AIAA 2005-4243
41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit
10 - 13 July 2005, Tucson, Arizona
The Performance and Wear Characterization of a HighPower High-Isp NASA Hall Thruster
Peter Y. Peterson*
QSS Group Inc., Cleveland, Ohio, 44135, US
David T. Jacobson*, David H. Manzella†, and Jeremy W. John*
NASA Glenn Research Center, Cleveland, Ohio, 44135, US
The performance of a 50-kilowatt-class Hall thruster designed for high voltage operation
was measured using both xenon and krypton propellants. The thruster was operated at
discharge powers ranging from 4-46 kW on xenon and 5-65 kW on krypton. The device
produced thrust ranging from 0.3 to 2.1 N at discharge voltages between 200 and 1050 V.
Maximum anode specific impulses of 3370 and 4940 sec. were demonstrated at discharge
voltages of 600 V on xenon and 1050 V on krypton, respectively. The peak anode efficiencies
were 72% at 600 V on xenon and 68% at 1050 V on krypton. In addition to performance
testing the thruster was operated on krypton at 700 V and 53 A to characterize the thruster
wear. The observed wear characteristics of the thruster were compared to previous xenon
Hall thruster wear results.
Nomenclature
A
GC
Isp
Id
=
=
=
=
=
Ampere
Gas correction factor
Anode specific impulse
Discharge current
Anode propellant mass flow rate
[A]
[-]
[s]
[A]
[mg/s]
v&a
=
=
=
=
=
=
=
=
=
Newton of Force
Anode efficiency
Base pressure of the facility
Indicated pressure of the facility
Corrected pressure of the facility
Standard Cubic Centimeter Per Minute
Second
Thrust
Anode propellant volumetric flow rate
[N]
[%]
[Torr]
[Torr]
[Torr]
[-]
[sec.]
[N]
[sccm]
Vd
V
= Discharge voltage
= Voltage
m& a
N
ηT
pbase
pindicated
pc
SCCM
sec.
T
I
[V]
[V]
I.
Introduction
n 2003, a decade after the termination of the U.S. Government’s multi-agency, SP-100 space nuclear power
development program [1], the Nuclear Systems Initiative (NSI) program was established. This program was
conducted under the auspices of the National Aeronautics and Space Administration (NASA) in partnership with the
Department of Energy [2]. The program objectives included the development of radioisotope power systems and
nuclear electric propulsion technologies required for ambitious exploration of the solar system, which is central to
NASA’s mission to explore the universe and search for life. In 2004, NASA renamed the effort ‘Project
*
†
Research Engineer, Electric Propulsion Branch, 21000 Brookpark Road, MS 301-3, and AIAA Member.
Senior Research Engineer, Electric Propulsion Branch, 21000 Brookpark Road, MS 301-3, and AIAA Member.
1
American Institute of Aeronautics and Astronautics
Copyright © 2005 by the American Institute of Aeronautics and Astronautics, Inc.
The U.S. Government has a royalty-free license to exercise all rights under the copyright claimed herein for Governmental purposes.
All other rights are reserved by the copyright owner.
Prometheus’ and the first application for the nuclear electric propulsion technology was identified as the Jupiter Icy
Moons Orbiter (JIMO). Ion thruster technology was to propel the JIMO spacecraft to Jupiter’s three icy moons,
Callisto, Ganymede, and Europa in search of ocean life.
In addition to the technology development work being performed in support of the proposed JIMO mission,
broad-based research and development has been conducted for future missions under the sponsorship of the
Prometheus Advanced Systems and Technology project. NASA Glenn Research Center (GRC) has investigated
Hall thruster operation at power levels and specific impulses consistent with mission objectives of the project.
Initially, the performance of an existing high-power Hall thruster operating on krypton propellant was measured [3].
The specific impulse and thruster efficiency goals (>4000 seconds, >60%) were achieved, which indicated that
further development was warranted. An improved Hall thruster, designated the NASA-400M was designed and
fabricated for further investigation of high-power, high-specific impulse operation.
The work presented here describes the measured performance of the NASA-400M operating on xenon and
krypton propellants and wear characterization of the thruster operating on krypton. The experimental facilities,
thruster, thrust stand, and laser profilometery system used to measures the performance and wear characteristics are
described.
II.
Experimental Apparatus
A. Hall Thruster
The NASA-400M was design to operate at highpower and high-specific impulse (Isp). The thruster
is based on the NASA-457M high-power Hall
thruster that demonstrated operation at power levels
up to 98 kW [3-6]. The NASA-400M discharge
channel had a diameter of 400 mm with an
anode/propellant distribution system similar to the
NASA-457M system described in Ref. [5]. The
NASA-400M
thruster
design
incorporated
improvements resulting from NASA-457M
development. These improvements include an
enhanced magnetic field topology and a higher field
strength in the discharge channel. A modified
discharge channel geometry was also employed to
improve the performance at high discharge voltages Figure 1. A photograph of the NASA-400M.
and krypton operation. A photograph of the NASA400M is shown in Figure 1. A hollow cathode,
capable of providing 100 A of emission current, was
mounted in the center of the thruster with the tip of
the cathode extending approximately 25 mm
downstream of the exit plain of the discharge
channel. Further details of this cathode can be
found in Ref. [7].
B. Vacuum Facilities
The performance and wear characterization of
the NASA-400M was conducted in vacuum facility
5 (VF-5) at NASA GRC. VF-5, shown in Figure 2,
is 4.6 m in diameter by 19.2 m in length chamber
with a pumping speed in excess of 3,500,000 liters
per second (air) provided by a combination of
twenty 0.9 m diameter oil diffusion pumps and over
40 m2 of liquid helium cryopanel surface. The
facility includes isolated ports that allow tests to be
conducted without the need to cycle the main Figure 2. Vacuum Facility 5 exterior with the high power
chamber to atmosphere. In 2001, a high power test port.
electric propulsion test port (1.8 m in diameter by
2
American Institute of Aeronautics and Astronautics
2.4 m in length) was installed on the end of VF-5 to expedite evaluation of large-scale Hall thrusters. High power
thrust stand was installed in the test port on a rail system that allows the stand and the thruster to be moved into and
out of the test port.
