Optimization of a Faraday Cup Collimator for Electric Propulsion Device Beam Study: Case of a Hall Thruster

Abstract

A Faraday cup (FC) is an instrument dedicated to current measurement in beams, jets and plasmas. It consists of a set of polarized electrodes mounted in such a way plasma sheath effect can be neglected, yielding accurate and reliable results. A FC is composed of three main parts, namely a collector or cup, which collects the current, a collimator, which defines the collection area and can contribute to limit electrons from entering the cup and a housing which protects the instrument from perturbation caused by the surrounding medium. In this paper, we provide experimental results of the effect of the collimator upon the measured ion current within the beam of a low-power Hall thruster. Different collimator materials, aperture diameters and polarization voltages are studied to determine the optimum design. Minimum dimension as well as appropriate materials are given as a conclusion in the case of low-power Hall thruster beam investigation.

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Optimization of a Faraday Cup Collimator for Electric
Propulsion Device Beam Study: Case of a Hall Thruster
Valentin Hugonnaud, Stéphane Mazoure
To cite this version:
Valentin Hugonnaud, Stéphane Mazoure. Optimization of a Faraday Cup Collimator for Electric
Propulsion Device Beam Study: Case of a Hall Thruster. Applied Sciences, MDPI, 2021, 11 (5),
pp.2419. �10.3390/app11052419�. �hal-03165095�

applied
sciences
Article
Optimization of a Faraday Cup Collimator for Electric
Propulsion Device Beam Study: Case of a Hall Thruster
Hugonnaud Valentin 1,2,* and Mazouffre Stéphane 2


Citation: Valentin, H.; Stéphane, M.
Optimization of a Faraday Cup
Collimator for Electric Propulsion
Device Beam Study: Case of a Hall
Thruster. Appl. Sci. 2021,11, 2419.
https://doi.org/10.3390/app11052419
Academic Editor: Jochen Schein
Received: 10 February 2021
Accepted: 2 March 2021
Published: 9 March 2021
Publisher’s Note: MDPI stays neutral
with regard to jurisdictional claims in
published maps and institutional affil-
iations.
Copyright: © 2021 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
1ENPULSION GmbH, Viktor Kaplan Straße 2, 2700 Wiener Neustadt, Austria
2CNRS-ICARE, 3 Avenue de la Recherche Scientifique, 45100 Orléans, France;
stephane.mazouffre@cnrs-orleans.fr
*Correspondence: valentin.hugonnaud@enpulsion.com
Featured Application: Over the last decade electric propulsion devices have evolved from labora-
tory units to qualified space hardware. Due to the diversity of concepts numerous electric thruster
technologies are available on the new space market. Each technology has a specific working prin-
ciple which implies a wide variety of plasma discharges and ion beams. Currently, it is still
difficult to compare, without bias, these plasmas to each other with standard devices and proce-
dures. This work aims at contributing to the effort towards standardization of a specific type of
plasma diagnostic called a Faraday cup. This instrument is of great importance as it measures the
ion current density in electric thruster plumes. This physical quantity provides information on
key parameter for thruster development and production such as thrust, beam divergence, ioniza-
tion degree and propellant use. In this contribution we describe and validate the optimization of
a Faraday cup collimator in the case of Hall thrusters.
Abstract:
A Faraday cup (FC) is an instrument dedicated to current measurement in beams, jets and
plasmas. It consists of a set of polarized electrodes mounted in such a way plasma sheath effect can
be neglected, yielding accurate and reliable results. A FC is composed of three main parts, namely a
collector or cup, which collects the current, a collimator, which defines the collection area and can
contribute to limit electrons from entering the cup and a housing which protects the instrument from
perturbation caused by the surrounding medium. In this paper, we provide experimental results
of the effect of the collimator upon the measured ion current within the beam of a low-power Hall
thruster. Different collimator materials, aperture diameters and polarization voltages are studied to
determine the optimum design. Minimum dimension as well as appropriate materials are given as a
conclusion in the case of low-power Hall thruster beam investigation.
Keywords:
faraday cup; hall thruster; optimization; collimator; plasma diagnostic; electricpropulsion
1. Introduction:
The space industry has now fully opened its doors to electric propulsion (EP)
devices [
1
–
4
]. To provide space operators with an accurate map of electric thruster perfor-
mance and behavior, EP manufacturers must study plasma and beam properties of the sold
product. Electrostatic EP devices such as Hall thrusters (HT), gridded ion engines (GIE)
and Field Emission Electric Propulsion (FEEP) thrusters, provide thrust by accelerating
and ejecting ions at very high speed. To avoid any charge up effect of the device and the
satellite during operation the ion beam must be neutralized with the help of an electron
gun, also termed cathode [
5
,
6
]. Consequently, the beam of an EP device is composed of
ions and electrons during operation. Many techniques exist to analyze EP ion beams [
7
–
18
].
Beam diagnostics by means of electrostatic probes is of interest in terms of implementa-
tion, use, data collection and cost. Probes can provide information about temperature,
density, velocity, energy as well as flux and current. This data can lead to the assessment
Appl. Sci. 2021,11, 2419. https://doi.org/10.3390/app11052419 https://www.mdpi.com/journal/applsci

Appl. Sci. 2021,11, 2419 2 of 29
of the thruster performance, its beam divergence angle and current use. The electrostatic
probe family is wide. It includes Langmuir probes [
19
], simple planar and guarded
probes [
16
,
17
], retarding potential analyzers (RPA) [
7
,
20
,
21
], magnetically filtered Faraday
probes [22]
, E
×
B probes [
12
,
23
] and Faraday cups [
15
,
24
]. A FC is certainly one of the
most accurate tools to access ion current in the beam.
The functioning principles of a FC are similar to that of planar probes. A negative
potential is applied to the diagnostic collector to attract and collect ions and repel electrons.
Although planar probes are heavily impacted by sheath expansion and secondary electron
emission (SEE), the geometry of a FC is thought to reduce and suppress these disturbances.
Faraday cups architecture differs from planar probes as they use a hollow cylinder closed
at one end as a collector and an additional electrode, called collimator, placed at the front
of the probe. This electrode defines the collection solid angle, which confines the flux going
through the collector. Due to the cylindrical shape of the collection surface, plasma sheath
effects are negligible which greatly improve the accuracy of ion current measurement. The
collimator along with the cavity shape, material properties and dimensions provide extra
degrees of freedom enabling recollection of secondary electrons, a phenomenon which
tends to artificially increase the ion current. Please note that many studies were conducted
to prove the advantages of using a Faraday cup instead of a planar probe design [
16
,
25
,
26
]
to study the plasma produced by an EP device. However, published work dealing with
Faraday cup optimization can only be found for fields [
15
,
24
,
27
,
28
] where ion energies
are three to six orders of magnitude larger (MeV) than expected energies in the electric
propulsion filed (eV to keV). More precisely, previous research on an optimum collimator
design for a Faraday cup was mostly performed in the field of nuclear physics where the
ion energy is in the keV—MeV range [
15
,
28
,
29
]. In those cases, the collimator is mainly
used to suppress secondary electrons produced by the collector. A negative potential,
with a magnitude higher than the collector voltage, is applied to the collimator to repel all
secondary electrons back into the cavity therefore avoiding large overestimate of the ion
current. Considering the high energy of the ion in nuclear physics, thermal simulations
as well as material sputtering yield determination are of great relevance [
15
,
24
]. In the
field of EP, collimated Faraday cups are of interest as they give the possibility to shield
the collection electrode against SEE and charge-exchange collisions (CEX). CEX collision
events correspond to collision between slow neutrals and fast ions. They therefore produce
fast neutrals and slow ions. This collision type is very often encountered in the beam of EP
devices [
30
]. CEX collisions have two main origins, namely: the residual gas background
pressure and the neutral particles flow at the thruster outlet. CEX is known to be the cause
of an increase in the measured current [
31
], see Section 3.2. Eventually, studies upon the
dimensioning of a collimator can be found in [27,32].
In this work different Faraday cup collimator aperture sizes and materials were
studied. Each design was used to determine the ion current density in the far-field plasma
plume of the 200 W-class ISCT200 laboratory model Hall thruster operated with ion energies
from a few eV to 250 eV. The experimental campaign has been split in three main parts. First,
measurements have been performed with different collimator materials, as this element
is the most exposed to the beam. Secondly, the collimator aperture diameter has been
varied to examine the impact on the measured ion flux. Finally, the collimator was placed
behind the housing. With this configuration the collimator is a simple electrode, and the
housing orifice determines the collection solid angle. Different potentials were applied
to the collimator to study its capacity to better screen electrons and prevent CEX ions to
be collected by the ion collector. As we shall see this approach gives a great flexibility for
FC operation.
2. Experimental Arrangement
2.1. Vacuum Chamber, Instrument and Procedure
All experiments have been performed in the cryogenically pumped New Experiments
on Electric Thrusters (NExET) vacuum chamber. It is a 1.8
×
0.8 m stainless steel vessel. The

