DESIGN AND TESTING OF A GAS DISTRIBUTION METHOD FOR PULSED 
INDUCTIVE THRUSTERS 
 
Except where reference is made to the work of others, the work described in this thesis is 
my own or was done in collaboration with my advisory committee.  This thesis does not 
include proprietary or classified information. 
 
 
_______________________________ 
Robert E. Miller III 
 
 
 
 
 
 
 
 
 
 
Certificate of Approval: 
 
 
 
______________________     ______________________ 
John Cochran       Roy J. Hartfield, Jr., Chair 
Profesor       Profesor 
Aerospace Engineering     Aerospace Engineering 
 
______________________     ______________________ 
Brian Thurow       Frank Rose 
Assistant Professor      Vice President of Research 
Aerospace Engineering     Radiance Technologies Inc. 
 
        
______________________ 
       George T. Flowers   
  Dean 
  Graduate School 
DESIGN AND TESTING OF A GAS DISTRIBUTION METHOD FOR PULSED 
INDUCTIVE THRUSTERS 
 
 
 
Robert E. Miller III 
 
 
 
 
 
A Thesis 
Submitted to 
the Graduate Faculty of 
Auburn University 
in Partial Fulfillment of the 
Requirements for the 
Degree of 
Master of Science 
 
 
 
 
 
 
 
 
 
 
Auburn, Alabama 
December 19, 2008 
 
 iii
DESIGN AND TESTING OF A GAS DISTRIBUTION METHOD FOR PULSED 
INDUCTIVE THRUSTERS 
 
 
 
 
Robert E. Miller 
 
 
 
Permission is granted to Auburn University to make copies of this thesis at its discretion, 
upon request of individuals or institutions and at their expense.  The author reserves all 
publication rights. 
 
 
 
 
______________________ 
 Signature of Author 
 
______________________ 
 Date of Graduation 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 iv
THESIS ABSTRACT 
 
DESIGN AND TESTING OF A GAS DISTRIBUTION METHOD FOR PULSED 
INDUCTIVE THRUSTERS 
 
 
Robert E. Miller III 
 
Master of Science, December 19, 2008 
(B.S., Auburn University, 1997) 
 
64 Typed Pages 
 
Directed by Roy Hartfield 
 
 
 
A gas distribution manifold for use in a Pulsed Inductive Thruster has been 
designed and tested.  The Argon test gas is distributed radially outward over a flat disc 
from an enclosed manifold area.  The manifold was designed to meet a specific gas 
distribution time of one milli-second.  Initial design of the manifold is determined from 
isentropic gas distribution assumptions.  The manufactured prototype is tested at a 
vacuum background pressure of two to three milli-Torr.  Gas distribution time for the 
flow over a simulated Pulsed Inductive Thruster surface is measured with respect to the 
manifold?s exit using a modified form of Langmuir Probe.  Error analysis for the 
measurement is provided.  Measurement error range was less than 10% for all 
measurements. 
 
 v
ACKNOWLEDGEMENTS 
 
 The author would like to thank Radiance Technologies, and the Auburn 
University Space Research Institute for their support, patience and encouragement.  
Special thanks to Dr. Frank Rose, Zac Shotts, and Steve Best for guidance and assistance.  
Without their help, this project would not have been possible.    
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 vi
Style manual or journal used:   Modern Language Association Style Manual 
 
 
 
Computer software used:   Microsoft Office Word 2003 
      Microsoft Office Excel 2003 
      UGS Solid Edge V19 
 
 
 
 
 vii
TABLE OF CONTENTS 
 
 
 
LIST OF TABLES............................................................................................................. ix 
LIST OF FIGURES ............................................................................................................x 
NOMACLATURE ........................................................................................................... xii 
1. INTRODUCTION ......................................................................................................1 
    1.1   Overview..................................................................................................................1 
1.2 Historical Perspective ..........................................................................................6 
1.2.1 United States Air Force................................................................................6 
1.2.2 NASA...........................................................................................................8 
2.     METHODOLOGY ....................................................................................................10 
2.1 Gas Distribution Time Measurement (Overview) .............................................14 
2.2 Choice of Test Gas.............................................................................................15 
3. THEORY ...................................................................................................................17 
3.1 Internal flow through the distribution system....................................................17 
3.2  Testing Method ..................................................................................................24 
3.2.1 Modified Application of Dual Langmuir Probes.......................................24 
3.2.2 Verification of the Modified Dual Langmuir Probes.................................28 
3.2.3 Difficulties in Use of the Modified Dual Langmuir Probes ......................35 
 
 
 viii
4. RESULTS AND ERROR ANALYSIS .....................................................................37 
4.1 Experimental Data .............................................................................................37 
4.2 Error Analysis ....................................................................................................47 
5. CONCULSIONS AND RECOMMENDATIONS ....................................................50 
REFERENCES ..................................................................................................................52 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ix
LIST OF TABLES 
 
Table 1: Choked Test Nozzle Data Perpendicular Sensor Orientation..............................31 
Table 2: Choked Test Nozzle Data Parallel Sensor Orientation........................................32 
Table 3: Choked Test Nozzle Data Increased Supply Pressure.........................................32 
Table 4: Reduced Area Choked Test Nozzle Data ............................................................33 
Table 5: Supersonic Test Nozzle Data...............................................................................34 
Table 6: Test Data for Edge of the Disc and Height of 3 mm ...........................................38 
Table 7: Test Data for Edge of the Disc and Height of 5 mm. ..........................................39 
Table 8: Test Data for Edge of the Disc and Height of 10 mm .........................................40 
Table 9: Test Data for Edge of the Disc and Height of 15 mm .........................................41 
Table 10: Test Data for Edge of the Disc and Height of 30 mm .......................................42 
Table 11: Test Data for Edge of the Disc and Height of 45 mm .......................................43 
Table 12: Test Data for Edge of the Disc and Height of 60 mm .......................................44 
Table 13: Test Data for 50% of the Disc Length and Height of 5 mm..............................45 
Table 14: Summary of the Test Results for Measurements Taken at Disc Edge ..............46 
Table 15:  Summary of the Standard Deviation for all test data 68% probability range...48 
Table 16:  Summary of the Standard Deviation for all test data 96% probability range...48 
 
 
 
 
 
 
 x
LIST OF FIGURES 
 
Figure 1 ................................................................................................................................3 
Figure 2 ................................................................................................................................3 
Figure 3 ..............................................................................................................................11 
Figure 4 ..............................................................................................................................12 
Figure 5 ..............................................................................................................................13 
Figure 6 ..............................................................................................................................13 
Figure 7 ..............................................................................................................................16 
Figure 8 ..............................................................................................................................18 
Figure 9 ..............................................................................................................................18 
Figure 10 ............................................................................................................................25 
Figure 11 ............................................................................................................................26  
Figure 12 ............................................................................................................................27 
Figure 13 ............................................................................................................................29 
Figure 14 ............................................................................................................................29 
 
 
 
 
 
 
 
 
 
 
 xi
NOMACLATURE 
 
PIT  Pulsed Inductive Thruster 
M(z)  Mutual Inductance (nH) 
F  Force 
L
c
  Thruster coil unloaded inductance (nH) 
z
o
  Plasma decoupling distance (m) 
z  Distance between the coil and plasma current 
I
1
  Current in the drive coil 
I
2
  Current in the plasma 
I
sp
  Specific Impulse (seconds) 
m
gas
  Mass of the gas above the disc at time of field trigger (Kg) 
g  Gravitational constant equal to 9.8 m/s
2 
C
r 
 Cross sectional area of individual channel 
C  Capacitance (Farads) 
V  Voltage (Volts)  
?   Thrust Efficiency 
P
exit  
Manifold exit pressure (Pascals) 
P
init  
Static supply pressure (Pascals) 
?  Specific heat ratio 
M
exit  
Manifold exit Mach number 
T
exit
  Manifold exit Temperature (Kelvin) 
T
init
  Static supply Temperature (Kelvin) 
?
exit  
Density at the Manifold exit (Kg/m
3
) 
?
init  
Static supply density (Kg/m
3
) 
u
exit
  Manifold exit velocity (m/s) 
a
exit  
Speed of sound for the manifold exit temperature (m/s) 
R
Ar
   Gas constant for Argon equal to 208.1 J/(Kg-K) 
.
m   Mass flow rate (Kg/s) 
CTA  Constant Temperature Anemometry 
u
2  
Velocity in the ?(M) direction (m/s) 
v
r  
Radial component of velocity (m/s) 
r
inner
  Magnetic coil disc inner radius (m) 
r
outer
  Magnetic coil disc outer radius (m) 
?  Viscosity of Argon 
SNR  Signal to Noise Ratio 
Std  Standard Deviation 
Sm  Standard deviation of the mean 
 
 
 1 
 
 
 
 
1. INTRODUCTION 
1.1 Overview 
 A Pulsed Inductive Thruster (PIT) is a type of spacecraft electric propulsion that 
has been under research for over thirty years.  Electrical energy is stored in a capacitor 
bank and then inductively discharged through flat, circular coil.  A small amount, usually 
less than a tenth of a gram, of propellant is distributed over the coil in inert form prior to 
the electrical drive pulse.  The gas is distributed over the coil in way that keeps it as close 
to the coil surface as possible.  Gas is distributed from the center of the thruster from a 
manifold with a circumferential opening normal to the drive coil face.  The gas is pulsed 
outward radially over the drive coil surface.  The time of the gas distribution must be 
known such that the electrical pulse through the coil can be timed to the gas distribution.  
Upon initiation of the electrical pulse, the gas is first ionized either by the electrical drive 
pulse itself, or by a separate pre-ionization system.  The ionized gas then couples to the 
magnetic field in the drive coil caused by the drive pulse.  This induces a ring current 
parallel to the plane of the drive coil in the ionized propellant that is now a plasma.   This 
now meets the requirement of a current carrying conductor (plasma) in a magnetic field, 
therefore force is applied to the plasma pushing it away from the drive coil.  This applies 
an equal and opposite force on the drive coil, imparting an impulse thrust ?bit? to the 
thruster. 
 
