# Hollow Cathode and Low-Thrust Extraction Grid Analysis  for a

Authors: Richard Wirz; Regina Sullivan; JoHanna Przybylowski; Mike Silva
Journal: International Journal of Plasma Science and Engineering
 (2008)

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## Abstract

Miniature ion thrusters are well suited for future space missions that
require high efficiency, precision thrust, and low contamination in the mN to
sub-mN range. JPL's miniature xenon Ion (MiXI) thruster has demonstrated an
efficient discharge and ion extraction grid assembly using filament cathodes
and the internal conduction (IC) cathode. JPL is currently preparing to incorporate a miniature
hollow cathode for the MiXI discharge. Computational analyses anticipate that an axially
upstream hollow cathode location provides the most favorable performance and beam
profile; however, the hot surfaces of the hollow cathode must be sufficiently downstream
to avoid demagnetization of the cathode magnet at the back of the chamber, which can
significantly reduce discharge performance. MiXI's ion extraction grids are
designed to provide>3 mN of thrust; however, previous to this effort, the low-thrust
characteristics had not been investigated. Experimental results obtained with the
MiXI-II thruster (a near replica or the original MiXI thruster) show that sparse average
discharge plasma densities of ∼5×1015–5×1016m-3 allow the use of very low
beamlet focusing extraction voltages of only ∼250–500 V, thus providing thrust levels
as low as 0.03 mN for focused beamlet conditions. Consequently, the thrust range
thus far demonstrated by MiXI in this and other tests is 0.03–1.54 mN.


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## Body

## 1. Introduction

### 1.1. Background and Motivation

Ion thrusters are well known for their
ability to deliver continuous thrust at high efficiency (ηtot  ~60–70%, ηud  ~80–90%) and high
specific impulse (Isp  ~2 000–5 000 seconds)
with the use of benign propellants (e.g., xenon and argon). A miniature ion
thruster that can provide these performance advantages at a maximum thrust near
3 mN and minimum thrust <0.1 mN is attractive for a variety of
future space missions
[1].
Candidate mission include many of NASA’s and ESA’s Exoplanet finding
missions which require precision control of large spacecraft and formation
flying as well as Earth-orbiting missions that require precision orbit control.Historically, miniaturization of
ion thruster technologies has presented many design and performance challenges
that have put the concept out of reach for mission designers. However, recent
advancements have shown that reasonable performance is possible for small ion
thrusters if the development and validation of key technologies are continued. The miniature xenon ion (MiXI)
thruster, shown in Figure1, is a significantly scaled-down version of
conventional ion thrusters that has demonstrated an efficient discharge and a
high-performance ion extraction grid assembly [2]. Similarly to conventional
ion thrusters, the MiXI thruster uses electrons released from the cathode to
create a low-density (~1017 m−3) xenon plasma. The xenon
propellant can be introduced to the chamber through the back flange or through
the cathode if a hollow cathode is used. A 3-ring cusp magnetic field is used
to confine the plasma and improve discharge efficiency. Plasma ions are
accelerated out of the thruster at high velocities (~40,000 m/s) through the
ion extraction grid assembly by an applied thruster voltage of up to 1 kV, thus
providing high specific impulse of over 3 000 seconds. The physical
transparency of the screen grid is 0.67 and during ion extraction the
transparency is approximately 0.72–0.75 for the
conditions discussed herein. Additional
details on the thruster configuration and operation are given in Sections 2 and
3. Previous studies and performance tests with the MiXI have used filament
cathodes and the internal conduction (IC) cathode [2–4]. The IC cathode demonstrated high performance
but it is a risky
technology for ion thrusters due to its low maturity; therefore miniature
hollow cathodes were designed and built specifically for the MiXI thruster. In
future experimental investigations we will use one of these cathodes for the
thruster discharge and, as evident from other ion thruster discharge studies,
the axial location of the cathode has a strong effect on thruster performance.
Therefore, in this study, we use an ion thruster discharge model, DC-ION, to
help determine a favorable axial position of the hollow cathode within the discharge
before we position the cathode inside the thruster for testing [5].Figure 1
Miniature xenon ion (MiXI) thruster with basic schematic.Another important aspect of the
MiXI design is the miniature ion extraction grids. The MiXI grids are designed
to achieve thrust up to ~3.0 mN, and have thus far demonstrated high
performance at nominal thrust levels [4]. Since
MiXI is considered an attractive candidate for missions that require high precision and a
relatively large thrust range, this study investigates the minimum continuous
thrust that MiXI can achieve with the current grid set in an effort to find the
minimum thrust available for future candidate missions.


### 1.2. Objective

In Section2 computational
analysis is used to determine the optimal location of the hollow cathode in
MiXI’s discharge chamber. In Section 3 the MiXI ion extraction grid assembly is
experimentally and computationally characterized in the low-thrust regime to
determine the minimum thrust capability of the grids.


## 1.1. Background and Motivation

Ion thrusters are well known for their
ability to deliver continuous thrust at high efficiency (ηtot  ~60–70%, ηud  ~80–90%) and high
specific impulse (Isp  ~2 000–5 000 seconds)
with the use of benign propellants (e.g., xenon and argon). A miniature ion
thruster that can provide these performance advantages at a maximum thrust near
3 mN and minimum thrust <0.1 mN is attractive for a variety of
future space missions
[1].
Candidate mission include many of NASA’s and ESA’s Exoplanet finding
missions which require precision control of large spacecraft and formation
flying as well as Earth-orbiting missions that require precision orbit control.Historically, miniaturization of
ion thruster technologies has presented many design and performance challenges
that have put the concept out of reach for mission designers. However, recent
advancements have shown that reasonable performance is possible for small ion
thrusters if the development and validation of key technologies are continued. The miniature xenon ion (MiXI)
thruster, shown in Figure1, is a significantly scaled-down version of
conventional ion thrusters that has demonstrated an efficient discharge and a
high-performance ion extraction grid assembly [2]. Similarly to conventional
ion thrusters, the MiXI thruster uses electrons released from the cathode to
create a low-density (~1017 m−3) xenon plasma. The xenon
propellant can be introduced to the chamber through the back flange or through
the cathode if a hollow cathode is used. A 3-ring cusp magnetic field is used
to confine the plasma and improve discharge efficiency. Plasma ions are
accelerated out of the thruster at high velocities (~40,000 m/s) through the
ion extraction grid assembly by an applied thruster voltage of up to 1 kV, thus
providing high specific impulse of over 3 000 seconds. The physical
transparency of the screen grid is 0.67 and during ion extraction the
transparency is approximately 0.72–0.75 for the
conditions discussed herein. Additional
details on the thruster configuration and operation are given in Sections 2 and
3. Previous studies and performance tests with the MiXI have used filament
cathodes and the internal conduction (IC) cathode [2–4]. The IC cathode demonstrated high performance
but it is a risky
technology for ion thrusters due to its low maturity; therefore miniature
hollow cathodes were designed and built specifically for the MiXI thruster. In
future experimental investigations we will use one of these cathodes for the
thruster discharge and, as evident from other ion thruster discharge studies,
the axial location of the cathode has a strong effect on thruster performance.
Therefore, in this study, we use an ion thruster discharge model, DC-ION, to
help determine a favorable axial position of the hollow cathode within the discharge
before we position the cathode inside the thruster for testing [5].Figure 1
Miniature xenon ion (MiXI) thruster with basic schematic.Another important aspect of the
MiXI design is the miniature ion extraction grids. The MiXI grids are designed
to achieve thrust up to ~3.0 mN, and have thus far demonstrated high
performance at nominal thrust levels [4]. Since
MiXI is considered an attractive candidate for missions that require high precision and a
relatively large thrust range, this study investigates the minimum continuous
thrust that MiXI can achieve with the current grid set in an effort to find the
minimum thrust available for future candidate missions.


