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Microvacuum arc thruster design for a CubeSat class satellite

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This paper describes the University of Illinois 2-cube CubeSat (10 x 10 x 20 cm) designed for April 2003 launch. The Illinois Observing NanoSatellite (ION) includes a scientific mission to view the airglow layer of the atmosphere and a CMOS camera for space and Earth photography. ION will also be used as a test bed to demonstrate a number of technologies including an active 3-axis attitude control system, with a new propulsion system used for both attitude control as well as orbital maneuvers. The new vacuum arc thruster (VAT) propulsion system produces ion velocities of up to 30,000 m/s, driven mostly by local pressure gradients. A 12 V inductive energy storage circuit is used to provide the initial breakdown and to sustain the plasma. Four thruster heads can be controlled individually to produce arc pulses with adjustable pulse width and repetition rate. Size and mass have been driven by the CubeSat requirements and amount to 4 x 4 x 4 cm and 150 g, respectively. Thrust to power ratios are expected to be ≈10µN/W. The individual impulse will be close to 1µN-s/pulse. Challenges to the design and integration of the VAT into a CubeSat size satellite are presented. On board diagnostics and methods used to verify operation of the VAT are discussed.
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SSC02-I-2
Filip Rysanek 16th Annual/USU Conference on Small Satellites
1
MicroVacuum Arc Thruster Design for a CubeSat Class Satellite
Filip Rysanek and John William Hartmann
University of Illinois in Urbana and Champaign, 306 Talbot Lab, 104 S Wright St., Urbana
IL 61802, (217) 244-5598, frysanek@uiuc.edu
Jochen Schein and Robert Binder
Alameda Applied Sciences Corporation, 2235 Polvorosa Ave, San Leandro, CA 94577, (510)
483-4156, schein@aasc.net
Abstract
This paper describes the University of Illinois 2-cube CubeSat (10 x 10 x 20 cm) designed
for April 2003 launch. The Illinois Observing NanoSatellite (ION) includes a scientific
mission to view the airglow layer of the atmosphere and a CMOS camera for space and Earth
photography. ION will also be used as a test bed to demonstrate a number of technologies
including an active 3-axis attitude control system, with a new propulsion system used for
both attitude control as well as orbital maneuvers. The new vacuum arc thruster (VAT)
propulsion system produces ion velocities of up to 30,000 m/s, driven mostly by local
pressure gradients. A 12 V inductive energy storage circuit is used to provide the initial
breakdown and to sustain the plasma. Four thruster heads can be controlled individually to
produce arc pulses with adjustable pulse width and repetition rate. Size and mass have been
driven by the CubeSat requirements and amount to 4 x 4 x 4 cm and 150 g, respectively.
Thrust to power ratios are expected to be 10µN/W. The individual impulse will be close to
1µN-s/pulse. Challenges to the design and integration of the VAT into a CubeSat size
satellite are presented. On board diagnostics and methods used to verify operation of the
VAT are discussed.
Introduction
The Illinois Observing Nanosatellite (ION) is
a 2 kg, dual-cube, CubeSat-class satellite
currently under construction at the University
of Illinois at Urbana-Champaign. The satellite
was designed, and is being built by a student
group at the U of I, under faculty supervision,
as part of the larger CubeSat program. This
group consists of roughly 25 graduate and
undergraduate students, drawn from various
engineering disciplines, who are in charge of
all aspects of satellite design, construction,
and testing, as well as program management.
The U of I program was initiated in the Fall of
2001. Analysis of existing and planned
CubeSat missions identified several objectives
with potential to provide significant
contribution to the overall CubeSat program
and small satellite community. A satellite
mission was constructed around these
objectives in an effort to provide such a
contribution. Mission objectives include both
technological and scientific goals. Objectives
include: 1) acquisition of data on the Earth’s
airglow layer via photo-multiplier tube
instrumentation; 2) development of a magnetic
3-axis attitude control system; and 3) space
qualification of a miniature electric propulsion
system. All objectives are described in further
detail in the following sections.
Satellite design was completed in the Spring
of 2002 with transition to satellite fabrication
and systems testing occurring late Spring and
Filip Rysanek 16th Annual/USU Conference on Small Satellites
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Summer 2002. The current timeline targets
satellite delivery in January 2003. The
University of Illinois has partnered with
CubeSat Launch Corporation to deliver ION
to orbit.