 2 
Much of the early research and design work in the United States has been 
conducted by TRW, Inc. in conjunction with the Air Force Research Laboratories at 
Edwards Air Force base in California and later with NASA Glenn Research Center in 
Cleveland, Ohio.  Current PIT related propulsion research is also being conducted in 
parallel by NASA at the Marshall Space Flight Center in Huntsville, Alabama in 
conjunction with the Institute for Scientific Research (ISR) Inc. and Radiance 
Technologies.  This propulsion design has yet to be utilized in an operational spacecraft, 
but could potentially offer several advantages.
1, 2, 3
  These advantages include: 
1. Potential for low thruster specific mass (Kg/KW) as low as 15.6 Kg/KW
4
 
compared to other high power (? 10 KW), electric propulsion thruster 
designs under development.
5
 
2. Capable of a wide range of average power levels in a single device. 
3. Additional thrust control through throttled gas flow. 
4. The PIT design will work with several propellant gases. 
5. The PIT design is completely electrodeless.  The design is therefore less 
susceptible to operational wear due to chemical reactions and sputtering 
than electric propulsion designs that require electrodes.
6
 
PIT propulsion devices use a single pulsed magnetic field to first ionize the 
propellant gas and then accelerate the ionized propellant for thrust.  The field coils used 
to create the magnetic pulse are integrated into a flat circular disc.  The field coil 
geometry is shown on the right in Figure 1.  The un-ionized propellant is initially 
dispersed over the disc.  The disc and distribution manifold are shown on the left in 
 
 3 
Figure 1.  Then the magnetic pulse is timed to the gas distribution over the disc to achieve 
an optimum interaction between the magnetic field and the propellant.  
 
  
Figure 1:  Geometry of the PIT and Field Coils Tested by Radiance 
 Optimization of the process requires that the propellant gas be as evenly 
distributed over the disc in the radial (r) and angular (theta) axes as possible with the gas 
as close to the disc as possible in the axial (z) direction.  The cylindrical coordinate 
system is shown with respect to the device in Figure 2. 
 
Figure 2:  Cylindrical Coordinate System on the Disc 
 
 4 
Ideally, there should be a uniform interaction between the pulsed magnetic field 
and the gas over the disc.  This would lead to the best coupling efficiency between gas 
and magnetic field.  When the electrical drive pulse and the ionized propellant interact, 
the coupling between the two currents is a function of the mutual inductance between the 
current in the drive coil, I
1
, and the current ring, I
2
, formed in the ionized propellant 
(plasma).  The mutual inductance, given by eq. 1 is a function of unloaded coil 
inductance, L
o
, the separation between the coil and the gas, z, and the plasma decoupling 
distance, z
o
.
1
  The plasma decoupling distance is a measure of the significant distance 
away from the coil at which the plasma becomes decoupled from the drive pulse.  The 
force, F, generated due to the coupling between the two currents is given by eq. 2.   
?
?
?
?
?
?
?
??
=
o
C
z
z
LM exp     (1) 
?
?
?
?
?
?
?
??
=
?
?
?=
oo
C
z
z
z
LII
z
M
IIF exp
2
21
21
    (2) 
 The physical shape, and therefore the coupling efficiency, of the plasma is 
determined by the uniformity and nearness of the initial inert gas distribution prior 
ionization to the drive coil at the start of the electrical drive pulse.  If the gas is 
distributed near to the drive coil, well within the plasma decoupling distance, and in a 
uniform density, then the induced current, I
2
, will be a maximum, and the greatest amount 
coupling distance, z
o
, will be used for generated force during the plasma acceleration. 
The amount of gas used and the magnitude of the magnetic field can be adjusted, 
such that a maximum fraction of the electrical energy in the magnetic field can be 
imparted into the propellant as directed kinetic energy in the positive z direction.  If the 
 
 5 
gas distribution is not uniform, then there will be a non-uniform coupling between gas 
and magnetic field.  The amount of force generated by the acceleration of the plasma will 
be reduced. 
 The timing of the pulse for the field must also be coordinated to the gas 
distribution time for the same energy transfer reasons stated above.  To coordinate the 
times, the distribution time of gas over the plate must be known and should be consistent.  
If the gas distribution time is a known constant, then onboard sensors will not be required 
to monitor the gas distribution to determine the trigger time of electromagnetic field 
pulse.  It is also beneficial to make the distribution time as long as possible.  For a given 
disc radius, this can be accomplished by keeping the radial distribution velocity of the gas 
as low as possible.   
The gas is distributed over the disc in open space that is originally at vacuum 
levels of background pressure.  The gas will achieve supersonic speeds for any 
distribution method chosen due to the low background pressure.  The max velocity of the 
gas is given by eq. 3.  The distribution time for the disc radius selected (~ 0.5 meters) will 
be roughly between 0.1 to 1.0 milliseconds for the supersonic gas velocity obtainable for 
Argon at a static gas temperature of 300 Kelvin and all drive coil and gas distribution 
manifold radii combinations of interest.     
Tcv
p
2
max
=       (3) 
Achieving the slowest possible distribution time reduces the difficulty in timing 
the magnetic field pulse to the gas distribution.  Also, if the distribution time is greater 
than or equal to one millisecond, then it might be possible that the pulsed power circuits 
 
 6 
to the magnetic coils can be recharged fast enough to allow for near continuous gas 
supply and field pulses every one millisecond.  This greatly increases the propellant 
utilization percentage since the gas leftover in the distribution system is not lost after 
every shot. 
The design proposed in this thesis is one method to achieve the desired gas 
distribution time.  The results of the work will show that the design lengthens the 
distribution time to around one millisecond.  The uniformity of the gas distribution was 
not measured for this work, but could be measured at a later date using a Fast Ionization 
Gauge
1
.  
 
1.2 Historical Perspectives 
    1.2.1 United States Air Force  
 A one meter diameter PIT thruster was built and demonstrated by C.L. Bailey and 
R.H. Lovberg working for TRW Inc. under Air Force Research Laboratories contract 
during the 1970?s.
1, 2, 3
  This thruster preceded smaller devices (30 cm diameter) of the 
same design that were also tested.  The TRW researchers found that the one meter 
thruster could generate a specific impulse of 2240 seconds whereas the smaller devices 
were limited to 1200 seconds.  The conclusion was that the PIT design?s efficiency 
increased with disc diameter.  This was due to improved coupling between the ionizing 
gas and the pulsed magnetic field and therefore increased energy transfer.
 1
 
The TRW testing used a 20 ?F capacitor bank charged to 20 KV to supply the 
voltage pulse to the field coils through a set of spark gaps.  The sparks gaps were placed 
 
 7 
in parallel in the circuit and triggered simultaneously.   The design was sized to simulate 
a 25 Kilowatt mission.  Testing yielded an overall efficiency of 50% thrust efficiency for 
this device.  The efficiency is defined by eq. 4.
4 
( )
inenergyElectical
producedenergyKinetic
CV
Igm
spgas
==
2
2
2
1
2
1
?    (4) 
The gas distribution system used a radial, supersonic nozzle placed at the center 
of the disc.  The nozzle was mounted on a pylon several centimeters high.  The gas was 
fed to the nozzle under high pressure by a fast acting valve that provides a 150 
microsecond gas pulse in a single pulse operational mode.  The gas pulse fed to the 
supersonic nozzle was directed downward in the z direction and also expanded radially 
outward toward the plate by the nozzle.  This gas pulse exited the nozzle at 
approximately MACH 2.0.  The magnetic field pulse was then timed to coincide with the 
time at which the gas pulse would be nearest the disc.
 1
 
The gas distribution for the design used in the TRW work was measured with a 
fast ionization gauge.  A Schlieren system was also used with limited success due to the 
low gas distribution pressure.
3
  The TRW researchers found that a significant percentage 
of the propellant gas could be compressed into a reflected shock wave near the disc face.   
Losses still existed in this distribution design for three reasons.  First, some of the 
gas would radially expand past the edge of the disc, and was therefore not utilized as 
propellant.  Second, some of the gas was not contained in the shock wave near the plate, 
and was present above the disc at a height at which it could not interact with the magnetic 
field.  A portion of the gas was therefore not accelerated by the magnetic field, but 
 