## 1.2. Objective

In Section2 computational
analysis is used to determine the optimal location of the hollow cathode in
MiXI’s discharge chamber. In Section 3 the MiXI ion extraction grid assembly is
experimentally and computationally characterized in the low-thrust regime to
determine the minimum thrust capability of the grids.


## 2. Sensitivity Analysis for Employing a Hollow Cathode in MiXI’s Discharge Chamber

In this section JPL’s DC-
ION computational
model is used to anticipate the performance of the MiXI thruster for a range of
hollow cathode axial locations and cathode magnet strengths. These results will
guide future experiments in which MiXI’s miniature hollow cathodes will be used
as the discharge and neutralizer electron sources.


### 2.1. Miniature, Low-Flow Hollow Cathodes

Previous investigations show that attractive
performance is possible for the MiXI thruster with low-power electron sources
such as the hollow cathodes used in conventional ion thrusters. Hollow cathodes are a mature technology and
typically require less power per amp of emitted electrons than other discharge
cathode options. Cathodeless discharge options, such as the microwave and rf
discharges discussed in [3], will be investigated for the MiXI thruster if the
high efficiency of cathode discharges is not achieved with cathode options. Conventional-sized
hollow cathodes require a designated propellant feed (>1 sccm) that
can exceed the propellant needs for the entire MiXI discharge chamber
(typically 0.05–0.5 sccm),
which, may result in very low efficiencies and poor throttleability [3]. Previous
investigations into small hollow cathodes with a 1.22 mm insert ID have shown
that scaling down to the discharge currents and propellant flow rates of the
MiXI thruster (JD  ~50–500 mA and
0.2–1.0 sccm,
resp.) is difficult if the cathode is to run efficiently in self-heated
mode [5–7]. To address this challenge, JPL designed and built two miniature
hollow cathodes (Figure 2) specifically for MiXI’s low-flow and current
conditions. These hollow cathodes are a scaled-down version of conventional
hollow cathodes. They are designed to have sufficiently high current capacity
so that they may scale to larger ion thruster sizes (>3 cm) and small Hall
thrusters, and may also provide a reliable and efficient option for neutralizing
the plumes of other small electric propulsion thrusters such as electrospray
(i.e., colloid and FEEP) thrusters.Figure 2
MiXI’s miniature hollow cathodes.


### 2.2. Hollow Cathode Axial Location Analysis

In this study, JPL’s ion thruster
model (DC-ION) simulates MiXI thruster performance at a range of axial
locations of a miniature hollow cathode inside the discharge. For ring cusp
discharges of this orientation, the axial placement of the cathode (for a given
magnetic field geometry) can drastically change the paths the electrons take to
the anode and hence the quality of the electron confinement; which, in turn,
can greatly affect ionization efficiency and performance. Details of the DC-
ION model and hollow
cathode simulations with DC-ION are given in [4, 8, 9]. For
this analysis, the entire discharge propellant flow is assumed to come from the
hollow cathode. The primary electrons produced from the hollow cathode exit are
assumed to exhibit an accelerated half-Maxwellian velocity distribution as used
for the hollow cathode input for the NSTAR thruster in [5]. At this time, the hollow cathode is assumed to operate at similar voltages and
electron tempe
ratures
as the NSTAR hollow cathode at TH12, resulting in the model inputs shown in Table 1 for nominal MiXI operation.Table 1
MiXI Throttle Point THM1.
Total flow [sccm]JD [mA]VD [V]JB [mA]VB [V]VA [V]Model specific inputsVp [V]Tp [eV]0.2928025.0~201000−20020.03.0The DC-ION discharge model was
used to compare the propellant efficiency and beam flatness for several hollow
cathode orifice plate and grid separation distances; which are shown as “x” in Figure 3 and are normalized by the discharge length “L.” Results from the DC-ION analysis shown in Figure 4 suggest that an upstream
cathode location ion thrusters yields the best propellant efficiency and beam
profile for nominal MiXI operation. Upstream cathode placements are also used
in larger ion thrusters to increase the field-free region available for
ionization. One must be careful to place the cathode orifice beyond the
magnetic maximum of the cathode magnet ring to avoid magnetic mirror effects;
therefore, the maximum x/L (i.e., 0.67)
is forward of the local cathode ring maximum in the MiXI discharge. Moving the
cathode further upstream (i.e., x/L>0.67) is also undesirable since the cathode heat can possibly demagnetize the
cathode magnets, as discussed later. Figure
5 gives the beam profiles for all the configurations
investigated herein and shows that the beam profile progressively peaks on-axis
as the hollow cathode is located closer to the extraction grids. This behavior
for closer spacing is due to the fact that the electrons emitted by the cathode
have a smaller distance to undergo a collision that will cause them to more
readily diffuse away the thruster axis where they will create more ions
off-axis, resulting in a flatter profile.Figure 3
Basic MiXI configuration showing axial distance between cathode face and screen grid,x, and discharge chamber length, L.Figure 4
Anticipated MiXI performance versus Cathode/Grid spacing
(x/L) using baseline MiXI configuration. Results
generated by DC-ION model.Figure 5
Anticipated MiXI beam profiles versus Cathode/Grid spacing
(x/L) using baseline MiXI configuration. Results
generated by DC-ION model.