C. Power Supply, Data Acquisition, and Control Systems
The performance and wear characterization of the NASA-400M was conducted with a high-power console
consisting of a discharge supply and various auxiliary power supplies. The discharge power supply was capable of
producing a constant voltage output ranging from 0-2000 V at current levels of 0-100 A for a total output power of
200 kW. The auxiliary power supplies included two electromagnetic coils supplies, and a heater and keeper supplies
for a NASA hollow cathode. This power console was installed and used during the performance evaluation of the
NASA-457M [3, 5, 6].
The data acquisition system used for the NASA-400M characterization was a 22-bit multiplexed datalogger with
computer interface. The datalogger monitored the voltages, currents, temperatures, propellant flow rates, chamber
pressure, and thrust every second during performance testing and every 5 minutes during the wear characterization.
The computer interface had the additional benefit of allowing a number of monitored channels to control a five-volt
transistor-transistor logic (TTL) output. The TTL output from the datalogger was routed to the power console and
propellant flow system. If an alarm condition was encountered, such as a variation in the discharge current beyond
the alarm limits, the datalogger discontinued the TTL output and the power console and propellant flow systems
were shut down. The uncertainties of the datalogger measurements were 0.05% for the voltage and current
measurements.
D. Flow System
The NASA-400M thruster utilized three
independent propellant flow controllers.
A
combination of two 500 SCCM flow controllers
provided propellant to the anode. A 100 SCCM
flow controller provided flow to the cathode. The
two propellants used for the evaluation of the
NASA-400M were 99.999% pure xenon and
krypton. The flow controllers were calibrated
before and after testing using a constant volume
flow technique and a commercially available
volumetric flow rate calibration system.
The
observed error between flow calibrations for xenon
was no greater than 2.2% for the anode and 1.2%
for the cathode and for krypton no greater than 1.2%
for both the anode and cathode. The anode flow
error was attributed to a 500 SCCM flow controller Figure 3. Illustration of the laser profilometry technique.
that exhibited higher than normal uncertainty of
4.2% for xenon operation and 2.5% for krypton
operation.
E. Thrust Stand
The performance characterization of the NASA400M was measured with an inverted pendulum
null-type thrust stand. This thrust stand had an
accuracy of 1% full scale for forces ranging from a
few mN to several Newtons of thrust. The
operation and theory of the inverted pendulum nulltype thrust stand were described in detail in Refs.
[8, 9]. The high-power thrust stand was operated in
a null-type configuration, which allows the thruster
to remain stationary while testing. The thrust stand
was also equipped with a closed loop inclination
control circuit, which utilized a piezoelectric
element to minimize thermal drift during
Figure 4. Circumferential Erosion Survey System.
3
American Institute of Aeronautics and Astronautics
performance testing. The thrust stand was calibrated in-situ with calibrated masses on a pulley system connected to
a stepper motor. The thrust stand was calibrated before and after each performance mapping period. No thermal
drift was observed during testing
F. Laser Profilometry
A laser profilometry system previously used during the T-220, D-80, and NASA-120M wear investigations [1012] was employed to measure the channel wear. This system utilized a cylindrical lens and a laser to produce a
plane of light perpendicular to the eroded discharge channel. The interaction of the laser light on the surface of the
sample formed a line that was imaged by a charged coupled device (CCD) camera located at a different angle, as
shown in Figure 3.
The CCD camera was equipped with a telecentric lens to limit the effect of image distortion from magnification.
The laser, CCD camera, and thruster were mounted on a rigid, aluminum frame as illustrated in Figure 4. The
thruster was affixed to a rotation stage and the laser was adjusted such that the plane of light crosses the center of the
thruster. The wear profiles for the inner and outer walls of the discharge channel were mapped by one-degree
increments. The uncertainty was less than ±0.05
mm for both radial and axial directions. The error
was determined by examining the distortion width
of the imaged beam profiles and comparing them to
known scales in the images.
III.
Results and Discussion
Anode Efficiency
A. Performance Characterization
The NASA-400M thruster was operated with
xenon and krypton propellants at power levels
ranging from 4-65 kW. The 100 A hollow cathode
was operated with the same propellant as the
thruster.
A photograph of the NASA-400M
Krypton
operating with krypton propellant is shown in
Figure 5.
Figure 5. A photograph of the NASA-400M operating on
During the performance testing of the NASA- krypton.
400M, the cathode flow rate was varied to maintain
a cathode floating voltage
75%
greater than -20 volts and stable
thruster operation. As a result,
the cathode flow varied from
70%
12-34% of the anode flow. The
optimized cathode flow rate for
Hall thrusters with discharge
65%
powers greater than 1 kW were
typically 5-10% of the anode
mass flow rate [13, 14]. The
60%
operation of the NASA-400M
required an increase in the
cathode flow rate for both
55%
xenon and krypton operation
beyond the optimized ratios of
Xe (21 mg/s, 215 sccm)
5-10% of the anode mass flow
50%
Xe (38 mg/s, 389 sccm)
rate.
The increase in the
Xe (60 mg/s, 615 sccm)
cathode flow for the NASAXe (72 mg/s, 737 sccm)
400M reduced the total
45%
efficiency and Isp of the
1200
1600
2000
2400
2800
3200
3600
thruster by 3-11% (absolute)
Anode Isp [sec]
and up to 550 sec., respectively,
as compared to operation with a Figure 6. The anode efficiency as a function of the anode Isp for the NASAcathode flow of 5-10% of anode 400M operating on xenon propellant.
4
American Institute of Aeronautics and Astronautics
75%
70%
65%
Anode Efficiency
mass flow rate. Due to the
abnormally high cathode flow
rates required by the laboratory
100 A cathode, performance
characteristics are discussed
based on the anode (discharge)
efficiencies and anode Isp.
Anode Isp [sec]
1. Xenon
60%
The performance of the
NASA-400M was measured
with anode xenon propellant
55%
flow rates ranging from 20 to
72 mg/s and discharge voltages
ranging from 200 to 600 V.
Xe (21 mg/s, 215 sccm)
50%
Xe (38 mg/s, 389 sccm)
The discharge voltage was
Xe (60 mg/s, 615 sccm)
limited to 600 V during the
Xe (72 mg/s, 737 sccm)
xenon testing due to an anode
45%
isolation issue that was
100
200
300
400
500
600
700
addressed prior to krypton
Discharge Voltage [V]
testing. The xenon performance
results are tabulated in Table 1 Figure 7. The anode efficiency as a function of the discharge voltage for the
in the Appendix. The anode NASA-400M operating on xenon propellant.
efficiency as a function of
anode Isp is shown in Figure 6.