 8 
entrained by gas that did interact with the field.  This leads to a lower overall I
sp
, and a 
reduction in efficiency.  Third, this design employed a much higher gas density near the 
center pylon, with the gas density decaying exponentially radially.  This resulted in an 
uneven gas distribution profile across the disc with respect the radial direction, reducing 
the effective ability to couple the magnetic field to the gas propellant.
3
  
The magnetic field timing window required to effectively take advantage of the 
gas distribution produced by this design is less than one microsecond in breadth.  This 
requires a very accurate means to time the magnetic field pulse to the gas distribution 
with very little room for timing error.  In addition, due to the high z velocity component 
of the gas during distribution, the compressed shock wave spends less than four 
microseconds in a band below a reasonably useable height for interaction with the 
magnetic field.  Therefore, the magnetic field pulse used with this system should be 
compressed down to no more than three to four microseconds in pulse width to 
effectively couple with the gas before the gas moves outside effective range.   
    1.2.2 NASA 
 During the past decade NASA has been working with the TRW one meter 
diameter PIT thruster at the Glenn Research Center at Cleveland, Ohio.  This effort 
entails attempting to replace the spark gaps switches with solid state devices, and 
operational testing of the thruster at high repetition rate to evaluate its performance.  The 
power supply for this testing is a 250 KJ capacitor bank that can supply 30 Megawatts for 
two milliseconds.   
 
 9 
The effort also includes an attempt to model the plasma formation and 
acceleration using the MACH2 code.  The magneto hydrodynamics MACH2 model is a 
time-dependent, two-dimensional, axis-symmetric, multi-material code based upon a 
time-advanced finite-volume spatial differencing method.  The model treats the gas as a 
compressible, viscous fluid.
6
  These efforts are in concert with other electric propulsion 
research in an attempt to develop a high-power electric thruster.
 7
   
 In 2004 research into alternative technology application for the pulsed inductive 
thruster design began at Radiance Technologies.  These studies included the application 
of a Vector Inversion Generator to replace the capacitor bank, pre-ionization of the 
propellant gas, and simplification of the magnetic field design and pulse delivery 
mechanism.  The design and testing described in this thesis was also conducted under this 
contract. 
 The basic goal of this work was to provide a gas distribution system for use in PIT 
that would distribute the gas close to the thruster in a known amount of time.  The desired 
distribution time should be more than 1 millisecond.  This would allow the thruster to be 
operated in a burst rep-rate mode at a 1 Khz rep-rate.  By operating in this mode, the 
thruster could work with a slower gas valve, since the pulse time of the valve would be 
determined by the time duration of the burst, and not the time duration of the individual 
pulse.  A radial distribution of the gas was chosen since this should keep the gas close to 
the thruster face.  The gas distribution was not measured for this work.  Experimental 
focus was on the gas pulse distribution time. 
 
 
 10 
 
 
 
 
2. METHODOLOGY 
 The design considerations outlined in the introduction provided the 
starting point for design of the gas distribution manifold.  In order to simplify the 
solution, the flow was approximated as steady state.  If the flow is considered steady 
state, then the isentropic nozzle equations can be used to characterize the gas velocity.  
The flow is a gas pulse, and is therefore inherently dynamic.  The starting background 
pressure inside the manifold is at vacuum.  Prior to establishing a steady state pressure 
distribution inside the manifold the gas would be under-expanded and would therefore 
accelerate to above the speed of sound inside the nozzle.  The exit of the manifold 
becomes the choke point of the flow after the steady state pressure distribution inside the 
nozzle is established.  The results of the testing will show that the approximation of the 
flow as steady state did predict the measured distribution times with an accuracy suitable 
for practical design purposes.  A CAD model of the manifold is shown in figure 3. 
 
 
 11 
 
Figure 3: Cross Sectional Cutaway of the Gas Distribution System and Disc 
 
If the flow were unsteady inside the manifold, the expected gas velocity would 
reach the speed of sound prior to exiting the nozzle.  For Argon at a static temperature of 
300 K the speed of sound is 322.9 m/s.  During experimental measurement of the flow, 
the time that it takes the flow to go through the manifold was measured to 0.97 
milliseconds by the modified Langmuir method that will be described later in the thesis.  
The length of the flow path through the manifold is 0.18 meters.  The average speed of 
the flow in the manifold is given by eq. 5. 
sm
meters
time
lengthpathflow
V
avg
/6.185
sec1097.0
18.0
3
=
?
==
?
  (5) 
 In the steady state condition, the flow accelerates from approximately zero 
velocity in the radial (r) direction to Mach one at the manifold exit.  The average 
subsonic velocity calculated based upon the measured travel time is evidence that the 
flow is either near or at steady state conditions.  If the flow were not near steady state, a 
sonic or supersonic average velocity would be more likely.   
 
 12 
The design chosen constrains the geometry of the enclosed portions of the device 
to ensure that the exit point of the gas (from the manifold) is a convergent nozzle for a 
steady state flow.  The manifold is pictured in Figures 4 through 6.  The exit is the 
smallest cross sectional area encountered by the gas during distribution.  The gas will 
accelerate to supersonic speeds over the plate due to free expansion.  However, the gas 
starts this expansion from the lowest speed possible for the given negligible background 
pressure, which is Mach one, set by the convergent nozzle geometry.  This ensures that 
the speed of the gas will be as low as possible during distribution over the disc for a 
maximum distribution time. 
 
 
 
 
 
 
 
Figure 4: Manifold Internals Part A 
 
 
 
 
 
 
 
 13 
 
 
Figure 5: Manifold Internals Part B 
 
 
 
Figure 6:  Nozzle Exit Side View 
 
 
 
 
 
 
 
 
 14 
2.1 Gas Distribution Time Measurement (Overview) 
 Ultra Heavy Molecular Weight (UHMW) polypropylene was selected as the 
material due to its ease in milling.  The full assembly with the manifold and disc are 
pictured in Figure 1.  
The device was placed into a vacuum chamber on a test stand.  Constant 
Temperature Anemometry (CTA) was the first attempted means to measure the gas 
distribution time.  The gas density proved too low to make CTA a viable measurement 
tool.  A technique utilizing a modified form of Langmuir probe
8
 was developed to detect 
the passage of the gas.  A Langmuir probe is a form of electrical plasma instrumentation 
that is typical used to measure plasma electron temperature and plasma ion density.  For 
further information on this system, please see ref. 8.  Two such instruments were used to 
monitor for passage of the gas.  One probe was placed at the exit of the manifold and the 
other at the edge of the plate.  Therefore, the time difference between the trigger points of 
the two detectors would be the distribution time.  The sensor setup is shown in Figure 7. 
The distribution time of the gas, as measured would then provide a rough estimate 
of the best time to trigger the magnetic field pulse.  The flow across the plate is a pulse 
instead of steady state for pulsed operation of the thruster.  For pulsed operation, the 
optimum gas distribution may occur over a relatively small amount of time (with respect 
to the distribution time) before or after the initial front of the gas pulse has passed.  
Therefore, the optimum trigger time would likely be some time near but not exactly equal 
to the distribution time.  This optimum time could be identified on a fully operational 
thruster by varying the magnetic field pulse time in small increments in the time range 
 
 15 
slightly past the time when the initial gas front reaches the edge of the disc.  The thrust 
could be measured for the different trigger times of the magnetic field pulse until an 
optimum trigger time could be found.   
In a continuous gas supply thruster design the gas supply is not pulsed for each 
shot.  The optimum time for the magnetic field pulse trigger in this design would likely 
be coincident with the distribution time. Since the flow is steady state for this design 
consideration, the optimum achievable gas distribution is likely that predicted by the 
model.    
2.2 Choice of test gas 
 Argon was chosen as the gas to be used for testing of the device.  The PIT design 
will work with several types of gases; however, Argon has several advantages for testing.  
Argon is monatomic therefore; its specific heat ratio is a constant for a large temperature 
range.  Argon is easily ionized, readily available for testing purposes, safe to handle, and 
remains a gas at relatively low temperatures.  Helium has many of the same properties as 
Argon, but has a higher gas speed.  This would result in a faster distribution time for 
Helium as compared to Argon. 
Argon is easily ionized and its Paschen curve has been well characterized.
9
  This 
simplified the calibration of the probes since the applied voltages were chosen such as to 
trigger ionization with a minor change in Argon gas pressure.  The sensitivity of the 
probes was on the order of one milli-Torr increase in Argon gas pressure above the 
starting two to three milli-Torr background pressure. 
 