Appl. Sci. 2021,11, 2419 3 of 29
overall pump stack warrants a background pressure as low as 2
×
10
−5
mbar-Xe during
operation of a 200 W input power plasma source. The grounded vacuum chamber is used
as potential reference for all experiment series. A schematic of the experimental set-up
is drawn in Figure 1. The Faraday cup is attached to an aluminum structure designed to
automatically align the probe with the thruster equatorial plane. The mechanical frame
is mounted on a URS1000BCC motorized rotation stage and controlled by a SMC100 unit
provided by Newport. An in-house computer program was used to interface with the
controller, record and save data. The pivot point of the rotating structure is aligned with
both the thruster axis and exit plane. The system allows for a 180
◦
scan on the horizontal
plane with respect to the thruster. Probe alignment with the EP device is made using a laser
system. The thruster centerline is referred to as the 0
◦
angular position of the probe. The
distance between the FC collimator entrance and the thruster exit plane (
R
) is here limited
by the vacuum chamber diameter. Consequently,
R
is fixed at 27.4
±
0.2 cm (
∼
6 thruster
mean channel diameters). The far-field plume is usually defined as the region where
R
is greater than four thruster diameters [
17
]. In the far-field plume domain the thruster
is assumed to be a point ion source [
25
,
33
,
34
]. The whole probe system is electrically
connected to the common ground reference.
Figure 1.
Schematic (not to scale) of the experimental set-up for fare-field plume measurements of
the ISCT200 Hall Thruster. The probe is aligned with the thruster centerline at 0°.
A calibrated Keithley 2410 sourcemeter in voltage source mode has been used to
measure the ion current collected by the Faraday cup. A TTI-EX752M dual output 300 W
power supply that can deliver up to
±
75 V in single output mode is used to define the
desired potential on the collimator. Both instruments are referenced to ground.
A standard procedure has been followed for each measurement. The different steps
are listed in Table 1. For all measurement series, the rotation of the arm that supports the
FC always follows the same cycle: start at
−
90
°
, angular sweep up to +90
°
and back to
−90° the rest position. Here the angle refers to the FC angle. The angular step size is 1°.

Appl. Sci. 2021,11, 2419 4 of 29
Table 1. Heat-up, ignition, measurements and shut down procedure of the ISCT200.
Step Action Duration
# # min
1 Cathode heating (16–18 A) 20
2 Thruster ignition (200 V and 1 mg/s)
3 Hall thruster stabilization 30
4 Setting of the operation point and stabilization 5
5 Measurements
6 Next operation point and stabilization 5
Repeat step 5 and 6 if needed
7 Thruster shutdown
8 Cathode shutdown
2.2. 200 W-Class Hall Thruster
A Hall thruster is an electrical propulsion device that uses a plasma discharge with
magnetized electrons to ionize and accelerate a propellant gas [
34
–
37
]. The principle relies
upon a magnetic barrier and a low-pressure dc discharge generated between an external
cathode and an anode. The latter is located at the upstream end of a coaxial annular
dielectric channel that confines the discharge. A fraction of the electrons emitted by the
thermionic cathode flows downstream to neutralize the ion beam. The remaining part
travels toward the anode to maintain the plasma discharge. The propellant gas, typically
xenon, is introduced at the back of the channel. Magnetizing coils or permanent magnets,
incorporated into a magnetic circuit, provide a radially directed magnetic field of which the
strength is maximum in the vicinity of the channel exhaust. The magnetic field is chosen
to be strong enough to make the electron Larmor radius much smaller than the discharge
chamber characteristic dimensions, but weak enough not to affect ion trajectories. The
electric potential drop is mostly concentrated in the final section of the channel owing
to the low axial mobility of electrons in this restricted area. The electric field governs
the propellant atoms ionization and the ion acceleration. The combination of the radial
magnetic field with the axial electric field generates an E
×
B electron drift in the azimuthal
direction, the so-called Hall current. The latter is responsible for the very efficient ionization
of neutral atoms inside the channel.
The ISCT200 Hall thruster is a 200 W-class HT with a classical magnetic field topology.
Details about the ISCT200 series and thruster architecture can be found in [
34
,
38
]. The
annular channel walls of the ISCT200 are made of BN-SiO2 ceramic. The channel geometry
is in the so-called 2
S0
configurations, which means the channel cross-sectional area is
twice the one of the well-known Russian SPT100 [
39
,
40
]. The 2
S0
configuration ensures
a high ionization degree. The magnetic field is generated by way of small cylindrical
samarium–cobalt magnets. The xenon propellant gas is injected homogeneously inside
the channel using a high porosity mullite ring ceramic placed behind the channel back
plate. The anode is a wide stainless steel ring placed at the back of the channel against
the outer wall. During operation, the thruster body is floating. A heated 5 A-class hollow
cathode with a disk-shaped LaB
6
emitter was used to generate the electron current [
5
,
41
].
The cathode is located outside the channel with its orifice in the vertical plane that contains
the channel outlet, tilted towards the thruster. The cathode, which is operated with a
constant xenon mass flow rate (
Φc
) of 0.3 mg/s, is electrically connected to the thruster
anode and floating.
The Faraday cup has been tested in the NExET chamber with the 200 W-class ISCT200
Hall thruster. Figure 2shows the ISCT200 in operation with Xenon at 200 V during the
campaign. One can notice the slight deviation of the inner beam to the positive side of
the angular distribution (left in the picture). The deviation is visible in the measured ion
current profiles display in next sections. The origin of the deviation is not completely
known. However, we expect the phenomena to be caused by inhomogeneous or asymmet-
rical distribution of the magnetic field in the azimuthal direction because, for versatility

Appl. Sci. 2021,11, 2419 5 of 29
purpose, we use an assembly of small magnets that are not perfectly identical. The use
of a magnet ring instead would make the topology symmetrical yet at the expense of
magnetic flexibility.
Figure 2.
Front view of the ISCT200 firing with xenon. The 5-A cathode is located above the
thruster body.
Throughout the whole test campaign two different operating conditions were chosen
for the thruster, see Table 2. The discharge current was kept constant to allow accurate
comparison between each firing parameter. For each of them, specific design of the FC was
used to characterize the beam (I–V characteristics) and to map the angular current density
of the plume (jiprofiles).
Table 2. Hall thruster firing parameters.
Discharge Voltage (Ud) Discharge Current (Id) Anode Mass Flow Rate (Φa)
V A mg/s
200 0.66 0.815
250 0.66 0.79
Finally, current oscillations acquired with a LECROY-HDO6104A oscilloscope during
thruster operation at 0.66 A, 200V and 250 V are plotted in Figure 3. The standard deviation
as well as uncertainty computed for both whole data sample is also given.
Figure 3.
Discharge current oscillation when the thruster fires at 0.66A, 200 V (
blue
) and 250 V (
red
).
For both curves, the standard deviation (
σ
) and uncertainty averaged (
um
) over the whole data
sample is given.
Parameters calculated from the ion current density measured by a FC are given
considering uncertainties (
u
) from our measurements. The final uncertainty is always given

