ELF/VLF Phased Array Generation via Frequency-matched Steering of a Continuous HF Ionospheric Heating Beam

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ELF/VLF PHASED ARRAY GENERATION VIA
FREQUENCY-MATCHED STEERING OF A CONTINUOUS HF
IONOSPHERIC HEATING BEAM
A DISSERTATION
SUBMITTED TO THE DEPARTMENT OF
ELECTRICAL ENGINEERING
AND THE COMMITTEE ON GRADUATE STUDIES
OF STANFORD UNIVERSITY
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
Morris Bernard Cohen
October 2009

c
Copyright by Morris Bernard Cohen 2010
All Rights Reserved
ii

I certify that I have read this dissertation and that, in my opinion, it
is fully adequate in scope and quality as a dissertation for the degree
of Doctor of Philosophy.
(Umran S. Inan) Principal Adviser
I certify that I have read this dissertation and that, in my opinion, it
is fully adequate in scope and quality as a dissertation for the degree
of Doctor of Philosophy.
(Timothy F. Bell)
I certify that I have read this dissertation and that, in my opinion, it
is fully adequate in scope and quality as a dissertation for the degree
of Doctor of Philosophy.
(Butrus T. Khuri-Yakub)
Approved for the University Committee on Graduate Studies.
iii

.
To life, to life, l’chaim!
L’chaim, l’chaim, to life!
iv

Abstract
The radio spectrum between 300 Hz and 10 kHz (ELF/VLF) has broad applications
to global communication, remote sensing of the ionosphere and magnetosphere, and
subterranean prospecting. While lightning is a dominant source of these radio waves,
artificial generation of these waves has posed an enduring challenge to scientists and
engineers, due to the extremely long wavelengths (30-1000 km) and the lossiness of
the Earth’s surface at these frequencies.
Recently, ELF/VLF waves have been successfully generated by high frequency
(HF, 3-10 MHz) heating of the lower ionosphere (60-100 km altitude), which changes
the atmospheric plasma conductivity. In the presence of natural currents such as the
auroral electrojet, ON-OFF modulation of this HF energy can impose an ELF/VLF
alternating current onto those natural currents. This technique turns the lower
atmosphere into a large antenna, which radiates energy downward into the Earth-
ionosphere waveguide and upward into the magnetosphere.
While this technique remains one of the few means of reliable ELF/VLF wave
generation, HF to ELF/VLF conversion efficiencies remain quite low. Utilizing the 3.6
MW HAARP HF heating facility in Alaska, we show that proper utilization of motion
of the HF beam can boost the generated ELF/VLF wave power by as much as tenfold.
Furthermore, as a result of having effectively created the world’s first controllable
large-element ELF/VLF phased array, directional launching of this energy becomes
possible. We utilize theoretical models of the HF heating and cooling process, and of
ELF/VLF wave propagation, to illuminate the observations and identify the physical
mechanisms underlying the wave generation, particularly as it relates to motion of
the HF beam.
v

Acknowledgements
I begin with a slightly paraphrased quote from the ancient Jewish law book Talmud,
Pirkei Avot, Chapter 3, attributed to Rabbi Yochanan Ben Zakai.
If you have learned much (scholarly wisdom), do not take credit for your-
self; it is for this reason that you have been formed.
Indeed, it may be my name printed on the front of this thesis, but really none of
it would have happened without the support of a lot of other people.
First and foremost, I’ve been blessed with a fantastic family. My parents have
truly been role models to me for my entire life. I say with no qualification that I have
the best parents I possibly could have. My brothers, Sam and Dave, have always
been terrific and very supportive, and I’m delighted that both of them have grown
the family, with my sisters-in-law Fern and Audria, and their children Josh, Ian,
Rachel, and Ethan.
I thank my teachers and friends from Beth Tfiloh School in Pikesville, Maryland,
where a great general education was complemented with a firm grounding in Jew-
ish teachings that I still proudly carry. I thank all my friends from my Stanford
undergraduate years, who made my early years on ‘The Farm’ a great experience.
I owe another thanks to all the VLF group members with whom I’ve interacted.
Marek Go lkowski has been a very able collaborator in planning so many HAARP
experiments (and absurd arctic adventures), and a reliable scientific counsel. Denys
Piddyachiy and George Jin were extensive contributors to the late night chat room
watches during campaigns. Robb Moore, Joe Payne, and Nikolai Lehtinen paved
the way for this thesis with excellent earlier work. Tim Bell provided some valuable
counsel with this dissertation.
vi

Justin Tan and Eddie Kim were critical in developing the ‘AWESOME’ receiver
with me, which has by now gotten so much use worldwide, and serves as the primary
source of data for this thesis. Ev Paschal, with his decades of experience in hardware
design, was a treasure trove of information on VLF receivers and field installation.
Although not part of this dissertation effort, for the exciting ‘AWESOME’ Inter-
national Heliophycial Year (IHY) global distribution program, I worked extensively
with Sheila Bijoor, Ben Cotts, and Naoshin Haque. Debbie and Phil Scherrer were
instrumental in the program’s development. I thank all our AWESOME collaborators
and site hosts around the world for their friendship.
Many other VLF members have been colleagues and friends. I’ve learned a lot
from Ryan Said, Prajwal Kulkarni, Jeff Chang, Charles Wang, Mark Daniel, Brant
Carlson, Bob Marshall, Dan Golden, Nader Moussa, Kevin Graf, Robert Newsome,
Max Klein, and others.
I thank Shaolan Min and Helen Niu for keeping so much important VLF group
business running smoothly, and Dan Musetescu for managing so much data and keep-
ing it all organized.
The operation of the HAARP facility has been possible thanks in part to the hard
work of Mike McCarrick, Helio Zwi, and David Seafolk-Kopp. I would like to thank
Doyle and Norma Traw, of Chistochina Bed and Breakfast, in Alaska, for helping with
receiver maintenance and always being great hosts during my various trips there.
The experience working with my advisor, Umran Inan, has been terrific, as from
it I have learned so much. The journey has been long since I took on my first
VLF project (rather unrelated to this thesis) as a college junior, but through several
different widely disparate projects I was never short of opportunities to grow, develop,
and pursue new ideas. For that reason my time in this research group has never felt
static at all. Thanks for giving me the chance.
This work has been supported by the Defense Advanced Research Projects Agency
and the Air Force Research Laboratory under Office of Naval Research (ONR) grants
N00014-09-1 and N00014-06-1-1036 to Stanford University.
vii

Contents
Abstract v
Acknowledgements vi
1 Introduction 1
1.1 Theionosphere .............................. 1
1.2 Magnetosphere-ionosphere coupling . . . . . . . . . . . . . . . . . . . 4
1.3 ELFandVLFwaves ........................... 7
1.4 ELF/VLF wave generation . . . . . . . . . . . . . . . . . . . . . . . . 9
1.5 Somehistory ............................... 13
1.6 Reviewofpastwork ........................... 18
1.6.1 Local geomagnetic conditions . . . . . . . . . . . . . . . . . . 19
1.6.2 Earth-ionosphere waveguide injection . . . . . . . . . . . . . . 20
1.6.3 Harmonic radiation and saturation . . . . . . . . . . . . . . . 21
1.6.4 Magnetospheric injection . . . . . . . . . . . . . . . . . . . . . 22
1.6.5 Mobile heated region . . . . . . . . . . . . . . . . . . . . . . . 23
1.6.6 Beampainting........................... 24
1.6.7 Alternative methods . . . . . . . . . . . . . . . . . . . . . . . 24
1.6.8 Ionospheric array . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.7 Scientific contributions . . . . . . . . . . . . . . . . . . . . . . . . . . 26
1.8 Approach ................................. 27
2 ELF/VLF Generation and Propagation Physics 28
2.1 Wavesinplasmas............................. 28
viii

2.1.1 Plasma properties . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.1.2 Magnetic field and the whistler wave . . . . . . . . . . . . . . 30
2.1.3 Anisotropy............................. 31
2.1.4 Collisions ............................. 32
2.1.5 The D-region ........................... 35
2.2 HFheatingtheory ............................ 38
2.2.1 Electron temperature . . . . . . . . . . . . . . . . . . . . . . . 39
2.2.2 Modified ionosphere . . . . . . . . . . . . . . . . . . . . . . . 41
2.2.3 HF wave propagation . . . . . . . . . . . . . . . . . . . . . . . 44
2.3 Modelconstruction ............................ 45
2.3.1 Energy balance at one altitude . . . . . . . . . . . . . . . . . . 45
2.3.2 Vertical structure . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.3.3 Extensionto3D.......................... 57
2.4 The Earth-ionosphere waveguide . . . . . . . . . . . . . . . . . . . . . 65
2.4.1 Reflection coefficients . . . . . . . . . . . . . . . . . . . . . . . 68
2.4.2 Modalsolutions.......................... 70
2.4.3 Propagation model . . . . . . . . . . . . . . . . . . . . . . . . 70
2.5 Modelresults ............................... 73
3 HF Beam Motion: Experiments 79
3.1 ELF/VLF generation and beam motion . . . . . . . . . . . . . . . . . 80
3.2 Implementation .............................. 84
3.3 Experimentalsetup............................ 85
3.4 Comparative frequency response . . . . . . . . . . . . . . . . . . . . . 90
3.4.1 Generated amplitudes from beam painting . . . . . . . . . . . 91
3.4.2 Directionality from beam painting . . . . . . . . . . . . . . . . 93
3.4.3 Generated amplitudes from geometric modulation . . . . . . . 94
3.4.4 Directionality from geometric modulation . . . . . . . . . . . . 95
3.4.5 Geometric modulation compared to oblique-AM . . . . . . . . 95
3.4.6 Summary of ground-based observations . . . . . . . . . . . . . 97
3.4.7 Magnetospheric injection . . . . . . . . . . . . . . . . . . . . . 99
ix

4 HF Beam Motion: Modeling 100
4.1 Modulatedcurrents............................ 100
4.2 Fields on the ground . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.3 Magnetospheric injection . . . . . . . . . . . . . . . . . . . . . . . . . 112
4.4 Directional pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
5 Physical Mechanisms 120
5.1 Heat-cooldutycycle ........................... 120
5.2 Phasing from oblique heating . . . . . . . . . . . . . . . . . . . . . . 127
5.3 HFpulsing................................. 132
5.4 ELF/VLF phased array control . . . . . . . . . . . . . . . . . . . . . 136
5.5 Phased array parameters . . . . . . . . . . . . . . . . . . . . . . . . . 140
5.6 Discussion................................. 143
6 Summary and Suggestions for Future Work 144
6.1 Futurework................................ 145
6.1.1 Equatorial electrojet . . . . . . . . . . . . . . . . . . . . . . . 146
6.1.2 Intersweep delay times . . . . . . . . . . . . . . . . . . . . . . 146
6.1.3 HF heating model with lookup table . . . . . . . . . . . . . . 146
6.1.4 Parallel conductivity changes . . . . . . . . . . . . . . . . . . 147
6.1.5 Directional pattern . . . . . . . . . . . . . . . . . . . . . . . . 147
6.1.6 Beam painting diurnal variations . . . . . . . . . . . . . . . . 148
6.1.7 Variation with HF frequency . . . . . . . . . . . . . . . . . . . 148
6.2 Concludingremarks............................ 148
A Long Distance Reception 149
B HAARP HF Radiation Pattern 152
C ELF/VLF Reception and Detection 155
C.1 Antenna characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . 156
C.2 Systemdesign............................... 158
C.3 Calibration ................................ 162
x