3500
The anode efficiency and Isp as
a function of discharge voltage
are shown in Figure 7 and
3000
Figure 8, respectively.
The
anode
efficiency
increased with anode Isp for all
the flow rates investigated and
2500
did not exhibit a maximum as
observed in other Hall thrusters
[15-18] and discussed in detail
2000
in Refs. [19, 20]. At the lowest
xenon flow rate (21 mg/s), the
Xe (21 mg/s, 215 sccm)
anode efficiency did not
Xe (38 mg/s, 389 sccm)
increase at the same rate as the
Xe (60 mg/s, 615 sccm)
1500
higher flow rates.
This
Xe (72 mg/s, 737 sccm)
behavior has been associated
Theoretical Isp (Singly-Charge)
with a decrease of the
Theoretical Isp (Multi-Charge)
1000
propellant utilization efficiency
100
200
300
400
500
600
700
as a result of decreased
Discharge Voltage [V]
propellant density [19].
A
maximum of 72% xenon anode Figure 8. The anode and theoretical Isp curves as a function of the discharge
efficiency was measured at 600 voltage for the NASA-400M operating on xenon propellant.
V and a flow rate of 60 mg/s.
The minimum xenon anode efficiency of approximately 48% occurred at the lowest voltage tested, 200 V, and a
flow rate of 60 mg/s.
The anode Isp increased as a function of the discharge voltage, and ranged between 1320 to 3370 sec. on xenon,
as shown in Figure 8. For a given voltage the measured anode Isp at the lowest flow rate was less than the Isp at the
higher flow rates. These results were attributed to operating the thruster below an optimal neutral particle density
and thereby resulting in a decreased propellant utilization. Figure 8 includes two theoretical Isp curves calculated
for an ionized propellant undergoing complete acceleration at the applied potential. The first theoretical Isp curve
relates single charged propellant as a function of discharge voltage and the second curve relates multiple charged
5
American Institute of Aeronautics and Astronautics
propellant as a function of discharge voltage [21]. In the multiple charged theoretical Isp curve, the fraction of
double charged ions was assumed to be approximately 27%. This fraction of the multiple charged ions was based
on the highest double charged ion species fraction data collected from the NASA-457M operating on xenon with an
ExB probe.
Anode Efficiency
Anode Efficiency
2. Krypton
The performance of the NASA-400M operating on krypton was measured with anode propellant flow rates
ranging from 11.6 to 44.6 mg/s and discharge voltages ranging from 300 to 1050 V. The discharge voltage was
limited to 1050 V during krypton testing due to additional voltage isolation issues. The results of the krypton
performance are tabulated in
70%
Table 2 in the Appendix. The
krypton anode efficiency as a
68%
function of anode Isp for the
66%
NASA-400M is shown in
Figure 9. The anode efficiency
64%
and Isp as a function of
discharge voltage are shown in
62%
Figure 10 and Figure 11,
respectively.
60%
The
anode
efficiency
58%
increased with anode Isp and
discharge voltage for all the
56%
flow rates investigated. The
Kr (25 mg/s, 401 sccm)
anode efficiency of the NASA54%
Kr (31 mg/s, 504 sccm)
400M did not decrease with
Kr (38 mg/s, 610 sccm)
increasing discharge voltage, as
52%
Kr (45 mg/s, 716 sccm)
discussed with the use of xenon
50%
propellant. This indicated that
2000
2500
3000
3500
4000
4500
5000
the electron leakage current and
propellant utilization were
Anode Isp [sec]
maintained with increasing
Figure 9. The anode efficiency as a function of the anode Isp for the NASAdischarge voltage.
Further
400M operating on krypton propellant.
thruster plume diagnosis of the
70%
thruster could indicate the
actual influence of the current,
68%
charge, voltage, and propellant
utilization
efficiencies
on
66%
thruster operation [19, 20].
However,
recent
krypton
64%
performance
and
plume
62%
characterizations of the NASA173M
provided
sufficient
60%
insight into the operation of
NASA Hall thrusters on
58%
krypton [22]. Since these Hall
thrusters share similar magnetic
56%
field characteristics, such as
Kr (25 mg/s, 401 sccm)
54%
field topology and radial
Kr (31 mg/s, 504 sccm)
magnetic field profiles across
Kr (38 mg/s, 610 sccm)
52%
the discharge channel, the
Kr (45 mg/s, 716 sccm)
conclusions of the NASA-173M
50%
krypton testing were deemed
200
300
400
500
600
700
800
900
1000
1100
appropriate.
Discharge Voltage [V]
The results of the NASA173M operating on krypton Figure 10. The anode efficiency as a function of the discharge voltage for the
showed improved performance NASA-400M operating on krypton propellant.
6
American Institute of Aeronautics and Astronautics
Anode Isp [sec]
Anode Isp [sec]
5000
as compared to previous
krypton studies [23-27], but not
to the same extent as observed
4500
during high power Hall thruster
krypton studies [3]. This has
been
attributed
to
the
4000
configuration of the discharge
channel geometry and the radial
profiles of the applied magnetic
3500
field of higher power devices.
In previous Hall thruster
investigations, the thruster
3000
efficiency operating on krypton
Kr (25 mg/s, 401 sccm)
Kr (31 mg/s, 504 sccm)
was lower than the efficiency
Kr (38 mg/s, 610 sccm)
operating
on
xenon
for
2500
Kr (45 mg/s, 716 sccm)
equivalent volumetric flow rates
Theoretical Isp (Singly-Charge)
[23-27]. These studies have
Theoretical Isp (Multi-Charge)
shown that some of the
2000
performance loss can be
200
300
400
500
600
700
800
900
1000
1100
compensated for by increasing
Discharge Voltage [V]
the volumetric flow rate until
the mass flow rate of krypton Figure 11. The anode and theoretical Isp curves as a function of the discharge
was equal to xenon flows rates. voltage for the NASA-400M operating on krypton propellant.
However, even with the
increased mass flow rate of krypton, the thruster efficiency was still less than xenon, and the resulting thruster Isp
was at best equal to the xenon Isp at the same mass flow rates [23]. Furthermore, by increasing the volumetric flow
rate of the krypton, the neutral propellant density in the discharge channel was increased beyond that of xenon at
equivalent volumetric flow rates. This resulted in greater current and power densities for krypton operation as
compared to xenon, which could limit the operation of the thruster due to thermal and/or lifetime issues.
