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The Pennsylvania State University
The Graduate School
Department of Aerospace Engineering
INVESTIGATION OF ELECTROMAGNETIC
ACCELERATION OF NONIONIZED GASES
A Thesis in
Aerospace Engineering
by
Cristian Paunescu
© 2009 Cristian Paunescu
Submitted in Partial Fulfillment of the Requirements
for the Degree of
Master of Science
May 2009
The thesis of Cristian Paunescu was reviewed and approved* by the following:
Michael M. Micci Professor of Aerospace Engineering Thesis Advisor
Sven G. Bilén Associate Professor of Engineering Design, Electrical Engineering, and
Aerospace Engineering
George A. Lesieutre Professor of Aerospace Engineering Head of Department of Aerospace Engineering
*Signatures are on file in the Graduate School
iii
ABSTRACT
Electric propulsion methods have always relied on the interactions between charged
particles and electromagnetic fields and, as such, have the shortfall of requiring energy to be
wasted in ionizing propellant. Polar propulsion is a completely revolutionary methodology for
accelerating gaseous fuel by a unique interaction between static magnetic fields and electric fields
modulated at microwave frequencies. The purpose of this project was to simulate and
experimentally validate that this method achieves accelerations and specific impulse figures
comparable with other current electromagnetic propulsion systems, but without requiring ionized
propellant. Using molecular dynamics simulations and a small scale experimental setup, this work
attempts to demonstrate the viability of this method and lay the groundwork for the future
development of this propulsion method.
iv
TABLE OF CONTENTS
LIST OF FIGURES .................................................................................................................vi
LIST OF TABLES...................................................................................................................viii
LIST OF SYMBOLS ...............................................................................................................ix
ACKNOWLEDGMENTS .......................................................................................................xii
Chapter 1 Introduction ............................................................................................................1
Chapter 2 Theory ....................................................................................................................8
Paschen minima ...............................................................................................................12 Collision frequency ..........................................................................................................14
Chapter 3 Simulation ..............................................................................................................17
Two-particle molecule .....................................................................................................17 Square electric field strength profile ........................................................................22
Three-particle molecule ...................................................................................................25 Constant electric field profile ...................................................................................26 Constant electric field profile with collisions...........................................................28
Pressure as an independent variable .................................................................32 Collision frequency peak position as an independent variable.........................34
Sinusoid electric and magnetic field strength profiles .............................................35 Phase shift as an independent variable .............................................................36
Simulation results.............................................................................................................36 Two-particle molecule..............................................................................................36 Three-particle molecule............................................................................................39
Square electric field strength profile ................................................................39 Constant electric field profile with collisions...................................................43 Sinusoid electric and magnetic field strength profiles......................................46
Chapter 4 Experiment .............................................................................................................48
Experimental Configuration.............................................................................................48 Procedure .........................................................................................................................54
Low voltage DC setup..............................................................................................55 High voltage DC setup .............................................................................................55 Pulse generator setup................................................................................................56
Chapter 5 Results ....................................................................................................................58
Experimental results.........................................................................................................58
v
Constant electric field strength profile .....................................................................59 Square electric field profile ......................................................................................59
Chapter 6 Conclusions ............................................................................................................61
Appendix Determination of usable E field cross-section for experimental test setup ............67
Analytical approach .........................................................................................................67 Numerical Approach ........................................................................................................68 Results and Conclusions ..................................................................................................69
References................................................................................................................................ 71
vi
LIST OF FIGURES
Figure 1.1: NSTAR efficiency data. [1]...................................................................................5
Figure 1.2: Total efficiency with xenon propellant, simple ionization. [1]. ............................6
Figure 2.1: Dipole moment distribution in a gas. Overall moment of inertia, P = 0.. .............10
Figure 2.2: Dipole moment distribution with electric field. dP/dt > 0.....................................11
Figure 2.3: Abraham effect in a magnetic field.. .....................................................................11
Figure 2.4 Breakdown rms field strength vs. total pressure with 100-µsec pulse length [5]... ..................................................................................................................................13
Figure 3.1: Lithium hydride simulation particle paths with “sawtooth” profile description.. ......................................................................................................................19
Figure 3.2: Custom dipole water molecule simulation particle paths, equal particle masses and charges.. ........................................................................................................21
Figure 3.3: Molecule center of mass velocity in electric field strength sawtooth profile.. .....22
Figure 3.4: Velocity components in x-y plane of two-particle molecule and electric field pulse... ..............................................................................................................................24
Figure 3.5: Velocity of center of mass in z direction resulting from one electric field pulse... ..............................................................................................................................25
Figure 3.6: Rotational frequency of water molecule based on constant electric field strength.............................................................................................................................27
Figure 3.7: Collision frequency distribution function, water vapor at 0.5 atm and 100°C.. ...29
Figure 3.8: Center of mass velocity (mm/s) in the z direction with collisions marked, at a magnetic field strength of 25 tesla... ................................................................................31
Figure 3.9: Linear extension formula for Paschen curve.. .......................................................32
Figure 3.10: Average acceleration over pressure range of 0 to 1 atm, or 0 to 101325 Pa.. .....33
Figure 3.11: Average acceleration over pressure range of 0 to 1 atm, 25-tesla magnetic field.. ................................................................................................................................35
Figure 3.12: Molecule center of mass velocity in electric field strength sawtooth profile, lithium hydride molecule... ..............................................................................................37
vii
Figure 3.13: Molecule center of mass velocity in electric field strength sawtooth profile, custom two-particle water molecule... .............................................................................38
Figure 3.14: Velocity increment per electric field pulse, effect of frequency and duty cycle. SPC/E molecule at 20,000 V/m electric field amplitude and 25-tesla magnetic field.. ................................................................................................................................40
Figure 3.15: Acceleration from pulsed electric field strength, effect of frequency and duty cycle. SPC/E molecule at 20,000 V/m electric field amplitude and 25-tesla magnetic field...................................................................................................................41
Figure 3.16: Acceleration calculation based on center of mass position data.........................42
Figure 3.17: Acceleration data based on pressure variation, 0 to 1 atm., 3-tesla magnetic field.. ................................................................................................................................44
Figure 3.18: Acceleration data based on peak collision frequency, 0 to 120 GHz. ................45
Figure 3.19: Acceleration data based on phase shift between sinusoidal waveforms.............46
Figure 4.1: Experimental setup diagram. ...............................................................................49
Figure 4.2: Test section model...............................................................................................51
Figure 4.3: Detailed view of test section, showing polymer stand, magnets, and copper plates, without transformer core.......................................................................................52
Figure 4.4: “Flapper” device, as part of disassembled test section. .......................................53
Figure A.1: Usable cross sectional area and field lines, ideal case.........................................69
Figure A.2: Usable cross sectional area and field lines, lower plate shorted to sides.............70
viii
LIST OF TABLES
Table 1.1: Comparison of propulsion systems.........................................................................3
Table 3.1: Symmetric 2-particle molecule approximation of water... .....................................20
Table 3.2: SPC/E water molecule model characteristics... ......................................................26
Table 4.1: Setup devices with corresponding model numbers.................................................50
Table 6.1: Total variable matrix for experiment continuation... ..............................................62
Table 6.2: Electric field recommendations... ...........................................................................64
Table 6.3: Magnetic field recommendations............................................................................64
Table 6.4: Field relative orientation and propellant recommendations....................................65
Table 6.5: Reactor configuration and metrology recommendations... .....................................66
ix
LIST OF SYMBOLS
ε0 vacuum permittivity, electric constant, C2-N/m2
Tη total efficiency
Θ molecular collision frequency, s−1
λ mean free path, m
mµ
dipole moment to mass ratio, C-m/kg
ρ electric charge density, C/m3
φ electric potential, V
χ( ) speed distribution function, m/s
∇ divergence operator
yx ∂∂
∂∂ , partial derivatives with respect to x, y
2∇ Laplace operator
eA exit area, m2
a acceleration, m/s2
B magnetic field strength, Tesla (Wb/m2)
B magnetic field vector, Tesla
By magnetic field strength, y direction, Tesla
C1,C2,C3 Cartesian velocity vector components, m/s
C molecular speed, m/s
C average molecular velocity, m/s
x
d molecular diameter, m
E electric field vector, V/m
Ex electric field strength, x direction, V/m
ionizationE ionization energy, J
xenonionizationst 1E first ionization energy for xenon, J
F force vector, N
f( ) velocity distribution function
fx, fy, fz force components, x, y and z directions, N
g gravitational acceleration at Earth surface, m/s2
I impulse, N-s
Isp specific impulse, s
k Boltzmann constant, m2-kg/s2-K
propellantKE propellant kinetic energy, J
M molecular mass, kg/mol
m mass flow rate, kg/s
PM propellant mass, kg
Pm propellant flow rate, kg/s
propellantm propellant mass, kg
m mass, kg
n number of moles
NA Avogadro’s constant
n0 number of molecules per unit volume, m−3
P polarization, C-m
xi
ap ambient pressure, Pa
ep exit pressure, Pa
PR pressure, Pa
TOTALP total input power, W
dtdP
rate of change of polarization, C-m/s
q charge, C
R universal gas constant, J/mol-K
T temperature, K
τ thrust, N
∆t change in time, s
eu exit velocity, m/s
equ equivalent velocity, m/s
ux, uz molecular velocity components, x and z directions, m/s
V volume, m3
propellantv propellant velocity, m/s
∆v change in velocity, m/s
xii
ACKNOWLEDGMENTS
I’d like to thank and acknowledge the support of many great people in the research of this
thesis, namely: Dr. Michael Micci, for the opportunity to work on this groundbreaking project
and for his guidance along the way; Dr. Sven Bilén for his help in understanding the world of
microwaves; Dr. Deborah Levin for her insights in molecular dynamics simulation; my labmates
Peter Hammond, Jacob Blum, and Jeff Hopkins, for bringing me into the fold of the lab and their
valuable insights and assistance; Mr. Doug Smith, for his expert glass work; and last but certainly
not least, the Air Force Office of Scientific Research for funding the project.