Science Objectives
The main science objective for ION is to study
the airglow layer of Earth’s upper atmosphere.
This layer is located approximately 100 km
above the Earth’s surface. The airglow
phenomenon is caused by atomic oxygen-
driven chemistry that emits light at a
wavelength of 760 nm. At this wavelength,
light is absorbed by Earth’s lower atmosphere,
preventing study by Earth-based sensors. ION
will study the airglow phenomenon using a
photo-multiplier tube (PMT). The PMT is
treated as the main payload for ION. Upon
delivery, ION will use the PMT to study the
airglow phenomenon from low Earth orbit;
specifically, the imaging and tracking of
wave-like structures ranging from 20 to 200
km in size that are created in the airglow layer
by atmospheric winds.
As a secondary mission, a complimentary
metal-oxide semiconductor (CMOS) camera
will be utilized for earth imaging. While
successful implementation of the CMOS
camera is primarily a technology validation
objective, it is hoped that data collected from
this sensor can be used for atmospheric study
as well.
Technology Objectives
ION Technology objectives include the
development and/or space qualification of
several components. The on-board CMOS
camera is one of these components. It is
hoped that successful utilization of this sensor
will enable future use for Earth-observing
missions, as well as the potential use of
similar CMOS devices for on-board star
tracking. High-efficiency solar cells provided
by the Emcore Corporation will also be flown
and demonstrated. In addition, the flight
computer being used on ION is also being
flight validated. The small integrated data-
logger (SID), supplied by Tether Applications
Inc., will be space qualified for future use in
small satellites. The U of I team is also in the
process of developing an active, magnetic
three-axis control system using free-air torque
coils as actuators. Three mutually orthogonal
torque coils will be combined with a three-
axis magnetic sensor and mathematical
models to interact with Earth’s magnetosphere
and control ION’s attitude via SID.
The primary technology mission for ION,
however, is the space qualification of a micro
vacuum arc thruster (µVAT) propulsion
system. This propulsion system is being
developed cooperatively with Alameda
Applied Space Sciences Corporation. The
propulsion system aboard ION will consist of
one power-processing unit (PPU) that supplies
power to four µVAT thruster heads. The
µVAT thrusters work in a manner similar to a
spark plug, with an electric arc being created
from anode to cathode. The interaction
between electric arc and cathode results in
cathode material being ejected from its surface
at high velocity. This produces a highly
efficient, low-thrust method of propulsion. In
the case of ION, the aluminum frame of the
satellite will serve as the cathode material
(with the electric arc localized to specific
areas), effectively utilizing the frame as
propellant in a self-consuming fashion.
Space qualification of the system will be
accomplished by verification of successful
firing using various on-board diagnostics.
Validation of this system will enable its future
use for attitude control, orbit maintenance, and
perhaps even orbital maneuvers such as orbit
raising/lowering and de-orbit. Such capability
opens the door to missions that were
previously impossible for satellites of ION’s
Filip Rysanek 16th Annual/USU Conference on Small Satellites
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size, and provides the promise of lower launch
costs and increased launch opportunities by
allowing CubeSat-class satellites to piggy-
back on vehicles with non-ideal orbits,
followed by transfer to final desired orbit.
Specific details of the propulsion system are
provided in the following sections. The basic
theory of vacuum arc thrusters is discussed
first. This is followed by a description of
components specific to ION and specifications
of their design. Operation and control are also
discussed. On-board diagnostics and methods
for space qualification are then explained,
with conclusions following.
Vacuum Arc Thrusters
Basic Theory
The initial µVAT design was coaxial. The
cathode was a 3 mm diameter metal rod
inserted into a small ceramic tube which in
turn was inserted into a ~6 mm diameter
copper tube, serving as the anode. The
insulator is coated with a thin film of the
cathode material to provide the ‘self-triggered’
or ‘triggerless’ operation. This kind of
operation allows for an arc to ignite at
voltages as low as 100V. More detailed
information about this process can be found
elsewhere1,2,3
Use of the self-triggered vacuum arc enables
use of a low mass PPU that utilizes inductive
energy storage (IES). Figure 1 shows a
schematic drawing of µVAT. A
semiconductor switch is triggered to draw a
current I from a DC power supply (5V-35V)
through an inductor L. The moment the switch
opens, a voltage peak L dI/dt is produced
which ignites the arc by driving current
through the thin-film coating on the ceramic
between anode and cathode. Subsequently,
plasma is established at a hot spot at the
cathode-coating interface and the stored
energy in the inductor supports the plasma.