 
 16 
 
Figure 7:  Testing Setup in the Vacuum Chamber 
 
 
 
 17 
 
 
 
 
3. THEORY 
All aspects of the design and testing are presented in this section in detail.  The 
gas distribution is divided into two main areas.  The first area presented is the flow of gas 
through the internal area of the manifold.  Distribution over the disc is then discussed.  
The section concludes with a description of the testing instrumentation and setup. 
3.1 Internal flow through the distribution system 
The flow path for the gas starts at the center of the manifold shown in Figure 3.  It 
is delivered by a pulsed solenoid valve supplied by a relatively constant pressure 
Reservoir.  The gas expands radially outward in six equal areas defined by the ribs, 
between the two halves of the manifold.  Each area of expansion has a slightly decreasing 
cross sectional area as the gas moves outward in the radial direction.  This was 
accomplished by narrowing the distance between the upper and lower halves of the 
manifold as a function of the manifold?s radius.  The internal portions of the gas 
distribution system, or manifold are shown in figures 8 and 9. 
 
 18 
 
Figure 8: Diagram Cutaway of the Gas Distribution System and Disc 
 
Figure 9: Control of the crossectional area by varying height 
 
 19 
The initial radius, where the ribs begin to divide the flow into six separate 
channels is 50 mm.  The cross sectional area, C
r
, for each of these six flow areas 
corresponding to this radius is given by eq. 6. 
()()heightxthicknessribRadiusC
r
62
6
1
?= ?    (6) 
The rib thickness is 10 mm.  The height between the plates at radius of 50 mm is 
4.5 mm.  This provides a cross sectional area of 190.6 mm
2
 for each of the six flow areas.  
The total cross sectional area at this radius is 6 x 190.6 mm
2
 = 1143.7 mm
2
.  The outer 
radius of the enclosed flow area is 180.0 mm.  The height between the plates at this point 
is 1.0 mm.  This results in a cross sectional flow area for each of the six areas of 178.5 
mm
2
 at the outer edge of the manifold.  The total cross sectional area at this radius is 6 x 
178.5 mm
2
 = 1071.0 mm
2
. 
Since the cross sectional area at the outer edge of the plate is maintained slightly 
smaller than for all radial cross sections on the interior of the manifold, this outer edge 
becomes the nozzle throat.  The geometry established is that of a converging nozzle.  
Therefore, the maximum velocity that can be obtained within the internal area of the 
manifold is Mach one for steady flow.  This is the assumed speed at the throat of the 
nozzle, where the flow becomes choked.   
The flow exits the manifold at Mach one, which is the lowest Mach number 
attainable for steady flow in any nozzle geometry, given that the flow is under expanded.  
An under expanded flow being one in which the exit pressure of the flow is greater than 
that of the exit surroundings.
10
  For steady flow under these conditions, the throat is 
guaranteed to have a choked flow condition.  The Mach number at the throat will be 
 
 20 
Mach one.  (Since the manifold deposits the gas into a vacuum, the flow will always be 
under expanded.) 
The gas properties at the exit of the manifold can be approximated from the 
steady isentropic nozzle equations.  For the purpose of this analysis the Mach number at 
the exit of the manifold is fixed at one, and ? for Argon is a fixed number equal to 1.67.  
The steady isentropic nozzle equations are presented in eqs. 7 through 9.
10
  
1
2
2
1
1
?
?
?
?
?
?
?
? ?
+=
?
?
?
exitinitexit
MPP     (7) 
 
1
2
2
1
1
?
?
?
?
?
?
?
?
+=
exitinitexit
MTT
?
     (8) 
 
1
1
2
2
1
1
?
?
?
?
?
?
?
? ?
+=
?
?
??
exitnitiexit
M     (9) 
 
   
These equations can be reduced to simpler statements for Argon exiting the 
manifold as shown in eqs. 10 through 12. 
initexit
PP 49.0=      (10) 
 
initexit
TT 75.0=      (1) 
 
initexit
?? 65.0=      (12) 
 
 
The velocity at the exit of the manifold is then given by eq. 13. 
 
exitArexitexitexitexit
TRMaMu ?==     (13) 
 
 The method for determining the mass flow rate at the exit of the nozzle is 
dependent upon the delivery method.  The delivery method can be split into two distinct 
 
 21 
categories.  The gas could be delivered either from a relatively small measured volume 
(constant volume source) or from a supply line or large reservoir (constant pressure 
source).  The first method would be the most likely method to use for a pulse over a short 
time frame.  The second method would be the most likely method for a continuous gas 
supply.  The continuous gas supply scheme would require delivery from a supply line 
(constant pressure source) since a measured volume for this scheme would be 
impractically large.  In addition, the constant volume would not be able to provide a 
constant mass flow rate due to large pressure drop over time, a problem inherent to the 
constant volume source.  
Regardless of supply scheme, a fast acting valve with a cross sectional area larger 
than the total cross sectional area at the manifold exit would be required at the entrance of 
the manifold for future designs.  A poppet type or diaphragm type valve would be 
appropriate for this application.  This would ensure that amount of gas wasted (not on the 
disc at time of magnetic field pulse) would be minimized and that the manifold exit cross 
sectional area would remain the choke point for the gas flow.  
A slower acting poppet type valve was used for the purpose of testing.  The cross 
sectional area of the valve is larger than one of the six sections of the manifold.  Of the 
six sections on the manifold, all but one was sealed off for measurement of the flow 
times.  The solenoid operated, poppet type supply valve was placed outside the vacuum 
chamber to simplify design of the gas supply system.  This resulted in a long leg of 
supply piping joining the supply valve and the manifold.  The amount of gas wasted per 
pulse was not a consideration for this stage of design and testing, since the sole purpose 
 
 22 
of the experimental setup was to measure the flow time over the disc.  The additional 
length of piping did not prove to be an inhibiting factor to the testing. 
The gas was supplied to the poppet valve by a large gas reservoir that experienced 
less than a 1% change in static, supply pressure per shot.  Since the pressure change in 
the reservoir per shot was minimal, it could reasonably be considered a constant pressure 
source.  This reservoir is larger than would be reasonable for use on a flight ready 
thruster due to space and weight considerations.   
 The mass flow rate equation for a steady state constant pressure source method 
using a nozzle is given by eq. 14. 
()12
1
2
.
2
1
1
?
+
?
?
?
?
?
?
? ?
+=
?
?
??
MM
TR
AP
m
initAr
init
   (14) 
 
 The choked nozzle exit design factor requires that the manifold exit remain the 
point at which the flow is choked to control mass flow rate.  This places a constraint on 
the gas supply system, in that the supply line prior to entry to the manifold must have a 
cross sectional area greater than the combined cross sectional area for the manifold exit.  
The manifold?s combined cross sectional area at the exit is given in eq. 15. 
22322
66.110071.110715.1786
sec
inmxmmmmx
areationalcrossExit
comb
===
=
?
 (15) 
 This corresponds to a radius of 18.46 mm or 0.727 inches for a circular pipe.  
Therefore, the supply line prior to entry to the manifold, where the static conditions are 
measured, must be greater than or equal to this radius in size.  For testing purposes, this 
constraint was impractical due the necessity to feed the gas into the vacuum chamber 
through a bulkhead fitting.  This fitting was slightly smaller than the required radius.  To 
 
 23 
alleviate this constraint, all but one the six sections in the manifold were closed off from 
flow.  This was done through the application of duct seal, a putty material, to inlet of 
these areas.  This ensured the desired flow geometry was maintained.  
 The desired mass distributed across the disc is 1 x 10
-5
 kg .  The mass bit size was 
selected based upon prior work by Loveberg and Dailey on pulsed inductive thrusters of 
this diameter.
1
  The desired distribution time is one millisecond.  The resulting design 
mass flow rate is 1 x 10
-2
 kg/s.  A supply temperature of 300 K is assumed.  The 
isentropic equations for flow through a convergent nozzle are presented in eqs. 7 through 
14 for the required supply pressure.  Note that viscous effects on the supply gas inside the 
distribution system are ignored.  Substituting in the values for geometry, gas properties 
and Mach number gives eq. 16. 
 
KPaPaP
init
208.33208 ==           (16) 
 
The equation can also be solved as a function of temperature; 
 
initinit
TP 2.104=      (17) 
 
 The supply temperature cannot practically be much less than 300 K to ensure that 
the propellant, Argon, does not reach its critical temperature of 151 K inside the manifold 
and subsequently interfere with the gas distribution over the disc.  The lower supply 
temperature limit to prevent this is 202 K. 
 The following factors have not been taken into account in the design and were 
considered to be relatively unimportant for preliminary design purposes here; 
1. The time dependence of the flow field governing eqs. 
2. Frictional heating of the gas in the manifold 
 
 24 
3. Heat transfer between the manifold and disc components and the gas flow 
4. Possibility of temporal flow instabilities internal to the manifold 
5. Turbulence 
6. Flow interaction with the disc during expansion over the disc  
3.2 Testing Method 
 The testing phase of this project focused primarily on determining the gas 
distribution time across the plate.  Initial attempts to measure density distribution were 
conducted using constant temperature anemometers.  This method proved unsuccessful 
and a method using gas detection through gas ionization was pursued as an alternate 
method.  This alternate method proved successful in measuring the gas distribution time.  
   