1
Chapter 1
Introduction
Currently there are many established and extensively researched electric propulsion
systems, all of which share the characteristics of having high efficiency but low thrust compared
to conventional liquid or solid rocket propellant systems. Most electric propulsion systems can be
lumped into three subgroups: electrostatic (ion thrusters), electrothermal (arcjets), and
electromagnetic (plasma thrusters). Electric propulsion (EP) was conceived independently by
Robert Goddard in the United States in 1906 and by Tsiolkovskiy in Russia in 1911, with
concepts and analysis work being done all over the world ever since. Significant research
programs were not established until the 1960s, when entities such as the National Aeronautics
and Space Administration (NASA) Glenn Research Center, Hughes Research Laboratories,
NASA’s Jet Propulsion Laboratory (JPL), and various institutes in Russia started work on EP
applications such as satellite station-keeping and deep-space prime propulsion. Experimental
flights started as early as the 1960s in both the US and Russia, with US efforts focusing, for the
most part, on ionic propulsion and Russian efforts on Hall thrusters.
Successful launches of systems such as Hughes’ Xenon Ion Propulsion System (XIPS) in
1997 and NASA’s Solar Electric Propulsion Technology Applications Readiness (NSTAR) ion
thruster aboard the Deep Space 1 probe in 1998 established EP for operational use [1].
Established concepts, such as ion and Hall thrusters, have enjoyed constant improvement in
efficiency and lifetime due to the large amount of background work available, and no new
concepts have recently emerged as equals in the EP field. Polar propulsion shows promise in
being different enough to capitalize on avoiding some of the problems with which current
2
methods are plagued and, at the same time, providing the benefits that are expected from EP
systems.
In order to compare various propulsion methods, appropriate comparison metrics must be
developed, which, for electromagnetic systems, usually include thrust, specific impulse, and
efficiency.
To derive specific impulse one must first find the thrust of a propulsion system, which is
given as
( ) eaee Appum −+=τ . (1-1)
For convenience it is helpful to define an equivalent exhaust velocity as
eae
e Am
ppuu ⎟
⎠⎞
⎜⎝⎛ −
+=eq . (1-2)
In turn, this helps define the simplified thrust and specific impulse quantities that are useful in
comparing propulsion systems, that is
equm=τ , (1-3)
∫ =⋅= equMdtI Pτ , and (1-4)
g
ugM
IIP
eqsp == . (1-5)
From this formulation, it is understood that specific impulse is a measure of the
efficiency of a thrust-producing system and that it is directly proportional to the propellant’s exit
velocity. In this case, we consider that the effect of exterior pressure is relatively minimal on the
equivalent exhaust velocity and, indeed, for EP systems the exhaust velocity of the thruster is far
larger than the velocity induced by the pressure difference between the thruster and environment.
3
EP systems have the advantage of having really high propellant exhaust velocities but at
low mass flow rates, resulting in high specific impulse but low thrust, as compared to chemical
rocket propulsion. Table 1.1 displays comparative figures for chemical versus EP systems.
The major breakthrough that the polar propulsion concept is trying to achieve is the
dramatic increase in efficiency granted by no longer requiring propellant to be ionized. For ionic
propulsion methods, the energy expended in turning non-ionized propellant — whether it is
hydrazine, xenon, or other propellants — into usable charged particles is lost after the propellant
is exhausted. In fact, not only does the energy required for ionization happen to be one or two
orders of magnitude larger than the single ionization energy of a type of propellant due to
recombination and radiation losses, but the expelled charged particles have to be neutralized by
an electron gun mounted next to the exhaust. The generation of electrons is required to make sure
the exhaust and the spacecraft are relatively neutral charge-wise, or the exhaust would be
electrically drawn to the spacecraft, negating the thrust.
Total electrical efficiency is defined as the fraction of the beam power to the total input
power, which is the sum of the beam power and energy loss mechanisms, primarily ionization
energy, but also ion recombination, boundary absorption, and radiation, and is given as
Table 1.1: Comparison of propulsion systems.
System Isp (sec) Thrust (N) Application
Rocketdyne SSME 455 2,090,664 Space shuttle main engine [2]
Pratt & Whitney RD-180 311 3,826,360 Atlas V [2]
Fakel SPT-140 1750 0.3 Station keeping (Hall thruster) [1]
Hughes 13-cm XIPS 2500 0.018 Station keeping (ion thruster) [1]
NSTAR 1979 – 3127
0.0207 – 0.0927
Primary propulsion, Deep Space 1 probe (ion thruster) [1]
4
TOTAL
JET
PP
T =η . (1-6)
In a real system such as the NSTAR xenon ion thruster, the total electrical efficiency [1]
TOTAL
2 12 Pm
T
PT ⋅
⋅=η (1-7)
is derived by using thrust, measured with a static stand, propellant mass flow, and total power
input to the thruster.
Energy losses due to propellant ionization affect the performance of ion thrusters by only
allowing them to be efficient at performance states of high specific impulse, as demonstrated in
the Figure 1.1 below. This results from a change in the ratio of energy that is used in ionization
and the energy used for thrust generation. For a system to operate efficiently, the majority of the
available energy is used for propelling a small amount of ionized fuel, which achieves a large
exhaust velocity. Since the acceleration portion of the system is more efficient than the ionization
portion, the system works optimally when most of the energy is expended in acceleration, and
less is expended in ionization, serving the additional purpose of using a small amount of fuel.
5
The influence of specific impulse on efficiency can be established by looking at a
simplified model of total efficiency, whereas the only loss mechanism is ionization energy
xenonionizationst 1ionization 100EE = , (1-8)
which is assumed to be 100 times the ionization energy of the xenon. Deriving the velocity of the
propellant
g
Iv sp
propellant = (1-9)
from the specific impulse allows the expression of the kinetic energy of the propellant as
( )2propellantpropellantpropellant 21 vmKE = . (1-10)
Total efficiency is then defined as
Total efficiency vs Isp for NSTAR Xenon ion thruster
y = 0.018x + 3.8919
40
45
50
55
60
65
1500 1700 1900 2100 2300 2500 2700 2900 3100 3300
Isp (sec)
Effic
ienc
y (%
)
Figure 1.1: NSTAR efficiency data. [1]
6
ionizationpropellant
propellant
EKEKE
T +=η , (1-11)
the kinetic energy imparted to the propellant divided by the total energy used for propulsion,
which includes the kinetic energy of the propellant and the energy required to ionize the
propellant.
It is readily apparent from looking at the Figure 1.2 that in the Isp range of the NSTAR
data, the simplified version of total efficiency is relatively linear, and a slope measurement can be
done. The two curves represent different constants used to modify the simplified ionization
model, one using a factor of 100 times the ionization energy as mentioned in equation (1-8), and
the other using a factor of 240, a number chosen so that the slope is within 0.5% of the linear fit
for the measured NSTAR data.
Total efficiency with simplified ionization, Xenon fuel
y = 0.0181x + 12.27
0
10
20
30
40
50
60
70
80
90
100
0 1000 2000 3000 4000 5000 6000 7000
Isp (sec)
Effic
ienc
y (%
)
240xNSTAR range100x
Figure 1.2: Total efficiency with xenon propellant, simple ionization. [1]
7
The data presented in Figure 1.2 show that, with a simplified ionization efficiency based
on a constant factor multiplying first ionization energy of the atom, a proper simulation of the
effect of ionization on total efficiency has been achieved.
Polar propulsion systems avoid the ionization energy loss entirely by employing the
Abraham effect in accelerating polar molecules. This thesis develops the foundation for
demonstrating the concept of polar propulsion as a viable EP system by predicting the molecular
dynamics of polar propulsion at the molecular level and by experimentally confirming the
simulation results.
Presented first is the derivation of, and early work on, the Abraham effect, with a focus
on the capabilities that a prototype system would have when built. This theoretical background, in
conjunction with relevant molecular dynamics considerations, forms the basis for the simulation-
aided investigation into polar propulsion. The various conditions explored by the simulation code
are then replicated by an experimental setup with the purpose of confirming the validity of the
simulation results. Finally, based on the conclusions derived from both simulation and
experimental work, this thesis provides recommendations for the advancement of the polar
propulsion concept in the future.