L
R
VS
VAT
switch
Figure 1 Principle schematic of the coaxial
vacuum arc assembly
After the initial vacuum arc formation, a fully
ionized metal plasma is produced from a
macroscopically cold cathode. The metal
plasma plume, produced at cathode spots in a
way reminiscent of laser plasma production,
streams outward to achieve velocities of 1-3
x106 cm/s over a wide range of elements from
Carbon to Tungsten, making the µVAT
suitable for 1000-3000 s specific impulse
missions. Time-of-flight measurements of the
charge state distributions have shown that the
ions are predominantly of charge states 1+ to
3+ depending on the metal species used and
the arc current density.1 Arc discharges are
produced with arc currents from tens of
amperes to many kA. Pulse lengths can be
from a few microseconds upwards, and the
pulse repetition rate can readily be up to a few
hundred pulses per second. This implies a
very wide dynamic thrust range. The µVAT
can be operated in a pulsed mode with an
average power of 1-100 W and masses of
about 0.1 kg. For orbit transfer and orbit
maneuvering of a satellite, high thrusts are
desired to save time, while for station keeping
the required thrusts are relatively low. The
µVAT has the potential of providing a wide
dynamic range of thrusts without efficiency
loss for these missions.
Filip Rysanek 16th Annual/USU Conference on Small Satellites
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ION Design
Power Processing Unit
The University of Illinois power processing
unit, designed and built by Alameda Applied
Sciences Corp. and shown in Figure 2
incorporates the same inductive energy
storage design. The ION PPU was designed
to control 4 thrusters individually. The PPU
has a modular design (Figure 3) with one main
board housing the inductor and timing circuit.
Each thruster is connected to a separate
control board which houses the semiconductor
switch used to control the current through the
inductor. PPU size and mass have been driven
by the CubeSat requirements and amount to 4
x 4 x 4 cm and 150 g, respectively. The PPU
is powered from a 12-24 V power bus.
Four TTL level control signals determine
which thrusters are operational. Multiple
control signals can be sent in order to fire
multiple thrusters simultaneously. In this
case, the arc will randomly initiate on one of
the two thruster heads. Another way to fire
two thrusters simultaneously is to alternate the
control signal. In this fashion, the relative
power ratio going to each thruster can be
controlled.
Figure 2 Vacuum Arc Thruster PPU
designed for use aboard ION
Figure 3 Vacuum Arc Thruster PPU
designed for use aboard ION, Open View
The ION PPU can be fired in two modes of
operation. First, an onboard timing circuit can
be used to fire the thrusters at a pre-set pulse
frequency and power. This mode of operation
requires only a single activation control signal.
The second mode of operation for the PPU is
one where the ION on-board computer sends
the PPU a square wave signal generated by a
pulse width modulator circuit (PWM) to
control the switch for each thruster. In this
manner, the computer can control the pulse
frequency as well as the energy per pulse.
Thrusters
The original µVAT design incorporated a
cylindrical thruster. With this design, the
thruster was to be placed in the feet of the
satellite. It was determined that the
cylindrical geometry would require significant
insulation, as well as tight tolerance
machining to operate reliably. It was also
unclear if a cylindrical design would
withstand launch vibration. A sandwich or
"BLT" geometry was adopted instead. In
testing, the BLT geometry proved to be more
reliable, as well as easier to manufacture. The
first BLT design is a sandwich of copper,
ceramic, and titanium. The arc forms between
the center (titanium) and outer electrodes.
The original BLT design was scaled to
approximately a 1 cm wide µBLT.
Filip Rysanek 16th Annual/USU Conference on Small Satellites
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During the initial design, the high density and
high Isp of the tungsten electrode were
favored. The tungsten could provide the
highest V given a limited mass and volume;
however, in order to demonstrate a thruster
system with a large volume of fuel for
possible future missions, the µBLT thrusters
were incorporated into the satellite structure in
such a way that the aluminum structure
became the fuel. The final design of the
µBLT is shown in Figure 4. The anode is
separated from the structure (cathode) with
two high-alumina ceramic plates. The arc will
either attach to the satellite structure or to the
aluminum bar used to clamp the µBLT
together. When the thrusters are assembled
and prepared for operation, the ceramic closer
to the aluminum bar will not be plated with
the conductive layer, increasing the chance
that the arc will form between the anode and
satellite structure.