During the present investigation the anode Isp increased as a function of the discharge voltage and ranged
between 2200 to 4940 sec., as shown in Figure 11. Figure 11 includes two theoretical Isp curves calculated for an
ionized propellant undergoing complete acceleration at the applied potential. The first theoretical Isp curve relates
single charged propellant as a
6000
function of discharge voltage,
and the second curve relates
multiple charged propellant as a
5000
function of discharge voltage.
A double charged ion fraction
of 16% was used to estimate the
4000
multiple charged theoretical Isp
curve in Figure 11.
This
fraction of the multiple charged
3000
ions was based on the highest
double charged ion species
fraction data collected from the
2000
NASA-457M operating on
krypton with an ExB probe.
Xenon
The ExB probe data of the
1000
NASA-457M indicated that the
Krypton
double charged species fraction
of krypton was less than the
0
observed results with xenon.
0.00
0.50
1.00
1.50
2.00
2.50
These results were consistent
Thrust [N]
with the NASA-173M results
[22], the fact that krypton has a Figure 12. Performance regime of the NASA-400M operating on xenon and
higher
first
and
second krypton.
7
American Institute of Aeronautics and Astronautics
ionization potential, and krypton has a lower ionization frequency due to decreased resident time in the discharge
channel. The lower double charged species-fraction results also indicated that higher order ionization could be
dismissed as an explanation for describing krypton decreased performance. Therefore, the propellant utilization
efficiency was likely the primary factor influencing krypton Hall thruster performance.
Anode Isp [sec]
Anode Efficiency
3. Xenon and Krypton Comparison
The NASA-400M Hall thruster performance regimes for both xenon and krypton propellants are shown in Figure
12. Xenon propellant are suitable for low Isp and high thrust mission requirements. The improved krypton Hall
thruster operation provides the
75%
opportunity for using Hall
thrusters for missions that
require higher Isp and still
70%
moderate thrust densities.
A previous investigation
demonstrated efficient krypton
65%
operation using the NASA457M Hall thruster [3]. The
anode efficiency of the NASA60%
400M as a function of discharge
power is shown in Figure 13 for
xenon and krypton propellants.
55%
Figure 13 also illustrates the
efficiency of the NASA-457M
for krypton operation.
As
Xenon
50%
mentioned in section II-A, the
Krypton
NASA-400M included several
Krypton (NASA-457Mv1)
design
improvements
to
45%
increase the performance of the
0
5
10
15
20
25
30
35
40
45
50
thruster at higher Isp conditions,
Discharge Power [kW]
and optimize krypton operation,
as compared to the NASA- Figure 13. The NASA-400M anode efficiency as a function discharge power for
xenon and krypton, including the krypton performance results of the NASA457M.
The
drop
in
anode 457M.
5500
efficiency between the xenon
and krypton operation with the
5000
NASA-400M was not as great
as previously measured with
4500
other Hall thrusters [3, 22-24,
27]. The improved krypton
4000
Hall thruster efficiency resulted
in greater Isp for a given
3500
volumetric flow rates and
discharge
voltage.
A
3000
comparison of the anode Isp of
the NASA-400M as a function
2500
of discharge power is shown in
Figure 14.
The improved
2000
Xenon
krypton Hall thruster operation
Krypton
of this Hall thruster may
1500
provide mission design greater
flexibility in choosing a
1000
propulsion system.
0
5
10
15
20
25
30
35
40
45
50
B. Thruster
Characterization
Wear
Discharge Power [kW]
Figure 14. The NASA-400M anode Isp as a function of discharge power for
xenon and krypton.
8
American Institute of Aeronautics and Astronautics
Normalized Radial Wear
Axial Position
The second component of
the NASA-400M investigation
0°
was to gain an understanding of
the wear characteristics of a
high-power, high-voltage Hall
C
90°
270°
thruster operating on krypton
propellant.
The
wear
180°
characteristics of a magnetic
layer Hall thruster operating
above 500 V, and using a
Inner BN Wall
Outer BN Wall
lighter atomic mass propellant,
have not been previously
reported.
A previous highInitial Profiles
voltage wear characterization,
Profiles (86 hours, 344 mm^3/hr)
of a magnetic layer Hall
Profiles (220 hours, 253 mm^3/hr)
thruster, was the 1000 hour
Profiles (292 hours, 177 mm^3/hr)
wear test of the T-220 [11].
The T-220 was operated at 500
V and 20 A, with xenon as a
Radial Position
propellant. It was determined
that the krypton wear test of the Figure 15. The inner and outer wall erosion profiles of the NASA-400M
NASA-400M
would
be
operating on krypton at 700 V and 37 kW.
conducted at a discharge
voltage of 700 V and a power level of 37 kW. This condition demonstrated stable operation and performed well
with an anode efficiency and Isp of 65% and 4000 sec., respectively. The discharge channel was replaced prior to
the beginning of the wear characterization to provide known initial wall profiles. The original goal of the wear test
was to operate the thruster for 1000 hours, however due to facility and thruster issues the test was terminated after
292 hours. The termination of the wear test was due to anomalous operation, which led to a failure of the thruster.
The cause of the unexpected operational characteristics are unknown, but may be attributed to sputtered material
deposition on the thruster, which lead to frequent shorting of the discharge plasma. The original test matrix called
for wear measurements to be made approximately every 200 hours, however due to unscheduled shutdowns, the
wear measurements were obtained at 86, 220, and 292 hours of operation at a single radial position.
The inner and outer wall
1.2
wear profiles of the wear test of
Outer Wall
the NASA-400M are shown in
1
Figure 15. The wear region of
0.8
the inner wall begins slightly
upstream of the outer wall. The
0.6
beginning of the inner and outer
0.4
NASA-400M Inner Wall
wall wear regions correspond
NASA-400M Outer Wall
approximately to the axial
0.2
T220 Inner Wall
locations where the radial
Decreased radial wear rates
T220 Outer Wall
0
for the T-220 at ~550 hours
magnetic field is ~80% of the
Inner Wall End of Life
maximum of the radial field for
-0.2
Outer Wall End of Life
this operating condition. This
-0.4
relationship was also observed
on the NASA-120M discharge
-0.6
channel material investigations
-0.8
in Ref. [12]. In addition, the
ionization region of a Hall
-1
Inner Wall
thruster has been shown to
-1.2
occur at the axial location
0
200
400
600
800
1000
1200
where ~80% of the maximum
Time
[hours]
of the radial magnetic field is
located [28, 29]. Therefore any Figure 16. The normalized radial wear at the exit regions of the inner and outer
discharge channel wear should walls of the NASA-400M compared to the T-220.