Appl. Sci. 2021,11, 2419 6 of 29
for 95% confidence level (i.e., 2
u
). Therefore, the current and propellant use are given with
±5% interval and divergence angles with ±2° accuracy.
3. Faraday Cup
3.1. Architecture
Measurements of the ion current density in the plasma plume or ion beam of
electric propulsion devices are of great relevance as the flux of ejected ions determines
the thruster properties such as the thrust level, the specific impulse, the propellant
use and it plays a key role in overall thruster performance. Moreover, an accurate
and comprehensive knowledge about ion current density is critical for the validation
of plume modelling and numerical simulations [
42
,
43
], for thruster acceptance tests,
for the study of facility effects [
44
,
45
] and for understanding the interactions between
plasma plume and spacecraft elements [
46
–
49
]. The ion current density can be measured
using an electrostatic probe that basically consists of a conducting electrode, termed the
collector, polarized to a high negative voltage with respect to the local floating potential
to repel electrons and capture ions. There are various configurations of probes from a
simple metal disk to architectures with collimators, filters and guard rings with various
materials [
16
]. A FC is a special kind of electrostatic planar probe. It is basically an isolated
conductive cup dedicated to the detection of charged particles in a low-pressure or vacuum
environment [16].
When a Faraday cup operates as an ion collector, which means the cup
is negatively biased with respect to the floating potential, the ion current in the probe
direction can be accurately measured. Contrary to other electrostatic probes, edge effects
due to plasma sheath formation are negligible with a FC owing to the closed geometry.
In this study, FCs with collimator diameters of 10, 7, 5, 3 and 1 mm have been built. A
large orifice collimator minimizes the impact of the neutral gas inside the cup. As a FC is
collimated, the collection solid angle is below 2
π
, contrary to a planar probe, therefore a
fraction of the thermal ion current is not captured [
16
,
17
]. Nevertheless, a collimator has a
key role to define the velocity vector of ions entering the device. Moreover, the collimator
also limits the ion flux, which avoids saturation of the measurement signal when the FC is
placed in the center of the ion beam, especially for high-power EP devices. A schematic
view of the FC is shown in Figure 4. The FC assembly is composed of 5 different parts.
The collimator (3) is used to screen the electrons and define the solid angle of collection,
see Table 3. In this work the FC is bombarded by high energy xenon ions. Graphite and
molybdenum have thus been employed. The orifice dimensions are assessed in
Section 5.3
.
A trade-off must be considered between increasing velocity filtering and minimizing
pressure inside the cup. Indeed, if the FC is not evacuated a large pressure inside the cup
enhances charge-exchange collision events, which may disturb the ion flux. The collimator
is electrically isolated from the FC body and cup enabling independent potential variation.
Figure 4. Scheme showing the 5 main parts of a Faraday Cup.

Appl. Sci. 2021,11, 2419 7 of 29
Figure 5.
Cross section view showing the main components of the Faraday cup, collimator geometries
and materials used in this study.
Table 3. Solid angle for a given collimator diameter.
Diameter Solid angle
mm °
10 11.4
7 8.0
5 5.7
3 3.4
1 1.1
A metal foam ion collector (1) forms the back of the cup (1 + 2). The collector is
mechanically attached to the cup without welding. The cup is a stainless steel hollow
cylinder. The diameter of the collector is 12 mm. The aluminum foam was provided by
Exxentis. The type used in this study is an open-cell AlSi7Mg foam Nr. 4. Each pore
has a diameter between 0.4 and 1 mm and are connected to each other via channels
with diameters from 0.15 to 0.2mm. The whole volume porosity is 60
±
5%. The
complex structure of a foam should reduce secondary electron emission and prevent
ion rebounds [
50
–
54
]. The active length of the stainless steel cup is 50 mm (
lcup
). The total
volume of the cup is therefore 5.65cm
3
. The length should be longer than space-charge
sheath thickness inside the probe to ensure the measurement outcomes are insensitive to
the local plasma properties. The on-axis electron density and temperature in the ISCT200
plume far-field are typically
≈
10
16
m
−3
and
≈
3 eV [
55
]. It gives a Debye length
λD
close
to 0.1 mm [
11
]. Due to the relatively large voltage applied to the collector
eV kBTe
,
where
kB
is the Boltzmann constant, the sheath thickness can be estimated assuming the
current is space charged limited. Therefore, the sheath is governed by the Child-Langmuir
law [56], and the sheath thickness sis given by:
s≈λD|V|
b
Te3/4
≈1 mm lcu p. (1)
A small FC also reduces the amount of sputtered material in the plasma beam and it
minimizes flow disturbances. The cylinder plus the collector are maintained at a potential
well below the floating potential to capture positively charged particles. The cup design
limits the perturbation introduced by the SEE process: the cylindrical geometry allows the

Appl. Sci. 2021,11, 2419 8 of 29
capture of most of the secondary electrons emitted by the collector surface. The length
minimizes but does not completely compensate SEE effect.
The FC is encapsulated into a cylindrical aluminum pod (4) to protect the external
PEEK insulator from ion bombardment and from the thermal load and to prevent ambient
plasma to disturb cup measurements. The pod is grounded with respect to the local plasma
potential (i.e., facilities ground). The pod (or housing) is also used to attach the probe to
the rotating arm.
The spacers (5) act as electrical insulators. They electrically uncouple the cup from the
collimator, as graphite and molybdenum are conductors, same as the housing. The size is
chosen to reduce the occurrence of short-circuit between the collimator and the cup. The
back of the cup is used to implement and accommodate wires and connections.
Figure 5displays the different designs tested in this work. To prevent confusion a
nomenclature (ID) is used to refer to a specific FC design. The ID is split into three parts
(
X
.
X
.
X
). The first component gives information about the material used to equip the
front of the FC. It can be either G, Mo, or Al which respectively correspond to graphite,
molybdenum and aluminum. The second component refers to the diameter of the inlet
aperture. Therefore, one can have numbers 01, 03, 05, 07 and 10. Finally, the last part of
the ID indicates information whether the collimator is exposed to or protected from the
beam, using the letter E and P respectively. So, designs labelled
X
.
X
.
P
differ from designs
X
.
X
.
E
as the housing aperture diameter decreases while the collimator diameter behind
becomes larger. Please note that with configuration
X
.
X
.
P
the collimator can be grounded
or biased while in configuration
X
.
X
.
E
the latter is always grounded (see Section 6.3). As
an example, the FC
G
.07.
E
corresponds to a collimator made of graphite with an aperture
diameter of 7 mm and is exposed to the beam.
3.2. Perturbations
Introducing an object inside the main beam of an EP device disturbs the plasma.
Therefore, one must minimize the exposed surface and reduce the size of the probe as much
as possible. Figure 6shows the three physical mechanisms which depend on material
properties during ion or electron bombardment: reflection, sputtering and secondary
electron emission (SEE).
Figure 6.
Schematic of three physical mechanism occurring on different FC parts which can lead to
measurement perturbation. The arrows have arbitrary length and direction.
In this study, ion reflection events are considered minimal due to the length of the cup
and the properties of the collector foam at the cup rear side. Indeed, the pores of the foam
material should increase the probability to trap ions. If not, the reflected ion would not be
able to reach the top of the cup entrance due to its length.
In contrast to ion reflection, SEE has a great impact on the measured ion current. The
rate of electron emitted by a material depends on its properties, the projectile energy and
angle of incidence [57–63]. In our study, we consider two possibilities:
•
First, we consider an electron emitted by either the FC housing front or collimator. If
the electron manages to reach the collector, the measured ion current will artificially
be lowered and would read: Imeasured =Ii−ISEE1with ISEE1>0.