8
Chapter 2
Theory
The Abraham effect is a proven mechanism of matter and electromagnetic field
interaction that describes how a polar molecule can be accelerated in a given direction as
interaction between a static magnetic field and an electric field modulated at a specific frequency
[3].
Walker proved that the resulting force on a dipole solid of barium titanate [7,8], for the
most part, was influenced by the time rate of change of polarization crossed with the magnetic
field. The force vector
BdtPdF ×= (2-1)
describes this relationship. Acceleration provided by this force depends on the molecule used.
Using a polar molecule without magnetic moment, this acceleration
t
Bm
a∆
=µ
(2-2)
would be resultant from the action of the molecule aligning with the electric field.
Conceptually speaking, a collection of polar molecules outside the influence of any
electric field will have a net zero polarization due to random molecular orientation. When an
electric field is applied, the dipole moments of the molecules will attempt to align themselves
with the electric field lines at a rate that is a function of the electric field strength and the
molecular rotational moment of inertia. According to Newton’s second law, acceleration can be
expressed as the force experienced divided by the mass of the molecule. Therefore, in order to
9
achieve high exhaust velocity through high acceleration of molecules, the selected propellant
must have a high dipole-moment-per-mass ratio.
Water has one of the highest permanent dipole-moment-per-mass ratios at 2.07×10−4
C-m/kg [4], with lithium hydride (1.4×10−3 C-m/kg) and potassium fluoride (2.99×10−4 C-m/kg)
being good alternatives, but not as readily available as water.
Since it is possible for this alignment of molecules to occur in the timeframe of 10−9 to
10−10 seconds, using electric radiation in the microwave frequency range allows for considerable
velocity differential over a small acceleration region. Using lithium hydride as an example, with a
stable 25-tesla magnetic field and a 10-GHz electric field, the resultant acceleration would be
7.4×108 m/s2. Over an acceleration region of only 6.75 cm, this would translate to an exhaust
velocity of 10,000 m/s.
Since multiple pulses are to be applied to the polar fuel in order to generate acceleration,
an analysis based on momentum would yield a time-based exhaust velocity figure. Assuming
conservation of momentum, the substitution of the simple definition of acceleration
tva∆∆
= (2-3)
into (2-2) will yield an expression for the velocity increase that each pulse would deliver,
Bm
v µ=∆ (2-4)
So, considering the same 25-tesla magnetic field with lithium hydride, the increment would be
0.037 m/s per pulse, but with a pulse frequency of 10 GHz, a target exhaust velocity of 50,000
m/s would be reached in only 0.135 seconds.
The principle of operation at work in polar propulsion can be understood more clearly
with a graphical representation of the sequence of steps involved. The starting state of the
10
propellant is gaseous with a random distribution of dipole moments for the molecules that
comprise the gas (see Figure 2.1)
When the electric field is activated, Figure 2.2 shows that the polar molecules behave in
such a way as to align with the direction of the field lines, which in turn causes them to
experience an increase in the polarization rate of change. This effect is built into the electric field
strength profile, which increases linearly from zero to a set value during the accelerating portion
of the signal.
Figure 2.1: Dipole moment distribution in a gas. Overall moment of inertia, P = 0.
11
The resulting rate of polarization, interacting with a steady magnetic field whose field
lines are perpendicular to those of the electric field, result in a force, defined as the Abraham
effect. Figure 2.3 shows that using one of the direction vectors of the electric and magnetic field
lines to define a plane, the resulting force would act in a direction perpendicular to the plane
containing those vectors.
Figure 2.2: Dipole moment distribution with electric field. dP/dt > 0.
Figure 2.3: Abraham effect in a magnetic field.
12
After the acceleration period, the electric field would be turned off in order to allow
random re-orientation of the polar molecules. This would return the system to the original state
and then the process would repeat, at frequencies intended to be in the range of 10 GHz. The
combination of a linear increase in electric field strength followed by an off period defines the
“sawtooth” profile required to generate acceleration with the Abraham effect.
Paschen minima
The breakdown of the water molecule is as equally important for polar propulsion as it is
for ionic propulsion, but in an inverse sense. In order for polar propulsion to work, the water
vapor being propelled has to contain, for the most part, whole water molecules. In order to avoid
situations where water vapor at low pressure and high enough electric field would experience
breakdown, the data of Bandel and MacDonald [5] was used to provide a good set of limiting
cases.
Figure 2.4 presents a plot of a Paschen curve, in which it is apparent that, for a low
pressure water vapor environment being exposed to microwave radiation, there is a threshold past
which molecular breakdown occurs.
13
The results of this study are relevant to the polar propulsion experiment because they
outline water-vapor environments, with electric fields being pulsed at microwave frequencies, in
a chamber with a gap similar in height (1.27 cm) to the one between the copper plates in this
experimental setup (1.7 cm). The pressure range of experimental procedure varied from 5 to 50
Torr for the most part, and the electric field strength stayed in the range of 0 to about 1200 V/cm,
specifically 0 to 0.88 V/cm for the low voltage DC test, 2.94 V/cm for the pulse generator test
(which had an amplitude of 5 V), and only reached close to the breakdown strength with 1176
V/cm during the high voltage DC test. Using experimental conditions represented by data points
under the breakdown electric field strength presented in Figure 2.4 ensured that the majority of
the water vapor molecules in the experimental setup test section stayed together as dipoles, which
is required for the Abraham effect to work.
Figure 2.4: Breakdown rms field strength vs. total pressure with 100-µsec pulse length [5].
14
Collision frequency
Modeling molecular physics phenomena is a fairly complex undertaking because any sort
of simulation involving volumes of gas requires analysis with considerable computing power and
powerful algorithms like the Monte Carlo method. Since the molecular collision frequency
inherent in a gas was deemed to be an important phenomenon in molecular dynamics, it was
included in the single molecule simulation code employed to demonstrate that polar propulsion
works. Collisions between gas molecules are both a loss and a beneficial mechanism for this
propulsion method, with the effect of smoothing the velocity distribution after the propulsion
system accelerates most of the molecules.
With a sawtooth electric field strength profile there are two ways collision frequency
affects the behavior of the gas in the acceleration portion of the waveform. During the
acceleration portion, when the electric field is on, collisions between molecules being accelerated
are considered part of a loss mechanism. Collisions between an accelerated molecule and another
that is moving at a relatively slower rate would result in a redistribution of energy between the
two molecules, resulting, on average, with two molecules each moving slower than the
accelerated molecule initially. When the electric field is off, molecular collisions serve to bring
most molecules to the same energy level, within a certain distribution. Most importantly, though,
collisions are required so that polar molecules that were being aligned to the electric field during
the acceleration stage become randomly oriented again.
The derivation of the collision frequency distribution function starts with the Maxwellian
velocity distribution
( )⎥⎦⎤
⎢⎣⎡ ++−⎟
⎠⎞
⎜⎝⎛= 2
322
21
23
2exp
2)( CCC
kTm
kTmCf i π
, (2-5)
15
which at first is described in the Cartesian coordinate system. Converting this formulation, by
using spherical coordinates, into a more manageable form
2)2/(22
3
24)( CkTmeC
kTmC −⎟
⎠⎞
⎜⎝⎛−=
ππχ , (2-6)
is important since the independent variable becomes the molecular speed. This simplification is
relevant due to the fact that, for the purposes of this simulation, knowing the velocity vector is not
important, just the overall speed.
To get a distribution function of collision frequency, the relationship between collision
frequency and molecular speed, which is denoted
λC
=Θ , (2-7)
and after solving for molecular speed
λ⋅Θ=C (2-8)
is substituted into the molecular speed distribution function (2-2), which results in
( ) ( )2)2/(223
24)( λλ
ππχ ⋅Θ−⋅Θ⎟
⎠⎞
⎜⎝⎛−=Θ kTme
kTm
, (2-9)
a temperature and mean free path dependent expression. Under the assumption that the density of
the medium is constant, the mean free path formulation
2
021
dnπλ = (2-10)
can be simplified using the expression
RT
PNPnRT
nNV
nNn RA
R
AA ===0 (2-11)
to become
16
RA PNd
RT22π
λ = , (2-12)
seen to be a temperature and pressure dependant variable [6].
The collision frequency distribution function in Equation (2-9) is used as part of a
mechanism in the molecular simulation code that replicates the effect of collisions on the
molecule whose behavior is simulated.
17
Chapter 3
Simulation
The majority of the work in proving polar propulsion is a viable concept, within the scope
of this project, is generating a baseline software model to predict the behavior of the real system.
The initial work was derived from an experiment by Walker [7,8] with a solid as the medium, in
order to prove the Abraham Effect, which was later adopted as a proposed thruster concept in
Cox’s 1981 work [9]. In 1985, Micci [10] conducted an investigation of the concept proposed by
Cox and concluded that the oscillating high power magnetic fields could not be generated with
the technology available at that time. Continuing the development of the polar propulsion concept
thus required the inception of a molecular level simulation of the concept, complete with the
electromagnetic field conditions in the current concept.