  3.2.1 Modified Application of Dual Langmuir Probes 
After failure of the CTA probes, it was suggested by Auburn Space Research 
Institute Lab Manager Steve Best that given the extremely low operating background 
pressures of the manifold the gas flow could possibly be ionized under high voltage 
potential.  This basic concept is used by Dual Langmuir Probes which are often used to 
study low density plasmas.
9
  The electrical characteristics of the gas medium (Argon in 
this case) are described by the Paschen curve shown in figure 10.
9
 
 
 25 
160
170
180
190
200
210
220
230
240
250
024681012141618
Pd (torr-cm)
B
r
eakdo
w
n V
o
lta
g
e (v
olt)
 
Figure 10: Paschen curve for Argon 
The Paschen curve predicts the conditions under which the Argon gas will ionize 
taking into account the applicable dimension of the probe ? lead separation.  The curve 
provides the threshold voltage across the sensor leads required to ionize the Argon gas 
versus the compound parameter of gas pressure multiplied by the probe lead separation.  
The operational range of interest for this measurement falls to the far left side of the 
Paschen curve.  For regions of very low pressure (in the milliTorr range) found in the 
present investigation, the curve is nearly vertical.  Therefore, a sensor separation of one 
to three millimeters will allow for a high resolution of pressure change detection.  The 
sensors used had a lead separation distance of 2.0 mm.  This lead separation was found to 
work best in practice. 
 
 26 
Initial testing proved this application to be viable.  Negatively biased DC voltage 
potential just low enough to not cause discharge (gas ionization) without gas flow was 
applied.  When the gas was pulsed through the manifold, passing the point where the 
probe was placed, ionization occurred and a detectable signal was produced.  The sensor 
described was connected to a circuit that provides a capacitive voltage of three to six 
kVDC negatively biased potential to the sensor.  The Voltage level is set such that the 
sensor will not trigger at background pressure, but will trigger with a pressure increase of 
one to three milli-Torr overall at the probe location.  Starting background pressure in the 
vacuum chamber was established between two to three milli-Torr for each measurement.  
When the sensor is triggered by the gas, a path is established to discharge the capacitor 
across the sensor leads.  The voltage potential for the capacitor of each sensor was 
monitored by oscilloscope.  An electrical schematic for a single channel of the sensor 
system is provided in Figure 11.   
 
Figure 11:  Sensor Schematic  
 
 27 
 
An initial attempt to use this sensor for gas distribution time utilized two 
independent sensors of the design described above.  The first one placed at the manifold 
exit and the second placed at the outer edge of the PIT disc.  The RF signal generated by 
the firing of the first sensor was large enough to trigger the second sensor.  To prevent 
this effect, the sensor lines required electrical shielding up to and as close as possible to 
the probe leads for all connecting wiring inside the vacuum chamber.   
It was also determined that sharp edges on the probe leads created a field 
geometry that was not conducive to this application.  Distribution times measured with 
probe leads of this type were very random.  To overcome this problem, the probe leads 
were made tear-drop shaped through the application of solder, such that no sharp edges 
were left on the leads.  The final configuration of the sensor leads is shown in Figure 12. 
 
 
Figure 12:  Close-up View of a Sensor 
 
 
 28 
    3.2.2 Verification of the Modified Dual Langmuir Probes 
With the sensor design established, the next step was to test their operation.  The 
manifold and PIT simulation disc were removed from the chamber leaving only the gas 
supply line.  A third monitor point for the oscilloscope was added.  This point was the 
voltage supply for the solenoid valve used to supply the gas pulse.  The solenoid valve is 
shown in Figure 13.  The power supply for the solenoid valve was a capacitor bank, 
whose voltage drop upon valve pulse initiation could be consistently used to mark the 
start of the gas pulse.  An electrical schematic for the solenoid valve?s pulsed power 
supply is provided in Figure 14. 
Since the oscilloscope?s initial trigger point was independent of the sensors, any 
deviation in the distribution time could be isolated to one or the other sensors.  The 
measurement method using the third time point was used for all measurements including 
those taken on the disc after sensor validation.  
  
 
 29 
 
 
Figure 13:  Solenoid Used to Pulse Gas to the Manifold 
 
 
 
Figure 14:  Solenoid Valve Operation Circuit 
 
The exit cross sectional area of the supply line was reduced such that the exit 
became a choked nozzle for the supply line.  One sensor was placed at the nozzle exit and 
the second was placed 390 millimeters directly out in front of the nozzle.  To verify the 
 
 30 
sensors, five different test runs were executed.  Each of the five tests included at least ten 
data points.  The data presented in Tables 1 through 5 represents the time at which the 
sensors triggered after the initiation of the gas pulse at the solenoid valve by the 
application of the electrical pulse from the capacitor bank.  The time difference between 
the trigger points for the two sensors is the distribution time, or travel time, for the gas 
between the two sensors.  All time measurements are in milliseconds. 
Three of the tests used the same nozzle exit cross sectional area of 197.9 mm
2
.  
This area was calculated to be small enough to provide choked nozzle exit geometry for 
supply line.   The first two tests compare alternate sensor orientations with respect to the 
gas flow.   One run was conducted with the sensors oriented perpendicular to the gas 
flow.  This data is presented in Table 1.  The second run (Table 2) was conducted with 
the sensor oriented parallel to the gas flow.  This was done to show that trigger time of 
the sensors was independent of sensor orientation to the gas flow.  The distribution time 
for both orientations was the same within measurement error.  The distribution time for 
each of these runs agreed with the predicted distribution time within one standard 
deviation for both data sets.   Note that the standard deviation of the mean, Sm, is given 
for all data sets by eq. 18 as a function of the standard deviation, Std, and n, the number 
of data points in the test set. 
n
Std
S
m
=       (18) 
During the third test run with a nozzle exit cross sectional area of 197.9 mm
2
, the 
supply pressure was increased.  The data for this test is presented in Table 3.  This was 
done to verify that the nozzle exit was choked.  Since the distribution time measured for 
 
 31 
this test did not vary from the two lower supply pressure runs, it provides verification that 
the nozzle was indeed choked.   
As a comparison, if the gas distribution time is estimated considering the Mach 
number to be constant at a value of one over the entire disc, then the distribution time is 
1.4 milliseconds.  If the gas distribution time is estimated considering the Mach number 
to be constant at a value of two over the entire disc, the distribution time is 0.93 ms. 
 
 
 
Table 1: Choked Test Nozzle Data Perpendicular Sensor Orientation 
Choked test nozzle (197.9 mm
2
) with a sensor separation of 390 mm, 10 PSIA 
of supply pressure and sensors oriented perpendicular to the gas flow.  All data 
in milliseconds 
Sensor 2   trigger time Sensor 1   trigger time distribution   time 
10.84 9.92 0.92 
10.84 9.96 0.88 
11.12 10.36 0.76 
11.28 10.20 1.08 
11.00 9.96 1.04 
10.84 9.92 0.92 
11.20 10.00 1.20 
11.04 9.76 1.28 
10.88 9.84 1.04 
11.04 9.96 1.08 
average average average 
11.01 9.99 1.02 
standard deviation of the 
mean 
standard deviation of the 
mean 
standard deviation of the 
mean 
0.05 0.05 0.05 
 
 
 
 
 32 
Table 2: Choked Test Nozzle Data Parallel Sensor Orientation 
Choked test nozzle (197.9 mm
2
) with a sensor separation of 390 mm, 10 
PSIA of supply pressure and sensors oriented parallel to the gas flow.  All data 
in milliseconds 
Sensor 2   trigger time Sensor 1   trigger time distribution   time 
10.80 9.96 0.84 
11.56 10.28 1.28 
11.60 10.16 1.44 
11.28 10.04 1.24 
10.96 10.00 0.96 
11.28 9.92 1.36 
10.84 9.96 0.88 
11.28 9.88 1.40 
11.20 9.80 1.40 
10.52 9.76 0.76 
average average average 
11.13 9.98 1.16 
standard deviation of 
the mean 
standard deviation of 
the mean 
standard deviation of 
the mean 
0.11 0.05 0.08 
 
Table 3: Choked Test Nozzle Data Increased Supply Pressure 
Choked test nozzle (197.9 mm
2
) with a sensor separation of 390 mm, 14 PSIA of 
supply pressure and sensors oriented perpendicular to the gas flow.  All data in 
milliseconds 
Sensor 2   trigger time Sensor 1   trigger time distribution   time 
10.72 9.76 0.96 
10.64 9.72 0.92 
10.64 9.80 0.84 
10.32 9.80 0.52 
10.68 9.76 0.92 
10.68 9.76 0.92 
10.84 9.76 1.08 
10.96 9.72 1.24 
11.08 9.72 1.36 
10.76 9.76 1.00 
average average average 
10.73 9.76 0.98 
standard deviation of the 
mean 
standard deviation of the 
mean 
standard deviation of the 
mean 
0.06 0.01 0.07 
 