Appl. Sci. 2021,11, 2419 9 of 29
•
Secondly, we consider now an electron emitted by the collector but not recollected by
the latter. Therefore, the measured ion current will be higher than reality and would
read: Imeasured =Ii+ISEE2with ISEE2>0.
In both cases the real ion current is not properly measured. Therefore, one must
minimize and control the rate of SEE.
Lastly, sputtering is characterized by its yield (
γ
) which defines the ratio of emitted
atoms per incident ions. This parameter depends on the projectile and the target inner
properties as well as the energy of impacting ions. Table 4shows the yield for graphite,
molybdenum and aluminum for ion energy corresponding to different thruster discharge
voltages. These figures were obtained with the software SRIM [
64
], see Section 6.1. The
primary danger with material sputtering is the collector deterioration which leads to a
decrease of ion collection efficiency and prevent long operation. Another issue concerns
particle deposition caused by sputtered material. It can lead to short-circuit between
electrodes and create a current leak. Neutral sputtered atoms cannot directly contribute
to the measured ion current. However, a collision between a neutral and the collector or
collimator can create a secondary electron, which can lead to change the measured ion
current as previously mentioned. A Hall thruster beam is composed of high kinetic energy
ions and low temperature electrons [
26
,
65
]. A negative potential is therefore applied to the
cup preventing any primary and secondary electrons to be captured. Section 5.4 shows the
trade-off which must be considered between ion collection and electron repulsion.
Table 4.
Sputtering yield coefficient computed for different discharge voltages with the software
SRIM [64].
Material Sputtering Yield (200 V) Sputtering Yield (250 V)
Atoms/ions At oms/ions
Carbon (Graphite) 0.0018 0.0056
Molybdenum 0.13 0.18
Aluminum 0.11 0.16
A Hall thruster plume is subject to charge-exchange collisions (CEX). These events
occur when a fast ion and a slow atom collide inelastically, resulting in a change of velocity
distribution for both particles. The collision results in a slow ion with a random velocity
distribution and a fast atom. The latter moved towards the edge of the plume which
increase the so-called “wings” of the thruster, see Section 5.3. The probe becomes a
potential sink which trap these ions with low energy and random velocity distribution.
This effect occurs at large angle where the ion density is low, and the Debye length is large.
CEX can occur in the HT channels or in the plume core due to high level of ion and neutrals
density. Therefore, it increases when the propellant flow rate or the ionization efficiency
increases. Consequently, higher ion current at the thruster “wings” increases the whole ion
current measured. Nevertheless, a collimator can prevent such phenomena to disturb the
measured current as it shields the cup from the ambient plasma [32].
4. Ion Current
4.1. Total Ion Current and Divergence Angle Determination
The ion current
Iiexp
corresponds to a flux of positive charges going through a surface
per unit of time. It reads:
Iiexp =Z Z jidS. (2)
The ion current density j
i
(A/m
2
) is assumed to be collinear to the outward pointed
unit normal vector to the surface. A spherical coordinate system is often used to determine
dS
and compute
Iiexp
. The probe is usually fixed at a distance
R
and the thruster is supposed
to be a point source at the center of a sphere. To compute
Iiexp
it is needed to know
ji(θ
,
φ)
,
where
θ
is the latitude and
φ
the longitude. When the current density is solely recorded in

Appl. Sci. 2021,11, 2419 10 of 29
a plane that contains the thruster axis, e.g., following the angle
θ
from
−π/
2 to
π/
2, one
can assume a cylindrical symmetry of the ion beam around the thruster axis to determine
ji(θ
,
φ)
and compute
Iiexp
. It is in fact easier to use a cylindrical coordinate system to solve
Equation
(2)
. In that case the coordinate system is depicted in Figure 7along with the
elementary arc
ds
. The thruster exit plane points toward the
x
axis. Measurements are
performed at a fixed distance
R
and defined by the angle
θ
. Cylindrical symmetry implies
a constant
ji
inside the element with radius
y
and thickness
ds
. The sum of these elements,
each weighted with ji(θ), gives the ion current:
Iiexp =ZR
0j(x,y)2πyds, (3)
with
ji(x
,
y)
=
ji(θ)
. With the help of several mathematical conventions and simplifica-
tions [66] we obtain the general final form of the ion current:
Iiexp =2πR2Zπ
2
0ji(θ)sin(θ)dθ. (4)
This form is also used by Brown et al. [
17
] in his recommended guidelines for use of
Faraday probes.
Figure 7.
Cylindrical coordinate system used to express the current density
ji
. The latter is constant
on a ring of radius yand thickness ds.
The divergence half-angle
θdiv
refers to the width of the beam. It quantifies the beam
deviation from a straight ion beam. The thrust is directly impacted, and it significantly
decreases when the divergence angle gets large. The divergence half-angle
θdiv
of the ion
beam is defined as the angle for which the ion current corresponds to a given fraction of the
total ion current. In general, the ratio is 0.95. Therefore, the half-angle is mathematically
related to Iiaccording to:
Iiθdiv =πr2Zθdiv
0ji(θ)·sin(θ)·dθ=0.95 ·Ii. (5)
Equation
(5)
shows that the way
Ii
is calculated, as well as the treatment of the angular
distribution of the ion current density (smoothing, fitting, filtering, interpolation), greatly
influence the value of θdiv for a given dataset.
4.2. Current and Propellant Use
The current use (
ηb
) is of importance for Hall thrusters as those devices are not
operated with direct ion current control. A Hall thruster provides thrust when delivering a

Appl. Sci. 2021,11, 2419 11 of 29
discharge current (
Id
) that incorporates both ion and electron contribution. The current use
is the ratio between the experimental ion current and Id.
ηb=Ii
Id
. (6)
This ratio is around 0.8 for HTs [
34
,
67
]. That means about 20% of the current is
provided by the electrons which do not contribute to the thrust. The propellant mass use
α
is the ratio of the ion mass flow rate to the propellant mass flow rate. It corresponds to the
fraction of the propellant mass flow rate injected into the discharge channel that is ionized.
This quantity directly characterizes the ionization efficiency, hence it must be maximized.
The propellant use reads [68,69]
α=˙
mi
˙
m=1
˙
mm∑
n=1
In+
ne , (7)
where
˙
mi
and
˙
m
are the ion mass flow rate and the atom mass flow rate, respectively,
m
is the atomic mass,
e
is the elementary charge and
In+
the current associated with ions
having a
n+
electric charge. Please note that multiple-charged xenon ions with charges
up to 5
+
have been detected in the plume of high-power Hall thruster. As the multiple-
charged ion fraction is often unknown, the ion beam is assumed to be solely composed of
singly-charged ions. The propellant use αis then given by the following formula:
α=1
˙
m
Ii
em. (8)
Please note that the above equation overestimates the value of
α
when multiple-
charged ions are present in the thruster plasma plume [
68
]. For high-power Hall thrusters
this ratio lies between 85% and 95%. For low-power HTs the current use is much lower
with values around 70%. In all cases accurate FC measurements are used to get more
precise and reliable values for the current ionization as this quantity plays a key role in
HT optimization.
5. Impact of the Collimator Characteristics
5.1. I–V Curves
In this work, three different collimator designs were studied. The first series of
experiments deals with the collimator material: graphite vs molybdenum. For the two
other series the collimator is made of graphite. The second series evaluates the impact of
the FC collection solid angle upon the ion current density. The last experiments investigate
the influence of having the collimator screened from the ion beam. For all FC configurations
the geometry and properties of the collector are unchanged. Configuration G.10.E, see
Figure 4, is taken here as the reference. A current density profile is measured for all FC
configurations. The thruster was operated at 200 V and 250V with a fixed discharge current
I
d
= 0.66 A. The discharge power is 132 W and 165W, respectively. The heat load on the
thruster channel walls prevents the operation of the ISCT200 thruster above 250V at 0.66 A.
Prior to FC measurements, current-voltage characteristic curves must be acquired to
verify the proper design and functioning of the probe. Figure 8shows I–V traces recorded
at various angles in the plume of the ISCT200 Hall thruster firing at 250 V and 0.765 mg/s
anode mass flow rate, see Figure 4. Measurements were carried out 27.4 cm downstream
the thruster exit plane. A broad negative potential range must be swept to get an accurate
picture of the FC behavior. Faraday cups provide reliable information upon the ion current
as electrons are screened and sheath expansion effect and SEE are cancelled. Consequently,
the ion branch, the part of the I–V curve where the probe is negatively biased, should be
horizontal. This constant ion current is termed the saturation current [
10
]. The potential
to apply to the collector is determined from the ion current saturation extracted from I–V
curves. The latter is used to measure the current density angular distribution profile of the