### 2.3. Magnetic Field Analysis

Currently, MiXI employs a
relatively weak cathode magnet since favorable performance was found with
filament discharges in previous efforts [2]; however, conventional ion thrusters (such as
NASA’s NSTAR thruster), which use hollow cathodes, typically use high cathode
magnet strengths. Therefore, when MiXI uses a hollow cathode in the discharge,
it may prove beneficial to strengthen the cathode magnet as done in
conventional ion thrusters. At the other extreme, due to the small size of the
MiXI discharge, there is some concern that the heat from the hollow cathode may
demagnetize the cathode magnet, especially if the cathode is positioned far
upstream. To address these potential scenarios, DC-ION runs were used to simulate the impact
of changing MiXI’s cathode magnet strength. In the following analysis, “High Field”
is the condition where cathode magnet strength is increased by a factor of two by doubling the
dimension along the magnetization direction, while “Low Field” assumes the
cathode magnet has been entirely demagnetized by cathode heat (in the computations
the magnet strength was set to zero). Previous
experimental results show that loss of the cathode magnet can reduce the
discharge performance by over 10% [4]. Figure 7 shows the anticipated performance for the Baseline, High
Field, and Low Field configurations at cathode locations x/L=0.42 and 0.67. These x/L conditions were chosen since they give the two highest propellant efficiencies
and represent downstream and upstream cathode positions, respectively. Figure
6 shows the beam profiles for these scenarios. As expected, the performance effects are most
pronounced when the cathode is in the most upstream position (i.e., x/L=0.67), closest to the cathode
magnet.Anticipated MiXI thruster performance versus Cathode/Grid spacing (x/L) at different cathode magnet strengths. Results generated by DC-ION model.
(a)(b)Anticipated MiXI thruster performance for different MiXI cathode magnet strengths.
Results generated by DC-ION model.
(a)(b)


## 2.1. Miniature, Low-Flow Hollow Cathodes

Previous investigations show that attractive
performance is possible for the MiXI thruster with low-power electron sources
such as the hollow cathodes used in conventional ion thrusters. Hollow cathodes are a mature technology and
typically require less power per amp of emitted electrons than other discharge
cathode options. Cathodeless discharge options, such as the microwave and rf
discharges discussed in [3], will be investigated for the MiXI thruster if the
high efficiency of cathode discharges is not achieved with cathode options. Conventional-sized
hollow cathodes require a designated propellant feed (>1 sccm) that
can exceed the propellant needs for the entire MiXI discharge chamber
(typically 0.05–0.5 sccm),
which, may result in very low efficiencies and poor throttleability [3]. Previous
investigations into small hollow cathodes with a 1.22 mm insert ID have shown
that scaling down to the discharge currents and propellant flow rates of the
MiXI thruster (JD  ~50–500 mA and
0.2–1.0 sccm,
resp.) is difficult if the cathode is to run efficiently in self-heated
mode [5–7]. To address this challenge, JPL designed and built two miniature
hollow cathodes (Figure 2) specifically for MiXI’s low-flow and current
conditions. These hollow cathodes are a scaled-down version of conventional
hollow cathodes. They are designed to have sufficiently high current capacity
so that they may scale to larger ion thruster sizes (>3 cm) and small Hall
thrusters, and may also provide a reliable and efficient option for neutralizing
the plumes of other small electric propulsion thrusters such as electrospray
(i.e., colloid and FEEP) thrusters.Figure 2
MiXI’s miniature hollow cathodes.


## 2.2. Hollow Cathode Axial Location Analysis

In this study, JPL’s ion thruster
model (DC-ION) simulates MiXI thruster performance at a range of axial
locations of a miniature hollow cathode inside the discharge. For ring cusp
discharges of this orientation, the axial placement of the cathode (for a given
magnetic field geometry) can drastically change the paths the electrons take to
the anode and hence the quality of the electron confinement; which, in turn,
can greatly affect ionization efficiency and performance. Details of the DC-
ION model and hollow
cathode simulations with DC-ION are given in [4, 8, 9]. For
this analysis, the entire discharge propellant flow is assumed to come from the
hollow cathode. The primary electrons produced from the hollow cathode exit are
assumed to exhibit an accelerated half-Maxwellian velocity distribution as used
for the hollow cathode input for the NSTAR thruster in [5]. At this time, the hollow cathode is assumed to operate at similar voltages and
electron tempe
ratures
as the NSTAR hollow cathode at TH12, resulting in the model inputs shown in Table 1 for nominal MiXI operation.Table 1
MiXI Throttle Point THM1.
Total flow [sccm]JD [mA]VD [V]JB [mA]VB [V]VA [V]Model specific inputsVp [V]Tp [eV]0.2928025.0~201000−20020.03.0The DC-ION discharge model was
used to compare the propellant efficiency and beam flatness for several hollow
cathode orifice plate and grid separation distances; which are shown as “x” in Figure 3 and are normalized by the discharge length “L.” Results from the DC-ION analysis shown in Figure 4 suggest that an upstream
cathode location ion thrusters yields the best propellant efficiency and beam
profile for nominal MiXI operation. Upstream cathode placements are also used
in larger ion thrusters to increase the field-free region available for
ionization. One must be careful to place the cathode orifice beyond the
magnetic maximum of the cathode magnet ring to avoid magnetic mirror effects;
therefore, the maximum x/L (i.e., 0.67)
is forward of the local cathode ring maximum in the MiXI discharge. Moving the
cathode further upstream (i.e., x/L>0.67) is also undesirable since the cathode heat can possibly demagnetize the
cathode magnets, as discussed later. Figure
5 gives the beam profiles for all the configurations
investigated herein and shows that the beam profile progressively peaks on-axis
as the hollow cathode is located closer to the extraction grids. This behavior
for closer spacing is due to the fact that the electrons emitted by the cathode
have a smaller distance to undergo a collision that will cause them to more
readily diffuse away the thruster axis where they will create more ions
off-axis, resulting in a flatter profile.Figure 3
Basic MiXI configuration showing axial distance between cathode face and screen grid,x, and discharge chamber length, L.Figure 4
Anticipated MiXI performance versus Cathode/Grid spacing
(x/L) using baseline MiXI configuration. Results
generated by DC-ION model.Figure 5
Anticipated MiXI beam profiles versus Cathode/Grid spacing
(x/L) using baseline MiXI configuration. Results
generated by DC-ION model.