C.4 Gain and sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
C.5 Timingaccuracy ............................. 167
C.6 Cross-modulation and cross-coupling . . . . . . . . . . . . . . . . . . 171
D Power Line Interference Mitigation 174
D.1 Adaptivefiltering ............................. 177
D.1.1 Theory............................... 178
D.1.2 Implementation.......................... 180
D.2 Least squares estimation . . . . . . . . . . . . . . . . . . . . . . . . . 186
D.3 Examples ................................. 190
E ON/OFF Duty Cycle Observations 193
xi

List of Tables
1.1 Ionospheric heating facilities . . . . . . . . . . . . . . . . . . . . . . . 15
B.1 Radiated power (and ERP), in Megawatts, of HAARP beam modes . 154
xii

List of Figures
1.1 Theionosphere .............................. 2
1.2 The magnetosphere in the solar wind . . . . . . . . . . . . . . . . . . 5
1.3 The auroral electrojet . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 AVLFtransmitter ............................ 11
1.5 Illumination by an ionospheric source . . . . . . . . . . . . . . . . . . 13
1.6 The HAARP HF heating facility . . . . . . . . . . . . . . . . . . . . . 18
2.1 Coordinate system for ionospheric conductivity . . . . . . . . . . . . 33
2.2 Ionospheric plasma parameters . . . . . . . . . . . . . . . . . . . . . . 37
2.3 Variations of ionospheric conductivities as a function of temperature . 42
2.4 Heating and cooling dynamics at 75 km altitude . . . . . . . . . . . . 47
2.5 Hall conductivity modulation vs. height, frequency, and HF power . . 49
2.6 Power density reaching higher altitudes . . . . . . . . . . . . . . . . . 51
2.7 Absorption of HF energy at 3.25 MHz . . . . . . . . . . . . . . . . . 53
2.8 Ionospheric modification at varying altitudes . . . . . . . . . . . . . . 55
2.9 HF power at 60 km from HAARP . . . . . . . . . . . . . . . . . . . . 57
2.10 2D interpolation of HF parameters . . . . . . . . . . . . . . . . . . . 59
2.11 Three-dimensional HF heating model results . . . . . . . . . . . . . . 61
2.12 Time-evolution of vertical modulated currents . . . . . . . . . . . . . 64
2.13 Propagation in the Earth-ionosphere waveguide . . . . . . . . . . . . 66
2.14 Reflection coefficients as a function of incidence angle . . . . . . . . . 69
2.15 ELF/VLF propagation simulations . . . . . . . . . . . . . . . . . . . 74
2.16 Hall, Pedersen, and Parallel conductivity contributions . . . . . . . . 76
2.17 Horizontal magnetic field from current sources . . . . . . . . . . . . . 77
xiii

3.1 Amplitude modulation, beam painting, and geometric modulation . . 82
3.2 Classification of modulation techniques . . . . . . . . . . . . . . . . . 84
3.3 Map showing location of HAARP and ELF/VLF receivers . . . . . . 86
3.4 Transmission format and sample data from AWESOME receiver . . . 88
3.5 The generated amplitudes from beam painting . . . . . . . . . . . . . 91
3.6 Directionality associated with beam painting . . . . . . . . . . . . . . 93
3.7 The generated amplitudes from geometric modulation . . . . . . . . . 94
3.8 Directionality associated with geometric modulation . . . . . . . . . . 95
3.9 Comparison between oblique-AM and geometric modulation . . . . . 96
3.10 Experimental frequency response of HF heating . . . . . . . . . . . . 98
4.1 Modeled Hall currents from modulated HF heating . . . . . . . . . . 102
4.2 Modeled fields on the ground from 5 kHz modulated HF heating . . . 104
4.3 Modeled ground magnetic field compared, 5 kHz . . . . . . . . . . . . 106
4.4 Modeled ground magnetic field compared at 2 kHz . . . . . . . . . . 109
4.5 Theoretical response of modulated HF heating (on ground) . . . . . . 111
4.6 Modeled fields at 700 km altitude from modulated HF heating . . . . 113
4.7 Modeled frequency variation of ELF/VLF power to 700km altitude . 114
4.8 Directional patterns in the Earth-ionosphere waveguide . . . . . . . . 117
4.9 Directionality of the sawtooth-sweep as a function of frequency . . . . 118
5.1 Schematic effect of duty cycle on ELF/VLF generation . . . . . . . . 121
5.2 Heating and cooling areas in geometric modulation . . . . . . . . . . 123
5.3 Observed effect of duty cycle on ELF/VLF generation . . . . . . . . . 124
5.4 Generated amplitude as a function of HF ON and OFF durations . . 126
5.5 Schematic of oblique HF heating effect . . . . . . . . . . . . . . . . . 128
5.6 Received signals for oblique-AM HF heating at different azimuths . . 130
5.7 Comparison of oblique-AM with geometric modulation . . . . . . . . 131
5.8 Temporal conductivity changes for rapid power modulation . . . . . . 133
5.9 Effectiveness of beam painting by ERP and duty cycle . . . . . . . . 135
5.10 ELF/VLF phased array concept . . . . . . . . . . . . . . . . . . . . . 137
5.11 Point-source, free space model of received fields . . . . . . . . . . . . 138
xiv

5.12 Circle-sweep and sawtooth-sweep magnetic field on the ground . . . . 140
A.1 Global detection of ELF signals from HAARP . . . . . . . . . . . . . 150
B.1 HF power into the ionosphere from HAARP beam modes . . . . . . . 153
C.1 Photos and block diagram of the AWESOME receiver. . . . . . . . . 159
C.2 AWESOME Anti-aliasing filter . . . . . . . . . . . . . . . . . . . . . 161
C.3 Measured performance characteristics of the AWESOME receiver . . 165
C.4 AWESOME receiver timing . . . . . . . . . . . . . . . . . . . . . . . 169
C.5 Cross modulation in the AWESOME receiver . . . . . . . . . . . . . 172
D.1 Power-line frequency tracking . . . . . . . . . . . . . . . . . . . . . . 183
D.2 Spectrum of ELF/VLF data as aand bparameters are varied . . . . 184
D.3 Variations of aparameter ........................ 185
D.4 Time series data for varying values of a................. 187
D.5 Examples of power-line filtered data . . . . . . . . . . . . . . . . . . . 191
E.1 Amplitudes of generated ELF waves as a function of duty cycle . . . 194
E.2 Efficiency of generated ELF waves as a function of duty cycle . . . . 196
xv

Chapter 1
Introduction
Hello and welcome to my thesis. Relax and enjoy the ride. We will explore the gener-
ation of extremely low frequency and very low frequency (ELF/VLF) electromagnetic
waves between 300 Hz−30 kHz. We consider a method of generation in which the
Earth’s upper atmosphere (60−100 km) is modified in such a way that it becomes a
large antenna. The modification occurs by heating of free electrons with High Fre-
quency (HF) waves between ∼3 and 10 MHz. The applicability of this method arises
from the fact that at ELF/VLF frequencies, wavelengths are extremely long (10−1000
km), making a more conventional antenna structure difficult, costly, and limited in
ability. In this chapter, we discuss the general problem at hand and describe the
physical environment in which our experimental observations and theoretical models
operate. We also review the history of experimental and theoretical efforts in the field
of ELF/VLF wave generation via ionospheric HF heating.
1.1 The ionosphere
The Earth’s atmosphere on the surface, where we breathe, consists almost entirely of
neutral nitrogen and oxygen gas molecules. On the other hand, the space environment
surrounding the Earth (known as the magnetosphere), consists almost entirely of
charged particles (electrons, protons, or ions), the densities of which are many orders
of magnitude lower than the air on Earth. Because the particles in the magnetosphere
1

CHAPTER 1. INTRODUCTION 2
8 9 10 11 12
0
100
200
300
400
500
Altitude (km)
Layers of the Ionosphere
log10Ne, (cm−3)
Day
Night
D
E
F
4 6 8 10
50
60
70
80
90
100
The D Region (High Latitude)
log10Ne, (m−3)
Night
Day
Winter
Summer
Figure 1.1: The ionosphere
are so spread out, collisions with one another and with ever fewer neutral molecules
are rare, and their motion is greatly affected by the Earth’s magnetic field. The
ionosphere is essentially the transition between these two regions, extending over
altitudes above the Earth’s surface between 50 km and 1000 km. Both the ionosphere
and magnetosphere are examples of plasmas, nominally the fourth state of matter
(after solid, liquid, gas). In a plasma, a substantial number of charged particles exist
to create a shielding effect (known as Debye shielding) which tends to acts against
the development and maintenance of quasi-static electromagnetic fields (at least in
a plasma without an externally applied magnetic field), since the charged particles
rearrange so as to cancel out those fields. More details on the relevant physics are
given in Chapter 2.
The left hand panel of Figure 1.1 shows the structure of the ionosphere’s vertical
profile, with electron density (Ne) in logarithmic scale on the horizontal axis, as a
function of the altitude above the Earth’s surface on the vertical axis. The daytime
ionospheric profile is shown with a solid line, the nighttime ionospheric profile in
dashed line. The data come from the International Reference Ionosphere (IRI) 2007
model, an empirical model of ionospheric parameters taking into account basic diur-
nal, seasonal and geographic variations, for 01-Jan-2009, at the geographic location
(0,0), at 00 UT (midnight) and 12 UT (high noon).
The sun’s radiation dominates the dynamics of the ionosphere, as the impingement

CHAPTER 1. INTRODUCTION 3
of high energy (extreme ultraviolet and higher) photons on the atmospheric molecules
is the primary source of ionization. For this reason, the structure of the ionosphere is
radically different between nighttime and daytime. At night, with the sun’s ionization
source gone, the Fregion ionization level is maintained by a diffusive flow of plasma
from the inner magnetosphere (where recombination is much slower, so the ionization
persists), and this flow is subsequently forced back out during the daytime [Tascione,
1994, pg.96]. The Dand Eregions, on the other hand, are maintained at nighttime
by a steady flow of cosmic rays from extrasolar sources.
The dynamics of the Dand Eregions are complicated. On top of strong diurnal
and seasonal changes, the electron density can change drastically and rapidly as a
result of energetic particle precipitation or other magnetospheric activity, particularly
at night. The right panel of Figure 1.1 shows more detail on the electron density in
the lower portion of the ionosphere, and its variability from day to night, and winter
to summer. The IRI typically does not define the electron density in the lowest parts
of the Dregion, since the numbers become so small and variable. Below this altitude,
the electron densities are generally extrapolated with an exponential decrease, in line
with a two-parameter ionosphere described by Wait and Spites [1964], defined by
Ne(h) = Nhmin
ee−βh (1.1)
where Nhmin
eis the lowest defined electron density in the IRI, and his km below that
altitude. The steepness parameter, β, is taken to be −0.15 km−1in the daytime, and
−0.35km−1in the nighttime. Some typical values of a two-parameter ionosphere in
the Dand Eregions can be found in Thomson et al. [2007] and Thomson [1993].
The IRI inputs are calculated for the location 62.39◦N, 214.85◦E, where the re-
search facility in Alaska central to this work is located. The summer ionospheres are
calculated for 01-Jul-2000, and winter ionospheres for 01-Jan-2000. The nighttime
ionospheres are calculated for 02:00 local time, and the daytime ionospheres for 14:00
local time. The four ionospheres shown here are referred to repeatedly in this disser-
tation. The IRI also gives the ambient temperature, which varies between 180 and
240 K in this altitude range, and the neutral molecular densities.