Appl. Sci. 2021,11, 2419 12 of 29
EP plume, see Sections 5.3 and 5.4. In Figure 8, the collected ion current does not depend
upon the cup voltage at large angles. The slow increase in ion current with the voltage at
small angles finds its origin in an increase of secondary electron emission.
Figure 8.
I–V characterization at different
θ
of the ISCT200 firing at 250 V, 0.66A with 0.765 mg/s of
anode mass flow rate. The measurements are conducted 27.4 cm from the thruster.
5.2. Collimator Material
In this experiment, the probe is equipped with either a 10mm graphite (G.10.E) or a
10 mm molybdenum (Mo.10.E) grounded collimator. Figure 9shows I–V curves for the
two configurations at two different discharge voltages measured on the HT axis (
θ
= 0
°
).
The slope is of the order of 10
−5
mA/cm
2
for the two configurations. The ion current
saturation is relatively constant indicating that most electrons are properly screened. The
main difference between the two designs is the amplitude of the measured current. The FC
equipped with a molybdenum collimator gives a current density which is about 20% lower.
As can be noticed in Figure 9the gap between the two curves increases when the voltage is
ramped up for a fixed value of Id.
Figure 9.
On-axis (
θ
= 0
°
) I–V curves I
d
= 0.66 A, U
d
= 200 V (
top
) and 250 V (
bottom
). Faraday cup is
in G.10.E (blue) and Mo.10.E (red) configuration.
The total ion current is obtained from the current density profile as explained in
Section 4.1
. We use Equations
(6)
and
(8)
to obtain the current and propellant use.
Figure 10

Appl. Sci. 2021,11, 2419 13 of 29
shows the value of
ηb
and
α
for two thruster operating conditions and two FC configu-
rations. Both parameters are lower for the molybdenum collimator configuration. The
difference remains true whatever the thruster discharge voltage with constant discharge
current. For the two configurations
ηb
is larger at 250 V because the ionization degree in-
creases with voltage. Numerical simulations are used in Section 6.1 to discuss the behavior
observed experimentally.
Figure 10. Current and propellant use obtained from jiprofile with designs G.10.E and Mo.10.E
5.3. Collimator Diameter
Here, the collection solid angle of the FC is modified using five grounded graphite
collimators with different aperture diameters (
d
): 10 mm (G.10.E), 7 mm (G.07.E), 5 mm
(G.05.E), 3 mm (G.03.E) and 1 mm (G.01.E). The length of the cup is 50mm. On-axis I–V
characteristics are displayed in Figure 11. At
Ud
= 200 V, the current density measured by
G.01.E is constant until 100 V then it starts to rise. This behavior remains so far unexplained.
At higher discharge voltage I–V curve measured with G.01.E is more unstable than the
other curves. With a diameter of 1 mm the probe alignment with the thruster axis is difficult.
A slight deviation of the probe pointing vector can lead to a large decrease in the measured
ion current. Misalignment could then explain the different behavior observed between
200 V and 250 V. Figure 11 indicates the current density decreases when the collimator
diameter is reduced.
Figure 11.
On-axis I-0V curves obtained at 200 V and 250V and with different collimator diameters
(I
d
= 0.66 A). FC are equipped with a grounded graphite collimator. Configurations used are G.01.E,
G.03.E, G.05.E, G.07.E and G.10.E.

Appl. Sci. 2021,11, 2419 14 of 29
Narrowing down the inlet aperture of the probe can prevent some thermal ions from
being collected; however, the ion thermal current is small in the ISCT200 plasma plume [
70
].
Additionally, the drop in current does not vary linearly with the reduction of the collimator
diameter. Figure 12 shows the rate of change of the current density for different collimator
diameters factor of reduction. It refers to the aperture diameter diminution compared to a
10 mm diameter (
G
.10.
E
). The Hall thruster fires at 250 V and 0.66A. We observe a linear
increase of the current density until a factor 6. After, the rate of change slows down and
reaches a maximum when the diameter of the collimator is reduced by a factor 10.
Figure 12.
Evolution of the current density rate of change with collimator reduction factor. Faraday
cup is 50 mm long with a Foam collector. It is equipped with a grounded graphite collimator. Hall
thruster is operated at 250 V and 0.66 A.
Figure 13a,b show the beam profile of the HT for 200V and 250 V at constant
Id
. The
double peak shape visible on the thruster axis is due to the annular geometry of HTs. It is
better seen at high voltages. Note when operated at 200 V and 0.66A the thruster plume
has instead a rounded shape. At this power level the thruster operates with a low efficiency.
As can be seen in Figure 13, we observe four distinct zones, unrelated to the probe design
and characteristic of the Hall thruster plume. For a given zone the differences observed
between each profile is due to the probe configuration. The zone width depends on the
thruster discharge voltage. Each zone is defined by a sharp change in current density slope.
Zone 1 depends the most on the thruster operation. Indeed, we note that at 200 V zone
1 lies
between
−
15
°
and 24
°
while at 250 V the zone width does not exceed 12
°
. This is due
to the thruster performance. Indeed, at 200 V the thruster ionization process is not optimal
which implies that ions travelling on the thruster axis have broader energy distributions
and their velocity vector deviates more easily from the thruster firing axis. Therefore, when
the aperture diameter of the FC is reduced it diminishes the probability for an ion to reach
the collector. In contrast, at 250 V the ionization is better which creates a more focus beam
with narrower ion energy distributions. Therefore, zone 1 is narrower. Please note that
within zone 1, a major current density drop is observed with FC G.03.E. Moreover, in this
zone the current density rate of change between each FC configuration is constant between
200 V and 250 V. Eventually, zone 2, 3 and 4 are larger at higher discharge voltage. Zones
3 and 4 are usually referred to the Hall thruster wings. They contain most of the slow
ions with random velocity vectors induced by CEX and scattering collisions [
71
]. Please
note that other thruster design parameters such as electric field distribution and zone of
the ionization contribute to Hall thruster wings [
70
,
72
]. The ion density decreases fast in
the plume of Hall thrusters when moving away from the centerline. The change of slope
between each zone becomes less visible at higher discharge voltage. At 250 V, the ionization
process in the thruster channel is more efficient. Consequently, the ion population increases.
When the of ion density increases the rate of CEX becomes higher in the thruster channel
and within the plume. Therefore, these two processes contribute to enlarge the beam