Figure 4 µBLT design incorporated into
satellite structure.
The four thrusters are located on the satellite
in such a way as to allow both translation and
2 axis rotation. Two thrusters are placed on
each of the 10 cm x 10 cm faces of the
satellite. Each thruster is in the opposite
corner of that face as shown in Figure 5. With
this layout, when thrusters 1 and 2 or thruster
3 and 4 are fired simultaneously, the satellite
experiences translation. When thrusters 1 and
3 or thruster 2 and 4 are fired, the satellite
experiences rotation about one axis. Firing
thrusters 1 and 4 or thrusters 2 and 3 rotates
the satellite about another axis.
To estimate the effect that the thrusters will
have on the satellite, a theoretical analysis was
conducted which provided an estimate of
thrust with an aluminum cathode to be 13.5
µN-s/W.4 With this thruster layout, each
thruster will have approximately 5 cm of lever
arm about the axis of rotation. It is assumed
the satellite has the moment of inertia of a
uniform density block (8.3x10-3 kg-m2) and
the thruster fires at a nominal 4 Watts,
producing 54 µN of thrust. The pair of
thrusters produce 5.4x10-6 N-m of torque.
This results in an angular acceleration of
6.56x10-4 rad/s2. This means that by firing the
thrusters continuously for approximately 4
seconds, the satellite will turn 90 degrees in 10
minutes.
This estimate is only an approximation to the
actual motion of the satellite. Due to the
location of the thrusters, torque will not be
applied through the center of mass, thus likely
resulting in something other than pure
rotation. The dynamics of this motion are yet
to be simulated; however, the simplified
model described above is sufficient to
estimate an approximate effect that the
thrusters will have.
Satellite Structure
Filip Rysanek 16th Annual/USU Conference on Small Satellites
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Figure 5 µBLT Thruster locations on
Satellite
Diagnostics
One issue that has often confronted mission
designers is whether the exhaust from
thrusters will redeposit on solar panels or
optical experiments. Such deposition can
reduce solar panel lifetime and efficiency. In
order to estimate this effect, a conductive
deposition monitor (CDM) experiment will
be flown to help determine the amount of
deposition accumulating on the satellite due to
the thruster.
The CDM is a 1 cm square ceramic plate, with
wire leads attached to opposite sides. As the
fuel from the thrusters deposits on the ceramic
plate, the resistance between the two wires
will fall. A circuit measures the resistance
between the leads. Since a very small amount
of deposition is expected, the circuit is
designed to be very sensitive between infinite
resistance and 10 M.
A number of methods have been devised to
help verify the operation of the thrusters. At
the very basic level, the attitude control
system will be able to detect any change in
attitude using the on-board magnetometer.
Although this is not a direct determination that
the thrusters are functioning properly, it is
enough to verify that an end has been
achieved.
The attitude control system will also be
capable of compensating for the thrust with
the on-board torque coils. The amount of
current through the torque coils necessary to
compensate for the thrusters can then be
converted into a force or torque produced by
the thrusters. This method can be used as an
in-flight thrust-stand to measure the exact
thrust produced by the thrusters.
The ION computer system is capable of
measuring the temperature of the satellite in
up to 63 locations. The temperature of the
inductor, as well as one of the IGBT switches
and it's corresponding thruster will be
monitored. This will provide a means to
protect the PPU and thrusters from
overheating due to normal operation. In case
of a failure resulting in a short circuit, the
temperature measurement will help to protect
and diagnose the system for future operation.
One final diagnostic tool is a Channel Island
Circuits model 711B current probe, used to
measure the current through one of the
thrusters. This current probe is a torroidal
inductive probe that measures the derivative
of the current between the PPU and the
thruster head. A circuit was designed to
integrate the derivative signal and return the
actual current to the analog input of the
computer. This data will be used as a
diagnostic tool and possibly in conjunction
with a pulse counter.
Conclusions
The University of Illinois has designed the
Illinois Observing Nanosatellite (ION), a
(
1
)
(
2
)
(
3
)
(
4
)
Filip Rysanek 16th Annual/USU Conference on Small Satellites
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CubeSat-class satellite with a scientific
payload, an active 3-axis attitude control
system, and a 4 vacuum arc thruster
propulsion system capable of 2-axis control
and orbit translation. This mission is a
stepping-stone toward a versatile satellite
system capable of carrying a payload,
changing orbits, and finely controlling
attitude.