CHAPTER 1. INTRODUCTION 4
1.2 Magnetosphere-ionosphere coupling
Although electromagnetic radiation from the sun and cosmic rays are chiefly respon-
sible for the formation of the ionosphere, a larger region around the Earth, known as
the magnetosphere, is shaped by the interaction of the so-called ‘solar wind’ with the
Earth’s magnetic field. The solar wind consists mostly of protons and electrons at
1 keV energy, originating from the sun, traveling at ∼400−500 km/s, and consisting
typically of ∼5 protons or electrons per cm3[Tascione, 1994, ch.3]. The geomagnetic
field of the Earth, however, acts to block this flow and deflect these particles. The re-
sult is that Earth’s magnetic field lines (which have roughly a magnetic dipole pattern
within a few Earth radii of the surface) are squashed in on the day side of the Earth,
and elongated into a tail on the night side. Figure 1.2 (available from NASA) shows
the basic structure of the Sun-Earth system and formation of the magnetosphere (not
to scale). The resulting current systems and dynamics of the magnetosphere driven
by the solar wind interaction with the geomagnetic field are in general very compli-
cated, and lead to a broad array of phenomena. For instance, some of the solar wind
that penetrates into the magnetosphere becomes trapped by the geomagnetic field,
forming two bands of energetic particles known as the Van Allen radiation belts.
In this dissertation, we are interested in one particular aspect through which the
magnetosphere system couples with the ionosphere. Above a portion of the high lati-
tude ionosphere known as the auroral zone, strong electric fields in the magnetosphere
accelerate energetic electrons in the magnetosphere. Since electrical conductivity is
much higher along the magnetic field in a magnetized plasma, the resulting current
moves primarily along the geomagnetic field line. At high latitudes, the geomagnetic
field lines are close to vertical, connecting the ionosphere to the magnetosphere, and
driving a current upward into the magnetosphere (or, electrons accelerated downward
into the atmosphere). The collision of these ‘precipitating’ electrons with the neutral
atmosphere is primarily responsible for the aurora borealis (in the northern hemi-
sphere) and the aurora australis (in the southern hemisphere), pictured in the right
part of Figure 1.3, which arise from photons emitted as a result of these collisions.
Since these currents typically persist far longer than charges can be sustained in

CHAPTER 1. INTRODUCTION 5
Figure 1.2: The magnetosphere in the solar wind
the plasma, the currents must in general be closed in a loop. An opposite current
therefore must also be present coming into the ionosphere, forming what are often
called Birkeland currents. The Birkeland currents connect at different latitudes, so
there must also be electric fields horizontally within the ionosphere connecting these
upward and downward currents, and this system is known as the auroral electrojet.
Figure 1.3, left panel, shows a schematic of the typical auroral electrojet system,
as would be viewed from a point one Earth radius above the surface. The magnetic
north pole is located at 82.7◦N, 110.8◦W as of 2005. The so-called ‘auroral oval’ is
shown in shades of red, and is the portion of the ionosphere with elevated conductivity
as a result of electron precipitation, with brighter red indicating higher conductivity.
The precipitation (and the conductivity) tends to be higher on the night side of the
oval [Baumjohann, 1983]. In addition, the auroral oval is not exactly centered around
the magnetic north pole, but is shifted by ∼4◦away from the sun [Baumjohann,
1983].
The auroral electrojet is highly variable. Its size and extent is largely a function
of solar and geomagnetic activity. During geomagnetic storms, the auroral electrojet

CHAPTER 1. INTRODUCTION 6
Magnetic Pole
HAARP
to Sun
0o Lon180o
90o W
90o E
30o N
45o
60o
75o
Electric
Field
Figure 1.3: The auroral electrojet

CHAPTER 1. INTRODUCTION 7
region expands southward. The right hand photos in Figure 1.3 are taken near Chis-
tochina, Alaska, of roughly the same portion of the sky, but only 4 minutes apart
(the top photo being earlier), on the morning of 11-March, 2006. The structure and
color of the aurora can be seen to dramatically change despite the small time between
the two photos, showing that this particular signature of magnetosphere-ionosphere
coupling can exhibit rapid variations.
The arrows in Figure 1.3 indicate the electric field lines, which are typically pointed
roughly in the north-south geomagnetic direction, but there are two diurnal discon-
tinuities [Baumjohann, 1983]. In the few hours before midnight, the direction of the
electric field changes from northward to southward, and this transition is known as
the Harang discontinuity [Baumjohann, 1983]. At midday, the auroral electrojet fields
typically are weaker.
The electric field generally in the north-south geomagnetic direction also generates
horizontal currents that are in the east-west direction (due to the anisotropic iono-
spheric conductivity discussed in Chapter 2). In this thesis, we consider a method of
ionospheric variation which modulates a small geographic portion of these typically
east-west auroral electrojet currents, by changing the conductivity of the ionosphere
with radio frequency (RF) heating. The RF heating facility is known as the High
Frequency Active Auroral Research Program (HAARP), whose location (indicated in
green on the map) is typically near the southern edge of the auroral oval, at Gakona,
Alaska.
1.3 ELF and VLF waves
The Dregion of the ionosphere lies at altitudes that are very difficult to access for
the purpose of taking measurements. The current record-high (unmanned) balloon
flight height reached 53 km, by Japan Aerospace Exploration Agency, in 2002. On
the other hand, satellites cannot orbit below 200−400 km altitude, since the drag
forces of the atmosphere would be too high. The inaccessibility of these altitudes to
direct measurements have consequently earned the Dregion the title ‘ignorosphere’.
One method of deriving information about the ionosphere is to send rockets

CHAPTER 1. INTRODUCTION 8
through it, and record during the upward and downward passes. While rocket passes
can provide direct information on the structure of the ionosphere, remote radio sens-
ing is the only reliable means of continuous ionospheric monitoring. In particular,
radio frequencies in the so-called Extremely Low Frequency (ELF, defined here as
300−3000 Hz) and Very Low Frequency (VLF, defined here as 3−30 kHz) are uniquely
well suited to remote sensing of the Dregion, due to the fact that the Dregion re-
flects a significant portion of ELF/VLF energy (as is discussed in Chapter 2). Hence,
changing conditions in the Dregion manifest as changes in the reflection conditions
of these ELF/VLF waves. Disturbances in the Dregion can be associated with a
wide variety of natural events, including solar flares [Mitra, 1974], lightning-induced
heating and ionization [Inan et al., 1993], lightning-induced electron precipitation
[Peter and Inan, 2007], auroral precipitation [Cummer et al., 1997], cosmic gamma-
rays [Fishman and Inan, 1988; Inan et al., 2007b], geomagnetic activity [Peter and
Inan, 2006; Rodger et al., 2007], and possibly earthquakes [Molchanov and Hayakawa,
1999].
ELF and VLF waves have also been observed to significantly impact the dy-
namics of energetic particles in the Van Allen radiation belts. For instance, it has
long been known that lightning-generated ELF/VLF waves can escape the atmo-
sphere, and propagate in the so-called whistler-mode, with right hand circular po-
larization in the magnetospheric plasma [Helliwell, 1965]. Under certain conditions,
these whistler waves can interact with energetic electrons, causing precipitation of pre-
viously trapped particles [Inan et al., 2007c]. In addition, the propagating whistler
wave can exchange energy with the particles, and as the wave and particle properties
evolve, the whistler wave can be amplified and exhibit nonlinear triggering of different
frequencies [Gibby et al., 2008, and references therein]. The magnetosphere can also
generates its own ELF/VLF waves such as chorus [Sazhin and Hayakawa, 1992] and
hiss [Hayakawa and Sazhin, 1992] under certain conditions.
Furthermore, the Earth (both land and sea) is a good conductor at ELF/VLF,
so that wave energy is trapped in the so-called Earth-ionosphere waveguide between
the ground and the D/Eregion, and signals can travel to global distances with
minimum (a few dB per Mm) attenuation [Davies, 1990, pg.389]. For instance, it

CHAPTER 1. INTRODUCTION 9
has long been known that lightning strokes emit the bulk of their electromagnetic
energy in the ELF/VLF frequency range [Uman, 1987, pg.118], due to the typical
time scales involved. The electromagnetic signatures of these strokes, known as radio
atmospherics, or ‘sferics’, can be detected at global distances from the source [Cohen
et al., 2006], and often reveal information about the characteristics of the lightning
source [Reising et al., 1996; Cummer and Inan, 1997; Inan et al., 2006] as well the
D-region ionospheric path in between [Cummer et al., 1998].
In addition to its uses for geophysical remote sensing, the high reflectivity of
ELF/VLF waves off the Dregion (and the Earth) suggests a number of practical
benefits. For instance, precise navigation can be achieved by receiving signals from
multiple VLF transmitters, and applying phase-coherent triangulation. The ‘Omega’
system [Swanson, 1983], in operation until 30-September 1997, enabled precise nav-
igation on the surface of the Earth long before the advent of the Global Positioning
System (GPS), using a set of VLF transmitters between 10 and 15 kHz frequencies
scattered around the world. The smaller ‘Alpha’ system [Inan et al., 1984], oper-
ated by Russia, is still in operation with three transmitters across Russia. The LOng
Range Aid to Navigation (LORAN) network [United States Coast Guard, 1980], still
in operation, utilizes waves in the Low Frequency band (∼100 kHz), with dozens of
transmitters around the world [Frank, 1983].
ELF/VLF waves are also practical for communications with submerged submarines,
due to the extremely long wavelengths (10−1000 km), enabling the energy to pene-
trate many meters into highly conductive (σ∼
=4) seawater, via the skin effect. The
ground-penetrating applications of ELF/VLF waves also make it useful for geophys-
ical prospecting [McNeil and Labson, 1991], and imaging of underground structures.
1.4 ELF/VLF wave generation
Despite the broad applications to remote sensing, navigation, communication, and
geophysical prospecting, ELF/VLF waves are difficult to generate for the purpose of
controlled experiments. Different kinds of traditional and novel antennas for electro-
magnetic wave generation are used for a dizzying array of applications, like television,