## 2.3. Magnetic Field Analysis

Currently, MiXI employs a
relatively weak cathode magnet since favorable performance was found with
filament discharges in previous efforts [2]; however, conventional ion thrusters (such as
NASA’s NSTAR thruster), which use hollow cathodes, typically use high cathode
magnet strengths. Therefore, when MiXI uses a hollow cathode in the discharge,
it may prove beneficial to strengthen the cathode magnet as done in
conventional ion thrusters. At the other extreme, due to the small size of the
MiXI discharge, there is some concern that the heat from the hollow cathode may
demagnetize the cathode magnet, especially if the cathode is positioned far
upstream. To address these potential scenarios, DC-ION runs were used to simulate the impact
of changing MiXI’s cathode magnet strength. In the following analysis, “High Field”
is the condition where cathode magnet strength is increased by a factor of two by doubling the
dimension along the magnetization direction, while “Low Field” assumes the
cathode magnet has been entirely demagnetized by cathode heat (in the computations
the magnet strength was set to zero). Previous
experimental results show that loss of the cathode magnet can reduce the
discharge performance by over 10% [4]. Figure 7 shows the anticipated performance for the Baseline, High
Field, and Low Field configurations at cathode locations x/L=0.42 and 0.67. These x/L conditions were chosen since they give the two highest propellant efficiencies
and represent downstream and upstream cathode positions, respectively. Figure
6 shows the beam profiles for these scenarios. As expected, the performance effects are most
pronounced when the cathode is in the most upstream position (i.e., x/L=0.67), closest to the cathode
magnet.Anticipated MiXI thruster performance versus Cathode/Grid spacing (x/L) at different cathode magnet strengths. Results generated by DC-ION model.
(a)(b)Anticipated MiXI thruster performance for different MiXI cathode magnet strengths.
Results generated by DC-ION model.
(a)(b)


## 3. Low Thrust Analysis for Extraction Grids

In this section a combination of
experimental and computational investigations are used to assess the low thrust
characteristics of the MiXI ion extraction grids.


### 3.1. Ion Extraction at Low Thrust Levels

The plasma sheath immediately
upstream of the ion extraction grids will change shape based on the
extractor geometry, voltages, and plasma properties. In general, for given
upstream plasma properties and extractor geometry, the sheath will increase in
size with increasing total voltage,VT,
to provide the space-charge current determined by the Child-Langmuir law [10]. Figure 8 shows how the sheath adjusts at different total voltage values (assuming all other properties, such as
upstream plasma density, are constant). In this figure Vfoc is the limit below which we observe direct ion
impingement on the accel grid, and Vxo is the voltage beyond which we observe cross-over impingement on the accel grid.
The process of changing VT to achieve the nominal operating condition in Figure
8(a) is called
“focusing.” From this behavior one can also see that increasing the
discharge chamber plasma density increases the current density at the screen
hole plasma sheath, thus increasing Vfoc for a given grid geometry.Screen hole plasma sheath and ion trajectory envelope for
constant upstream plasma conditions. (a) Nominal
(Vxo>VT>Vfoc), (b) direct impingement (VT<Vfoc), (c) cross-over impingement
(VT>Vxo).
(a)(b)(c)


### 3.2. Experimental Testing Apparatus

A second lab model of the 3 cm
diameter MiXI thruster “MiXI-II” for characterization of MiXI components,
performance, and beam. MiXI-II is identical to the original 3-ring cusp MiXI
thruster [1] except that the thruster mount (at the aft end of the thruster) is
simplified and the grid mounts were modified to provide improved contact between the grids and
the electrical leads. Figure 9
shows MiXI-II mounted in the vacuum chamber. As shown
schematically in Figure 9, MiXI uses a 3-ring cusp discharge that is 3 cm in
diameter with two ion extraction grids at the downstream end of the discharge. In
this study, MiXI-II is used to analyze the grid performance at low thrust levels.MiXI-II thruster with plasma screen ((a), note filament
neutralizer) and without plasma screen (b). A schematic of the
MiXI 3-ring configuration is shown at (c).
(a)(b)(c)


#### 3.2.1. MiXI’s High-Performance Extraction Grids

A combination of experimental and
computational analyses
was used to design the MiXI grids [2]. These
grids provide high performance since they employ a small hole accelerator grid (SHAG)
design that exhibits low neutral transparency while still providing sufficient
ion transparency to allow over 3 mN of thrust. As described in [1], the current MiXI grid set was designed with
relatively high grid thickness to provide longer grid life and lower susceptibility
to thermal deflections relative to earlier designs. The maximum thrust capacity
with the current MiXI grid set is ~3 mN (assuming a conservative beam flatness
of 0.52, typical MiXI beam flatness is over 0.6). In this analysis we investigate
the lower thrust limit of the MiXI grid set by examining the direct impingement
limits with computational and experimental analyses. For this investigation, MiXI-II uses
filament cathodes for the neutralizer (shown in Figure 9) and discharge electron sources to provide a simple
robust system for grid performance analysis. The use of a discharge filament
cathode, as opposed to a hollow cathode, will have some effect on overall
performance (increased cathode heater power and likely reduced propellant efficiency) but should
not dramatically change the discharge performance. Depending on cathode
location, the filament will likely provide a similar but different beam profile
when compared with a hollow cathode (possibly flatter due to the more
omnidirectional electron emission behavior of the cathode, but similar due to
the relatively high average magnetic field strength within the MiXI discharge).


#### 3.2.2. Vacuum Facility

The experiment was conducted in the 2 m diameter vacuum chamber (see Figure10) outfitted with 3 diffusion pumps and 2 cryopumps, as
well as several mechanical pumps. In these experiments, only the diffusion
pumps were used. The vacuum achievable with these pumps was between 1×10−6 and 5×10−6 Torr depending on propellant flow rate. The MiXI-II
thruster was pointed along the chamber axis towards the far end of the chamber,
and was offset horizontally 0.15 m from the centerline.Figure 10
JPL’s building 149 vacuum chamber  (2 m diameter).