9
American Institute of Aeronautics and Astronautics
Normalized Volumetric Wear Rate
not occur upstream of the ionization region. The further downstream from the beginning of the ionization region,
the more energy the ions gain due to the applied potential. The exact physical mechanism that causes the ionized
propellant to be directed towards the wall is not completely understood and theories range from radial electric fields
formed from wall sheaths [30] to simple elastic collisions between ions and neutrals [31]. In Ref. [31] the axial
location of ~80% of the radial maximum field corresponded to the axial location in which the model predicted that
the accelerated ions reach the minimum cutoff potential for sputtering, also described as the threshold energy for
sputtering of a target material [32]. The results from the experiment wear studies and the wear modeling suggest
that the wear, and lifetime, of a Hall thruster can be influenced by the configuration of the applied magnetic field.
The end of life for a Hall thruster has been defined when the discharge plasma erodes through the wall material
to expose the magnetic circuit. Once the magnetic circuit is exposed, the plasma will begin to erode the material of
the magnetic circuit. Over time, the erosion of the magnetic circuit will begin to influencing the applied magnetic
field in the discharge channel of the thruster. Once the applied magnetic field begins to change the operation of the
thruster is no longer optimized and the operational characteristics of the thruster may vary.
A comparison of the normalized radial wear, as a function of time, at the exit plane of the magnetic circuit for
the NASA-400M and the T-220 are shown in Figure 16. The radial wear has been normalized to the width of the
inner and outer channel walls for each thruster for comparison purposes. The radial wear data of the T-220, from
Ref. [11], indicated two distinct radial wear rates. The higher initial radial wear rate occurred to approximately 550
hours and then decreased to a lower rate for the remainder of the T-220 test. Similar wear trends were observed
with the life test of the SPT-100 [33, 34]. Further evidence of this Hall thruster wear characteristic is shown in
Figure 17, a comparison of the normalized volumetric wear rates of the SPT-100, T-220, NASA-120M, and the
NASA-400M. The volumetric wear rates in Figure 17 begins with a large wear rate then asymptotes to a smaller
rate after approximately the first 500 hours.
The volumetric wear rate, in Figure 17, was normalized by the channel cross-section area and the width of the
discharge channel. The formulation and results of a Hall thruster lifetime model [31] indicated that inelastic
collisions between the ionized and neutral propellant particles are primarily responsible for the change in wear rate
with time. The results from Ref. [31] also suggest that the width of the discharge channel may play an important
role in the lifetime of a Hall thruster. Increasing the channel width of a Hall thruster, at a fixed cross-sectional area,
will decrease the likelihood of the deflected ionized particles intersecting the channel walls and causing sputtering.
Therefore, it was determined that normalization of the volumetric wear rates by both the cross-sectional area of the
discharge channel and the width of the channel was appropriate. By normalizing the wear rate in this fashion, a
thruster with a large diameter and small width could be compared to a channel with the same cross-sectional area
and larger width.
The normalized volumetric
wear rates of the NASA-120M,
2.5
T-220, and the NASA-400M as
a function of time was less than
that of the SPT-100 results.
2
The SPT-100 was operated at
its nominal operating condition
where as the other thrusters
T-220
were either operated at a
1.5
reduced power level than
SPT-100
nominal, had a non-symmetric
NASA-400M
discharge channel, and/or a
NASA-120Mv1
1
lighter atomic mass propellant.
The
NASA-120M
wear
investigation was conducted at
0.5
one operation condition for 200
hours for each material studied
[12]. The volumetric wear rate
of the NASA-120M, shown in
0
Figure 17, was conducted at a
0
500
1000
1500
2000
2500
3000
3500
4000
lower power level than the
Operating Time [hours]
nominal design point and the
exit plane was located slightly Figure 17. The normalized total wear rate of the NASA-400M compared to the
upstream of the nominal axial SPT-100, T-220, and the NASA-120M.
10
American Institute of Aeronautics and Astronautics
location due to the particular design of the thruster. The volumetric wear rate results of the T-220 were obtained at
the nominal operating condition of the thruster, however the outer wall of the discharge channel ended further
upstream than the inner wall. Given that the outer wall ended closer to the axial location of the ionization region
than the inner wall, the accelerated ionized propellant that was directed or redirected towards the outer wall had a
smaller probability of actually contacting the outer wall. This offset of the axial location of the discharge chamber
walls makes it problematic to compare the volumetric wear rates of the T-220 with other thrusters. The NASA400M was operated on krypton propellant at a lower power level than the nominal xenon design condition.
Experimental and phenomenological model studies of different atomic mass ionized gases at equivalent energies,
charge, and angle of incidence impacting on the same target material have shown that the sputtering of target
material to be dependent on the momentum of the ionized gas [35-37]. Examining the ratio of the momentum of
single charged krypton to xenon ions at equivalent energies, and neglecting the influence of the angle of incidence, a
krypton ion will impact a target material at approximately 81% of the momentum of a xenon ion. Comparing this
simple result to the sputtering rate data collected by Kim in Ref. [35] and the species fraction data presented in
section III-A, the 30-50% reduced sputtering data of krypton, compared to xenon, is understandable. The ion
species fraction measurements of the NASA-457M indicated that operating a Hall thruster on xenon provides a
greater amount of multiple charged ions than compared to krypton operation. This increase of multiple charged
xenon ions will result in increased momentum that will be imparted on the target surface, therefore an increase in the
amount of sputtered material and therefore shorter lifetime.
IV.
Conclusion
The performance characterization of the NASA-400M demonstrated the highest xenon and krypton performance
of any previously recorded Hall thruster. The NASA-400M successfully demonstrated up to 5000 sec. anode Isp at
anode efficiency of 68% with krypton propellant. The thruster produced a maximum thrust of 2.1 N and an anode
efficiency of 72% with xenon. The NASA-400M krypton performance was improved compared to previous krypton
Hall thruster performance results. The improved krypton operation of the NASA-400M compared to the NASA457Mv2 validated the design improvements made to the NASA-400M and indicated possible further improvements
that can be made for high-power krypton Hall thruster operation.