Appl. Sci. 2021,11, 2419 15 of 29
divergence angles by increasing the ion density in zone 4. Please note that the current ratio
between the core and large angle wings can reach three orders of magnitude in HT plumes.
(a)0.66 A, 200 V
(b)0.66 A, 250 V
Figure 13.
Current density angular distribution measured with different collimator diameters (G.10.E,
G.07.E, G.05.E, G.03.E). The thruster fires at 0.66A, 200 V (
a
) and 250 V (
b
). Profiles are displayed
with a linear (top) and logarithmic (bottom) scale. Numbers refer to the different zones.
5.4. Screened Collimator
In this experiment the probe is equipped with an aluminum housing (Al.05.P) with
a front aperture of 5mm. A 10 mm diameter graphite collimator is placed behind and is
electrically isolated. The collector remains a foam. The first study is made with both hous-
ing and collimator grounded. The second study is performed with a polarized collimator
while the housing is kept grounded. In both studies a voltage sweep is applied to the
collector. Measurement outcomes are compared with the ones obtained with FC G.05.E
configuration. The aperture diameter is similar for the two designs.
The beam profiles of the first study are displayed in Figure 14a,b (G.05.E and Al.05.P).
At both discharge voltages Al.05.P measures the highest ion current density. On the thruster
axis, the signal acquired by configuration X.X.P is 15 to 20% higher than X.X.E. The differ-
ence in current density is observed all over the beam profile. Actually, the current density
decreases when the potential is more negative on the collimator. When the collimator is
biased to −75 V, jiis near 5% less than the one obtained with a grounded collimator.

Appl. Sci. 2021,11, 2419 16 of 29
(a)0.66 A, 200 V
(b)0.66 A, 250 V
Figure 14.
Current density angular profile with (G.05.E) and without (Al.05.P) exposure to the plasma
beam. The thruster fires at 0.66 A, 200V (
a
) and 250 V (
b
). Profiles are displayed with a linear (
top
)
and logarithmic (bottom) scale.
In the second part of the experiment four different potentials (
−
15 V,
−
25 V,
−
50 V and
−
75 V) have been applied to the collimator in the FC configuration Al.05.P. I–V curves at
θ
= 0
°
are plotted in Figure 15. One can notice all I–V curves are relatively flat when the FC
potential is below
−
100 V. As mentioned in previous studies [
73
] SEE is characterized by a
drop of ion current when the potential applied to the collector is higher than the electrode
placed at the entrance of the FC (housing, collimator). Such behavior is not observed in
Figure 15, which confirms the choice of FC architecture to suppress SEE.
Figure 16 shows I–V curve with a voltage sweep applied to the collimator while the
collector is grounded, the current density measured on the collimator increases when the
voltage applied is more negative. This trend is characteristic for I–V curves of Langmuir
and non-guarded planar probes [
16
]. The collimator is a simple disk electrode with no
specific design to reduce SEE. Moreover, sheath expansion effect is no longer negligible.
This results in an artificial ion current increase as displayed in Figure 16.

Appl. Sci. 2021,11, 2419 17 of 29
Figure 15.
On-axis I–V curves with the collimator unexposed (Al.05.P) to the plasma beam for
different collimator potentials (Vr). The thruster fires at 0.66 A and 250V.
Figure 16.
On-axis I–V curves acquired with design Al.05.P. A voltage sweep is applied to the collima-
tor electrode while the collector is grounded. Thruster parameters are 250 V, 0.66A,
Φa= 0.802 mg/s
.
Figures 15 and 16 suggest that applying a negative voltage to the collimator, prevents
a part of the ion current to reach the collector. To better understand changes observed in
the measured ion current density, simulations have been carried out with the SIMION
software [74]. The outputs of numerical simulations are discussed in Section 6.3.
Figure 17a,b show the beam profile obtained with FC Al.05.P with the collector
potential fixed at
−
50 V and the collimator grounded (blue) or biased at
−
75 V (red)
with the thruster firing at 200 V and 250 V, respectively. Only zones 1 and 4 introduced
in
Section 5.3
with Figure 13a,b are plotted. These zones are the most influenced by the
probe voltage configuration. Indeed, in zone 1 there is a non-negligible drop of the current
density measured by the FC configuration with
−
75 V applied to the collimator. In contrast,
in zone 4 the current density measured with V
r
at
−
75 V overtakes the grounded collimator
configuration. The lower signal measured by the
−
75 V configuration in zone 1 is caused
by larger ion energy distribution, see Section 5.3. Low energy ions will tend to be directly
or indirectly (Section 6.3) collected by the collimator. The higher signal in zone 4 is another
clue for the presence of CEX within a Hall thruster plume. In this zone low energy ions
with random velocity vectors caused by CEX are predominant. Therefore, they will be more
sensitive to any potential drop in their vicinity, such as the collimator voltage (
Section 6.3
),

Appl. Sci. 2021,11, 2419 18 of 29
and will be attracted [
71
]. Since with this configuration the collimator is placed behind the
housing and the collector is biased to −50 V, they will be directed towards the latter.
(a)0.66 A, 200 V
(b)0.66 A, 250 V
Figure 17.
Current density angular profile without exposure to the plasma beam (Al.05.P configura-
tion) for different collimator potentials. The thruster fires at 0.66 A, 200 V (
a
) and 250 V (
b
). Profiles
are displayed with a linear (top) and logarithmic (bottom) scale.
6. Discussions
6.1. FC Material
Experiments showed the influence of the material on the measured ion current. The
software SRIM (Stopping and Range of Ions in Matter) was used to find the sputtering
yield of Al, C (
≡
graphite) and Mo with Xe as the projectile. SRIM includes a group of
programs which calculate the stopping and range of ions into matter. They use a quantum
mechanical treatment of ion-atom collisions where projectile atoms are considered to be
“ion” and target atoms as “atoms” [
64
]. Simulations that included 10000 singly-charged
xenon ions were run to compute the yield and heat losses. The latter corresponds to the
energy transferred by projectiles to the target materials and subsequently converted into
heat.
Figures 18 and 19
show results for carbon (i.e., graphite) and molybdenum under
singly-charged Xe ion bombardment. Simulation outcomes give an idea on how the target
behaves under Xe ions bombardment.

Appl. Sci. 2021,11, 2419 19 of 29
Figure 18.
Carbon (
top
) and molybdenum (
bottom
) sputtering yields and threshold value for 250 eV
Xe ions computed with the SRIM software.
The software computes the sputtering yield based on the binding surface energy
(
Esur f
) specific to each target. When this value is not known the heat of sublimation is used
instead [
64
]. Moreover,
Esur f
strongly depends on the material cleanliness and roughness.
These properties will change over time as the target gets bombarded. It can lead to quick
change of the sputtering yield. For instance, Figure 18 shows the sputtering yield as a
function of the target atom’s energy which reach the surface of the material. Singly-charged
xenon ions are used as projectile and targets are made of carbon (top) and molybdenum
(bottom). The vertical blue line, which defines the average surface binding energy, marked
7.4 eV and 6.8 eV for the carbon and molybdenum targets respectively. The arrow, to the
left of this line, with the legend “not sputtered” implies the number of atoms which reached
the surface with more than 7.4 eV (C) or 6.8 eV (Mo) is 0.005 and 0.18, respectively. These
values correspond to the sputtering yield and are listed in Table 4. The vertical blue line
will shift towards the left when the material surface gets damaged. The filled area shows
how much effect small changes of the surface roughness (
≡Esur f
) will make on the final
sputtering yield. It is seen that the two materials experience a fast degradation of the yield
when the material surface is damaged. However, the maximum sputtering yield for carbon
remains small (0.32 atoms/ion) compared to Mo yield that is 10 times higher.
Molybdenum targets release 3 to 1 ratio sputtered atoms per incoming ion which is
not negligible. This is coherent with a simple comparison based on the atomic number
between target and projectile. Xenon has an atomic number close to molybdenum, 54 and
42 respectively, while it is 6 for carbon. Since C is much lighter than Xe, the singly-charged
xenon ions need numerous collision events to start sputtering carbon materials.