### 3.3. Experimental Analysis of Low Thrust Regime

During each test, the discharge current,JD,
was set at a
specified value while the total voltage between the two grids, VT, was varied. Discharge
voltage, VD, was held at
25 V for all tests. To simulate a steady discharge with a constant ion
density, the discharge current was held within 5% of the reported average value
over the entire range of total extraction voltage. As expected, with increasing
total voltage, JB reaches
a near-constant maximum value while JA reaches a near-constant minimum value for all the discharge current levels. The
data in Figure 11
show that the beam “focuses” at increasing voltages
for increasing discharge current level and that cross-over impingement is not
achieved for the densities and voltages investigated.JB and JA  for low JD
values for MiXI-II.
(a)(b)(c)(d)This experiment was primarily aimed at the low-discharge current regime
since potential missions considering the MiXI thruster, such as NASA’s exoplanet
finding missions and the Space Interferometer Mission (SIM), desire that MiXI
produces thrust over a large thrust range, mN to sub-mN levels. Therefore, test cases were conducted with
very low discharge currents (i.e., <20 mA). Two test cases at low
discharges are shown in Figure12. For an average JD of 17 mA, the focusing voltage, Vfoc,
at which JA and JB become approximately
constant occurs at around 400 to 450 V. For the 13 mA case, this appears to
occur at around 450 to 50 V, although it is difficult to tell the exact point
due to the inconsistencies in the data trend (especially the JA curve). During data
acquisition, the low JD test cases exhibited more noticeable fluctuations in JB and JA than those conducted at higher values of   JD,
so approximate values are reported. Further
examination is needed to explain why the focusing voltage and maximum beam
current are greater for the 13 mA versus the 17 mA case, which is contrary to the
expected trends from Figure
11. The increase in JA at higher voltages for the 17 mA case does not
appear to signify cross-over impingement due to the constantly increasing
levels of beam current.JB  and JA  for very low JD  values for MiXI-II.
(a)(b)The results in Figures11
and 12 follow the expected space-charge current limited
operation where the “focusing voltage”
increases with upstream ion density (or in this case, discharge current). This
is apparent in Figures 13 and 14
where all data are plotted on the same scale for
comparison with the computational data in the following section.Figure 13
Summary of beam current data.Figure 14
Summary of accel grid data.


### 3.4. Computational Analysis of Low Thrust Regime

The 2D ion optics model, CEX2D, was
used to simulate single beamlets of the MiXI grid geometry over a range of
upstream plasma densities and extraction voltages [8]. For the calculations
performed herein, the model requires grid geometry, grid voltages, upstream
plasma density, upstream electron temperature, and downstream electron temperature.
The plasma density is inferred as discussed below while the electron
temperatures are assumed equal to experimental values from similar experiments
[4]. As shown in Figure 15, the CEX2D model outputs example ion trajectories that
demonstrate the transition from direct-impingement to focused beamlet
conditions.Example of beam focusing forVB−VA=250V (a)
and for VB−VA=550V (b). Bottom of figures are the centerline of a axisymmetric beamlet.
Results produced by CEX2D.
(a)(b)The CEX2D model demonstrates the
behavior of a single beamlet. To predict the total beam current,JB, from CEX2D’s beamlet current
density, jB, we assumed an
average beam flatness, FB, over the MiXI grid area, such that (1)JB≈FB⋅jBπrgrid2, where jB is the current density
over the “hexagonal” computational area simulated by CEX2D [11]. We used a relatively low value for beam
flatness of only 0.52, a minimum of the beam flatness from previous MiXI beam profiles
at low discharge currents. For this first-order analysis, the beamlets are
assumed to exhibit identical focusing voltages as the beamlet modeled by CEX2D
(a more complete analysis would include consideration of the focusing behavior
at the range of densities typically found across the grid surface). Therefore, the average upstream plasma
density assumed inside the plasma discharge is obtained by multiplying the beam
flatness by the plasma density that is used by CEX2D to provide agreement with
the experimentally measured value of total beam current per the above equation.
Therefore, the upstream plasma densities are inferred from the measured total beam
current and are not directly measured. For these approximations, Figure 16
shows the expected beam current for a range of
extraction voltages for different average upstream plasma densities. As
expected, these results yield a narrow range of focusing voltages from 350 to 450 V
due to the single beamlet approximation, which is independent of the radial
distribution of densities upstream for an actual grid set. For the same reasons,
the accel grid current from the computational results quickly drops to zero over a small voltage range, as
shown in Figure 17.Figure 16
Beam
current versus accelerating voltage for averaged discharge plasma densities
(m−3). Results averaged from
CEX2D beamlet results.Figure 17
Accel grid current versus total voltage
for averaged discharge plasma densities (m−3). Accel current values
are zero from 600 to 1300 V. Results averaged from CEX2D beamlet results.


### 3.5. Discussion of Low-Thrust Analysis of Extraction Grids

#### 3.5.1. Discussion of Experimental Results

For the experimental results, beam
focusing is the region of simultaneous decrease inJA and an increase in JB; and the value at which these currents both reach a
near zero slope is the focusing voltage, Vfoc. The focusing voltages and maximum beam
currents for the different discharge currents used in the experimental tests are
shown in Figure 18. The general trend of increased focusing voltage and
beam current for higher discharge current is expected as discussed in Section 3
and in [2, 9]. Further investigation is needed to explain the
increase in focusing voltage and beam current at the lowest discharge current
(13 mA) value. During the experimental tests, the extraction voltage was
increased beyond Vfoc in
an attempt to achieve
cross-over impingement; however, this point was not reached since increasing
the beam voltage beyond 1000 V caused the grids to short for these tests. The
relatively high ratio of JA/JB measured suggests that
low-thrust operation may lead to decreased grid life due to direct impingement.
Additional efforts are needed to determine to what level the high accel current
is caused by variation in upstream plasma density (low-beam flatness) which can
lead to cross-over impingement at the high radial gridlet locations. Also,
long-term erosion predictions and assessments will be needed to assess grid
life for given mission profiles.Figure 18
Focusing voltage and maximum beam current versus
discharge currents used in experimental tests.


#### 3.5.2. Comparison of Experimental Results and Computational Results

The computational results produce qualitative trends similar to those found in the measured data; however, the transition toVfoc occurs much more sharply in the computational data. This is due to the simplifying assumption in the computational analysis that characteristics of one beamlet represent the behavior of all beamlets. For actual ion thrusters, the radial variation in the ion density in the discharge chamber leads to a variation in focusing voltage across the grid surface. Thus the transition to focused operation should be more gradual as seen in the measured data. Also, the prediction of zero accel current is not realized in the measured data. After focusing occurs, we see a nominal accel current of at least 0.3 mA in the measured data, which is likely an effect of the nonuniform ion density, variation in the MEMS-fabricated hole sizes, and impingement of charge-exchange ions on the downstream surface of the accel grid. For these reasons, this first-order computational analysis also under-predicts the focusing voltage and over-predicts the rate at which the beam focuses. However, these effects do not greatly affect the total beam current predicted by the model and by comparing the maximum beam current values from the experimental (Figure 13)  and computational data (Figure 16) we can approximate the average discharge plasma
densities for the discharge currents used in the experiment. This comparison
yields the correlation of average discharge plasma density and discharge
current shown in Figure 19. Also in Figure
19, we approximate the thrust at the focusing voltages for each condition, assuming no beam divergence
or double ions losses [4].Figure 19
Approximate thrust and average discharge plasma density versus discharge
current.In light of the needs of future
efforts, it would be helpful for the CEX2D grid model to facilitate the
simulation of an entire grid set for a given upstream density profile as opposed
to single gridlets. Another possible improvement to the CEX2D model would be to
randomize the initial velocity direction of the ions that enter the plasma
sheath (currently the model assumes the ions enter the sheath with Bohm
velocity parallel to the beamlet axis), this modification would likely give a
more realistic value for direct accel grid impingement, that is, nonzero values
for focused cases, if a sufficient number of particles are used in the
simulation.