A significant point of commonality shared by all phases of the simulation is the field
setup in Cartesian three-dimensional space. The direction of the electric field, whatever the
electric field strength profile may be, is always taken to be in the positive x direction, while the
magnetic field line direction is always along the y axis, again in a positive direction. From the
initial work with lithium hydride, the direction of movement for the particle in question was taken
to be in the positive z direction and, as such, all later builds of the simulation code attempted to
generate movement in this direction.
Two-particle molecule
This iteration of the research uses a steady magnetic field and varies the electric field at
frequencies in the range of 109 to 1010 Hz. The starting point for the molecular simulation was
18
code written in Fortran to show the behavior of a lithium hydride molecule reacting to a particular
configuration of electromagnetic forces. The polar molecule was placed in an environment where
the steady magnetic field lines were perpendicular to the electric field lines, and the electric field
profile was described as a “sawtooth”, with a 50% duty cycle.
Simulating the behavior of the dipole molecule is achieved using a model that assumes
two oppositely charged particles constrained to be a certain distance apart based on the molecular
bond. Due to its proven success in molecular dynamics simulation, the velocity Verlet algorithm
[11] is utilized for incrementally calculating the position, velocity, and acceleration of each
particle in three dimensions. Constraining the molecule to retain its proper bond length required
the use of the RATTLE constrain dynamics algorithm [12]. The physical forces influencing the
particles are determined using Maxwell’s equations and the requirement of the magnetic and
electrical field lines to be perpendicular, with the electric field aligned to the x axis and the
magnetic field lines aligned with the y axis. The resulting force components are
( )yzxx BuEqf −= , (3-1)
0=yf , and (3-2)
yxz Bquf = . (3-3)
Figure 3.1 shows the paths of the lithium and hydrogen atoms in three dimensions for a
maximum electric field of 20,000 V/m and a steady magnetic field of 25 tesla.
19
Positive results of the aforementioned simulation prompted the move to a more readily
available substance with comparable dipole moment per mass ratio to lithium hydride (1.48×10−3
C-m/kg), namely water (2.07×10−4 C-m/kg). Adapting the code for use with this new three-
particle molecule was done incrementally due to the nature of the code.
The first stage used an approximation of the water molecule as a two-particle
configuration, adapting the mass, bond length, and charges to have the same polar moment as that
of a water molecule, and with the masses of the new atoms as half of the summed mass of the
original atoms in the water molecule. The charge was also distributed as a summation of the total
Figure 3.1: Lithium hydride simulation particle paths with “sawtooth” profile description.
E (V/m)
Time (sec)
20
charge, distributed equally to both atoms, so the fabricated molecule had the following statistics
displayed in Table 3.1. It is important to note here that while both charges are displayed as
positive, the simulation code always assigns one as positive and one as negative, so the molecule,
while not exactly real, behaves as an electrically polar molecule should.
Given that only certain parameters of the simulation changed while the molecule
remained a two-particle dipole, the results were, yet again, positive, leading to a further evolution
in the complexity of the model. All simulations involving dipole molecules showed positive
acceleration, as can be seen in Figure 3.2, where the maximum electric field was kept at 20,000
V/m and the steady magnetic field was kept at 25 tesla, with average values dependent on the
characteristics of the molecule.
Table 3.1: Symmetric 2-particle molecule approximation of water.
Particle A Mass: 1.4958×10−26 kg
Charge: 9.4357×10−20 C
Particle B Mass: 1.4958×10−26 kg
Charge: 9.4357×10−20 C
Bond length 6.5645×10−11 m
21
The plot in Figure 3.3 was generated using the equal-mass-and-charge dipole water
molecule model, at a magnetic field strength of 25 tesla and electric field amplitude of 20,000
V/m at 1 GHz frequency, to show that the influence of the electric field varies from pulse to
pulse. This variance is caused by the orientation in three-dimensional space of the molecule when
the field is turned on, and ultimately the degree of alignment of the dipole to the electric field
lines. Looking at the plane defined by the two intersecting lines, the dipole axis and one electric
Figure 3.2: Custom dipole water molecule simulation particle paths, equal particle masses and
charges.
22
field line, the largest velocity increase impulse would result from the two lines being closest to
perpendicular, and the least from being almost aligned.
Square electric field strength profile
One avenue of exploration was the square or pulsed electric field profile, which was
meant to investigate the relationship between molecular rotation frequency and electric field pulse
Figure 3.3: Molecule center of mass velocity in electric field strength sawtooth profile.
23
width. To this end, the two-particle simulation code was used to tune the pulse frequency to the
molecule’s rotation period to gauge the effects on the acceleration.
Simulation results led to an understanding of the interaction between the pulse and the
molecule to be simple in a certain respect. Depending on the orientation of the molecule in three-
dimensional space, providing a pulse in the electric field strength in the presence of a steady
magnetic field, would cause energy to be transferred to the molecule as rotational kinetic energy.
The behavior exhibited in Figure 3.4 is of the two-particle water molecule described in
Table 3.1, in a magnetic field of 25 tesla, with an electric field strength magnitude of 20,000 V/m,
excluding for now the effect of molecular collision frequency. What the plot displays is how the
molecule receives rotational kinetic energy as a result of the electric field pulse.
24
Looking at the velocity of the center of mass in the z direction as the electric field is
turned on, acceleration is observed, as well as a resulting slight oscillatory behavior occurring
when the field returned to the off position, as shown in Figure 3.5. This evidence of acceleration
was the driving force behind the investigation of a pulsed electric field on the three-particle
molecule.
Figure 3.4: Velocity components in x-y plane of two-particle molecule and electric field pulse.
25
Three-particle molecule
Finally, a more accurate portrayal of the water molecule was researched. There is not
agreement on a simulation model that acts exactly as water would experimentally, so the 3-
particle extended simple point charge (SPC/E) model was chosen from a set of possible candidate
configurations [13]. The SPC/E molecule characteristics are listed in Table 3.2.
Figure 3.5: Velocity of center of mass in z direction resulting from one electric field pulse.
26
Introducing a more realistic molecular configuration caused an increased amount of
complexity in the code but, most importantly, provided the molecule an additional rotational
degree of freedom. Subsequently, the behavior of the molecule in a high frequency electric field
became not only unpredictable, but it also stopped displaying a clear progression in either
direction on the z axis. Due to the fact that there were many variables to explore in order to
explain the behavior of the molecule, many versions of the simulation code were created in order
to test the effects of things like electric field strength, signal duty cycle and period, pressure, and
collision frequency distribution offset. Presented below are the simulations that match the
experimental conditions used in this study.
Constant electric field profile
Moving back to the simpler configuration with a constant electric field strength profile
allowed exploration of the effects of electric field strength on the rotational vibration frequency of
the water molecule. This effect was recognized to be periodic and predictable in the absence of a
magnetic field by observing the frequency of molecule’s rotation around the center of mass. Data
were recorded by plotting the positions of the three particles over time and generating an
Table 3.2: SPC/E water molecule model characteristics.
Hydrogen (H) atom Mass: 1.6739×10−27 kg
Charge: 6.79×10−20 C
Oxygen (O) atom Mass: 2.6568×10−26 kg
Charge: −1.358×10−19 C
O – H Bond length 1×10−9 m
H – O – H Bond angle 109.47°
27
averaged frequency based on the average period of all three particle plots. The molecule behaved
as predicted, namely oscillating in rotation around its center of mass while staying confined in the
x-y plane.
The information in Figure 3.6 came to be used as a baseline of the molecule’s behavior in
further developments in the evolution of the code, namely the pulsed electric field strength work
and the exploration of the effect of the collision frequency distribution.
Frequency vs E field strength
y = 1.7407x0.5106
1
10
100
0.1 1 10 100
E field strength (kV/m)
Freq
uenc
y (G
Hz)
Figure 3.6: Rotational frequency of water molecule based on constant electric field strength.
28
Constant electric field profile with collisions
The collision frequency investigation would allow a net unidirectional acceleration to be
established out of the rotation of the molecule by timing collisions correctly. Therefore, having a
collision occur as the molecule is at its farthest displacement in the desired direction, and causing
this effect repeatedly, would result in acceleration in that direction. The collision algorithm
simulates the effect of a collision on the water molecule by zeroing out all motion at the moment
of collision, except velocity in the z direction, and assigning a random orientation to the molecule,
using randomized collision timing derived from a Maxwellian collision frequency distribution.
The plot in Figure 3.7 shows the distribution function for the collision frequency of water at a
certain value of temperature and pressure.
29
In the simulation code, these parameters are set to values that reflect the operating mode
of the experimental setup so that the simulation results can be used to generate an expectation of
the experimental results. As a measure of randomization, a modified version of the ran2 [14]
random number generator was utilized to select the time between collisions that was actually used
in the code. The ran2 algorithm allowed for random numbers to be generated within a given
distribution, namely the collision frequency distribution function, and was found to work
relatively well. Also, the ran2 algorithm was called on to give the water molecule a semblance of
Figure 3.7: Collision frequency distribution function, water vapor at 0.5 atm and 100°C.