CHAPTER 1. INTRODUCTION 10
AM/FM radio, wireless phones, medical devices, aircraft communications, radars,
and much more. But ELF/VLF waves are not so easy to generate with conventional
antennas.
Consider the fact that the wavelength (λ) at these frequencies is between 10−1000
km. Construction of a half-wave dipole would therefore need an antenna of these
length scales. A practically realizable antenna, oriented vertically and powered from
the ground, invariably has an extremely short length compared to λ. For such elec-
trically short antennas, the entire conductor is quite nearly an equipotential surface,
since the time it takes for the voltages to propagate from the feed point to the ends
of the antenna is negligible compared to the ELF/VLF period. So applying a voltage
to the feed point generates a current signal which propagates out to the ends of the
antenna and reflects, with the reflected current nearly canceling the outgoing current.
With only small net currents, charges cannot be separated along the antenna, and so
potential differences along the antenna are also small. In essence, the resistance of
the antenna for radiating is small, since a large current creates only small potential
differences along the antenna. Antennas are often characterized by this ‘radiation
resistance’, which, for an electrically short monopole antenna above a ground plane,
is given by
Rs= 40 πh
λ2
(1.2)
where his the length of the antenna and λis the wavelength [Stutzman and Thiele,
1998, pg.66]. Rsis therefore only 6.3 mΩ for a 100 meter tall antenna at 15 kHz.
Therefore, radiation with any acceptable efficiency can only be achieved if the impedance
of the source driving the antenna is close to this value (and this includes any ohmic
losses from the finite conductivity of the antenna itself). Practically speaking, such
small output impedances requires tuning of reactive load elements to cancel out as
much of the impedance as possible, and this can only be achieved over a narrow res-
onant frequency range. A thorough discussion of the engineering tradeoffs involved
in this type of design is given by Watt [1967, ch.2]. Even within this narrow fre-
quency range, the voltages driving the antenna must be extremely high in order to

CHAPTER 1. INTRODUCTION 11
Figure 1.4: A VLF transmitter
have sufficient current, causing engineering problems with arcing. A number of these
VLF transmitters are, nevertheless, currently in operation. The left side of Figure
1.4, adapted from Figure 2.8.11 of Watt [1967], shows a diagram of the NAA trans-
mitter in Cutler, Maine, showing the complicated mast structure needed to erect and
support the large VLF transmitter. A satellite image of NAA from Google Earth
(44.646◦N, 67.281◦W), is shown on the right side of Figure 1.4.
Below 10 kHz, the requirements of the tuning elements become sufficiently ex-
treme (in order to match the small radiation resistance) that a vertical monopole is
not practical [Barr et al., 2000], and the radiation resistance must be increased with
a longer antenna. Koons and Dazey [1983] report some success with ELF/VLF gen-
eration via an antenna with one end lofted up to 1.5 km high on balloons, achieving
100 W of radiated power at 6.6 kHz, but such a system would be difficult and costly
to operate continuously. A second possible strategy is therefore to lay a long an-
tenna along the ground, which can in practice be made much longer. Unfortunately,
the presence of the conducting ground acts to effectively set up a nearly equal but
opposite image current just below the ground, which cancels out the radiation. For
instance, Dazey and Koons [1982] report on the use of 10.6 km long power trans-
mission line at Kafjord, Norway, in order to transmit signals to the SCATHA and
GEOS spacecrafts, but managed to radiate 0.17−0.79 W at 1280 Hz. The ELF fa-
cility located in Wisconsin and Michigan utilized grounded horizontal wire operated

CHAPTER 1. INTRODUCTION 12
at 76 Hz, but even with an antenna length of 150 km, managed to radiate only ∼10
W [Jones, 1995]. An ELF antenna operating at Siple Station, Antarctica [Helliwell
and Katsufrakis, 1974], was able to effectively lift the antenna ∼2 km off the Earth
(and therefore separate the image current from the antenna current by 4 km), since
it was built on top of a thick (poorly conducting) antarctic ice sheet, but even so,
was able to achieve radiation efficiency of only a few percent [Raghuram et al., 1974]
between 1 and 10 kHz. More recently, a 6.25 km long horizontal dipole antenna has
been constructed at the South Pole for use as a VLF beacon, radiating a few hundred
watts at 19.4 kHz [Chevalier et al., 2007].
Both the vertical dipole (typically used for ∼10−30 kHz) and the horizontal dipole
(demonstrated at 76 Hz) are generally very expensive to build, cannot be moved,
operate in only a narrow frequency range, and have no directional control of the
radiated VLF waves.
A number of less conventional ELF/VLF wave generation techniques have tried
to overcome the limitations of these antenna constructions. Gould [1961] used a
conductor connected across an isthmus between two land masses in Scotland and
observed resonances due to current flow around the two landmasses. Although small
VLF fields were measured, the conductivity difference between the sea and the rocky
land was insufficient to be effective [Galejs, 1962]. Barr et al. [1993] tried making a
large loop antenna strung over the top of a mountain and through a tunnel passing
inside it, in New Zealand, but only radiated at 0.00075% efficiency at 10 kHz. Longer
VLF antennas deployed from balloons can achieve good efficiency [Field et al., 1989],
but obviously cannot be maintained and powered indefinitely.
In recent decades, considerable research effort has been directed toward the gener-
ation of a source of ELF/VLF waves embedded in the ionosphere. The idea is to turn
the lower ionosphere into a large radiating antenna by modulating the ionospheric
conductivity. In the presence of natural electric fields in the ionosphere, modulated
ionospheric conductivity will also modulate these currents. A more detailed discus-
sion of the physics is given in Chapter 2 of this dissertation. For now, it suffices to
say that the modification is achieved with intense Radio Frequency (RF) radiation di-
rected at the ionosphere in the presence of natural ionospheric currents. The auroral

CHAPTER 1. INTRODUCTION 13
Earth
Ionosphere
Geomagnetic
field lines
ELF/VLF
source
Underground
anomaly
Ionospheric
disturbance
Figure 1.5: Illumination by an ionospheric source
electrojet currents are one such possible natural current system.
Figure 1.5 shows how an ionospheric source would illuminate both the Earth-
ionosphere waveguide, and the magnetospheric region above. The Earth-ionosphere
waveguide energy can be used to remotely sense ionospheric disturbances, or un-
derground structures. Under special conditions, the ELF energy escaping into the
magnetosphere can interact with radiation belt particles, undergo amplification, and
be detected at the geomagnetic conjugate point or after reflection back to the source
region [Inan et al., 2004; Go lkowski et al., 2008]. Both illumination of the Earth-
ionosphere waveguide and magnetospheric probing with ELF wave injection are prac-
tical motivations for producing ELF/VLF waves via modulated HF heating.
1.5 Some history
Research in ionospheric modification with powerful RF waves, and more specifically,
ELF/VLF wave generation, has been conducted at a number of facilities worldwide for

CHAPTER 1. INTRODUCTION 14
the past few decades. These antenna arrays are able to focus RF energy in a narrow
beam upward, with constructive interference from an array of HF transmitters, often
in a grid pattern. In focusing the RF energy, the power density in the center of the
beam (Scenter )can be written as
Scenter =GPrad
4πr2(1.3)
where Gis the ‘gain’ or directivity of the antenna, ris the distance to the antenna,
and Prad is the total radiated power. Gis defined as the ratio of the maximum power
density at any angle from the source to the average power density over all angles from
the source, so Scenter is equivalent to the power density from an antenna that has no
directivity (G=1), but has radiated power GPrad. This quantity is known as the
‘effective radiated power’ (ERP), and measures the equivalent transmitting power
level that would be required to produce the center-of-beam power density, if that
transmitter radiated power evenly in all directions. Table 1.1 lists the ionospheric
heaters that we refer to in this dissertation, along with the location, Prad, ERP, and
RF frequencies. All but one of the facilities utilize RF radiation generally in the High
Frequency (HF, 3−30 MHz) range.
The earliest attempt (at least in the United States) to modify the ionosphere
with high power RF radio waves may have been spearheaded by Stanford University
[Potemra, 1963], but this effort apparently yielded no evidence of electron heating,
even in the Fregion, perhaps due to the use of only 40 kW of power in an 8-
element array. The first successful ionospheric modification experiments (at least in
the United States) took place in Platteville, Colorado beginning in 1968. The first
scientific results are given by [Utlaut, 1970], and the array itself is described in detail
by Carroll et al. [1974]. Nominally built for modification of the Fregion, a number
of measurable effects of the heating resulted, including spread-F, broadband echoes,
airglow, and infrared radiation [Utlaut and Cohen, 1971].
Dregion modification was also observed in the Platteville experiments, using the
technique of VLF remote sensing. When the HF heating was turned on, changes were
observed in the amplitude and phase of a VLF transmitter signal originating 64 km

CHAPTER 1. INTRODUCTION 15
Location and Year Coordinates f(MHz) Prad (kW) ERP (MW)
40.2◦N 2.75 2000 50
Platteville, Colorado (1968) 104.7◦W 10.0 2000 50
56.3◦N 4.62 130 15
Gor’kii, Russia (1973) 44.0◦E 5.75 130 22
56.3◦N 4.5 750 150
SURA, Russia (1982) 44.0◦E 9.0 750 320
67.9◦N
Monchegorsk, Russia (1976) 32.9◦E3.3 80 10
69.6◦N 2.75 1200 300
Tromsø, Norway (1980) 19.2◦E 8.0 1400 350
69.6◦N
Tromsø, Norway (1990) 19.2◦E5.42 1080 1000
18.5◦N 3.0 800 160
Islote, Puerto Rico (1980) 66.7◦W 12.0 800 320
12.0◦N
Jicamarca, Peru (1983) 76.9◦W49.9 350 5547
64.9◦N 2.85 800 70
HIPAS, Alaska (1987) 146.8◦W 4.53 800 70
62.4◦N 2.8 960 11
HAARP, Alaska (2003) 145.2◦W 9.5 960 330
62.4◦N 2.8 3600 420
HAARP, Alaska (2007) 145.2◦W 9.5 3600 3800
Table 1.1: Ionospheric heating facilities