## 3.1. Ion Extraction at Low Thrust Levels

The plasma sheath immediately
upstream of the ion extraction grids will change shape based on the
extractor geometry, voltages, and plasma properties. In general, for given
upstream plasma properties and extractor geometry, the sheath will increase in
size with increasing total voltage,VT,
to provide the space-charge current determined by the Child-Langmuir law [10]. Figure 8 shows how the sheath adjusts at different total voltage values (assuming all other properties, such as
upstream plasma density, are constant). In this figure Vfoc is the limit below which we observe direct ion
impingement on the accel grid, and Vxo is the voltage beyond which we observe cross-over impingement on the accel grid.
The process of changing VT to achieve the nominal operating condition in Figure
8(a) is called
“focusing.” From this behavior one can also see that increasing the
discharge chamber plasma density increases the current density at the screen
hole plasma sheath, thus increasing Vfoc for a given grid geometry.Screen hole plasma sheath and ion trajectory envelope for
constant upstream plasma conditions. (a) Nominal
(Vxo>VT>Vfoc), (b) direct impingement (VT<Vfoc), (c) cross-over impingement
(VT>Vxo).
(a)(b)(c)


## 3.2. Experimental Testing Apparatus

A second lab model of the 3 cm
diameter MiXI thruster “MiXI-II” for characterization of MiXI components,
performance, and beam. MiXI-II is identical to the original 3-ring cusp MiXI
thruster [1] except that the thruster mount (at the aft end of the thruster) is
simplified and the grid mounts were modified to provide improved contact between the grids and
the electrical leads. Figure 9
shows MiXI-II mounted in the vacuum chamber. As shown
schematically in Figure 9, MiXI uses a 3-ring cusp discharge that is 3 cm in
diameter with two ion extraction grids at the downstream end of the discharge. In
this study, MiXI-II is used to analyze the grid performance at low thrust levels.MiXI-II thruster with plasma screen ((a), note filament
neutralizer) and without plasma screen (b). A schematic of the
MiXI 3-ring configuration is shown at (c).
(a)(b)(c)


### 3.2.1. MiXI’s High-Performance Extraction Grids

A combination of experimental and
computational analyses
was used to design the MiXI grids [2]. These
grids provide high performance since they employ a small hole accelerator grid (SHAG)
design that exhibits low neutral transparency while still providing sufficient
ion transparency to allow over 3 mN of thrust. As described in [1], the current MiXI grid set was designed with
relatively high grid thickness to provide longer grid life and lower susceptibility
to thermal deflections relative to earlier designs. The maximum thrust capacity
with the current MiXI grid set is ~3 mN (assuming a conservative beam flatness
of 0.52, typical MiXI beam flatness is over 0.6). In this analysis we investigate
the lower thrust limit of the MiXI grid set by examining the direct impingement
limits with computational and experimental analyses. For this investigation, MiXI-II uses
filament cathodes for the neutralizer (shown in Figure 9) and discharge electron sources to provide a simple
robust system for grid performance analysis. The use of a discharge filament
cathode, as opposed to a hollow cathode, will have some effect on overall
performance (increased cathode heater power and likely reduced propellant efficiency) but should
not dramatically change the discharge performance. Depending on cathode
location, the filament will likely provide a similar but different beam profile
when compared with a hollow cathode (possibly flatter due to the more
omnidirectional electron emission behavior of the cathode, but similar due to
the relatively high average magnetic field strength within the MiXI discharge).


### 3.2.2. Vacuum Facility

The experiment was conducted in the 2 m diameter vacuum chamber (see Figure10) outfitted with 3 diffusion pumps and 2 cryopumps, as
well as several mechanical pumps. In these experiments, only the diffusion
pumps were used. The vacuum achievable with these pumps was between 1×10−6 and 5×10−6 Torr depending on propellant flow rate. The MiXI-II
thruster was pointed along the chamber axis towards the far end of the chamber,
and was offset horizontally 0.15 m from the centerline.Figure 10
JPL’s building 149 vacuum chamber  (2 m diameter).


## 3.2.1. MiXI’s High-Performance Extraction Grids

A combination of experimental and
computational analyses
was used to design the MiXI grids [2]. These
grids provide high performance since they employ a small hole accelerator grid (SHAG)
design that exhibits low neutral transparency while still providing sufficient
ion transparency to allow over 3 mN of thrust. As described in [1], the current MiXI grid set was designed with
relatively high grid thickness to provide longer grid life and lower susceptibility
to thermal deflections relative to earlier designs. The maximum thrust capacity
with the current MiXI grid set is ~3 mN (assuming a conservative beam flatness
of 0.52, typical MiXI beam flatness is over 0.6). In this analysis we investigate
the lower thrust limit of the MiXI grid set by examining the direct impingement
limits with computational and experimental analyses. For this investigation, MiXI-II uses
filament cathodes for the neutralizer (shown in Figure 9) and discharge electron sources to provide a simple
robust system for grid performance analysis. The use of a discharge filament
cathode, as opposed to a hollow cathode, will have some effect on overall
performance (increased cathode heater power and likely reduced propellant efficiency) but should
not dramatically change the discharge performance. Depending on cathode
location, the filament will likely provide a similar but different beam profile
when compared with a hollow cathode (possibly flatter due to the more
omnidirectional electron emission behavior of the cathode, but similar due to
the relatively high average magnetic field strength within the MiXI discharge).