30
being part of a realistic collision by giving it a random orientation in space after every collision,
while keeping the center of mass in the same place.
Taking advantage of the versatility of the simulation, the collision frequency’s peak value
was given a shift parameter, so that the entire distribution could be adjusted to higher or lower
frequency ranges. The effect of the collision frequency distribution shift was one of the important
parameters tested for effect versus acceleration. An example of the velocity induced by the
collision frequency can be seen in Figure 3.8, where the simulation code recorded the velocity of
the center of mass and the number of collisions that occurred based on certain values of pressure
and temperature.
31
At this point, three parameters could be independently tested for their effect on the
resultant acceleration, but only pressure and collision frequency peak position were considered,
and temperature was kept at a constant 100°C.
Figure 3.8: Center of mass velocity (mm/s) in the z direction with collisions marked, at a
magnetic field strength of 25 tesla.
32
Pressure as an independent variable
Note that for this type of setup, the electric field strength was taken to be the maximum
allowed by the Paschen curve, i.e. the breakdown strength. Therefore, choosing a pressure would
determine the highest allowable electric field strength through a linear fit extension (Figure 3.9)
of the pressure range from 5 to 100 Torr of the Paschen curve (Figure 2.4).
Setting the collision frequency to have zero shift, i.e., based only on the set temperature
and the pressure value from a selected range, the simulation code output averages acceleration
values over multiple runs. The idea behind multiple runs is that, while one run can show an
average acceleration based on one random sequence of collisions, each run is unique in when and
Breakdown electric field strength
0.00E+00
2.00E+04
4.00E+04
6.00E+04
8.00E+04
1.00E+05
1.20E+05
0 5 10 15 20 25
Pressure (Torr)
E fi
eld
stre
ngth
(V/m
)
Figure 3.9: Linear extension formula for Paschen curve.
33
how many collisions occur. Overall, this has to be averaged over enough runs so that the final
value for acceleration is significant for comparison versus values derived at different pressure set
points.
The linear fit presented in Figure 3.10 exemplifies a set of data which averaged
acceleration over 100 independent runs, over a range of pressures from 0 atm to 1 atm, showing
also the electric field strength value corresponding to breakdown at that pressure. The choice of
number of runs to average over was chosen based on computational time elapsed, to provide a
large enough sample size without taking more than one day to compute.
Average Acceleration (B = 25 Tesla, 100 cases)
0.00E+00
5.00E+06
1.00E+07
1.50E+07
2.00E+07
2.50E+07
3.00E+07
0.0E+00 2.0E+04 4.0E+04 6.0E+04 8.0E+04 1.0E+05 1.2E+05
Pressure (Pa)
Acc
eler
atio
n (m
/s^2
)
0.0E+00 5.0E+05 1.0E+06 1.5E+06 2.0E+06 2.5E+06 3.0E+06 3.5E+06 4.0E+06
Breakdown E field (V/m)
Figure 3.10: Average acceleration over pressure range of 0 to 1 atm, or 0 to 101325 Pa.
34
Figure 3.10, therefore, displays the maximum amount of acceleration that can be
achieved at a given pressure and temperature (100°C) before the water vapor becomes plasma and
is no longer useful.
Collision frequency peak position as an independent variable
The same batch-processing function used for recording the effect of pressure was utilized
to test the effect of shifting the collision frequency. Over a limited range of frequencies, the trend
of the acceleration increases linearly, as shown in Figure 3.11. The particular range shown in
Figure 3.11 is centered on the value of 3.98 GHz, and extends in both directions by
approximately 1.5 GHz.
35
This acceleration trend continues, though, and brings into question the accuracy of the
simulation when considering collision frequencies two or more orders of magnitude higher than
the base collision frequency distribution peak value. To that effect, future work may involve
determining a more thorough way of investigating the collision frequency distribution function,
and the effect of its shape and range.
Sinusoidal electric and magnetic field strength profiles
Although earlier in this discussion it was established that magnetic field strength
modulation is something difficult to achieve even with today’s technology, it was deemed
Acceleration
3.98E+09 Hz
-1.E+06
0.E+00
1.E+06
2.E+06
3.E+06
4.E+06
5.E+06
6.E+06
7.E+06
8.E+06
9.E+06
2.00E+09 2.50E+09 3.00E+09 3.50E+09 4.00E+09 4.50E+09 5.00E+09 5.50E+09 6.00E+09
Frequency (Hz)
Acc
eler
atio
n (m
/s^2
)
Figure 3.11: Average acceleration over pressure range of 0 to 1 atm, 25-tesla magnetic field.
36
relevant to investigate the relationship between sinusoidal profiles for both electric and magnetic
fields. A separate version of code was developed in order to not only set up sinusoid functions for
both types of fields, but to be able to change the phase shift between the two waves and
investigate the effects of the shift.
Phase shift as an independent variable
In this situation there are still many variables left to tackle, with phase shift being thought
to have a significant effect on acceleration, if any is present. Simulation-wise the implementation
of sinusoid shape functions for both fields is not difficult, even with the added complication of a
phase shift angle, so the rest of the discussion on phase shift will continue in the next chapter.
Simulation results
Two-particle molecule
Data from the original simulation, a lithium hydride molecule under the influence of
perpendicular magnetic and electric fields, shows a definite linear increase in center of mass
velocity, as shown in Figure 3.12. With a constant magnetic field of 25 tesla, a “sawtooth” profile
electric field strength 20,000 V/m in amplitude and excluding of the effect of collisions, the
resultant average acceleration was calculated to be 1.1364×107 m/s2.
37
Similar results can be seen in Figure 3.13, where the custom water two-particle dipole,
described earlier in this chapter and specifically in Table 3.1, resulted in an average acceleration
value of 5.5×105 m/s2. The conditions for this simulation were a constant magnetic field of 25
tesla, a “sawtooth” profile electric field strength 20,000 V/m in amplitude and excluding the
effect of collisions.
Figure 3.12: Molecule center of mass velocity in electric field strength sawtooth profile, lithiumhydride molecule.
38
Since the conditions were exactly the same as the lithium hydride results, it is safe to
conclude that the lower acceleration of the custom water molecule is due to the dipole-moment-
per-mass ratio that is one order of magnitude lower (see Chapter 1) than that of lithium hydride.
Figure 3.13: Molecule center of mass velocity in electric field strength sawtooth profile,custom two-particle water molecule.
39
Three-particle molecule
Square electric field strength profile
The square pulse electric field strength configuration shows promise as a viable method
of accelerating polar molecules, even though the profile differs from the intended “sawtooth”
shape. As shown in this chapter, the effect of pulsing the field strength is to grant the molecule a
step up in velocity when the field is on, and to allow it to rotate freely when the field is off.
Multiple simulations were executed over two ranges of independent variables, namely duty cycle
and frequency. This simulation uses the SPC/E water molecule model at a magnetic field value of
25 tesla, electric field strength of 20,000 V/m and excluding the effect of collisions. The trend
visible in Figure 3.14 is to a certain extent predictable, since an increase in duty cycle would
logically increase the amount of energy transferred to the molecule, part of which is expressed as
acceleration on the molecule.
40
The other visible trend in Figure 3.14 is that the velocity increment also increases as the
frequency of the pulsed electric field strength decreases. The most likely explanation is that, at
higher frequencies, the water molecule no longer has the ability to react to the energy it is
provided.
In Figure 3.15, it is apparent that, while the duty cycle and frequency affect the velocity
increment, the acceleration experienced by the molecule remains at a relatively constant level.
Within a reasonable distribution, Figure 3.15 demonstrates that the electric field strength
amplitude value of 20,000 V/m for any type of pulsed performance corresponds to approximately
4.96 · 106 m/s2 of acceleration.
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 2 3 4 5 610%
30%
50%
70%
90%
0.0E+00
2.0E-03
4.0E-03
6.0E-03
8.0E-03
1.0E-02
1.2E-02
1.4E-02
1.6E-02
Velocity Increment of Pulse (m/s)
Frequency (GHz)
Duty Cycle
Figure 3.14: Velocity increment per electric field pulse, effect of frequency and duty cycle.
SPC/E molecule at 20,000 V/m electric field amplitude and 25-tesla magnetic field.
41
Figure 3.16 displays the result of a slight modification to the simulation code that outputs
the position of the center of mass on the z axis, and a cumulative average of the position. A
cumulative average generates a value based on the average of all points up to an including its own
point.
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 2 3 4 5 610%
30%
50%
70%
90%
4.88E+06
4.90E+06
4.92E+06
4.94E+06
4.96E+06
4.98E+06
5.00E+06
5.02E+06
Acceleration (m/s^2)
Frequency (GHz)
Duty Cycle
Figure 3.15: Acceleration from pulsed electric field strength, effect of frequency and duty cycle.
SPC/E molecule at 20,000 V/m electric field amplitude and 25-tesla magnetic field.