CHAPTER 1. INTRODUCTION 16
from Platteville and detected at a receiver site 64 km from Platteville in the opposite
direction [Jones et al., 1972]. Since VLF waves are reflected in the Dregion, this
observation implied that electron temperature and collision frequency were modified
well below the Fregion. The Platteville HF heater operated until 1984, but did not
conduct experiments on ELF/VLF wave generation via modulation of the HF energy.
Much of the development of ELF/VLF wave generation experiments were con-
ducted in parallel at facilities on both sides of the East-West Cold War division. How-
ever, the first observation that modulation of this HF heating can produce ELF/VLF
waves were made by Getmantsev et al. [1974], at a facility near Gor’kii, Russia, though
the initial suggestion dates back much earlier [Ginzburg and Gurevich, 1960]. For this
reason, ELF/VLF wave generation via modulated HF heating is referred to by some
Russian authors as the ‘Getmantsev effect’.
At Gor’kii, the HF power was amplitude modulated at a variety of frequencies
between 1.2 and 7 kHz, and small signals (0.02 µV/m) at the modulation frequency
were detected. Budilin et al. [1977] confirmed that the signals originated from the
lower ionosphere, by measuring the phase (and therefore the delay) as a function of
ELF/VLF frequency. These experiments generated only weak signals in large part
due to being at mid-latitudes, where only the weak ‘Sq’ wind-driven currents are
present in the ionosphere [Belyaev et al., 1987]. However, at the suggestion of Kotik
and Trakhtengerts [1975], experiments are presented by Kapustin et al. [1977] near
Monchegorsk, Russia, in the presence of the auroral electrojet. Although the lack of
calibrated data made it impossible to directly compare the signal strengths to the
mid-latitude observation, the amplitude of the resulting ELF/VLF signal is found
to be a strong function of the electrojet location (as determined with magnetometer
measurements) with a maximum when the electrojet was overhead, indicating that
the electrojet acts to strongly enhance the wave generation by providing a natural
current source. Research continued at the Gor’kii facility, and the HF heater was
later upgraded and named ‘SURA’.
The HF array facility near Tromsø, Norway, operated by the European Incoherent
Scatter Scientific Association (EISCAT), began operation in 1980 and was almost
immediately used for ELF/VLF wave generation [Stubbe et al., 1981], where one of

CHAPTER 1. INTRODUCTION 17
three different arrays (for three different HF frequency ranges) could be utilized. One
of the arrays was subsequently upgraded in 1990 [Barr and Stubbe, 1991a].
The Islote facility, near Arecibo, Puerto Rico, operated in the absence of a dom-
inant natural current system, similar to the facility in Gor’kii. Ferraro et al. [1982]
present data showing detection of signal levels of ∼10−9A/m, between 500−5000 Hz,
with further analysis of the signals by Ferraro et al. [1984].
The Jicamarca facility is a radar facility in the Very High Frequency (30−300
MHz) band. Although the operating frequency is much higher than the other facilities,
the Jicamarca radar was able to generate ELF/VLF radiation at 2.5 kHz with pulsed
(5% duty cycle) VHF [Lunnen et al., 1984]. Despite the pulsed nature and the
higher frequency (which, as is discussed later, is less advantageous for ELF/VLF
wave generation), the Jicamarca experiments had the advantage of lying beneath
another natural current system known as the equatorial electrojet. There have been
few experiments on modulation of the equatorial electrojet, and this topic could be
a significant area of future research in ionospheric modification.
Two additional facilities were constructed in Alaska for the purpose of heating
the auroral ionosphere. The High Power Auroral Stimulation facility (HIPAS) uti-
lizes equipment and modified designs originally used at Platteville [Wong et al., 1990],
and began operation in 1987. Like the Tromsø facility, HIPAS was almost immedi-
ately utilized to demonstrate ELF/VLF wave generation [Ferraro et al., 1989], with
amplitudes as high as 0.8 pT.
The most recent facility to begin operation is the High Frequency Active Auro-
ral Research Program (HAARP). The HAARP facility was built in three stages, the
latter two being completed in 2003 and then 2007. Again demonstrating the strong
interest in ELF/VLF wave generation, Milikh et al. [1999] conduct experiments on
modulated heating even at the very early construction stage known as the ‘develop-
mental prototype’, which produced only 10 MW of ERP. Milikh et al. [1999] are also
the first to utilize two nearby HF heating facilities, with simultaneous detection of
ELF/VLF signals from HAARP and HIPAS HF heating. In this dissertation, we use
experimental data obtained with the HAARP facility. A picture of the HF antenna
array, known as the Ionospheric Research Instrument, is shown in Figure 1.6, as of

CHAPTER 1. INTRODUCTION 18
Figure 1.6: The HAARP HF heating facility
August 2005. The HAARP facility utilizes 3.6 MW of power, but some power is
reflected at the antenna array (due to imperfect impedance matching between the
near-field coupled antenna elements), so actual radiated power is slightly less. Ap-
pendix B discusses the actual transmitted powers and ERPs for a number of different
HAARP beam modes.
1.6 Review of past work
We now review some of the past efforts in the field of HF ionospheric heating, focusing
specifically on ELF/VLF generation. We consider a number of broad topics that have
been given significant research attention, both theoretically and experimentally.

CHAPTER 1. INTRODUCTION 19
1.6.1 Local geomagnetic conditions
Many of the earlier efforts in ELF/VLF wave generation concerned its connection
to geomagnetic activity, such as the auroral electrojet strength and orientation, and
ionospheric conditions above the heater. These studies essentially discuss the usage
of HF heating facilities as a diagnostic tool for the ionosphere. For instance, some
studies have compared ELF/VLF amplitudes with other instrumental diagnostics.
Rietveld et al. [1983] show that the polarization of ELF/VLF signals observed near
Tromsø were highly correlated with the direction of the auroral electrojet fields as
measured by the Scandinavian Twin Auroral Radar Experiment (STARE) radar.
Rietveld et al. [1987] tracked the measurements over a 32 hour period, comparing
also to STARE, and data from a riometer and magnetometer. Jin et al. [2009] also
compare ELF/VLF generated amplitudes with data from a series of magnetometers in
Alaska. Rietveld et al. [1986] transmit HF pulses of varying lengths and observed the
ionospheric response, thereby allowing estimation of the characteristic heating and
cooling time constants. Rietveld and Stubbe [1987] discuss the possibility of using the
pulses as a diagnostic for the horizontal electrojet field structure. Papadopoulos et al.
[2005] discuss similar results and experiments on the variation in the detected field on
the ground from HF heating of varying pulse lengths, at the HAARP facility. Rietveld
et al. [1989] present a comprehensive examination of the amplitude and ionospheric
source height as a function of ELF/VLF frequency.
At the HIPAS facility, Li and Ferraro [1990] discuss estimation of the D-region
electron density by transmitting a series of ELF/VLF signals in frequency steps,
coupled with theoretical calculations of the reflection and transmission coefficients.
Lee et al. [1990] use ELF/VLF signal amplitudes and phases to detect and characterize
geomagnetic pulsations. Milikh et al. [1994] present hypothetical calculations of the
electron temperature and density that would result from the HAARP facility. Payne
et al. [2007] use a model of ELF/VLF generation, and measurements of the vertical
electric field on the ground and around the HAARP heated region, to determine the
direction of the auroral electrojet currents and fields. Cohen et al. [2008a] also discuss
the direction of the auroral electrojet fields, using measurements of the polarization
of ELF/VLF pulses at ∼700 km distance from the HAARP facility.

CHAPTER 1. INTRODUCTION 20
1.6.2 Earth-ionosphere waveguide injection
A number of efforts have focused on characterization of the properties of the gen-
erated signals in illuminating the Earth-ionosphere waveguide. These studies have
addressed the feasibility of HF heating as a communication system for ELF/VLF
waves. Along with theoretical calculations, measurements are made at long enough
distances for propagating Earth-ionosphere waveguide modes to dominate the signal.
In a theoretical calculation, Barr and Stubbe [1984] evaluate the source power as a
function of frequency and ionospheric conditions, using the theory of reciprocity to
associate the ionospheric source with an equivalent ground-based source.
A number of experimental efforts have focused on detection of the ELF/VLF radi-
ation at increasingly long distances from the HF heating facility. Belyaev et al. [1987]
report that signals from Gor’kii were detected at ∼500 km distance, but provide no
other details. Another early effort is the report by Ferraro et al. [1982] of the possi-
ble detection of 2073 Hz signals in Pennsylvania, ∼6000 km distance from Tromsø,
although Barr et al. [1986] and Barr et al. [1991] strongly question the results. Barr
et al. [1985a] report a set of ELF/VLF detections in the Earth-ionosphere waveguide,
at distances of 200 km and 500 km from the Tromsø facility. Barr et al. [1986] made
use of the polarization of these signals, and showed that the frequency-dependence
of the polarization at these medium distance receivers is linked to ionospheric con-
ditions. Barr et al. [1991] detect signals at several frequencies ∼2000 km from the
Tromsø facility, and show a good match between the polarization of the received
signals, and predictions from a theoretical propagation model. Moore et al. [2007]
present a similar study at HAARP, with detection of 2125 Hz and 575 Hz at Midway
Atoll, ∼4400 km from HAARP, currently the most distant such detection. Signal
levels at Midway were ∼5 fT averaged over a 1-hour long integration. Using a prop-
agation model to link the received field value to a source power under a variety of
different ionospheric conditions, HF to ELF/VLF conversion efficiency of HAARP
into the Earth-ionosphere waveguide is estimated to be 0.0006% to 0.0032%. Cohen
et al. [2009, in press] present evidence of a much stronger detection at Midway Atoll,
shortly after the HAARP facility was upgraded. Signal amplitudes were in the range
15−20 fT, and were strong enough to be detected with integration times of less than a

CHAPTER 1. INTRODUCTION 21
second. This particular instance is also presented in Appendix A of this dissertation.
McCarrick et al. [1990] show that frequencies in the Schumann resonance range
(11−76 Hz) can be excited using an ‘array dephasing’ technique that spreads the
beam power over a wider area, and found that the received signal (detected 35 km
away from HIPAS) was well correlated with electrojet activity. Carroll and Ferraro
[1990] present computer simulations of ELF/VLF injection into the Earth-ionosphere
waveguide from an ionospheric source.
1.6.3 Harmonic radiation and saturation
Since the response of the ionospheric conductivity to HF heating is highly nonlinear,
the harmonic content of generated ELF/VLF signals is not the same as the harmonic
content of the HF heating modulation function. In addition, the nonlinear dependence
on the conductivity change with HF power has produced interest in a saturation
process, or a point of diminishing return beyond which increasing powers yield little
or no enhancement in ELF/VLF wave amplitudes. Alternatively, it is suggested that
an increasing HF power may eventually trigger the beginning of an electron runaway
process which increases the efficiency [Papadopoulos et al., 1990]. In response to these
questions, a number of studies have sought to quantify the relationship between HF
power levels and harmonic content of the ELF/VLF signals.
James [1985], Rowland et al. [1996], and Pashin and Lyatsky [1997] present a
theoretical model of the HF heating process, tracking the ionospheric conductivities
as a function of time, and analyzing the resulting harmonic content. Barr and Stubbe
[1993] derive the heating and cooling time constants in the ionosphere experimentally,
and find that odd and even harmonics apparently yield different time constants. Barr
et al. [1999] take this one step further, finding that the odd and even harmonics are
in fact generated at different altitudes. Oikarinen et al. [1997] present experimental
observations of the harmonic content. Barr et al. [1999] deduce the ionospheric heat-
ing and cooling time constants from the harmonic content and suggest that different
harmonics are sourced at different altitudes due to the nonlinear heating process.