## 3.2.2. Vacuum Facility

The experiment was conducted in the 2 m diameter vacuum chamber (see Figure10) outfitted with 3 diffusion pumps and 2 cryopumps, as
well as several mechanical pumps. In these experiments, only the diffusion
pumps were used. The vacuum achievable with these pumps was between 1×10−6 and 5×10−6 Torr depending on propellant flow rate. The MiXI-II
thruster was pointed along the chamber axis towards the far end of the chamber,
and was offset horizontally 0.15 m from the centerline.Figure 10
JPL’s building 149 vacuum chamber  (2 m diameter).


## 3.3. Experimental Analysis of Low Thrust Regime

During each test, the discharge current,JD,
was set at a
specified value while the total voltage between the two grids, VT, was varied. Discharge
voltage, VD, was held at
25 V for all tests. To simulate a steady discharge with a constant ion
density, the discharge current was held within 5% of the reported average value
over the entire range of total extraction voltage. As expected, with increasing
total voltage, JB reaches
a near-constant maximum value while JA reaches a near-constant minimum value for all the discharge current levels. The
data in Figure 11
show that the beam “focuses” at increasing voltages
for increasing discharge current level and that cross-over impingement is not
achieved for the densities and voltages investigated.JB and JA  for low JD
values for MiXI-II.
(a)(b)(c)(d)This experiment was primarily aimed at the low-discharge current regime
since potential missions considering the MiXI thruster, such as NASA’s exoplanet
finding missions and the Space Interferometer Mission (SIM), desire that MiXI
produces thrust over a large thrust range, mN to sub-mN levels. Therefore, test cases were conducted with
very low discharge currents (i.e., <20 mA). Two test cases at low
discharges are shown in Figure12. For an average JD of 17 mA, the focusing voltage, Vfoc,
at which JA and JB become approximately
constant occurs at around 400 to 450 V. For the 13 mA case, this appears to
occur at around 450 to 50 V, although it is difficult to tell the exact point
due to the inconsistencies in the data trend (especially the JA curve). During data
acquisition, the low JD test cases exhibited more noticeable fluctuations in JB and JA than those conducted at higher values of   JD,
so approximate values are reported. Further
examination is needed to explain why the focusing voltage and maximum beam
current are greater for the 13 mA versus the 17 mA case, which is contrary to the
expected trends from Figure
11. The increase in JA at higher voltages for the 17 mA case does not
appear to signify cross-over impingement due to the constantly increasing
levels of beam current.JB  and JA  for very low JD  values for MiXI-II.
(a)(b)The results in Figures11
and 12 follow the expected space-charge current limited
operation where the “focusing voltage”
increases with upstream ion density (or in this case, discharge current). This
is apparent in Figures 13 and 14
where all data are plotted on the same scale for
comparison with the computational data in the following section.Figure 13
Summary of beam current data.Figure 14
Summary of accel grid data.


## 3.4. Computational Analysis of Low Thrust Regime

The 2D ion optics model, CEX2D, was
used to simulate single beamlets of the MiXI grid geometry over a range of
upstream plasma densities and extraction voltages [8]. For the calculations
performed herein, the model requires grid geometry, grid voltages, upstream
plasma density, upstream electron temperature, and downstream electron temperature.
The plasma density is inferred as discussed below while the electron
temperatures are assumed equal to experimental values from similar experiments
[4]. As shown in Figure 15, the CEX2D model outputs example ion trajectories that
demonstrate the transition from direct-impingement to focused beamlet
conditions.Example of beam focusing forVB−VA=250V (a)
and for VB−VA=550V (b). Bottom of figures are the centerline of a axisymmetric beamlet.
Results produced by CEX2D.
(a)(b)The CEX2D model demonstrates the
behavior of a single beamlet. To predict the total beam current,JB, from CEX2D’s beamlet current
density, jB, we assumed an
average beam flatness, FB, over the MiXI grid area, such that (1)JB≈FB⋅jBπrgrid2, where jB is the current density
over the “hexagonal” computational area simulated by CEX2D [11]. We used a relatively low value for beam
flatness of only 0.52, a minimum of the beam flatness from previous MiXI beam profiles
at low discharge currents. For this first-order analysis, the beamlets are
assumed to exhibit identical focusing voltages as the beamlet modeled by CEX2D
(a more complete analysis would include consideration of the focusing behavior
at the range of densities typically found across the grid surface). Therefore, the average upstream plasma
density assumed inside the plasma discharge is obtained by multiplying the beam
flatness by the plasma density that is used by CEX2D to provide agreement with
the experimentally measured value of total beam current per the above equation.
Therefore, the upstream plasma densities are inferred from the measured total beam
current and are not directly measured. For these approximations, Figure 16
shows the expected beam current for a range of
extraction voltages for different average upstream plasma densities. As
expected, these results yield a narrow range of focusing voltages from 350 to 450 V
due to the single beamlet approximation, which is independent of the radial
distribution of densities upstream for an actual grid set. For the same reasons,
the accel grid current from the computational results quickly drops to zero over a small voltage range, as
shown in Figure 17.Figure 16
Beam
current versus accelerating voltage for averaged discharge plasma densities
(m−3). Results averaged from
CEX2D beamlet results.Figure 17
Accel grid current versus total voltage
for averaged discharge plasma densities (m−3). Accel current values
are zero from 600 to 1300 V. Results averaged from CEX2D beamlet results.


## 3.5. Discussion of Low-Thrust Analysis of Extraction Grids

### 3.5.1. Discussion of Experimental Results

For the experimental results, beam
focusing is the region of simultaneous decrease inJA and an increase in JB; and the value at which these currents both reach a
near zero slope is the focusing voltage, Vfoc. The focusing voltages and maximum beam
currents for the different discharge currents used in the experimental tests are
shown in Figure 18. The general trend of increased focusing voltage and
beam current for higher discharge current is expected as discussed in Section 3
and in [2, 9]. Further investigation is needed to explain the
increase in focusing voltage and beam current at the lowest discharge current
(13 mA) value. During the experimental tests, the extraction voltage was
increased beyond Vfoc in
an attempt to achieve
cross-over impingement; however, this point was not reached since increasing
the beam voltage beyond 1000 V caused the grids to short for these tests. The
relatively high ratio of JA/JB measured suggests that
low-thrust operation may lead to decreased grid life due to direct impingement.
Additional efforts are needed to determine to what level the high accel current
is caused by variation in upstream plasma density (low-beam flatness) which can
lead to cross-over impingement at the high radial gridlet locations. Also,
long-term erosion predictions and assessments will be needed to assess grid
life for given mission profiles.Figure 18
Focusing voltage and maximum beam current versus
discharge currents used in experimental tests.