The wear characterization of the thruster ended prematurely due to both thruster and facility issues. After 292
hours of operation, the wear test was terminated due to anomalous operation, which led to a failure of the thruster.
The cause of the unexpected operational characteristics are unknown, but may be attributed to sputtered material
deposition on the thruster, which lead to frequent shorting of the thruster. The wear data that was collected with the
NASA-400M was compared to previous Hall thruster studies and discussed. The NASA-400M wear results
illustrated similar volumetric wear rate and radial wear rates as has been previously observed with other Hall
thrusters that operated below their nominal design point or had asymmetrical discharge channel. The short duration
of the thruster wear characterization was not sufficiently long enough to estimate the lifetime of the NASA-400M
configuration and operating conditions. However, the radial and the volumetric wear rates of the NASA-400M, up
to 300 hours of operation, are comparative to previous Hall thruster lifetime measurements.
Appendix
Table 1. Xenon performance data for the NASA-400M.
Discharge
Voltage
(Vd) [V]
Discharge
Current (Id)
[A]
Discharge
Power
[kW]
Anode Mass
Flow Rate
[mg/s]
Anode
Volumetric
Flow Rate
[sccm]
Cathode
Floating
Voltage
[V]
200
301
401
501
601
201
300
401
499
601
201
301
400
501
600
201
17.8
20.2
21.1
21.2
21.5
27.8
30.3
32.6
32.6
32.5
39.4
41.6
46.3
45.4
45.1
52.4
4
6
8
11
13
6
9
13
16
20
8
13
19
23
27
11
20.9
20.9
20.9
20.9
20.9
29.1
29.1
29.1
29.1
29.1
38.3
38.3
38.3
38.3
38.3
48.6
214
214
214
214
214
298
298
298
298
298
393
393
393
393
393
497
-13.4
-11.1
-10.4
-10.2
-9.9
-13.7
-8.4
-8.2
-8.4
-9.1
-14.9
-8.6
-8.6
-8.4
-8.0
-16.8
Thrust
[mN]
Anode
SpecificImpulse
(Isp) [sec]
Anode
Efficiency
271
358
412
506
554
399
551
651
789
874
544
753
921
1113
1214
686
1322
1749
2014
2473
2707
1399
1931
2279
2765
3061
1446
2002
2451
2959
3229
1439
49%
51%
48%
58%
57%
49%
57%
56%
66%
67%
49%
59%
60%
71%
71%
46%
11
American Institute of Aeronautics and Astronautics
300
400
501
601
200
301
401
501
601
201
300
400
500
53.7
61.2
59.2
58.9
67.0
67.7
74.5
75.1
75.4
82.7
85.2
91.6
94.0
16
24
30
35
13
20
30
38
45
17
26
37
47
48.6
48.6
48.6
48.6
59.8
59.8
59.8
59.8
59.8
72.1
72.1
72.1
72.1
497
497
497
497
613
613
613
613
613
738
738
738
738
-9.2
-9.0
-8.7
-8.4
-10.1
-9.6
-9.5
-9.3
-9.2
-10.4
-10.3
-10.0
-10.0
970
1204
1410
1568
873
1184
1499
1755
1978
1077
1426
1851
2118
2037
2527
2960
3291
1488
2017
2555
2990
3370
1523
2016
2617
2995
60%
61%
69%
72%
48%
57%
63%
68%
72%
48%
55%
65%
66%
Anode
Efficiency
60%
51%
55%
47%
53%
51%
55%
53%
51%
54%
57%
51%
54%
55%
59%
52%
52%
55%
57%
56%
60%
58%
59%
62%
58%
66%
60%
58%
64%
60%
66%
62%
61%
67%
66%
67%
68%
68%
68%
50%
59%
53%
63%
56%
60%
55%
63%
59%
62%
62%
65%
56%
60%
58%
65%
65%
63%
60%
65%
64%
59%
65%
62%
Table 2. Krypton performance data for the NASA-400M.
Discharge
Voltage
(Vd) [V]
Discharge
Current (Id)
[A]
301
401
501
601
700
801
900
1002
1100
300
400
500
601
701
801
300
300
301
400
400
401
500
501
501
601
601
601
700
701
701
800
800
800
851
900
950
1001
1005
1050
300
300
301
400
401
401
500
500
501
501
600
601
601
700
700
700
700
701
750
751
800
801
801
801
16.8
17.8
17.9
18.0
18.3
19.2
19.5
19.8
19.8
26.3
27.7
28.0
28.0
29.2
29.4
36.5
37.0
37.6
38.0
37.9
38.9
38.3
38.9
39.4
39.0
40.0
39.3
40.4
41.2
40.4
41.0
41.1
40.7
41.0
41.2
41.3
40.9
40.7
40.8
47.7
48.8
47.4
49.8
49.0
48.8
49.9
49.8
50.3
49.4
50.4
50.5
50.4
52.5
51.8
53.5
53.3
52.6
52.5
53.6
53.4
52.8
53.0
52.2
Discharge
Power [kW]
Anode
Mass
Flow Rate
[mg/s]
Anode
Volumetric
Flow Rate
[sccm]
Cathode
Floating
Voltage
[V]
Thrust
[mN]
Anode
SpecificImpulse
(Isp) [sec]
5
7
9
11
13
15
18
20
22
8
11
14
17
20
24
11
11
11
15
15
16
19
19
20
23
24
24
28
29
28
33
33
33
35
37
39
41
41
43
14
15
14
20
20
20
25
25
25
25
30
30
30
37
36
37
37
37
39
40
43
42
42
42
11.6
11.6
11.6
11.6
11.6
11.6
11.6
11.6
11.6
18.2
18.2
18.2
18.2
18.2
18.2
24.8
24.8
24.8
24.8
24.8
24.8
24.8
24.8
24.8
24.8
24.8
24.8
24.8
24.8
24.8
24.8
24.8
24.8
24.8
24.8
24.8
24.8
24.8
24.8
31.4
31.4
31.4
31.4
31.4
31.4
31.4
31.4
31.4
31.4
31.4
31.4
31.4
31.4
31.4
31.4
31.4
31.4
31.4
31.4
31.4
31.4
31.4
31.4
186
186
186
186
186
186
186
186
186
292
292
292
292
292
292
398
398
398
398
398
398
398
398
398
398
398
398
398
398
398
398
398
398
398
398
398
398
398
398
504
504
504
504
504
504
504
504
504
504
504
504
504
504
504
504
504
504
504
504
504
504
504
504
-17.4
-16.3
-15.6
-15.3
-14.3
-12.9
-12.0
-11.3
-11.9