Appl. Sci. 2021,11, 2419 20 of 29
Figure 19.
Xenon ions energy losses per angstroms to carbon (
top
) and molybdenum (
bottom
) targets
computed with the SRIM software.
In the case of carbon, shortly after the vertical blue line, the yield becomes very small
and sputtered particle only have energies from 7.4 eV to 12 eV. Molybdenum sees its
sputter energy distribution to be more important. The atoms can reach energies from
6.8 eV
up to 20 eV. From these two plots we understand that molybdenum will tend to sputter
more atoms with an energy distribution broader than carbon. Any material subject to
bombardment undergoes a heating process. Its impact can be estimated with the software
SRIM as pictured in Figure 19. It shows the energy loss by the projectile for carbon and
molybdenum. The red curve labelled “IONS” is the direct energy transferred from the ion
to the target electrons. The blue curve, called “RECOILS”, represents the energy transferred
from recoiling target atoms to the target electrons. Both phenomena contribute to the
heating process of materials. Figure 19 pictures ion energy per angstrom losses with targets
made of carbon and molybdenum. Losses are smaller with C than with Mo. Additionally,
the energy loss decreases as the projectile goes deeper into the target. The energy loss
distribution in C is wider through the material thickness than molybdenum. Most energy
losses from Xe ions into Mo occurs near the surface enhancing local heating on the material.
Experimental results and numerical simulations can only suggest conservative mea-
sures to limit plasma–probe perturbations. The material chosen to be placed at the forefront
of a Faraday cup must have a low sputtering yield. It should also have a low and wide
energy absorption capacity to minimize the heating of the material surface.
6.2. Collimator Geometry
Figure 20 shows the evolution of the current utilization (top) and divergence angle
θdiv
(bottom) for different collimator diameters. Results for Hall thruster operation at 200 V
and 250 V with 0.66A are plotted. The divergence angle
θdiv
is not affected by the reduction
of the collimator diameter. The small observed differences are within the measurement
uncertainty. However, the current and propellant utilization computed with each FC
configuration decreases when the collimator diameter is reduced. At 250 V
ηb
and
α
are up
to 33% lower between the 10 mm and 3mm diameter. It leaves no doubt to a dependency of
the measured current density with the aperture diameter. One possible explanation is the
invalidity of the point source assumption that is often found in the literature. Ions originate
from an extended region of space that has an annular geometry. Moreover, the velocity

Appl. Sci. 2021,11, 2419 21 of 29
vector dispersion is large in the case of HTs due to the overlap between the ionization
and acceleration zones combined with many scattering and charge-exchange collision
events. For those reasons, the collected ion current strongly depends on the FC solid angle.
Note that this work reveals the thruster to probe distance necessary for the point source
assumption to be valid is different than four thruster diameters, a classical value often
encountered, if the collection surface is
≤
5 mm. In the conditions of our experiments, a
diameter larger than 5 mm seems correct to be used for further investigation.
Figure 20.
Evolution of the current utilization (
top
), propellant utilization (
middle
) and divergence
angle (
bottom
) computed from current density distributions obtained with different inlet apertures.
Hall thruster is operated at 200 V (blue), 250 V (red) and 0.66A.
6.3. Collimator as Electron Screen
When studying the ion beam of EP devices such as gridded ion engines [
73
] or
FEEPs [75]
with a Faraday cup the collimator is used to redirect secondary electrons back
to the collector while preventing thermal ions from entering the cup. Those EP devices
operate with ion energies from several hundreds to thousands of electron-volts. For plasma
diagnostic standardization we shall start to compare FC architectures and measurement
methods. Hall thrusters deliver high current densities with ion energy relativity low
compared to other EP technologies. Therefore, using electric field to enhance the ion
collection efficiency of a FC while working with a HT can be problematic. Voltages applied
to a Faraday cup are of the same order of magnitude than HT discharge voltages which
can greatly disturb the thruster behavior and properties.
We used SIMION to assess the plasma–probe interaction. SIMION is an ion optics
simulation program that models ion optics problems with 2D symmetrical and/or 3D
asymmetrical electrostatic and/or magnetic potential arrays. In our study, singly-charged
Xe ions with different kinetic energy are flown through a 2-D FC. Additionally, we used the
software to draw the field lines inside and outside the cup to evaluate possible perturbation
with the ambient plasma near the FC entrance. Two FC configurations were used, and
outcomes are shown in Figure 21. The Faraday cup located on the right corresponds to
X.X.P while the left one refers to X.X.E. The top of the figure shows potential lines inside FC
with the collimator (R) grounded and the collector (C) biased to
−
50 V. At the bottom
−
75 V
is applied to the collimator (R) and the collector (C) remains at
−
50 V. Field lines from
−
5 V
to
−
75 V are plotted. For a grounded collimator no major differences are observed between
the two configurations. However, when
−
75 V is applied to the collimator the X.X.P design
shields better field lines in the plasma in the probe vicinity.

Appl. Sci. 2021,11, 2419 22 of 29
Figure 21.
Field lines computed with SIMION. Configurations X.X.E (
left
) and X.X.P (
right
) with the
collimator grounded (top) and at −75 V (bottom).
The current density acquired by G.05.E and Al.05.P enable the computation of
ηb
,
α
and the divergence angle, see Figure 22. There both FC collectors are biased to
−
50 V while
the collimator (R) is grounded. Although there is no impact on the determination of the
divergence angle, we observe that
ηb
and
α
increases with the Al.05.P configuration. Both
parameters are around 10% higher when the Faraday cup housing front is used to collimate
the ion flux. With this design the collector is consequently further away from the point of
collimation. Therefore, primary and secondary electrons from the probe entrance region are
lost before reaching the collector. The latter is better shielded from external perturbations.
Figure 22.
Evolution of the current use (
top
), propellant use (
middle
) and divergence angle (
bottom
)
computed from current density distributions obtained with the collimator grounded and used as an
electron screen. HT operates at 200 V and 250V at 0.66 A.
Furthermore, SIMION was used to simulate the behavior of different monoenergetic
ion beams through the cup, see Figures 23 and 24. The Faraday cup configuration studied
is X.05.P. No material can be selected with the software. Two scenarios were considered.
In the first case, the simulation displayed in Figure 23 includes 200 singly-charged xenon
ions with energy of 5 eV (red), 10 eV (black), 100eV (green) and 250 eV (blue). Ions have a
velocity vector collinear to the Faraday cup axis. In the simulation a 10
°
divergence angle
was applied to maximize the number of ions entering the cup. The collector, represented
by the central cup, is biased to
−
50 V. Twice the potential of the collector is applied to
the collimator, which is only an electron screen now. Section 5.4 shows with such a FC

