms/go≃4390s$ obtained with the drift velocity $vmf≃43km/s$ of the fast ion group in Fig. 3(b). The difference supports the existence of additional physical mechanisms that contributes to the impulse in the alphie thruster.

The alphie plasma thruster is a gridded ion engine different from the conventional GIE concept,^8,9 and Table I summarizes its basic performances. With only one external cathode, ions and electrons flow through the orifices of its two-grid system whereas only ions are transported through the ion optics of GIEs.⁷ Its operation voltages are lower than GIEs and around double than in HETs. The separation gap of 2–3 mm between the grids is larger compared to conventional GIEs (generally 1 mm) and makes this thruster less prone to breakdown and short circuits.

In the alphie, the electric charges are accelerated in the self-consistent electric field created by the charge separation caused by opposite currents of ions and electrons and the electric potentials connected to the grids and its ionization chamber. Since ions are accelerated in a plasma, the exit ion beam current is not space–charge limited. The basic physics of positive and negative charge transport by the electric field has been validated by PIC numerical simulations.^11,12

The alphie plasma plume expansion region along its symmetry axis has been investigated with a combination of RFEA, emissive, and Langmuir probes. The RFEA only provides the velocity spectrum $fi(viz)$ of the ion speed component $viz$ parallel to its axis of symmetry. Although the one-dimensional IVDFs are limited, along with EEDFs obtained with Langmuir and emitting probes provide important information on the structure of the plasma plume and charge acceleration processes. In the region studied, $z=50−350mm$ the motion of electrons and ions is collisionless since the mean free paths for elastic and inelastic encounters are much longer than the characteristic size of our vacuum tank.

The flow from the thruster is a mesothermal plasma with a non-monotone plasma potential profile $Vsp(z)$ along the region studied. The local concentration of ions would be responsible for the acceleration of electrons and two electron groups have been observed, as in flows from Helicon plasma sources^23,24 and PIC numerical simulations.^5,6 The two electron groups merge along the axial direction of plume following the changes in the plasma potential profile. Numerical simulations also predict different electron groups with variable temperatures along the plasma expansion region.^5,6

The ion populations observed are of those accelerated by the self-consistent electric field and the low velocity group that comes from charge-exchange processes, possibly due to non-linear effects in the thruster we are exploring with PIC and kinetic codes. The thruster is the only source of ions in our experiments, as we use a thermionic cathode as an electron source. The two ion groups merge when the acceleration potential and the group driven by the electric field separate as this potential is increased. Contrary to electrons, the two ion populations remain unaltered along the axial symmetry axis of the plasma plume.

Within the limited spatial resolution of the RFEA, we have observed the fast ion group with $viz>0$ is concentrated in the transversal section of the plasma plume inside a circle defined by the projection of the two-grid holes. Since ions also have a radial velocity component, the transversal concentration of fast ions decreases along the axial distance.

The high ion temperatures of both ion groups are explained by the heating of the neutral gas inside the discharge chamber by the high-energy ionizing electron group. The ionization and momentum transfer collisions cross section for electrons are similar for energies over $≃100eV$⁠. In these inelastic encounters, fast electrons trapped in the magnetic field transfer a fraction of its kinetic energy to heavy species, increasing the average kinetic energy of these particles.

The direct measurement of impulses delivered of 0.8–3.5 mN gives high specific impulses of 13 900–20 000 s, higher than low power HETs. The throttle capability of the alphie acceleration potential has also been verified. However, this parameter produces a double effect, to increase the velocity of ions and also the energy transferred to the neutral atoms inside the ionization chamber by collisions.

The elevated specific impulses can be explained by the high temperatures of both ion and neutral gas. The last leaks through the orifices of the two-grid system and might contribute to the thrust, similarly to other electric propulsion systems.

The authors are grateful for the technical assistance of Mr. F. Sánchez and Mr. J. Damba to the Spanish FPI fellowship program. This work was funded by the Ministerio de Ciencia Innovación y Universidades of Spain under Grant No. RT2018-094409-B-100.

The authors have no conflicts to disclose.

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

The RFEA measures the one-dimensional current of ions with velocities $uz>0$ parallel to its axis of symmetry and its fundamentals are discussed in Refs. 14 and 20. Figure 8 shows the longitudinal cross section scheme of the one we used in our experiments. It is made with cylindrical symmetry and has an end collecting plate and four grids, all equally spaced.