-17.8
-16.9
-16.3
-16.3
-14.8
-14.6
-18.2
-13.8
-16.0
-17.6
-13.6
-15.8
-13.3
-16.8
-16.0
-16.2
-14.2
-12.7
-18.2
-12.9
-12.4
-12.4
-11.9
-17.4
-12.2
-12.1
-12.0
-12.1
-11.5
-11.8
-18.7
-13.0
-16.1
-12.3
-18.3
-16.2
-18.0
-17.0
-17.5
-15.6
-16.9
-15.0
-17.5
-20.4
-16.9
-14.8
-14.9
-14.4
-16.6
-14.5
-13.8
-16.3
-14.6
-16.4
265
291
338
342
395
425
473
495
507
394
479
507
572
642
708
534
536
555
657
651
683
743
754
777
818
884
839
899
960
920
1032
1004
989
1077
1102
1140
1173
1171
1201
668
734
686
885
834
857
925
990
965
981
1082
1109
1033
1180
1152
1234
1232
1212
1214
1284
1314
1250
1317
1275
2334
2561
2980
3015
3485
3744
4168
4363
4470
2210
2687
2844
3209
3602
3974
2196
2206
2284
2702
2680
2811
3059
3104
3197
3364
3637
3452
3698
3948
3784
4246
4131
4067
4432
4532
4688
4824
4817
4943
2171
2384
2227
2874
2707
2783
3005
3217
3134
3187
3513
3603
3356
3833
3741
4007
4003
3936
3944
4169
4269
4060
4279
4140
12
American Institute of Aeronautics and Astronautics
802
851
851
900
901
300
300
300
400
401
500
501
601
601
700
700
801
801
300
300
401
401
401
500
601
700
800
53.4
53.0
53.5
53.0
53.7
58.4
57.6
56.0
58.8
60.3
59.9
60.4
64.9
62.6
65.4
65.5
65.7
66.9
66.8
69.4
69.7
71.8
70.6
71.5
71.1
78.2
80.6
43
45
46
48
48
17
17
17
24
24
30
30
39
38
46
46
53
54
20
21
28
29
28
36
43
55
64
31.4
31.4
31.4
31.4
31.4
38.0
38.0
38.0
38.0
38.0
38.0
38.0
38.0
38.0
38.0
38.0
38.0
38.0
44.6
44.6
44.6
44.6
44.6
44.6
44.6
44.6
44.6
504
504
504
504
504
610
610
610
610
610
610
610
610
610
610
610
610
610
716
716
716
716
716
716
716
716
716
-18.9
-14.3
.14.2
-14.0
-14.1
-19.2
-18.9
-18.8
-18.8
-19.0
-18.2
-18.2
-17.3
-17.4
-18.1
-16.5
-16.3
-17.4
-23.1
-19.2
-23.7
-19.1
-24.3
-18.2
-17.4
-18.0
-16.8
1287
1361
1366
1410
1400
825
879
831
1041
1046
1204
1188
1359
1330
1465
1472
1578
1590
968
997
1212
1247
1230
1415
1577
1764
1915
4182
4420
4437
4580
4546
2213
2359
2231
2793
2807
3232
3189
3646
3568
3931
3951
4235
4267
2212
2279
2772
2850
2812
3235
3606
4033
4377
62%
65%
65%
66%
65%
51%
59%
54%
61%
60%
64%
61%
62%
62%
62%
62%
62%
62%
52%
54%
59%
61%
60%
63%
65%
64%
64%
References
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
G. L. Bennett, R. J. Hemler, and A. Schock, "Space Nuclear Power: An Overview," Journal of Propulsion and Power,
Vol. 12, No. 5, pp. 901-910, 1996.
C. M. Satter, "JIMO Follow-On Mission Studies," presented at Space Technology and Applications International
Forum, American Institute of Physics 0-7354-0230-2, Albuquerque, NM, 2005.
D. Jacobson and D. Manzella, "50 kW Class Krypton Hall Thruster Performance," presented at Joint Propulsion
Conference, AIAA-03-4550, Huntsville, Alabama, 2003.
D. Manzella, D. Jacobson, P. Peterson, and R. Hofer, "Scaling Hall Thrusters to High Power," presented at JANNAF,
Las Vegas, NV, 2004.
D. Manzella, R. Jankovsky, and R. Hofer, "Laboratory Model 50 kW Hall Thruster," presented at Joint Propulsion
Conference, AIAA-02-3676, Indianapolis, Indiana, 2002.
D. Manzella and D. Jacobson, "Investigation of Low-Voltage/High-Thrust Hall Thruster Operation," presented at Joint
Propulsion Conference, AIAA-03-5004, Huntsville, Alabama, 2003.
C. B. Carpenter and M. J. Patterson, "High-Current Hollow Cathode Development," presented at International Electric
Propulsion Conference, IEPC-01-274, Pasadena, Ca, 2001.
T. W. Haag, "Thrust stand for high-power electric propulsion devices," Review of Scientific Instruments, Vol. 62, No.
5, 1991.
T. W. Haag and M. Osborn, "RHETT/EPDM performance characterization," presented at Internal Electric Propulsion
Conference, IEPC-97-107, Cleveland, OH, 1997.
D. Jacobson, "High Voltage TAL Erosion Characterization," presented at Joint Propulsion Conference, AIAA-02-4257,
Indianapolis, Indiana, 2002.
L. S. Mason, R. Jankovsky, and D. Manzella, "1000 Hours of Testing on a 10 Kilowatt Hall Effect Thruster," presented
at Joint Propulsion Conference, AIAA-01-3773, Salt Lake City, UT, 2001.
P. Peterson and D. Manzella, "Investigation of the Erosion Characteristics of a Laboratory Hall Thruster," presented at
Joint Propulsion Conference, AIAA-03-5005, Huntsville, Alabama, 2003.
J. Fisher, A. Wilson, and L. Werthman, "The Qualification of a 4.5 kW Hall Thruster Propulsion Subsystem,"
presented at Joint Propulsion Conference, AIAA-03-4551, Huntsville, Alabama, 2003.
L. Albarede, V. Lago, P. Lasgorceix, M. Dudeck, A. I. Bugrova, and K. Malik, "Interaction of a Hollow Cathode
Stream with a Hall Thruster," presented at Internal Electric Propulsion Conference, IEPC-03-333, Toulouse, France,
2003.