 
 33 
For the fourth test, the cross sectional area of the choked nozzle was reduced to 
112.4 mm
2
.  The same distribution time was measured within one standard deviation for 
the data as for the larger, but still choked nozzles and the computer simulation prediction 
time.  This data is presented in Table 4.  
Table 4: Reduced Area Choked Test Nozzle Data 
Choked test nozzle (112.4 mm
2
) with a sensor separation of 390 mm, 10 PSIA of 
supply pressure and sensors oriented perpendicular to the gas flow.  All data in 
milliseconds 
Sensor 2   trigger time Sensor 1   trigger time distribution   time 
10.88 10.12 0.76 
11.68 10.04 1.64 
10.60 10.00 0.60 
11.16 10.00 1.16 
11.08 9.96 1.12 
11.52 9.96 1.56 
11.52 9.96 1.56 
10.92 9.88 1.04 
11.04 9.88 1.16 
10.72 9.88 0.84 
10.60 9.84 0.76 
average average average 
11.07 9.96 1.11 
standard deviation of the 
mean 
standard deviation of the 
mean 
standard deviation of the 
mean 
0.11 0.02 0.11 
 
For the fifth test, the nozzle exit cross sectional area was increased to 357.5 mm
2
.  
This area was calculated to be large enough to provide convergent ? divergent nozzle 
geometry for the distribution system exit.  Therefore, the exit velocity from the nozzle 
would be supersonic and the distribution time would be shorter.  The distribution time 
was estimated as follows.  The exit cross sectional area of 357.5 mm
2 
provides an area 
ratio of 1.81 for the given supply piping diameter.  From this area ratio, the initial Mach 
number was determined to be 2.25.  Since the supply temperature is 300K (relatively 
 
 34 
low), the distance of concern is relatively small (0.39 meters) and the initial Mach 
number was high, then the change in velocity for the expanding velocity is relatively 
small.  Based upon these assumptions, the distribution time was predicted to be 
approximately 0.8 milliseconds using the Mach 2.25 exit velocity condition.  The 
measured distribution time did concur with this estimated time as shown in Table 5. 
Table 5: Supersonic Test Nozzle Data 
Supersonic test nozzle (357.5 mm
2
) with a sensor separation of 390 mm, 10 PSIA of 
supply pressure and sensors oriented perpendicular to the gas flow.  All data in 
milliseconds 
Sensor 2   trigger time Sensor 1   trigger time distribution   time 
10.72 10.12 0.60 
10.84 10.08 0.76 
10.64 10.00 0.64 
10.64 9.84 0.80 
10.56 9.80 0.76 
10.64 9.88 0.76 
10.64 9.84 0.80 
10.72 9.80 0.92 
10.96 9.92 1.04 
10.52 9.80 0.72 
average average average 
10.69 9.91 0.78 
standard deviation of the 
mean 
standard deviation of the 
mean 
standard deviation of the 
mean 
0.04 0.04 0.04 
 
The sensor?s trigger time is dependent upon lead separation, gas pressure, and 
applied voltage.  This behavior as discussed is characterized by the Paschen curve for the 
gas used, which in this case is Argon.  The operational region chosen for the sensor is in 
an area where the Paschen curve is nearly vertical.  In this region, the gas ionization 
threshold is on the order of a few milli-Torr in pressure difference.  The pressure 
contacting the sensors from the gas pulse for this testing was several orders of magnitude 
 
 35 
larger than this threshold.  The sensors? response time is therefore several orders of 
magnitude smaller than the characteristic time scale, and its response to the gas passage 
reliable.  Overall, the accuracy range of the instrument appears to be reasonable, based 
upon the standard deviation of the mean showing the repeatability of the measurements 
and the correlation of the measured flow times to the expected values based upon 
calculated flow properties. 
 
    3.2.3 Difficulties in Use of the Modified Dual Langmuir Probes 
It is noted that the sensors do experience an anomalous behavior after 
approximately fifteen gas pulses.  After approximately this number of pulses, it was 
repeatedly observed that the second sensor would take several milliseconds longer to 
trigger than previous readings.  This would occur for two to three pulses and then the 
sensor would not respond at all.  To restore operation, the vacuum chamber would be re-
pressurized to atmospheric pressure and then pumped back down to an initial test 
pressure of two to three milli-Torr.  After the pressure cycling of the chamber, the sensor 
would return to normal operation for approximately another fifteen pulses.  This behavior 
occurred without fail for every test run. 
The cause of this behavior could not be determined, but is believed not to be 
indicative of the gas distribution.  The longer time responses just prior to sensor failure 
were disregarded.  The sensors were operated taking into account this behavior with the 
vacuum chamber pressure cycled as necessary to restore sensor operation.  
 
 36 
In addition to the above anomalous behavior, the sensors also proved to be 
temperamental in operation.  The problems experienced with the sensors ranged from a 
failure to trigger at all to erratic readings.  The erratic readings included trigger times that 
indicated impossibly short or impossibly long distribution times.  In any instance that the 
readings became erratic with widely varying readings, the test run was terminated.  The 
entire experimental setup was inspected for problems and the test run was repeated.  If 
erratic readings continued, then the sensor leads were rebuilt.  In every case during which 
erratic readings were experienced, normal operation of the sensors could be restored.  
Since the erratic readings could be cleared by rebuilding the sensors and no other change 
in the experimental setup, it is reasonable to believe that the behavior was due solely to 
sensor malfunction and not attributable to the gas distribution.  
 
 
 
 
 
 
 
 
 
 
 
 
 37 
 
 
 
4. RESULTS AND ERROR ANALYSIS 
4.1 Experimental Data 
 After verifying the operation of the sensor system the PIT disc and manifold were 
reinstalled into the vacuum chamber as shown in Figure 6.  The sensors were placed such 
that the first sensor was at the manifold exit and the second was at the edge of the disc.  
At the edge of the PIT simulation disc (radius of (180+390) mm), measurements were 
taken at heights (distance perpendicular off the disc face) of 3 mm, 5 mm, 10 mm, 15 
mm, 30 mm, 45 mm, and 60 mm.   
 A single testing point at 50% of the distribution length, 195 mm, and a height of 5 
mm was also studied.  The results of this test run are presented in Table 13.  More test 
points at 25%, 50%, and 75% disc length were planned, but unfortunately the vacuum 
chamber experienced technical difficulties that prevented further testing.  All of the data 
collected is presented in Tables 6 through 13.   
 
 38 
Table 6: Test Data for Edge of the Disc and Height of 3 mm 
Cumulative data for the point at the disc edge at a height of 3 mm above the 
disc surface.  All data in milliseconds 
Sensor 2 trigger time Sensor 1 trigger time 
Distribution time         
  (S
2
 time ? S
1
 time) 
11.96 10.92 1.04 
12.20 10.96 1.24 
11.84 11.08 0.76 
12.12 11.04 1.08 
12.24 11.00 1.24 
11.92 10.92 1.00 
11.88 10.96 0.92 
11.64 10.92 0.72 
12.00 10.84 1.16 
12.60 11.24 1.36 
12.28 11.08 1.20 
12.28 11.08 1.20 
11.84 11.12 0.72 
12.72 11.12 1.60 
12.48 11.04 1.44 
12.04 11.04 1.00 
11.88 11.04 0.84 
11.88 10.92 0.96 
12.28 10.84 1.44 
12.20 11.24 0.96 
11.72 11.08 0.64 
11.88 11.00 0.88 
12.24 11.00 1.24 
11.68 10.80 0.88 
12.84 10.96 1.88 
average average average 
12.11 11.01 1.10 
standard deviation of 
the mean 
standard deviation of 
the mean 
standard deviation of 
the mean 
0.06 0.02 0.06 
 
 
 
 
 
 39 
Table 7: Test Data for Edge of the Disc and Height of 5 mm 
Cumulative data for the point at the disc edge at a height of 5 mm above the disc surface.  
All data in milliseconds 
Sensor 2 trigger time Sensor 1 trigger time 
Distribution time           
 (S
2
 time ? S
1
 time) 
12.12 11.08 1.04 
12.24 10.96 1.28 
12.48 11.00 1.48 
11.84 11.04 0.80 
12.12 11.12 1.00 
12.08 11.00 1.08 
12.32 10.88 1.44 
11.88 10.92 0.96 
11.96 10.92 1.04 
11.44 10.88 0.56 
11.88 10.92 0.96 
12.24 10.92 1.32 
11.84 10.92 0.92 
11.92 10.92 1.00 
11.84 10.88 0.96 
12.00 10.96 1.04 
12.48 10.88 1.60 
11.96 10.96 1.00 
12.04 10.84 1.20 
12.24 10.72 1.52 
11.52 10.88 0.64 
11.96 10.84 1.12 
12.52 11.04 1.48 
12.44 10.92 1.52 
12.28 10.88 1.40 
12.16 10.84 1.32 
11.36 10.84 0.52 
11.68 10.80 0.88 
11.96 10.76 1.20 
11.48 10.68 0.80 
12.08 10.68 1.40 
11.40 10.72 0.68 
11.64 10.52 1.12 
11.48 10.72 0.76 
12.16 10.68 1.48 
11.52 10.60 0.92 
11.88 10.72 1.16 
11.88 10.76 1.12 
11.32 10.56 0.76 
average average average 
11.94 10.85 1.09 
standard deviation of the 
mean 
standard deviation of the 
mean 
standard deviation of the 
mean 
0.05 0.02 0.05 
 