The flow of electrons and ions from the plasma pass through the first entrance grid (EG), held at the local floating potential. The plasma electrons are rejected by the second electron repeller (ER) grid set to the $VER=−30V$ voltage, thus only plasma ions reach the next ion discriminator (ID) grid. The voltage $VID$ of the latter can be varied, so only ions with kinetic energy $E≥eVID$ can reach the end ion collector plate to contribute to the RFEA current-voltage $(VID,IC)$ curve. The secondary electron suppressor (ES) grid is biased at $VES=−30V$ negative voltage and placed between the end plate and the ion discriminator grid. It is used to suppress the current of secondary electrons produced by energetic ions that impact the end collector plate.

The mesh used for all grids is 99% purity copper of $100μm$ thickness and varying 0.5–0.6 mm opening width. The four grids were aligned and a transparency of $T=18.6%$ for the set was determined by an optical method. The grids and the end plate are separated by $d=5mm$ from each other and were placed perpendicular to a cylindrical open channel of $23±0.1mm$ long with a diameter of $6.6±0.1mm$ where plasma particles move.

A computer-controlled power supply applied the voltage $VID=±500V$ to the discriminator grid and the ion current $Ic(VID)$ at its end collector plate was recorded using a digital multimeter Keithley 2000.^14,20 The resolution of RFEA^7,10 is $ΔE=±8eV$ for $400eV$ for single charged ions with velocities $viz>0$ parallel to the RFEA axis of symmetry. This is equivalent to $Δvir=±6km/s$ radial speed for ions with $viz=44km/s$⁠.

Assuming a perfect transparency of grids, the current density of ions of charge $e$ moving through the RFEA cylindrical open channel is $dJz=euzdni$ where $dni=niofi(z,uz)duz$ and $fi(z,uz)$ the ion velocity distribution at the $z$ coordinate.

For the fixed voltage $VID$ of the discriminator grid, only ions with kinetic energies $E≥eVID$ pass through and the minimum velocity of collected ions by the end collector plate is $umn=2eVID/mi$⁠, where $mi$ is the ion mass then

For a collector plate of surface $S$ and grid set of transparency $T<1$ to account for the ions lost at the grids, the collector plate current is

The derivation of $jz(z,eVID)$ with respect to $VID$ gives the ion energy distribution function (IEDF),

and substituting $umn=2eVID/mi$ the one-dimensional IVDF along the RFEA axis of symmetry can be obtained.

The calculation of the IEDF also requires the numerical evaluation of the derivative of the raw experimental data. In our case, the Savitzky–Golay algorithm was employed to approximate the experimental data⁷ and to evaluate the derivative of the IV curve. Figure 9 shows a typical curve of our RFEA and its numerical fit. The two separated plateaus indicate the existence of two groups of ions as shown in the IEDF calculated using Eq. (A1).

The currents corresponding to the slow $Is$ and fast ion $If$ groups can be evaluated using the above integral for $jz(z,eVd)$ and the voltage $Vr$ corresponding to the IEDF minimum between both groups of ions. The total ion current is obtained for the minimum energy $eVmn$ when all ions that enter in the RFEA are collected,

In Fig. 9, the ions of all energies contribute to the maximum current $Imx(z,eVmn)≃400μA$ at $Vmn≃−350V$⁠. The voltage $Vmn$ also corresponds to the minimum energy for the ions.

As the discriminator voltage $VID>Vmn$ grows, the current $Ic(z,eVd)$ decreases since only ions with enough kinetic energy reach the collector plate. For the voltage $Vr≃−30V$ in Fig. 9, all ions of the low energy group are rejected by the ion discriminator grid. Therefore, the measured ion current is

which is exactly the fast ion population current. Therefore, the ion current of the second plateau $Ir(z,eVr)≃120μA$ in Fig. 9 represents the contribution to the IV curve of fast ions and the difference,

is the current of the slow ion group. Both can be evaluated directly from the measured current $If(z,eVr)$ of the second plateau in the IV characteristic curve of the RFEA. Equations (A2) and (A3) were employed to evaluate the distribution of ion currents over a transversal section of the plasma plume in Fig. 4.