42
The second-order polynomial curve fit of the averaged position data is
14426 101105105 −− ×+×−×= xxy , (3-4)
which expresses the position (m) as a function of time (sec). Taking the second derivative of this
expression should result in a figure for acceleration, which is constant, since the second-order
polynomial is an excellent fit to the data. It is then confirmed that this value is consistent, since an
acceleration of 5×106 m/s2 is only 0.8% off from the average value (4.96×106 m/s2) resulting from
the batch processing method.
The pulsed electric field shows a lot of promise, but requires a more thorough
investigation of all the independent variables involved and their degree of influence on the
acceleration.
Position of center of mass over time
y = 5E+06x2 - 0.0005x + 1E-14
0.00E+00
1.00E-13
2.00E-13
3.00E-13
4.00E-13
5.00E-13
6.00E-13
7.00E-13
8.00E-13
9.00E-13
0.00E+00 5.00E-11 1.00E-10 1.50E-10 2.00E-10 2.50E-10 3.00E-10 3.50E-10
Time (sec)
Posi
tion
(Z a
xis)
(m)
Z_cmAvg. Z_cmPoly. (Avg. Z_cm)
Acceleration:5x10^6 m/s^2
B = 25 Tesla; E = 2x10^4 V/m; Period = 6x10^-11 sec; Duty Cycle = 17%; 5 Cycles
Figure 3.16: Acceleration calculation based on center of mass position data.
43
Constant electric field profile with collisions
Pressure as an independent variable
The plot presented in Figure 3.10 exemplifies one of many sets of data points generated
with the methodology of determining the collision frequency distribution and electric field
strength magnitude based on pressure alone. Given that the range explored was 0 to 1 atm, it
becomes relevant to try to restrict the range to pressures that are applicable to the intended
operating environment of an electric thruster.
Based on the data in Figure 3.10, the expectation for the maximum attainable acceleration
is 2.6607×107 m/s2 at atmospheric pressure. At the operating pressure of the experimental setup,
which is usually 0.50 psi (3447 Pa), based on the linear curve fit from Figure 3.10,
9984888.268 += xy , (3-5)
the expected acceleration value is 1.0268×106 m/s2.
Since the magnetic field available in the experimental setup was at least one order of
magnitude below the 25-tesla field strength assumed for most simulations, a few sets of data like
the one displayed in Figure 3.17 were generated with the field strength of 3 tesla.
44
At the operating pressure of 3447 Pa, the resulting acceleration can be estimated by a
sixth-order polynomial as
68292028.18107.1
10310110210623
37411516622
+−×+
+×+×−×+×−=−
−−−−
xxxxxxy
, (3-6)
which has the value of 3.732×104 m/s2.
Collision frequency peak position as an independent variable
Expanding on the discussion of pressure and its effect on acceleration started earlier in
this chapter, the next step was to expand the range of frequencies to which the peak value of the
collision frequency distribution function was shifted. The originally linear curve fit over the range
of 2.5 to 5.5 GHz had to be expanded to a larger range. Figure 3.18 shows the resultant plot over
a range of 0 to 120 GHz, and the adjusted curve fit.
Average Acceleration (B = 3 Tesla, 20 cases)
0.00000E+00
2.00000E+06
4.00000E+06
6.00000E+06
8.00000E+06
1.00000E+07
1.20000E+07
1.40000E+07
1.60000E+07
1.80000E+07
0.0E+00 2.0E+04 4.0E+04 6.0E+04 8.0E+04 1.0E+05 1.2E+05
Pressure (Pa)
Acc
eler
atio
n (m
/s^2
)
0.0E+00 5.0E+05 1.0E+06 1.5E+06 2.0E+06 2.5E+06 3.0E+06 3.5E+06 4.0E+06
Breakdown E field (V/m)
Figure 3.17: Acceleration data based on pressure variation, 0 to 1 atm, 3-tesla magnetic field.
45
Considering an operating pressure of 3447 Pa and a temperature of 100°C, the resulting
simple collision frequency
λC
=Θ (3-7)
is based on the average molecular velocity
MRTCπ8
= (3-8)
and the mean free path given in Equation (2-12). With a collision frequency of 1.4895×108 Hz,
the expected acceleration is determined from the Figure 3.18 curve fit to be
583741104103102 4214325 +×−×+×−= −−− xxxy , (3-9)
and the value of the acceleration is 5.2483×105 m/s2.
Acceleration
3.1840E+10
-2.E+07
0.E+00
2.E+07
4.E+07
6.E+07
8.E+07
1.E+08
1.E+08
1.E+08
2.E+08
0.0000E+00 2.0000E+10 4.0000E+10 6.0000E+10 8.0000E+10 1.0000E+11 1.2000E+11
Frequency (Hz)
Acc
eler
atio
n (m
/s^2
)
Figure 3.18: Acceleration data based on peak collision frequency, 0 to 120 GHz.
46
Sinusoidal electric and magnetic field strength profiles
Investigating the interplay between sinusoidal magnetic and electric field strength
profiles was considered an important part of the simulation. The conditions for the simulation
were a pressure of 0.5 atm and a frequency for both sine waves of 0.1 GHz. Electric field strength
amplitude remained as a variable, while the amplitude of the magnetic field was left at 25 tesla, as
in most previous constant field profile simulations.
Phase shift as an independent variable
Three settings for phase shift were considered, 0, 90 and 180 degrees, utilizing average
acceleration data from the batch processing simulation code, with sinusoidal waveforms for the
electric and magnetic fields. The data that were compiled are shown in Figure 3.19.
Sine phase shift data
-2.50000E+05
-2.00000E+05
-1.50000E+05
-1.00000E+05
-5.00000E+04
0.00000E+00
5.00000E+04
1.00000E+05
1.50000E+05
2.00000E+05
2.50000E+05
0 30 60 90 120 150 180 210
Phase shift (deg)
Ave
rage
Acc
eler
atio
n (m
/s)
10 runs at E=2e410 runs at E=5e2
Figure 3.19: Acceleration data based on phase shift between sinusoidal waveforms.
47
The two cases agree in that the closer the phases of the magnetic and electric fields are,
the higher the acceleration becomes.
Chapter 4
Experiment
Experimental Configuration
The core of the experimental setup is a quartz tube with square cross section, sealed at
both ends with two solid aluminum endplates enabling its attachment to the water vapor circuit
through Swagelok fittings. A vessel of solid aluminum containing approximately a liter of
distilled water connects to one end of the quartz tube. Temperature control for the water vessel is
provided by a hot plate that references a temperature probe inside the vessel, and flow control is
provided by a simple in-line needle valve. Pressure measurement for the system is achieved by
use of an OMEGA PX303-050A5V pressure transducer connected to the system at a branch
immediately following the water vessel’s valve (Valve 1). The pressure is displayed on a digital
meter in psi units. Temperature is recorded using two OMEGA CASS-14E-3-NHX
thermocouples with K-type connectors, one recording the air temperature in the lab and the other
recording the temperature of the water vapor right before it enters the quartz tube section of the
setup.
Figure 4.1 shows that at the other end of the quartz tube, an exit valve (Valve 2) provides
control of the flow rate of water vapor through the system, and finally connects to the vacuum
pump that provides the low pressure environment for the experiment.
49
The devices used with this setup and their model numbers are summarized in Table 4.1.
Multiple devices under the headings of electric field generators and oscilloscopes offer versatility
in the generation and measurement of electric fields in the setup.
Figure 4.1: Experimental setup diagram.
50
The main part of the setup is present at the center of the quartz tube, where a set of two
neodymium magnets are connected to a C-shaped transformer core, seen in Figure 4.2, to create a
horizontal magnetic field through the cross-section of the quartz tube, with a measured field
strength of 0.6-tesla.
Table 4.1: Setup devices with corresponding model numbers.
Setup Device Model Number Hot plate OMEGA LHS-730 Pressure transducer OMEGA PX303-050A5V Pressure transducer display OMEGA DP25-E-A Thermocouple display OMEGA HH-52 Vacuum Pump Welch DUOSEAL 1402 Heating tape 1 OMEGALUX STH051-080 Heating tape 2 OMEGALUX HTWC-101-002 E field generators
High voltage power supply Stanford Research Systems, Inc. PS350 5000 V – 25 W
Square wave/pulse generator Tektronix PG 502 - 250 MHz Oscilloscopes
500 MHz scope Agilent Infiniium Oscilloscope 1 GHz scope HP 54100D Digitizing Oscilloscope (Agilent)
51
Figure 4-2: Test section model.
The polymer tube in Figure 4.3 holds the two magnets apart and also allows for two
copper plates to be snugly attached to the exterior top and bottom of the quartz tube. With wires
soldered to the part of each plate that protrudes outside the polymer piece, an electric potential
can be applied between the plates, generating the electric field lines essentially in a vertical
direction through the cross-section.
52
Figure 4.3: Detailed view of test section, showing polymer stand, magnets, and copper plates, without transformer core.