 
 
 
 40 
Table 8: Test Data for Edge of the Disc and Height of 10 mm 
Cumulative data for the point at the disc edge at a height of 10 mm above the 
disc surface.  All data in milliseconds 
Sensor 2 trigger time Sensor 1 trigger time 
Distribution time         
(S
2
 time ? S
1
 time) 
12.24 11.08 1.16 
11.84 10.96 0.88 
12.32 10.88 1.44 
12.80 10.92 1.88 
11.84 10.84 1.00 
11.96 10.60 1.36 
11.76 10.68 1.08 
12.04 10.68 1.36 
12.28 10.72 1.56 
12.12 10.76 1.36 
11.64 10.92 0.72 
11.84 10.76 1.08 
11.72 10.64 1.08 
11.20 10.60 0.60 
11.76 10.56 1.20 
12.00 10.72 1.28 
12.08 10.72 1.36 
11.48 10.68 0.80 
11.64 10.76 0.88 
12.76 10.72 2.04 
average average average 
11.97 10.76 1.21 
standard deviation of 
the mean 
standard deviation of 
the mean 
standard deviation of 
the mean 
0.09 0.03 0.08 
 
 
 
 
 
 
 
 
 41 
Table 9: Test Data for Edge of the Disc and Height of 15 mm 
Cumulative data for the point at the disc edge at a height of 15 mm above the 
disc surface.  All data in milliseconds 
Sensor 2 trigger time Sensor 1 trigger time 
Distribution time         
(S
2
 time ? S
1
 time) 
12.12 11.04 1.08 
12.00 11.08 0.92 
12.16 11.00 1.16 
11.72 11.00 0.72 
11.80 11.00 0.80 
12.00 10.96 1.04 
12.20 11.04 1.16 
12.72 11.16 1.56 
11.64 10.96 0.68 
11.48 10.88 0.60 
12.32 10.96 1.36 
11.68 10.88 0.80 
12.40 10.96 1.44 
12.40 10.84 1.56 
12.56 11.00 1.56 
12.36 10.88 1.48 
12.04 10.96 1.08 
12.40 11.04 1.36 
12.08 11.00 1.08 
11.60 11.00 0.60 
11.88 11.08 0.80 
11.96 11.04 0.92 
11.68 10.88 0.80 
11.68 11.00 0.68 
11.72 10.84 0.88 
12.32 10.72 1.60 
11.64 10.68 0.96 
11.36 10.48 0.88 
12.24 10.60 1.64 
11.24 10.44 0.80 
average average average 
11.98 10.91 1.07 
standard deviation of 
the mean 
standard deviation of 
the mean 
standard deviation of 
the mean 
0.07 0.03 0.06 
 
 
 
 42 
Table 10: Test Data for Edge of the Disc and Height of 30 mm 
Cumulative data for the point at the disc edge at a height of 30 mm above the 
disc surface.  All data in milliseconds 
Sensor 2 trigger time Sensor 1 trigger time 
Distribution time         
(S
2
 time ? S
1
 time) 
12.04 11.12 0.92 
12.12 11.04 1.08 
12.72 11.16 1.56 
11.84 11.08 0.76 
12.08 10.96 1.12 
12.16 11.04 1.12 
12.40 11.40 1.00 
11.68 11.00 0.68 
11.80 10.80 1.00 
11.64 10.92 0.72 
12.04 11.12 0.92 
11.96 10.88 1.08 
11.96 10.96 1.00 
11.76 10.92 0.84 
11.96 10.88 1.08 
11.68 10.92 0.76 
12.64 11.00 1.64 
12.68 10.96 1.72 
12.76 11.36 1.40 
12.32 11.20 1.12 
11.72 10.96 0.76 
11.60 10.92 0.68 
12.40 11.04 1.36 
12.00 10.88 1.12 
11.52 10.76 0.76 
11.76 10.76 1.00 
11.92 10.68 1.24 
12.08 10.68 1.40 
average average average 
12.04 10.98 1.07 
standard deviation of 
the mean 
standard deviation of 
the mean 
standard deviation of 
the mean 
0.07 0.03 0.06 
 
 
 
 
 43 
Table 11: Test Data for Edge of the Disc and Height of 45 mm 
Cumulative data for the point at the disc edge at a height of 45 mm above the 
disc surface.  All data in milliseconds 
Sensor 2 trigger time Sensor 1 trigger time 
Distribution time         
(S
2
 time ? S
1
 time) 
11.84 10.88 0.96 
12.20 10.84 1.36 
11.72 11.04 0.68 
11.96 10.84 1.12 
12.12 10.80 1.32 
11.52 10.72 0.80 
11.88 11.12 0.76 
12.68 10.72 1.96 
12.32 10.64 1.68 
11.96 10.64 1.32 
12.04 11.04 1.00 
12.08 10.80 1.28 
11.56 10.76 0.80 
11.92 10.72 1.20 
11.72 10.80 0.92 
11.68 10.64 1.04 
12.36 10.76 1.60 
11.76 10.88 0.88 
12.40 11.00 1.40 
12.00 10.92 1.08 
average average average 
11.99 10.83 1.16 
standard deviation of 
the mean 
standard deviation of 
the mean 
standard deviation of 
the mean 
0.07 0.03 0.08 
 
 
 
 
 
 
 
 
 44 
Table 12: Test Data for Edge of the Disc and Height of 60 mm 
Cumulative data for the point at the disc edge at a height of 60 mm above the 
disc surface.  All data in milliseconds 
Sensor 2 trigger time Sensor 1 trigger time 
Distribution time         
(S
2
 time ? S
1
 time) 
12.56 11.44 1.12 
11.72 11.00 0.72 
11.44 10.80 0.64 
12.56 10.68 1.88 
11.64 10.88 0.76 
12.20 10.84 1.36 
11.96 10.84 1.12 
11.96 10.96 1.00 
11.60 10.80 0.80 
12.04 10.68 1.36 
12.16 11.16 1.00 
12.00 10.68 1.32 
12.36 10.68 1.68 
12.44 11.08 1.36 
11.72 10.60 1.12 
12.12 10.76 1.36 
average average average 
12.03 10.87 1.16 
standard deviation of 
the mean 
standard deviation of 
the mean 
standard deviation of 
the mean 
0.09 0.06 0.09 
 
 
 
 
 
 
 
 
 
 
 45 
Table 13: Test Data for 50% of the Disc Length and Height of 5 mm 
Cumulative data for the point 195 mm from the manifold exit (50% length) at a 
height of 5 mm above the disc surface.  All data in milliseconds 
Sensor 2 trigger time Sensor 1 trigger time 
Distribution time         
(S
2
 time ? S
1
 time) 
11.60 11.00 0.60 
11.24 10.88 0.36 
11.40 11.16 0.24 
11.84 11.16 0.68 
11.44 11.04 0.40 
11.96 11.44 0.52 
11.60 11.16 0.44 
11.56 11.08 0.48 
11.52 11.16 0.36 
11.76 11.16 0.60 
11.40 10.72 0.68 
11.64 11.24 0.40 
11.64 11.20 0.44 
11.52 11.00 0.52 
11.72 11.04 0.68 
11.52 11.04 0.48 
11.52 10.88 0.64 
11.48 10.88 0.60 
11.44 10.88 0.56 
11.16 10.76 0.40 
11.36 10.84 0.52 
average average average 
11.54 11.03 0.50 
standard deviation of 
the mean 
standard deviation of 
the mean 
standard deviation of 
the mean 
0.04 0.04 0.03 
 
 
 
 
 
 
 
 46 
Table 14: Summary of the Test Results for Measurements Taken at Disc Edge 
Summary of testing for all data taken at the edge of the disc - distance of 390 
mm.  All data in milliseconds 
Height above the disc 
Measured distribution 
time 
Standard deviation of 
the mean 
3 mm 1.10 0.06 
5 mm 1.09 0.05 
10 mm 1.21 0.08 
15 mm 1.07 0.06 
30 mm 1.07 0.06 
45 mm 1.16 0.08 
60 mm 1.16 0.09 
 
 A summary of the average gas distribution time measurements for various 
heights, z, is given in table 14.  These measurements show that the gas distribution time 
is slightly greater than one millisecond, and that the manifold does fulfill this aspect of 
the design criteria.  If further studies were done to study the density distribution over the 
drive coil, this data could contribute to understanding the flow properties overall.  
However, no data other than the distribution time is available at this time, there are no 
further conclusions about the flow characteristics that can be made from these few data 
points. 
 In addition to the data collected on the distribution time across the disc it can also 
be said that the average time the gas spends in the manifold is 0.97 milliseconds.  This is 
based upon the difference between the cumulative time average for the time to the 
manifold entrance from the solenoid valve and the time to the manifold exit from the 
solenoid valve.  The time through the gas supply piping downstream of the solenoid 
 