CHAPTER 1. INTRODUCTION 22
Barr and Stubbe [1991a] experimentally explore the amplitude of generated ELF
and VLF waves as a function of ERP of the HF beam at Tromsø, and find no evidence
of a saturation process. On the other hand, Moore et al. [2006] explore the second
and third harmonics, and conclude that saturation is detectable with the earlier 960
kW HAARP facility. Moore [2007] present statistics indicating that detection of
saturation is a function of the HF frequency level, and the location of the receiver.
1.6.4 Magnetospheric injection
Some of the interest in ELF/VLF wave generation is based on its potential uses
for magnetospheric injection, for the purpose of controlled experiments on magneto-
spheric and radiation belt processes, such as wave-particle interactions and electron
precipitation. A large number of satellites (mostly in low earth orbit, or LEO, <1000
km altitude) have observed ELF/VLF signals generated with HF heating. However,
the nature of LEO satellite passes (i.e., rapid motion of the satellite during the brief
pass) has made it difficult to fully characterize (at least experimentally) the extent
and properties of magnetospheric injection.
James et al. [1984] observe ELF/VLF radiation from Tromsø on the ISIS-1 satel-
lite and compare to simultaneous ground measurements. James et al. [1990] subse-
quently observe signals with the DE-1 spacecraft, and discuss the harmonic content
of the received signal, spectral broadening and propagation delays. Lefeuvre et al.
[1985] observe ELF/VLF signals on the Aureol-3 satellite, from the Tromsø facility.
Kimura et al. [1991] and Kimura et al. [1994] observe signals from HIPAS and Tromsø,
respectively, on the Akebono satellite. Yagitani et al. [1994] construct a theoretical
model of the radiation to LEO altitudes, with Nagano et al. [1994] then presenting
an experiment at HIPAS with accompanying theoretical calculations.
A number of more recent detections have focused on the HAARP ELF/VLF signal
radiated into space. The particular interest in HAARP arises from its location, which
is just inside the plasmapause much of the time, therefore making it a good candidate
for magnetospheric injection that may lead to an amplification process, in particular,
after propagation in a ‘duct’ guiding structure. Platino et al. [2004] observed signals at

CHAPTER 1. INTRODUCTION 23
27−29 Mm altitude, on the CLUSTER spacecraft. Platino et al. [2006] subsequently
observed signals at LEO altitudes on the DEMETER spacecraft. Further analysis
on DEMETER observations are presented by Piddyachiy et al. [2008], regarding a
narrow column of radiation (predicted by Lehtinen and Inan [2008]) extending into the
magnetosphere. Finally, magnetosperic injection with HAARP has yielded the first
examples of detectable wave-particle interactions initiated by ELF/VLF signals from
modulated HF heating, first reported by Inan et al. [2004], with additional analysis by
Go lkowski et al. [2008]. Go lkowski et al. [2009] also report cross modulation between
the signals returning to the HAARP region after two magnetospheric hops (and ∼8
seconds delay) and the modulated HF-heated ionosphere, strong evidence that the
magnetospherically propagating signals are injected very close to the HAARP facility.
1.6.5 Mobile heated region
Rietveld et al. [1984] introduce beam steering to the Tromsø array, by varying the
phase of the HF waveform along the rows of the array. This capability enabled
direction of the beam in the north-south direction, up to 37◦from vertical in each
direction, so that the heated region of the ionosphere could effectively be moved
horizontally. Variations in the ELF/VLF amplitude at a nearby receiver as the beam
is directed are observed to be to connected to changes in the auroral electrojet field
strengths, as separately measured by the STARE radar [Rietveld et al., 1984].
Barr et al. [1985b] observe diffraction or scattering of VLF waves off of the HF-
heated portion of the ionosphere, detected at more distant transmitters. Using the
beam steering capability to move the heated region and therefore change the transmit-
ter to heated region to receiver angle, the scattering is found to be almost exclusively
in the forward direction, meaning it could be observed only on receivers positioned
such that the transmitter to receiver path crosses the heated region.
Barr et al. [1987] measure the ELF/VLF signal at a receiver ∼500 km to the
South of Tromsø, as a function of the beam steering angle (also in the north-south
direction), and showed that the phase of the data received could be largely attributed
to Earth-ionosphere waveguide properties. Barr et al. [1988] subsequently presented

CHAPTER 1. INTRODUCTION 24
the amplitude data, and found that Earth-ionosphere waveguide propagation was not
sufficient to explain the results, but that the signal was also affected by the differences
in phase between different portions of the heated region, owing to the fact that the
HF energy took a finite time to reach the ionosphere, and this time delay varied across
the width of the HF beam.
1.6.6 Beam painting
In a significant effort to raise the efficiency of HF to ELF/VLF conversion, Papadopou-
los et al. [1989] and Papadopoulos et al. [1990] introduce a technique which subse-
quently became known as ‘beam painting’. The basic idea of beam painting is that
‘matching the operation of he HF heater to the nonlinear response of the ionospheric
plasma’ [Papadopoulos et al., 1989] can be achieved utilizing motion of a very high
ERP beam at rapid rate. The specifics of beam painting are described in Chapter
3, but it suffices here to say that the technique involves effectively increasing the
size of the ionospheric antenna. Barr and Stubbe [1991b] and Barr et al. [1999] both
perform tests with the Tromsø facility and find that the ERP of the HF beam (the
highest in the world at that time) is not sufficiently high for beam painting to yield
any practical benefit. It has therefore fallen to the upgraded HAARP facility, with
its unprecedented ERP and rapid beam steering ability, to address this possibility
more directly.
1.6.7 Alternative methods
In a continuing effort to increase the generated amplitudes of ELF/VLF waves, other
generation methods have been explored, particularly as an alternative to simply uti-
lizing amplitude modulation. Both Villase˜nor et al. [1996] and Barr and Stubbe [1997]
discuss a ‘dual frequency’ or ‘CW’ mode (respectively named) in which the HF array
is split into two halves, and driven with HF frequencies differing by the ELF/VLF
frequency to be generated, essentially a beat-frequency method. Both studies con-
clude that amplitude modulation generates stronger ELF/VLF signals than the beat-
frequency technique. However, Barr and Stubbe [1997] suggested, based on theoretical

CHAPTER 1. INTRODUCTION 25
calculations, that the CW technique would become substantially stronger for frequen-
cies above ∼3 kHz, in the direction from the array where the lower of the two HF
frequencies drives the array. Kuo et al. [1998] present further theoretical calculations
comparing beat-frequency with amplitude modulation.
Milikh and Papadopoulos [2007] discuss a method of increasing efficiency in which
the ionosphere is first heated continuously for several minutes, in order to build up a
higher electron density in the D-region and sharpen the gradient of the ionospheric
electron density profile, by lowering the electron-neutral attachment through long-
timescale heating. The higher and sharper electron densities could then be used in
ensuing minutes to generate ELF/VLF with better efficiency.
1.6.8 Ionospheric array
Along with a search for increased HF to ELF/VLF conversion efficiency, or higher
generated amplitudes, some effort has been made to generate an array of ionospheric
sources using HF heating. Such an array would have the advantage of providing
directionality to injected ELF/VLF signals, since ordinary VLF transmitters (and
amplitude modulated HF heating) are unable to provide any directional control. A
straightforward way to provide directional control would be to build several VLF
transmitters nearby, and operate them in a phased-array configuration, but given
the expense and difficulty of constructing and operating one VLF transmitters, the
resources required to operate several would be prohibitive.
The most prominent experimental example of an ELF/VLF array is that of Barr
et al. [1987], who discuss a novel experiment in which the HF beam is alternated
between two locations in the ionosphere, one to the north, and one to the south,
at rates up to 5 kHz. This operation creates two heated regions in the ionosphere,
displaced by an amount that could be controlled, undergoing ON-OFF heating with
modulation functions 180◦out of phase. By varying the separation between the two
regions, and measuring the signal at a receiver ∼500 km from Tromsø, it is found that
the two regions act as a two-element ELF/VLF array. A signature of constructive and
destructive interference is detected, since the maximum signal at the receiver occurred

CHAPTER 1. INTRODUCTION 26
when the two heated regions were separated by one half wavelength, representing the
180◦phase shift between the two regions. Villase˜nor et al. [1996] describe a similar
technique performed at the HIPAS facility, referred to therein as ‘demodulation mode’.
Some theoretical work has also occurred on the topic of an ionospheric array.
Werner and Ferraro [1987] derived an array factor specifically for ionospheric sources.
Papadopoulos et al. [1994] discuss the effect of Cerenkov radiation, when a source of
ELF/VLF radiation is moving close to the speed of light, with a particular emphasis
on injection of ELF/VLF energy into the magnetosphere. Borisov et al. [1996] extend
this discussion to illumination of the Earth-ionosphere waveguide.
1.7 Scientific contributions
The following advances to the field of ELF/VLF wave generation are developed and
reported in this dissertation:
•A novel method is introduced of ELF/VLF wave generation via frequency-
matched steering of a continuous HF beam (herein referred to as ‘geometric
modulation’), an alternative to amplitude modulation in which the beam power
is left on, but the beam is steered in a geometric pattern at the desired ELF/VLF
generation frequency. Using amplitude modulation as a baseline for comparison,
it is demonstrated that ∼7-11 dB higher ELF/VLF amplitudes, and ∼11-15 dB
directional dependence result from geometric modulation, compared to ampli-
tude modulated vertical HF heating.
•A previously proposed technique known as ’beam painting’ is successfully im-
plemented for the first time, in which rapid (100 kHz) beam motion effectively
increases the area of the radiating region of the ionosphere. Beam painting is
directly compared with geometric modulation, as well as amplitude modulation.
•The HF heating and electron cooling processes are theoretically modeled in three
dimensions, yielding the predicted spatial distribution of the ionospheric current
sources generated. These results feed into a second model simulating ELF/VLF
propagation in the Earth-ionosphere waveguide (and into the magnetosphere),

CHAPTER 1. INTRODUCTION 27
to determine the radiated patterns up to 1000 km along the Earth, and up to
700 km into the ionosphere.
•Using a combination of experimental and theoretical results, the results achieved
with geometric modulation are interpreted in terms of a controllable ELF/VLF
multi-element phased array, which allows controllable directional launching of
ELF/VLF energy in the Earth/ionosphere waveguide.
1.8 Approach
We have now introduced the environment that dominates the problem we consider,
motivated the need for ELF/VLF wave generation, and reviewed past efforts in the
field. The remainder of this dissertation is as follows: In Chapter 2, we illuminate the
physics of the problem by describing a theoretical model, including HF ionospheric
modification resulting in ELF/VLF generation, whose output drives a full-wave model
of ELF/VLF wave propagation. In Chapter 3, we apply the experimental techniques
to a set of modulation schemes which involve motion of the HF beam during the
ELF/VLF period. In Chapter 4, we then analyze the theoretical modeling results,
compare to experiment, and thereby predict features of the modulation techniques
which would be measurable with additional receivers. In Chapter 5, we utilize a com-
bination of theory and experiment to illuminate the degree to which four particular
physical mechanisms impact our experimental and theoretical approach. Finally, in
Chapter 6 we summarize and suggest additional future efforts.