Indicating the flow rate in the quartz tube is achieved simply by a non-static plastic
curtain with a thickness of 0.8 mil, the “flapper”, which is inserted in the center of the quartz tube
through a slot in the top surface of the tube (See Figure 4.4). This curtain is sized to cover the
cross section almost entirely.
53
Figure 4.4 shows that vacuum putty was used for the dual purpose of sealing the slot
through which the “flapper” was inserted into the quartz tube and also to secure the top copper
plate to the test section. This arrangement was chosen so that the “flapper” is situated close
enough to the test section to allow for observation of minute and localized flow rate changes, but
not too close to interfere with the volume of water vapor being accelerated.
Figure 4.4: “Flapper” device, as part of disassembled test section.
54
Procedure
Given the nature of this experiment, the procedure described in the following paragraphs
aims at reducing the inherent lack of precision in measurements through rigorous conditioning
and resetting of the reactor and the system so that correlating repetitive measurements increases
the accuracy of the experimental methodology. An example of such a behavior is the fact that the
pressure settings for various steps do not directly translate to vapor concentrations in the test
section because the setup does not include any devices to measure that parameter. To that effect,
the repeatability of the experiment centers around the process steps being repeatable, which
depend mainly on the system pressure reading and the “flapper” inclination.
Starting with every device in the off state, the first step is powering on all the required
devices, namely the hot plate, thermometer display, pressure gauge, and vacuum pump. After
making sure all Swagelok connections and quartz tube seals are secure, the vacuum pump is
turned on to evacuate the quartz tube. At this starting stage Valve 1 is completely closed and
Valve 2 is completely open, so the system should have as little water vapor in it as possible. At
this stage the system is pumped down to as low pressure as is possible, in the range of 0.10 psi,
until the pressure stabilizes.
Adding water to the system requires only slightly opening Valve 1, making sure that the
temperature in the water vessel is stabilized beforehand by the hotplate’s temperature control
system. The target pressure after this step is never exactly the same, and depends somewhat on
the target pressure of the next step, when the flow is reduced to a small enough value. Again, it is
important that the pressure is stable at this point, as well as the temperature, which could vary as
an equilibrium flow is established.
55
The next step allows for the setting of a stable, low water vapor flow environment in the
quartz tube, which is checked mainly by watching the “flapper” closely while slowly closing
Valve 2. When the “flapper” returns to its resting position, the setup is ready to activate the
electric field required by the specific experimental conditions. At this point, since the test section
interior walls tend to condense water on their surface, care must be taken so that the process of
stabilization ends up with a balance between having the “flapper” be as close as possible to the
resting position without a lot of condensation occurring. Condensation in the test section is
usually alleviated by allowing the flow to be high enough so that the water vapor is not exposed
to the test area as much.
Low voltage DC setup
Based on different electric field configurations that were tested in during of this
experiment, different sources of electric potential were used. The first set of tests consisted of a
DC electric field that was provided by a simple 1.5-V AA battery adjusted through a
potentiometer. The resulting range of 0 to 1.5 V was tested, with a focus on the target voltage of
78 mV, chosen to be the level at which noticeable acceleration should be apparent. Throughout
the whole range, no visible effect was found, and a larger voltage range was attempted.
High voltage DC setup
Using the aforementioned high voltage power supply, a newly expanded range of 0 to
2000 V was explored, knowing that discharge between the copper plates would occur at 2450 V.
In the range between 0 and 20 V, the increment used was 1 V; from 20 to 100 V, the increment
was 10 V; and from 100 V to 2000 V, the increment was 100 V. Given that the simulation results
56
showed that the effect of higher electric fields on the water molecule was to increase the
rotational frequency, higher voltage ranges were not tested at small increments. The simulation
results gave an expectation that acceleration would occur when the rotational vibration frequency
is in a certain phase relationship with the collision frequency. This result was based on the
assumption that after a collision occurred, the molecule would be brought to rest in space. Since
the rotational frequency was the same as the displacement frequency of the center of mass of the
simulated water molecule along the direction of desired acceleration, it was theorized that having
a collision frequency four times higher than that of the vibration would bias the molecule to move
in one direction only. Since the experimental results proved this theory wrong, the experiment
moved into the direction of a pulsed electric signal.
Pulse generator setup
Simulation work supported the claim that acceleration in the water vapor medium could
be achieved with a square wave profile electric field, and specifically that high acceleration was
associated with low duty cycle and high amplitude. Testing this experimentally proved to be the
most difficult part due to the interactions between the pulse generator and the oscilloscopes used
to measure the signal and its accuracy. The Tektronix PG 502 pulse generator had a range of
signal frequencies from 100 Hz to 250 MHz, with an analog duty cycle selector that could be
modulated from 10% to almost 100%.
The original focus of this experiment was to modulate the electric field in the microwave
range (1–30 GHz), so the experiment focused on the higher frequency range of 100 to 250 MHz,
which brought some signal resolution problems. With oscilloscopes whose operating frequencies
are at 500 MHz, and sampling rates of 1 GSa/sec, one would expect good resolution of sinusoid
type signals, but a square wave consists of many sinusoidal signals that are superimposed. The
57
signals that allow the square wave to have well resolved edges have overtones at frequencies far
higher than that of the fundamental frequency of the signal and, as such, the oscilloscope would
only see a rounded version of the expected square signal. Working with a few different
oscilloscopes and accounting for signal loss issues like capacitance in the wires, the accuracy of
the high frequency signals being output by the pulse generator was never entirely determined.
The rest of the pulse generator frequency range could be properly tested and provided great
resolution, leaving the range of interest to be the only part in question. Better resolution was
achieved with the HP 54100D Digitizing Oscilloscope due to an automatic multi-sampling
feature, but the results from experiments performed with this oscilloscope as part of the setup
could not be included due to time constraints.
Chapter 5
Results
Experimental results
To date, attempts to experimentally reproduce the predicted simulation results have met
with many challenges. The goal of producing a noticeable flow increase from a steady magnetic
and electric field configuration, with the assumed influence of molecular collision frequency has
proven to be elusive. Changing the pressure and temperature of the setup under controlled
circumstances has allowed a degree of control over the quantity of water vapor present in the
quartz tube and its collision frequency probability distribution, but comparable results to the
simulation output have not been achieved.
With the recent addition of heating tape (Figure 4.1) to most of the test setup, the problem
of condensation for the most part was alleviated. It is important to note that, not only does
condensation affect visibility in the quartz tube, rendering any observation of “flapper”
inclination impossible, the condensation, as an exothermal process, also adds thermal energy to
the remaining flow. Again, looking at the experimental setup (Figure 4.1), it can be noted that the
position of the thermocouple that measures flow temperature is located before the quartz tube,
and hence the effects of condensing liquid could change the water vapor temperature in the test
section to become significantly different than that recorded at the thermocouple.
Based on the process described in Chapter 3, predictable conditions for the experimental
setup can be achieved if the process is followed accurately. Final water vapor temperature is
affected by a combination of water temperature in the source tank and settings on two heating
tape control units, with the temperature being monitored by the in-flow thermocouple. While
59
many temperatures can be achieved, the two main target temperatures explored were 80 and
100°F, and target pressures were on average around 0.50 psi. Reaching a stable temperature set
point takes time, mostly since temperature in the test section needs to stabilize after the initial
opening of the water tank valve to the system, and afterwards for the effect of the heating tape to
stabilize.
Constant electric field strength profile
The electric field strength profiles designed in Chapter 3 were all tested, within lab
capability, to check correlation between simulation and experimental results. The simplest profile
being the constant electric field strength, it was tested with both low and high voltage sources,
over almost the full range of the devices. In the case of the high voltage power source, the test
range ended at the point where breakdown of the water vapor occurred. Throughout the entire
range of 0 to 2000 V, which translated to a field strength range of 0 to 117600 V/m, no effects on
the flapper were observed.
Square electric field profile
Using the pulse generator source (Table 4.1), the range of frequencies from 100 Hz to 10
MHz was explored, at one order of magnitude intervals, each interval having a selectable duty
cycle of 50% and descending, again in orders of magnitude. The pulse generator’s highest
frequency set points of 100 and 250 MHz were the points of interest, since they are closer to the
microwave range of frequencies the experiment was meant to operate in. Unfortunately, due to
time constraints the testing of the pulsed electric field strength method was not able to be part of
60
this thesis, but further testing will continue, and the effects of pulsed electric fields on water
vapor acceleration will be determined.
61
Chapter 6
Conclusions
While the original intention of this project was to demonstrate the viability of polar
propulsion as a competitive electric propulsion method, the complexity of the molecular physics
and limitations in time and resources made it difficult to prove the concept is physically
realizable. In no way does the work presented here mean to imply that polar propulsion is
impossible to realize, quite the opposite is true since some of the simulation results yielded
encouraging results. However, the goal of providing practical solutions for this kind of electrical
propulsion, straying from the rather exotic conditions in which its feasibility was demonstrated
(25 T, 10 GHz, sawtooth, LiH), is a tough challenge and needs more work. This thesis, therefore,
aims to present a solid starting point to the realization of a total proof-of-concept setup, and to
establish a comprehensive outline of the experimental procedure required to understand the
underlying mechanisms of the application of the Abraham effect to space propulsion.