Appl. Sci. 2021,11, 2419 23 of 29
configuration a fraction of the ion current is collected by the collimator (electron screen)
instead of the collector, see Figure 15 and 16. We observe in Figure 23 no ions are captured
by the collimator. On the contrary the beam is better focused onto the cup for low energy
ions. We also notice that an important part of the beam is collected by the side walls of
the cup.
Figure 23.
Ion simulations computed with the software SIMION. Each configuration displays the
ion trajectory going through the FC. Potential is fixed at
−
50 V and
−
100 V for the collector and
collimator, respectively. Ion energies are 5eV (red), 10 eV (black), 100eV (green) and 250eV (blue).
The probe aperture diameter is 5mm
In the second scenario we assumed ion beam trajectories with different incident angles,
see Figure 24. At the top of the figure ions with low energy (10 eV) are flowing through
the cup. The bottom figure shows results for 250 eV ions. The ion energy range was
chosen based on the large ion energy distribution within the plume of a Hall thruster.
For experimental purposes, the incident angles were chosen randomly, and the slope was
accentuated to maximize the chance for an ion to be collected by the collimator. The goal
here being to assess the probability of an incoming ion to reach the collimator placed behind
the housing front. We observe that low energy ions are focused and directed towards the
cup. However, highly energetic ones get closer to the collimator and a small fraction
manage to touch it. Most of the ions are still collected by the side wall of the cup.
Figure 24.
Ion simulations computed with the software SIMION. Each configuration displays the
ion trajectory through the FC. The color code refers to different incident angles. Potential is fixed
at
−
50 V and
−
100 V for the collector and collimator, respectively. Ion energies are 10eV (
top
) and
250 eV (bottom).
Consequently, two additional simulations were run as shown in Figures 25 and 26.
Here, we consider ion reflection or rebound from the original beam to the cup side and rear
walls. The semi-half-angle of the possible reflected ions was maximized to 90
°
.
Figure 25
shows the results of 250eV ion reflection from the cup side walls at different locations for
35 mm (black), 40 mm (red), 45mm (green) and 50 mm (blue) the bottom of the cup. It is
assumed that in the best case reflected ions lose more than 95% of their energy and in the
worst case only 50%. Ions with 10 eV and 100 eV are flown with random horizontal velocity

Appl. Sci. 2021,11, 2419 24 of 29
vectors. For each case, the Faraday cup has a collector at
−
50 V and the collimator is either
grounded (top) or biased to
−
100 V (bottom). When the collimator is grounded, around
5% of the ions with high energy escape the cup while all low energy ones are completely
redirected back to the collector. However, once the collimator is at
−
100 V close to 10% of
low energy ions escape the cup or are collected by the collimator. Ions with 100 eV are not
affected by the change of equipotential field lines inside the cup.
Figure 25.
Ion simulations computed with the software SIMION. Each configuration displays the
possible trajectory of ion rebounds from the lateral side of the FC. The color refers to different
rebound location. The collector is at
−
50 V. The collimator is either grounded (top) or biased to
−100 V (bottom). Ion energies are 10eV (left) and 100 eV (right).
Figure 26 simulates ion rebounds from the bottom of the Faraday cup (50mm) for
energies of 10eV (black), 50 eV (red), 75 eV (green) and 100 eV (blue). The collector is
at
−
50 V while the collimator is either grounded (top) or
−
100 V (bottom). In the same
manner than ion reflection from the side walls, applying a potential to the collimator does
attract a small fraction of reflected ions from the cup bottom. Most of the ions collected by
the collimator are low energy ones.
Numerical simulations show the probability to collect primary ions from the original
beam with the collimator protected behind the FC housing is negligible. Using a more
negative potential on the collimator than on the collector enhances the ion trajectory
towards the cup. This, however, leads to a larger ion spread, hence a larger ion collection
on the side walls of the cup. Furthermore, ions reflected at the bottom and side walls
of the cup can be directed towards the collimator if the latter is biased more negatively
than the collector. As a result, a small fraction of the primary ions is not collected and the
measured ion current is lower as seen during experiments, see Section 5.4. In our study,
we used a collector disk made of aluminum foam which should reduce ions reflection and
enhance ions trapping. However, the collector is electrically and mechanically connected
to a stainless steel hollow cylinder, termed cup, see Section 3.1, which has no ion trapping
capacities. Further investigations shall be carried out with a cup fully made of foam. It
would bring more information about the influence of ion reflection inside a Faraday cup.
Finally, a Hall thruster plume is more complex than a simple ion beam. Consequently,
these simulations must be seen as a first, yet valuable, step to better grasp the ion behavior
inside a FC.

Appl. Sci. 2021,11, 2419 25 of 29
Figure 26.
Ion simulations computed with the software SIMION. Each configuration displays the
possible trajectory of ion rebounds from the bottom of the FC. The collector is at
−
50 V. The collimator
is either grounded (top) or biased to
−
100 V (bottom). Ion energies are 10 eV (black), 50eV (red),
75 eV (green) and 100 eV (blue).
7. Conclusions
In this paper, challenges in designing and using the collimator of a Faraday cup have
been investigated in the case of Hall thruster plume through both experiments and com-
puter simulations. Results allow us to propose general guidelines to optimize the architec-
ture of a Faraday cup collimator. First, the front of the probe should be made with material
that can sustain local heating and that exhibits a low sputtering yield (
Sections 5.2 and 6.1
).
Secondly, the distance between the point of collimation and the collector should be greater
than the plasma sheath (Section 6.3). Moreover, in the case where the far-field plasma
region of the ISCT200 is studied with FC architecture presented in this paper, the hypothesis
of a point source is valid if the probe aperture diameter is
≥
5 mm (Sections 5.3 and 6.2).
Further studies where the probe to thruster distance varies and the HT mean diameter
(D
HT
) changes could bring valuable information to find a limit and relation between HT
dimension, Faraday cup aperture diameter (d
a
) and probe-thruster distance (l). In our
case, we recommend for l
∼
6 D
HT
to use a FC with D
HT <
10d
a
. Additionally, the collector
must be biased negatively, the exact value must be determined with I–V characterization
since it depends on the thruster plume properties, to attract and capture primary ions
of the thruster plume (Section 5.1). Finally, the use of an additional electrode, placed
between the point of collimation and the collector, to enhance SEE recollection is not
necessary (
Sections 5.4 and 6.3
). Eventually, to reduce measurement perturbations due to
plasma–probe interaction (CEX, SEE), particular attention must be paid to the optimization
of the geometry and material properties of the cup and collector. Based on results obtained
in this study, we can propose an optimal Faraday cup front architecture to study the plume
of a low-power Hall thruster at a distance greater than four times the HT channel outer
dimension. The configuration X.X.P provides more reliable results and shield better the
collector against perturbation induced by ambient plasma in the cup vicinity. Therefore,
the FC should be equipped with a collimator used as electron screen and should use the
front of its housing to collimate the ion flux through the collector cup. Additionally, this
study did not assess the collector materials and dimensions. Nevertheless, based on our
experiments a long cup with a metallic foam placed at its rear side seems to be adequate.
Author Contributions:
Investigation, H.V.; Supervision, M.S.; Validation, M.S.; Writing—original
draft, H.V. and M.S.; Writing—review and editing, H.V. All authors have read and agreed to the
published version of the manuscript.

Appl. Sci. 2021,11, 2419 26 of 29
Funding:
V.H. benefits from an ENPULSION grant. Part of this research is financially supported by
the ESA, ESTEC under grant PO-5401003120, by the Région Centre-Val de Loire through the PEPSO-2
program and by the European Union’s Horizon 2020 research and innovation program under grant
agreement 730135 CHEOPS.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement:
Plume data obtained in the frame of this study are available upon re-
quest. Contact the corresponding author. Data about the ISCT200 Hall thruster design
are confidential.
Acknowledgments: The authors would like to thank Aumayr for his support on theoretical subject
regarding plasma diagnostics design and behavior. Additionally, we would like to thank T. Hallouin
for his help and expertise on Hall Thrusters.
Conflicts of Interest: The authors declare no conflict of interest.
Abbreviations
The following abbreviations are used in this manuscript:
CEX Charge-EXchange
EP Electric Propulsion
FC Faraday Cup
FEEP Field Emission Electric Propulsion
GIE Gridded Ion Engine
HT Hall Thruster
IIEE Ion Induced Electron Emission
ISCT200 Icare Small Customizable Thruster 200
NExET New Experiments on Electric Thrusters
SEE Secondary Electron Emission
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