D. H. Manzella, D. T. Jacobson, and R. S. Jankovsky, "High Voltage SPT Performance," presented at Joint Propulsion
Conference, AIAA-01-3774, Salt Lake City, UT, 2001.
D. T. Jacobson, R. S. Jankovsky, V. K. Rawlin, and D. H. Manzella, "High Voltage TAL Performance," presented at
Joint Propulsion Conference, AIAA-01-3777, Salt Lake City, UT, 2001.
B. Pote and R. Tedrake, "Performance of a High Specific Impulse Hall Thruster," presented at International Electric
Propulsion Conference, IEPC-01-35, Pasadena, Ca, 2001.
13
American Institute of Aeronautics and Astronautics
[18]
[19]
[20]
[21]
[22]
[23]
[24]
[25]
[26]
[27]
[28]
[29]
[30]
[31]
[32]
[33]
[34]
[35]
[36]
[37]
A. E. Solodukhin, A. V. Semenkin, S. O. Tverdohlebov, and A. V. Kochergin, "Parameters of D-80 Anode Layer
Thruster in One- and Two- Stage Operation Modes," presented at International Electric Propulsion Conference, IEPC01-032, Pasadena, Ca, 2001.
R. R. Hofer, "Development and Characterization of High-Efficiency, High-Specific Impulse Xenon Hall Thrusters," in
Department of Aerospace Engineering. Ann Arbor, MI: The University of Michigan, 2004.
P. Y. Peterson, "The Development and Characterization of a Two-Stage Hybrid Hall/Ion Thruster," in Department of
Aerospace Engineering. Ann Arbor, MI: The University of Michigan, 2004.
R. Hofer and R. Jankovsky, "A Hall Thruster Performance Model Incorporating the Effects of a Multiply-Charged
Plasma," presented at Joint Propulsion Conference, AIAA-01-3322, Salt Lake City, UT, 2001.
R. Hofer, P. Peterson, D. Jacobson, and D. Manzella, "Factors Affecting the Efficiency of Krypton Hall Thrusters,"
presented at APS Division of Plasma Physics, Savannah, GA, 2004.
C. Marrese, J. M. Haas, M. T. Domonkos, A. D. Gallimore, S. O. Tverdohlebov, and C. Garner, "The D-100
Performance and Plume Characterization on Krypton," presented at Joint Propulsion Conference, AIAA-96-2969, Lake
Buena Vista, FL, 1996.
A. I. Bugrova, A. I. Morozov, A. S. Lipatov, A. M. Bishaev, V. K. Kharchevnikov, and M. V. Kozintseva., "Integral
and Spectral Characteristics of ATON Stationary Plasma Thruster Operating On Krypton and Xenon," presented at
Internal Electric Propulsion Conference, IEPC-03-366, Toulouse, France, 2003.
S. Bechu, C. Perot, N. Gascon, P. Lasgorceix, A. Hauser, and M. Dudeck, "Operating Mode Investigation of a
Laboratory Stationary Plasma Thruster," presented at Joint Propulsion Conference, AIAA-99-2567, Los Angeles, Ca,
1999.
S. O. Tverdohlebov, "Study of Double-Stage Anode Layer Thruster Using Inert Gases," presented at Internal Electric
Propulsion Conference, IEPC-93-232, Seattle, WA, 1993.
V. Kim, G. Popov, V. Kozlov, A. Skrylnikov, and D. Grdlichko, "Investigation of SPT Performance and Particularities
of it’s Operation with Kr and Kr/Xe Mixtures," presented at International Electric Propulsion Conference, IEPC-01065, Pasadena, Ca, 2001.
J. M. Haas, "Low-Perturbation Interrogation of the Internal and Near-Field Plasma Structure of a Hall Thruster Using a
High-Speed Probe Positioning System," in Department of Aerospace Engineering. Ann Arbor, MI: The University of
Michigan, 2001.
V. M. Gavryshin, V. Kim, V. I. Kozlov, and N. A. Maslenikov, "Physical and Technical Bases of the Modern SPT
Development," presented at Internal Electric Propulsion Conference, IEPC-95-038, Moscow, Russia, 1995.
K. Sullivan, J. Fox, and M. Martinez-Sanchez, "Kinetic Study of Wall Effects in SPT Hall Thrusters," presented at
Joint Propulsion Conference, AIAA-04-3777, Fort Lauderdale, FL, 2004.
D. Manzella, J. Yim, and I. Boyd, "Predicting Hall Thruster Operational Lifetime," presented at Joint Propulsion
Conference, AIAA-04-3953, Fort Lauderdale, FL, 2004.
J. R. Roth, Industrial Plasma Engineering: Volume 2 Applications to Nonthermal Plasma Processing, vol. 2. London:
Institute of Physics Publishing, 2001.
S. K. Absalamov, V. B. Andreev, T. Colbert, M. Day, V. V. Egorov, R. U. Gnizdor, H. R. Kaufman, V. Kim, A. I.
Korakin, K. N. Kozubsky, S. S. Kudravzev, U. V. Lebedev, G. A. Popov, and V. V. Zhurin, "Measurement of Plasma
Parameters in the Stationary Plasma Thruster (SPT-100) Plume and its Effect on Spacecraft Components," presented at
Joint Propulsion Conference, AIAA-92-3156, Nashville, TN, 1992.
M. Day, N. A. Maslenikov, T. Randolph, and W. Rogers, "SPT-100 Subsystem Qualification Status," presented at Joint
Propulsion Conference, AIAA-96-2713, Lake Buena Vista, FL, 1996.
V. Kim, V. Kozlov, A. Semenov, and I. Shkarban, "Investigation of the Boron Nitride based Ceramics Sputtering Yield
Under it's Bombardment by Xe and Kr ions," presented at International Electric Propulsion Conference, IEPC-01-073,
Pasadena, Ca, 2001.
S. Scaglione, L. Caneve, and F. Sarto, "Sputtering Yield of Optical Materials: Sigmund's Model and Experimental
Results," Journal Vacuum Science Technology, Vol. 12, No. 4, pp. 1523-1527, 1994.
P. Sigmund, "Theory of Sputtering. I. Sputtering Yield of Amorphous and Polycrystalline Targets," Physical Review,
Vol. 184, No. 2, pp. 383-416, 1969.
14
American Institute of Aeronautics and Astronautics