Chapter 2
ELF/VLF Generation and
Propagation Physics
In this chapter, we introduce the physical phenomena ing propagation of electro-
magnetic waves in a magnetized plasma, and describe a theoretical model to apply
these principles to our problem of High Frequency (HF, 3−30 MHz) heating of the
ionosphere, and ELF/VLF wave generation and propagation.
2.1 Waves in plasmas
The Earth’s ionosphere and magnetosphere are both prominent examples of the
plasma state of matter. Plasmas are sometimes referred to as the fourth state of
matter, after solid, liquid, and then gas [Bittencourt, 2003, pg.1]. In a plasma, a
large enough number of molecules have been split apart into positive and negative
charged particles, like electrons, protons, and ions, with the net charge remaining
zero. Waves propagating in a plasma have a number of unique characteristics as
compared to propagation in simpler media, like free space or a dielectric. The effect
of an externally applied magnetic field (such as that of the Earth’s geomagnetic field)
alters the physics additionally, most notably by introducing anisotropy to the prob-
lem. Collisions between particles have a further complicating impact. We begin by
introducing the key concepts of plasmas that are needed to understand the problem.
28

CHAPTER 2. ELF/VLF GENERATION AND PROPAGATION PHYSICS 29
Note that for the remainder of this dissertation, we use the term ‘electrons’ to
refer exclusively to the free ionized electrons, as opposed to electrons which orbit
around molecules. Although by definition, a plasma is quasi-neutral, consisting of
equal amounts of positive and negative charge, it is the electrons that are chiefly
responsible for the physical processes we describe here, whereas the positive ions,
which are many orders of magnitude heavier (and thus harder to accelerate with
electromagnetic fields), play a negligible role at the ELF/VLF and HF frequencies
considered here.
Many treatments of plasma physics tend to give very mathematical descriptions of
the various phenomena involved in wave propagation in a plasma. This fact is largely
due to the highly complex nature of this subject, in which nearly all traditional
ways of simplifying electromagnetics problems (homogeneity, isotropy, linearity, non-
dispersiveness) are violated. On the other hand, while the mathematical results
(adequately treated in other works) may be too highly nuanced for basic intuition, the
basic physical processes which interplay to underlie all the physics of wave propagation
in a plasma are well within reason. It seems somewhat of a lost art to recapture the
physical intuition in plasma physics, so we focus here on illuminating the various
physical components which contribute to wave propagation.
2.1.1 Plasma properties
Consider first a plasma with no externally-applied magnetic field, and a negligible
number of collisions. The positive and negative particles can block electromagnetic
fields from having an impact any more than a short distance away, by rearranging
slightly to cancel out the fields, a phenomenon known as Debye shielding. Because
electrons are so much lighter than ions, they are able to rearrange much more quickly,
and thus in a typical plasma, the by-far dominant Debye shielding arises from elec-
trons. The denser are the electrons, the quicker is the Debye shielding process, and
this characteristic response time gives rise to the concept of the plasma frequency
ωpe =qrne
me0
(2.1)

CHAPTER 2. ELF/VLF GENERATION AND PROPAGATION PHYSICS 30
Where Neis the density of electrons, meis the mass of an electron, and qis the
charge of an electron. An example of the derivation of the plasma frequency is done
by Budden [1985, pg. 39]. The quantity ωpe can also be thought of as the natural
frequency of oscillation of the electrons.
A wave propagating in such a plasma is thus unable to propagate unless its elec-
tromagnetic fields change faster than the plasma can shield and cancel the fields, that
is to say, an electromagnetic wave is unable to propagate unless its frequency is above
ωpe.
Even the relatively small electron densities in the Dregion are sufficiently high
for Debye shielding to take place. For instance, the plasma frequency is 3 kHz for an
electron density of ∼1.1 ×105m−3, while electron densities in the Dregion (above
65 km) are substantially higher, as shown in Figure 1.1. So the plasma frequency is
well above the wave frequency at all ionospheric altitudes, for ELF/VLF frequencies.
2.1.2 Magnetic field and the whistler wave
Based on the fact that the plasma frequency exceeds the ELF/VLF wave frequency at
very low altitudes, it would seem that ELF/VLF waves should be blocked well before
they reach the Dregion. However, the effect of the magnetic field and collisions
prevent this from happening. Let us consider the effect of an externally applied
magnetic field to the plasma, since the Earth’s geomagnetic field appears across the
ionosphere and magnetosphere, but at this point, we assume there are still no particle
collisions.
Consider that in the presence of an externally applied magnetic field ~
B0(such
as the magnetic field of the Earth), a charged particle will experience the so-called
Lorentz force
~
F=q~v ×~
B0(2.2)
where meis the electron mass, ~v is the velocity of the particle, and B0is the applied
magnetic field. For a homogeneous magnetic field, the Lorentz force will cause the
particle to gyrate around the magnetic field at a specific frequency, known as the

CHAPTER 2. ELF/VLF GENERATION AND PROPAGATION PHYSICS 31
gyrofrequency, in response to an applied electric field with a component orthogonal
to the magnetic field. The gyrofrequency is given by
ωce =qB0
me
(2.3)
Thus, horizontal linear motion is allowed only along the magnetic field line, since
the Lorentz Force in that direction is zero. Motion in the plane perpendicular to
~
Bis constrained to follow circular motion. All the electrons present in a plasma
are therefore constrained to orbit the magnetic field line at ωce, with possibly some
additional linear motion along the magnetic field line.
For a right hand circularly polarized wave at frequency below ωce, the electron
response to the wave involves motion around the magnetic field line at the wave
frequency, and this motion then re-radiates electromagnetic energy that allows the
wave to propagate. In essence, Debye shielding (which would otherwise short-circuit
the wave electric field) is overcome because the electron response to the wave simply
recontributes the energy back to the wave via radiation. A nice discussion of this re-
radiation process is given by Ratcliffe [1959, ch.3]. This special mode of propagation
below the plasma frequency due to the applied magnetic field is known as the ‘whistler
mode’. The whistler mode energy propagates at a slower velocity than the speed of
light, particularly at frequencies well below ωce.
2.1.3 Anisotropy
A second effect of the magnetic field is to introduce anisotropy to the ionosphere.
For instance, consider that an electric field, ~
E, applied to the plasma causes electrons
to respond and generate a current, ~
J. In isotropic media, Ohm’s law tells us that
~
J=σ~
E, where σ, the conductivity, is a simple scalar. In a magnetized plasma, if
~
Eis applied parallel to the magnetic field, electrons are accelerated strictly in that
direction, since the Lorentz force equation (2.2) has no component along ~
B0. In
that sense, the magnetic field may as well not exist, and the scalar Ohm’s law is
obeyed, as defined by the so-called parallel conductivity. On the other hand, for ~
E
applied perpendicular to the magnetic field, electrons are not able to travel strictly

CHAPTER 2. ELF/VLF GENERATION AND PROPAGATION PHYSICS 32
along ~
Edue to the Lorentz force, and are forced also in the direction of ~
E×~
B0.
This forcing gives rise to the so-called Pedersen and Hall conductivities, referring to
the ionospheric currents generated parallel to and perpendicular to ~
E(respectively),
when ~
Eis perpendicular to ~
B0.
For this reason, we must write the conductivity as a tensor quantity (σ), so that
from Ohm’s law we calculate the currents generated as
~
J=σ~
E(2.4)
It is convenient to utilize a coordinate system in which the z-axis is along ~
B0, the
zaxis is perpendicular to both ~
Eand ~
B0, and the horizontal axis defined so as to set
up a right hand coordinate system (by×bz=bx). This coordinate system is shown in
Figure 2.1. We therefore have
σ=



σP−σH0
σHσP0
0 0 σk



(2.5)
where σP,σH, and σkare the Pedersen, Hall, and parallel conductivities, respectively.
The expressions for these conductivities are discussed later in this chapter.
2.1.4 Collisions
In the D-region of the ionosphere, the atmosphere is still thick enough that electrons
frequently collide with neutrals. (In this context, ‘frequently’ means that there is a
nonnegligible chance that an electron undergoes a collision during one cycle of the
wave period.) Since there are many more neutral particles than ionized particles,
collisions between two ionized particles are comparatively rare. The dominant form
of collision, between electrons and neutral molecules, is much like a ping pong ball
hitting a bowling ball, since the electron is extremely light compared to any neutral
molecule. In each collision, an electron is scattered in some direction, and so after a
few collisions, the electron carries no memory of what direction it moved earlier.