### 3.5.2. Comparison of Experimental Results and Computational Results

The computational results produce qualitative trends similar to those found in the measured data; however, the transition toVfoc occurs much more sharply in the computational data. This is due to the simplifying assumption in the computational analysis that characteristics of one beamlet represent the behavior of all beamlets. For actual ion thrusters, the radial variation in the ion density in the discharge chamber leads to a variation in focusing voltage across the grid surface. Thus the transition to focused operation should be more gradual as seen in the measured data. Also, the prediction of zero accel current is not realized in the measured data. After focusing occurs, we see a nominal accel current of at least 0.3 mA in the measured data, which is likely an effect of the nonuniform ion density, variation in the MEMS-fabricated hole sizes, and impingement of charge-exchange ions on the downstream surface of the accel grid. For these reasons, this first-order computational analysis also under-predicts the focusing voltage and over-predicts the rate at which the beam focuses. However, these effects do not greatly affect the total beam current predicted by the model and by comparing the maximum beam current values from the experimental (Figure 13)  and computational data (Figure 16) we can approximate the average discharge plasma
densities for the discharge currents used in the experiment. This comparison
yields the correlation of average discharge plasma density and discharge
current shown in Figure 19. Also in Figure
19, we approximate the thrust at the focusing voltages for each condition, assuming no beam divergence
or double ions losses [4].Figure 19
Approximate thrust and average discharge plasma density versus discharge
current.In light of the needs of future
efforts, it would be helpful for the CEX2D grid model to facilitate the
simulation of an entire grid set for a given upstream density profile as opposed
to single gridlets. Another possible improvement to the CEX2D model would be to
randomize the initial velocity direction of the ions that enter the plasma
sheath (currently the model assumes the ions enter the sheath with Bohm
velocity parallel to the beamlet axis), this modification would likely give a
more realistic value for direct accel grid impingement, that is, nonzero values
for focused cases, if a sufficient number of particles are used in the
simulation.


## 3.5.1. Discussion of Experimental Results

For the experimental results, beam
focusing is the region of simultaneous decrease inJA and an increase in JB; and the value at which these currents both reach a
near zero slope is the focusing voltage, Vfoc. The focusing voltages and maximum beam
currents for the different discharge currents used in the experimental tests are
shown in Figure 18. The general trend of increased focusing voltage and
beam current for higher discharge current is expected as discussed in Section 3
and in [2, 9]. Further investigation is needed to explain the
increase in focusing voltage and beam current at the lowest discharge current
(13 mA) value. During the experimental tests, the extraction voltage was
increased beyond Vfoc in
an attempt to achieve
cross-over impingement; however, this point was not reached since increasing
the beam voltage beyond 1000 V caused the grids to short for these tests. The
relatively high ratio of JA/JB measured suggests that
low-thrust operation may lead to decreased grid life due to direct impingement.
Additional efforts are needed to determine to what level the high accel current
is caused by variation in upstream plasma density (low-beam flatness) which can
lead to cross-over impingement at the high radial gridlet locations. Also,
long-term erosion predictions and assessments will be needed to assess grid
life for given mission profiles.Figure 18
Focusing voltage and maximum beam current versus
discharge currents used in experimental tests.


## 3.5.2. Comparison of Experimental Results and Computational Results

The computational results produce qualitative trends similar to those found in the measured data; however, the transition toVfoc occurs much more sharply in the computational data. This is due to the simplifying assumption in the computational analysis that characteristics of one beamlet represent the behavior of all beamlets. For actual ion thrusters, the radial variation in the ion density in the discharge chamber leads to a variation in focusing voltage across the grid surface. Thus the transition to focused operation should be more gradual as seen in the measured data. Also, the prediction of zero accel current is not realized in the measured data. After focusing occurs, we see a nominal accel current of at least 0.3 mA in the measured data, which is likely an effect of the nonuniform ion density, variation in the MEMS-fabricated hole sizes, and impingement of charge-exchange ions on the downstream surface of the accel grid. For these reasons, this first-order computational analysis also under-predicts the focusing voltage and over-predicts the rate at which the beam focuses. However, these effects do not greatly affect the total beam current predicted by the model and by comparing the maximum beam current values from the experimental (Figure 13)  and computational data (Figure 16) we can approximate the average discharge plasma
densities for the discharge currents used in the experiment. This comparison
yields the correlation of average discharge plasma density and discharge
current shown in Figure 19. Also in Figure
19, we approximate the thrust at the focusing voltages for each condition, assuming no beam divergence
or double ions losses [4].Figure 19
Approximate thrust and average discharge plasma density versus discharge
current.In light of the needs of future
efforts, it would be helpful for the CEX2D grid model to facilitate the
simulation of an entire grid set for a given upstream density profile as opposed
to single gridlets. Another possible improvement to the CEX2D model would be to
randomize the initial velocity direction of the ions that enter the plasma
sheath (currently the model assumes the ions enter the sheath with Bohm
velocity parallel to the beamlet axis), this modification would likely give a
more realistic value for direct accel grid impingement, that is, nonzero values
for focused cases, if a sufficient number of particles are used in the
simulation.


## 4. Conclusions

The computational analysis in Section2 of this paper suggests that a hollow cathode electron source in the existing
MiXI geometry should provide propellant efficiency of almost 90% and beam
flatness of approximately 0.63. As expected, the cathode provides better
performance and beam fla
tness
at upstream mounting locations. Increasing the cathode magnet strength does not
appear to significantly improve the performance; however, a noticeable
propellant efficiency loss of up ~12% is anticipated if the cathode magnet is
demagnetized by the cathode heat. These findings are currently under
implementation in the lab to guide the positioning of MiXI’s miniature hollow
cathode inside the discharge. The experimental data of the MiXI-II beam shows
that the existing grid set allows thrust levels ≤ 0.03 mN
at focused beamlet conditions. As shown by the computational analysis of the
beamlets, lower discharge plasma densities (on the order of ~5×1015–5×1016 m−3, which are
inferred from the experimental and computational results) allow very low total
extraction voltage of only ~250–500 V, thus
providing the lowest thrust levels thus demonstrated by MiXI. Consequently, the
thrust range demonstrated by MiXI in this and other tests is 0.03–1.54 mN,
assuming no beam divergence or double ion losses. As with many developmental
ion thruster efforts, these thrust values are inferred from beam voltage and
current; future tests will provide direct thrust measurements. This large
continuous thrust range at high efficiency is very attractive to a number of
future missions that desire the unique advantages of ion propulsion at the
sub-mN-to-mN scale.



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*Source: 693825-2008-08-03.xml*