Along with it's scientific mission, ION is a
technology demonstration mission. The
vacuum arc thruster propulsion system
consists of a 150 g power processing unit
designed and fabricated by Alameda Applied
Sciences Corporation (AASC). The PPU
controls up to four thrusters, firing any
thruster at a pre-set power level, or a power
level determined by the on-board computer.
The thrusters are a 1 cm wide sandwich (BLT)
configuration. The BLT design is a very
simple yet robust design, with inexpensive
manufacture costs. The thrusters are
incorporated into the structure to use the
structure as fuel, opening the possibility for
large fuel mass missions in the future.
For this technology demonstration, the VATS
provide 2-axis attitude control, as well as orbit
translation. The VATs, although limited in
functionality in this mission, have enormous
potential for future flights. The low mass
system makes the propulsion system viable for
almost any class satellite. The thrust scales
with power input which is delivered through a
12-24 Volt bus. This simple yet scalable
design makes the system viable for both
micro-sats in the CubeSat class, as well as
larger satellites.
Vacuum arc thrusters open many doors for
future CubeSat class satellites. They will
increase launch opportunities by allowing
launch on vehicles with non-ideal orbits.
They also give CubeSat class satellites a
maneuverability previously reserved for much
larger satellites.
References
1 A. Anders, I.G. Brown, R.A. MacGill, and
M.R. Dickinson, Journal of Physics D:
Applied. Physics., vol. 31, 584-587
(1998).
2 A. Anders, J. Schein, and N. Qi, “Pulsed
vacuum-arc ion source operated with a
'triggerless' arc initiation method”,
Review. Scientific. Instruments. 71, 827
(2000).
3 J. Schein, N. Qi, R. Binder, M. Krishnan, J
Ziemer, J. Polk, A. Anders "Inductive
energy storage driven vacuum arc
thruster" Review of Scientific
Instruments, 73(2), 925 2002
4 James E Polk, et al., "A Theoretical
Analysis of Vacuum Arc Thruster
Performance" 27th International Electric
Propulsion Conference, IEPC Paper 01-
211, Pasadena, CA, Oct 2001
... The apparent motion follows the law and is known in literature as "retrograde motion". This phenomenon is not yet fully understood, but there are many different models that try to explain it 75 [30]. It is worth reiterating that it is the process of arc spot extinction and reignition that creates the illusion of movement [32]. ...
... In 2002, the thruster planned for the Illinois Observing Nanosatellite (ION), a 2 U CubeSat from the University of Illinois at Urbana-Champaign, was presented [75]. The thruster was named µBLT due to its size and the fact that the cathode, insulators, and anode are "sandwiched" together ( Figure 10). ...
... The PPU was designed by Alameda Applied Sciences Corporation and is capable of controlling all four295 thrusters on the satellite. From[75], with copyright permission from the authors. ...
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Micropropulsion systems are rapidly gaining attention from the small satellite community as they can increase the mission lifetime and allow the satellite to perform complex maneuvers and precise attitude control. These systems need to be fully operational with the low power available on satellites. Various thruster concepts based on vacuum arcs are currently under development, predominantly in the pulsed regime due to the power constraints on small spacecraft. Pulsed vacuum arc thrusters are capable of efficiently producing highly-ionized supersonic plasma at very low average power. This Perspective article provides a critical analysis and a review of various aspects of electric propulsion technology based on vacuum arcs. Furthermore, we give a personal assessment of the present status and provide an outlook on the field, including the growing role in small satellites such as CubeSats. Vacuum arc micropropulsion systems could play an important role in mitigating the problem of space debris. Such a system could be integrated with a satellite so that, at the end of its mission and using metal components as solid fuel, it will lower the satellite’s orbit and accelerate reentrance into the atmosphere faster than by its natural decay rate.
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... This paper describes CAES using intrusive and non-intrusive plasma diagnostics methods. Figure 2a-b shows the system design con guration starting with an inductive energy storage circuit [2,21] to power the AES. The inductance, capacitance, switch, input DC voltage, PWM (pulse width modulation) width, frequency, and coil magnetic eld values at the arc interface were 550 µH, 6800 µF, IXYH50N120C3D1 IGBT, 18-30 V, 610-1020 µs, 1-10 Hz, and 0.014 T, respectively. ...