All of the sections marked in yellow in Table 6.1 are experimental capabilities of the
current setup, which have been investigated to the extents that were possible by equipment and
time restrictions. Each variable was provided with at most three separate categories of possible
experimentation and for each variable, i.e. frequency, magnitude, or pulse shape, the three ranges,
values, or shapes are not associated with entries in the same column, above or below. For
example, in the section on magnetic field, while one value to be explored for magnitude is 25
tesla, there is no implication that the pulse shape has to be sinusoidal for that magnitude, as the
pulse shape is to be an independent variable.
62
Table 6.1: Total variable matrix for experiment continuation.
Variable Range
Electric field
Frequency DC 100 Hz – 250 MHz pulsed 250 Hz – 30 GHz
Delivery Battery to electrodes Power supply to electrodes Waveguide
Magnitude 88.23 V/m (low) 1.176e5 V/m (high) Mid-range
Duty Cycle 50%, 5%, etc. 90%, 80%, etc. Completely variable %
Pulse shape Rectangular & Constant Saw Tooth Sinusoid
Magnetic field
Frequency Constant Matched to electric Other
Delivery Permanent magnet Electromagnet Waveguide
Magnitude 0.6 tesla 25 tesla Other
Pulse shape Constant Sinusoidal Other
Relative position
E vs. B field lines Perpendicular Angle Complex field
Propellant
Type Water Other
Pressure 0.50 psi Higher vacuum Atmospheric
Temperature Atmospheric Low temperature Boiling/High temperature
Flow rate Very low Stagnant High speed
63
Based on the lessons learned from the simulation and experiment, it is the goal of this
thesis to generate the guidelines along which the future work on this project will more than likely
reach its goal of proving the concept of polar propulsion viable.
Some of the recommendations overlap with variables that have already been explored,
and this by no means signifies that work in that subject is completed, but that a more thorough
investigation should follow. Tables 6.2 through 6.5 graphically display a comparison between the
covered experimental configurations (in yellow) and the ones recommended for future work (in
green).
For the electric field it has become apparent that a waveguide setup would ensure a better
amount of control over the shape of the field line distribution inside the test section. For a more
detailed discussion on this subject, please see the Appendix. The magnitude requirement covers
the entire range of magnitudes possible, with the understanding that future work should
comprehensively explore the entire range of electric field magnitudes from zero to breakdown
strength.
Out of all the signal shapes considered, the “sawtooth” remains the most likely to have a
real application to this process, and the ability to accurately change the duty cycle of the signal is
equally important in fully exploring the potential of this shape.
Reactor configuration
Setup cross section Square Rectangular Circular
Size 1.7 x 1.7 cm Other
Metrology
Method Flapper Doppler shift Mechanical, in-flow
64
While the permanent magnet currently being employed for the experimental setup is
fairly powerful, in order to reach accelerations comparable to other electric propulsion methods,
the magnitude of the field strength should be in the 25-tesla range, which could be achieved by
electromagnets. As far as the decision between a constant field versus a sinusoidal or other kind
of variation, there is not enough evidence to support an advantage either way, but based on
financial constraints, constant magnetic field strength would be more budget-friendly than any
other option.
The relative position of the electric and magnetic field lines has always been
perpendicular based on the theory described in Chapter 2, and for the purposes of this experiment,
changing the angle would more than likely result in needless energy losses. Different propellants,
especially dipoles, might not suffer from the problems that a complex molecule like water does,
Table 6.2: Electric field recommendations.
Variable Range
Electric field
Frequency DC 100 Hz – 250 MHz pulsed 250 Hz – 30 GHz
Delivery Battery to electrodes Power supply to electrodes Waveguide
Magnitude 88.23 V/m (low) 1.176e5 V/m (high) Mid-range Duty Cycle 50%, 5%, etc. 90%, 80%, etc. Completely variable %
Pulse shape Rectangular & Constant Saw Tooth Sinusoid
Table 6.3: Magnetic field recommendations.
Variable Range
Magnetic field Frequency Constant Matched to electric Other Delivery Permanent magnet Electromagnet Waveguide
Magnitude 0.6 tesla 25 tesla Other Pulse shape Constant Sinusoid Other
65
but a proper analysis of other propellants should be made. As for the pressure and temperature of
the propellant, future work should focus on working to best replicate the conditions of operation
encountered in space. The determination of the proper flow rate for the next iteration of the
experimental setup also needs to consider the operating conditions in which the thruster will
eventually operate. Ideally though, the most accurate measurements would be taken when the
water vapor velocity would be as low as possible to begin with, so the acceleration of the system
would not be lost in the noise and turbulence present in the flow section.
While no clear advantage can be claimed for the square cross section shape of the test
section, this shape may migrate towards a rectangular one if the electric field is to be generated in
a waveguide. Most importantly, the flow velocity measurement method that this experiment
would benefit from the most would be the laser absorption spectrum Doppler shift method, due to
its accuracy at low flow rates and complete lack of intrusion in the flow.
Table 6.4: Field relative orientation and propellant recommendations.
Variable Range
Relative orientation
E vs. B field lines Perpendicular Angle Complex field
Propellant Type Water Other
Pressure 0.50 psi Higher vacuum Atmospheric Temperature Atmospheric Low temperature Boiling/High temperature
Flow rate Very low Stagnant High speed
66
In closing, though the overall goal of demonstrating that the polar propulsion concept is
physically viable was not fully realized, the work presented here has laid a proper foundation for
the work required to eventually reach that goal.
Table 6.5: Reactor configuration and metrology recommendations.
Variable Range
Reactor configuration
Setup cross section Square Rectangular Circular
Size 1.7 x 1.7 cm Other
Metrology Method Flapper Doppler shift Mechanical, in-flow
67
Appendix
Determination of usable E field cross-section for experimental test setup
Analytical approach
After initial setup of the E-field plates, and subsequent testing under the conditions
derived from earlier simulation work, no acceleration effect was noticed in the test section. The
first theory to rectify this issue was that the capacitor plates were in contact with the magnet,
which was found to be conductive. This would result in a redistribution of the electric field lines
from perfectly perpendicular from one plate to the other, to another shape, which was not fully
understood.
In order to find this new shape, an attempt was made to find an analytical solution for the
electric field potential starting with Maxwell’s equations. Given proper boundary conditions, this
should have provided a good idea of the distribution of the electric field in the test setup. Starting
with Gauss’s law
0ερ
=⋅∇ E , (A-1)
and knowing that the electric potential
ϕ−∇=E , (A-2)
we can write
0
)(ερϕ −=∇∇ . (A-3)
So, for space devoid of charge, this becomes the Laplace equation
68
0)( 2 =∇=∇∇ ϕϕ . (A-4)
In two dimensions it may be written as
02
2
2
22 =
∂∂
+∂∂
=∇yx
V ϕϕ. (A-5)
At this point, solving this equation requires the method of separation of variables, but the
true trouble emerges when trying to define the boundary conditions. In the case of this
experiment, a prominent discontinuity in potential exists where the surfaces of the capacitor
plates meet with the magnet faces. Since the setup cross section is square, any two surfaces that
are electrically insulated from each other will cause the electric potential to go from one value to
another instantaneously. For this reason, an analytic solution is no longer viable due to the time
and resources available to spend on it.
Numerical Approach
COMSOL Multiphysics, a program designed to do physics simulation using FEA, offers
a timely alternative to analytic solutions. Setting up the entire 2D problem in the
Multiphysics/Electrostatics module, two situations were explored. The important one is the
situation where the plates are electrically insulated, since this is the manner in which the
experimental setup was adjusted. The best case scenario simulation was a simple capacitor, and
the resulting electric field was measured to be 0.433 V/m. The distance between the plates was set
to 18 mm with a potential difference of 7.8 mV DC.
Simulating two insulated magnet faces placed perpendicular to the electric field plates to
form a complete square resulted in a completely different field distribution, and most importantly
there were limited regions of the total area where the electric field was in the area of 0.433 V/m.
69
Results and Conclusions
Plotting the electric field values in 2D overlaid with the field lines shows which part of
the cross sectional area is usable, given the restrictions that the field lines must be mostly
perpendicular to the magnetic field lines, and the strength must be in the area close to 0.433 V/m.
Figure A.1 shows two plots, one of an area of electric field strength covering a range of
0.433±10% V/m and another using ±20%.
Visually, the estimated portion of the area that is useful is significantly less than 50% of
the cross-sectional area available. Based on these results, it would be best to use dielectric
magnets.
Figure A.2 shows the simulation of the two magnets being in contact with the bottom
plate was also explored, with the same ±10% and ±20% spread, respectively.
Figure A.1: Usable cross sectional area and field lines, ideal case.
70
From these plots it is apparent that the COMSOL Multiphysics simulation indicates that
the usable region is relatively small compared to the total area available.
Figure A.2: Usable cross sectional area and field lines, lower plate shorted to sides.
71
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