 47 
valve to the manifold entrance was taken from the average of the cumulative sensor one 
readings during the sensor verification testing.   
This measurement can be used for this purpose since the supply piping remained 
unchanged throughout the testing.  The time required for the gas to transit through both 
the supply piping and the manifold together can be determined from the sensor one data 
with the manifold and disc in place.  The difference between the two averaged time 
readings gives the estimate (0.97 milliseconds) of the gas distribution time through the 
manifold alone. 
4.2 Error Analysis 
 The standard deviation for all test measurements is presented with the data in 
Tables 1 through 13.  The standard deviation of the mean, ?, provides a measurement of 
the data spread.  For any single test run, given the average value of the measurement, x, 
there is a 68% probability that the actual value of x lies within the range of x? ?.  There is 
a 96% probability that the actual value of measurement lies within the range of x?2?.  
The average distribution time and standard deviation of the mean for the average 
distribution time for all the measurements taken with the manifold in place is summarized 
in Table 15 and 16.  For each reading the data range corresponding to the probability 
range is presented.  Also, as a metric, the percentage variation of average distribution 
time that this range corresponds to is presented.  
 
 
 
 
 48 
Table 15:  Summary of the Standard Deviation for all test data 68% probability range 
68% probability 
Test Run (by 
data table 
number) 
exp. 
measured 
avg. 
distribution 
time (ms) 
Standard 
Deviation 
(?) 
x?? range 
(ms) 
?% avg 
reading 
table 1 1.02 0.05 (0.97,1.07) 5% 
table 2 1.16 0.08 (1.08,1.24) 7% 
table 3 0.98 0.07 (0.91,1.05) 7% 
table 4 1.11 0.11 (1.00,1.22) 10% 
table 5 0.76 0.04 (0.72,0.80) 5% 
table 6 1.1 0.06 (1.04,1.16) 5% 
table 7 1.09 0.05 (1.04,1.14) 5% 
table 8 1.21 0.08 (1.13,1.29) 7% 
table 9 1.07 0.06 (1.01,1.13) 6% 
table 10 1.07 0.06 (1.01,1.13) 6% 
table 11 1.16 0.08 (1.08,1.24) 7% 
table 12 1.16 0.09 (1.07,1.25) 8% 
table 13 0.5 0.03 (0.47,0.53) 6% 
 
Table 16:  Summary of the Standard Deviation for all test data 96% probability range 
96% probability 
Test Run (by data 
table number) 
exp. measured 
avg. distribution 
time (ms) 
Standard 
Deviation 
(?) 
x?2? range 
(ms) 
?% avg 
reading 
table 1 1.02 0.05 (0.92,1.12) 10% 
table 2 1.16 0.08 (1.00,1.32) 14% 
table 3 0.98 0.07 (0.84,1.12) 14% 
table 4 1.11 0.11 (0.89,1.33) 20% 
table 5 0.76 0.04 (0.68,0.84) 11% 
table 6 1.1 0.06 (0.98,1.22) 11% 
table 7 1.09 0.05 (0.99,1.19) 9% 
table 8 1.21 0.08 (1.05,1.37) 13% 
table 9 1.07 0.06 (0.95,1.19) 11% 
table 10 1.07 0.06 (0.95,1.19) 11% 
table 11 1.16 0.08 (1.00,1.32) 14% 
table 12 1.16 0.09 (0.98,1.34) 16% 
table 13 0.5 0.03 (0.44,0.56) 12% 
 
 Table 15 indicates that there is a 68% probability that the actual average 
distribution time for any single test run is within ? 6% (on average) of the measured 
 
 49 
average value.  Table 16 indicates that there is a 96% probability that the actual average 
distribution time for any single test run is within ? 13% (on average) of the measured 
average value.   
Additional experimental measurements with more precise sensors should be made 
to determine the gas distribution over the thruster.  The time limit for the contract under 
which the research contained in this thesis was conducted expired prior to conducting 
additional testing.  Additional testing is planned in conjunction with future work. 
 
 
 
 
 
 
 50 
 
 
 
5. CONCLUSION AND RECOMMENDATIONS 
 
 The testing results for distribution time across the thruster showed that the gas is 
distributed in the desired time range.  Due to time constraints, an improved gas 
distribution measurement method was not employed at this time.  Additional 
measurements of the density distribution should be made to show that the distribution of 
the gas is adequately close to the thruster surface to ensure magnetic coupling to the 
thruster?s pulsed magnetic field.  
 Given that is takes 0.97 milliseconds for the gas to pass through the manifold 
compared to 1.06 milliseconds for it to travel over the PIT disc two recommendations can 
be made.  First, as dimensioned, this manifold would work well for a continuous gas 
supply PIT, but not for a single pulse PIT.  In a single pulse engine a large percentage of 
the gas would be wasted in the manifold not utilized on the disc.  If this manifold design 
were planned to be used with a PIT that would have partial duty as a pulsed unit, then I 
would recommend shortening the radius of the manifold and the disc proportionately.  
This would reduce the overall percentage of gas wasted in the manifold in a single pulse 
operational mode. 
The knowledge and experience gained during the research conducted by ISR and 
Radiance Technologies will be harnessed on a new electric propulsion project under the 
 
 51 
direction of the NASA Marshall Space Flight Center in Huntsville, AL.  This new 
research will focus on a similar electric propulsion design, the Faraday Accelerator with 
Radio-frequency Assisted Discharge (FARAD).  The electric propulsion design works 
the same way that the PIT does, except the propellant is pre-ionized prior to acceleration 
by the electromagnetic field.  A RF antenna that requires little energy when compared to 
the acceleration field pulse pre-ionizes the gas.  Therefore, the acceleration field pulse is 
not partially expended performing this function prior to accelerating the propellant.  This 
increases the efficiency of the engine since a larger fraction of the acceleration field pulse 
can be then used to accelerate the propellant.
11 
 
 The manifold design work conducted in this thesis will be incorporated into the 
FARAD project.  The FARAD thruster designed will be 30 cm in diameter, instead of 
the1 meter diameter used for the PIT project.  The manifold design will be scaled down 
to fit the 30 cm diameter thruster design.   
 
 
 
 
 
 
 
 
 
 
 52 
 
 
REFERENCES 
 
1. Dailey, C.L. and Lovberg, R.H., ?Large Diameter Inductive Plasma Thrusters?, 
AIAA paper 79-2093, Princeton/AIAA/DGLR 14
th
 International Electric 
Propulsion Conference, Princeton, New Jersey, October 1979. 
 
2. Dailey, C.L., ?Pulsed Electromagnetic Thruster?, Technical Report AFRPL-TR-
71-107, Air Force Rocket Propulsion Laboratory, Edwards Air Force Base, 
California, December 1971. 
 
3. Dailey, C.L. and Lovberg, R.H., ?Large Inductive Thruster Performance 
Measurement?, AIAA paper 81-0708R, American Institute of Aeronautics and 
Astronautics Journal, Vol. 20, No. 7, July 1982. 
 
4. Dailey, C.L. and Lovberg, R.H., ?Experimental Data for a One-Meter Diameter 
Pulsed Inductive Plasma Thruster with Application to a 25 KW mission?, 
unpublished. 
 
5. Martinez-Sanchez, M. and Pollard, J.E., ?Spacecraft Electric Propulsion ? An 
Overview?, Journal of Propulsion and Power, Vol. 14, No. 5, 1998, pp. 688 ? 699. 
 
6. Mikellides, Pavlos G., ?Pulsed Inductive Thruster (PIT): Modeling and Validation 
Using the MACH2 Code?, NASA/CR-2003-212714, NASA Glenn Research 
Center, Chelveland, Ohio, 2003. 
 
7. NASA Glenn Research Center, ?2001 Research and Technology?, NASA/TM-
2002-211333, NASA Glenn Research Center, Chelveland, Ohio, March 2002. 
 
8. Hopkins, M.B., ?Langmuir Probe Measurements in the Gaseous Electronics 
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Research of the National Institute of Standards and Technology, Vol. 100, No. 4, 
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9. Petraconi, G., et al., ?Longitudinal Magnetic Field Effect on the Electrical 
Breakdown in Low Pressure Gases?, Brazilian Journal of Physics, Vol. 34, No. 
4B, December, 2004 
 
 
 53 
10. Anderson, John D., Modern Compressible Flow With Historical Perspective, 
McGraw Hill, New York (2004) 
 
11. Polzin, Kurt Alexander, Faraday Accelerator with Radio-frequency Assisted 
Discharge (FARAD), Ph.D. Dissertation, Dept. of Mechanical and Aerospace 
Engineering, Thesis No. 3147-T , Princeton Univ., Princeton, NJ, 2006.