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The paper describes an arc electron source for air ionization applications in a self�neutralizing air-breathing plasma thruster. The arc electron source is an electron source with a prominent level of electron energy control that is required for the air-breathing plasma thruster. The mean energy of the electrons in the arc electron source is con�trolled by changing the grid voltage in the range of 0V–300V. The Langmuir/Faraday probes were used to obtain ion/electron current, electron temperature, and electron density as a function of pressure and electron energy. Ion current measurements con�cerning distance from the source were obtained as a function of pressure and grid volt�age. Optical emission spectroscopy was used to obtain electron temperature, spectral intensities, and ion formation rate. Additionally, a drift tube based on radial magnetic feld electron confnement was designed to detect the presence of negative ions. It has been shown that both positive and negative ions can be produced thus providing conditions for a self-neutralizing air-breathing plasma thruster.
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This article considers operational dynamics of a solar thermal propulsion unit (STPU) with a solar energy concentrator for CubeSat nanosatellites. It was shown that for a 6U CubeSat with a 1U propulsion system, a resulting delta V of more than 35 m/s in less than 24 h is possible. This delta V is enough to move apart two satellites to opposite points of a 600 km circular orbit in less than 5 days. An original scheme of the engine with a capillary feeder system and a Fresnel lens as the solar energy concentrator is proposed. A simplified mathematical model of the engine was created to make it possible to calculate hundreds of thruster operating cycles with different parameters in the chamber. The ODEs were numerically integrated using the Matlab-Simulink software package.
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Vacuum arcs can be initiated by simply applying a sufficiently high voltage (∼ 1 kV) between the anode and cathode, provided that there is a conducting path between these electrodes. Typically, the conducting path is obtained by coating the ceramic insulator. Plasma is formed explosively at the coating-cathode interface. Since neither a trigger supply nor a trigger electrode are required, the method has been dubbed “triggerless” arc initiation. Triggerless operation of a vacuum arc ion source was demonstrated for a number of cathode materials. It was found that triggerless operation is very reliable as long as the balance of deposition and erosion of the conducting material leads to a steady-state path resistance in the range from 1 Ω to 100 kΩ. © 2000 American Institute of Physics.
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In vacuum arc discharges the current is conducted through vapor evaporated from the cathode surface. In these devices very dense, highly ionized plasmas can be created from any metallic or conducting solid used as the cathode. This paper describes theoretical models of performance for several thruster configurations which use vacuum arc plasma sources. This analysis suggests that thrusters using vacuum arc sources can be operated efficiently with a range of propellant options that gives great flexibility in specific impulse. In addition, the efficiency of plasma production in these devices appears to be largely in-dependent of scale because the metal vapor is ionized within a few microns of the cathode electron emission sites, so this approach is well-suited for micropropulsion.
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A new type of vacuum arc thruster in combination with an innovative power processing unit (PPU) has been developed that promises to be a high efficiency (∼15%), low mass (∼100 g) propulsion system for micro- and nanosatellites. This thruster accelerates a plasma that consists almost exclusively of ions of the cathode material and has been operated with a wide variety of cathodes. The streaming velocity of the plasma exhaust varies with cathode material, from a low of 11 km/s for Ti up to 30 km/s for Al, with a corresponding range of specific impulse from 1100 s for Ta to 3000 s for Al. Initiation of the arc requires only a few hundred volts due to an innovative “triggerless” approach in which a conductive layer between the cathode and the anode produces the initial charge carriers needed for plasma production. The initial starting voltage spike as well as the energy to operate the vacuum arc are generated by a low mass (<300 g) inductive energy storage PPU which is controlled using +5 V level signals. The thrust-to-power ratio has been estimated to reach up to ≈20 μN/W. The vacuum arc thruster was tested at the Jet Propulsion Laboratory using W as cathode material. Experimental results are within 65% of the estimated values. © 2002 American Institute of Physics.
  • I G Anders
  • R A Brown
  • M R Macgill
  • Dickinson
Anders, I.G. Brown, R.A. MacGill, and M.R. Dickinson, Journal of Physics D: Applied. Physics., vol. 31, 584-587 (1998).
A Theoretical Analysis of Vacuum Arc Thruster Performance" 27 th International Electric Propulsion Conference
  • E James
  • Polk
James E Polk, et al., "A Theoretical Analysis of Vacuum Arc Thruster Performance" 27 th International Electric Propulsion Conference, IEPC Paper 01- 211, Pasadena, CA, Oct 2001