CHAPTER 2. ELF/VLF GENERATION AND PROPAGATION PHYSICS 33
Electric field
Pedersen current
Parallel current
Geomagnetic field
Hall current
B0
Electron
motion
Figure 2.1: Coordinate system for ionospheric conductivity

CHAPTER 2. ELF/VLF GENERATION AND PROPAGATION PHYSICS 34
The rapid electron-neutral collisions in the Dregion produce a mechanism by
which a propagating wave can lose energy. A nice discussion of the microscopic
reason for collisional damping of waves is given by Ratcliffe [1959, ch.5], and we
focus here on a detailed qualitative description, since the details of the mathematics
is adequately covered elsewhere. The basic idea is that the frequent collisions and
associated redirecting of the each electron’s velocity cause the orderly energy in the
propagating wave to be converted to random heat energy, first in the electrons, and
from there to the neutral molecules. (However, being composed of molecules that are
so much more massive than electrons, the neutral atmosphere exhibits essentially no
temperature rise as a result of this energy deposition, so in this context it is like an
infinite energy sink).
Let us consider the case where an electromagnetic wave is at a frequency above
the plasma frequency (such as for HF waves in the Dregion), so that Debye shielding
does not adequately take place, and the wave is propagating. At any given time,
electrons are being accelerated/decelerated by the electromagnetic field associated
with the propagating wave, so that some electrons are gaining energy, and some are
losing. The key, however, is that this combination results in a net gain of electron
energy. As a simple example, consider two electrons traveling in opposite directions,
with a speed v, in the presence of parallel electric field that changes the speed of
each by 0.1vin some given time span. One of the electrons is accelerated, the other
decelerated, but the total kinetic energy (1
2mv2) of two electrons with speeds of 1.1v
and 0.9vis higher than the total kinetic energy of two electrons both at speed v.
If there were no collisions, none of that would impact electron temperature, be-
cause whatever speed is gained/lost by an electron in the first half of the wave period
is promptly reversed in the second half of the wave period (since the electric field is
reversed), so that the electrons neither gain nor lose heat in the long term (i.e., this
back and forth would constitute ordered energy, not random heat motion). In the
presence of collisions, however, some number of electrons are accelerated/decelerated
during part of the wave period, but then collide with a neutral molecule before the
end of the wave period. The collisions scatter the added energy in random directions,
thereby converting that energy it into heat.

CHAPTER 2. ELF/VLF GENERATION AND PROPAGATION PHYSICS 35
Furthermore, the collision itself between an electron and a neutral molecule has a
tendency to transfer energy from the more energetic of the two to the less energetic.
As the electron temperature (or average energy) rises above the temperature of the
neutral molecules, there is therefore a tendency for the electrons to lose that gained
energy to the neutral atmosphere. A nice physical and mathematical discussion of
this is given by Huxley and Crompton [1962, edited by Bates, D. R.].
In this manner, a propagating electromagnetic wave can be damped as it crosses
a collisional plasma. The mathematics of this damping process are encompassed in
the so-called Appleton-Hartree equation discussed below, and this ability for HF wave
energy to be deposited onto free electrons via collisions as it crosses through this region
is in fact the key field-matter interaction that drives our ability to modify the D-
region with powerful HF waves. Unlike electron density, which in the Dregion varies
heavily, the collision frequency is essentially constant in time (for a given electron
temperature), since it depends on the neutral densities, which themselves remain
constant.
2.1.5 The D-region
The comparative effects of the plasma frequency, geomagnetic field, and collisions, are
often evaluated with three parameters which normalize the characteristic frequencies
to the wave frequency, ω. These three parameters are
X=ω2
pe
ω2(2.6)
Y=ωce
ω(2.7)
Z=νeff
ω(2.8)
where νeff is an effective electron-neutral collision frequency. Xnormalizes the wave
frequency to the plasma frequency, Ynormalizes the wave frequency to the gyrofre-
quency, and Znormalizes the wave frequency to collision frequency, so the three
parameters tell us the impacts of Debye shielding, the magnetic field gyromotion,

CHAPTER 2. ELF/VLF GENERATION AND PROPAGATION PHYSICS 36
and collisions, respectively, on the wave dynamics. For instance, Y'0 indicates that
the wave frequency is much higher than the gyrofrequency, so such a plasma can
be treated as nonmagnetized, meaning that removing the magnetic field would have
little or no impact on the dynamics. Z'0 implies that collisions are too rare to have
an impact on wave dynamics, therefore the plasma can be considered collisionless.
Figure 2.2 shows the three ionospheric parameters for the summer daytime and
winter nighttime ionosphere shown in Figure 1.1. The plasma frequency equals the
wave frequency (i.e. X=1) somewhere below 50 km in the daytime, and ∼73 km
at nighttime. In the absence of the geomagnetic field and collisions, a 3 kHz wave
would be reflected at those altitudes. However, the high rate of collisions prevent
the electrons from rearranging in an orderly matter, and this result then prevents
the Debye shielding from occurring if Z > X. The reflection of the 3 kHz waves
can thus be roughly considered to occur roughly at the point where collisions can
no longer counteract the effects of Debye shielding, i.e. X=Z. In the daytime
ionosphere shown here, and at 3 kHz, this condition occurs at ∼61 km, and for the
nighttime ionosphere, ∼80 km. Experimental results for VLF transmitter frequencies
around 20−30 kHz indicate that the reflection heights are more like 70 km and 85 km,
for daytime and nighttime mid-latitude ionospheres, respectively [Thomson, 1993;
Thomson et al., 2007].
The calculation of the refractive index, n, in a magnetized collisional plasma
requires use of the full Appleton-Hartree equation, which can be written in terms of
X,Y, and Z. The refractive index is an important quantity, since the real part drives
the propagation of the waves through the medium, whereas the imaginary part (or
the absorptive part) determines the absorption via collisions (a negative imaginary
part indicates absorption). This important equation is:
n2= 1 −X
1−jZ −Y2sin2θ
2(1−X−jZ )±YqY4sin4θ
4(1−X−jZ )2+ cos2θ
(2.9)
where θis the angle between the wave k-vector and the geomagnetic field. A derivation
of the Appleton-Hartree equation is found in Budden [1985, ch.4]. The aforementioned
phenomenon where an ELF/VLF wave refects generally near the altitude where X=Z

CHAPTER 2. ELF/VLF GENERATION AND PROPAGATION PHYSICS 37
−4 −2 0 2 4
40
50
60
70
80
90
100
Plasma Parameters
f = 3 kHz
log10(X, Y, or Z)
Altitude (km)
XNight
XDay
Y
Z
−6 −4 −2 0
Refractive Index
f = 3 MHz
log10(n)
+Re
−Im
5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10
−8
−6
−4
−2
Absorption coefficient variation with electron density
log10(Im(n))
f = 3 MHz
log10(Ne) (m−3)
60 km
70 km
80 km
90 km
Figure 2.2: Ionospheric plasma parameters

CHAPTER 2. ELF/VLF GENERATION AND PROPAGATION PHYSICS 38
can be seen mathematically, as well, since for X > 1 and ZX, the second term
on the right side has a negligible effect. Budden [1961b, ch.16] gives a mathematical
description of this reflection process in terms of a sharpening of the gradient of the
refractive index with altitude near where X=Z.
The top right panel of Figure 2.2 shows the real and the negative of the imaginary
part of the refractive index for a 3 MHz wave, for both the daytime (orange) and
nighttime (blue) ionospheres. The real part of the refractive index remains close to
1 until ∼85 km. Above 85 km, the real part of the daytime refractive index rapidly
shrinks, and the refractive index is dominated by the imaginary part. At night,
though, electron densities are sufficiently low that the refractive index is dominated
by the real part, which remains very close to 1.
The refractive index in the HF realm also demonstrates one important property
which we refer to later in this chapter. As stated, the collision frequency does not
change as a result of the highly variable electron densities. We can thus plot the
absorptive part of nas a function of electron density, for several different altitudes, as
is shown in the bottom panel of Figure 2.2. The important property to take note of
is that over a wide range of electron densities and altitudes, the collisional absorption
is essentially proportional to the electron density.
2.2 HF heating theory
We now describe the theoretical formulation of the HF heating model utilized in this
dissertation. We are concerned with the generation of ELF/VLF waves based on
Equation 2.4, where σhas a quasi-static component (driven by ionospheric ambient
conditions), and a component at the ELF/VLF frequency, driven by ionospheric
modification. Since ~
Eis the effectively constant electric field of the auroral electrojet,
our goal is to determine the component of σwhich changes at ELF/VLF frequencies
as a result of HF heating. So we seek to simulate and characterize a phasor value of
σat the frequency of interest, which may vary spatially across the three dimensional
volume of the ionosphere affected by HF heaitng.

CHAPTER 2. ELF/VLF GENERATION AND PROPAGATION PHYSICS 39
2.2.1 Electron temperature
Our first goal is to track the electron energy distribution in the ionosphere as it
responds to the heating (and as it subsequently recovers from lack thereof). In the
absence of an external driving force, an ambient collisional plasma will tend toward
a distribution of electron velocities known as the Maxwell-Boltzmann distribution
Bittencourt [2003, pg.165],
fe=Neme
2πkBTe3
2
e−mev2
e
2kBTe(2.10)
where Neis the number density of electrons, veis the electron velocity, kBis Boltz-
mann’s constant, and Teis the electron temperature. By integrating the distribution
over ve, the average energy turns out to be 3
2kBTe, proportional to temperature.
The problem of tracking the evolution of this distribution in response to an exter-
nal driving force may in general be quite complicated, since different electron energy
levels absorb the wave energy, and then subsequently recover, at different rates. As
a result, the heating and cooling dynamics must be separately tracked at all electron
energies. For instance, in association with very intense heating of the ionosphere
(such as heating from the electromagnetic pulse of lightning [Taranenko et al., 1993])
the electron energies do not in general remain Maxwellian. A complete formulation
therefore must track the more complete electron energy distribution as it evolves in
time.
However, a number of past studies [Stubbe and Kopka, 1977; James, 1985; Moore,
2007] assumed that even the most powerful HF waves considered in ionospheric heat-
ing experiments are not powerful enough to significantly perturb the basic Maxwellian
shape of the electron energy distribution. Although the electron temperature Temay
drastically change, the electron energy distribution remains roughly ‘Maxwellian’ [Bit-
tencourt, 2003, pg.165]. This assumption greatly simplifies our task, since we can
track the entire electron energy distribution with just a single parameter (Te), which
gives us exceptional computational efficiency. We therefore apply this assumption
for the remainder of this dissertation, and no longer refer to electron energies, but
represent heating only in terms of the electron temperature.

CHAPTER 2. ELF/VLF GENERATION AND PROPAGATION PHYSICS 40
The temporal evolution of the electron temperature requires the tracking the HF
energy absorbed by the electrons as well as the energy lost to other particles (both
occurring via collisions). The effects two balance out to a rate of change of electron
energy 3
2NekB(dTe/dt), in an equation (adapted from James [1985]) that takes the
form
3
2NekB
dTe
dt = 2kχS −Le(2.11)
where kis the wavenumber of the HF wave (2π/λ), −χis the imaginary part of the
refractive index n(calculated from the aforementioned Appleton-Hartree equation),
and Sis the power density of the HF wave. In this equation, the left hand term
shows the time-varying electron energy, the first term on the right is the absorbed
HF power, and the second term (Le) is the electron loss rate.
The electron loss term, Le, is a sum of losses from elastic collisions, rotational
excitation, and vibrational excitation, for both molecular nitrogen (N2) and oxygen
(O2). These equations are compiled by Rodriguez [1994, pg.175-178], with the elastic
loss rates given by Banks [1966], the rotational excitation loss rates given by Mentzoni
and Row [1963] and Dalgarno et al. [1968], and the vibrational excitation loss rates
given by Stubbe and Varnum [1972]. These equations are as follows:
LN2
elast = 1.89 ×10−44NeNN2(1 −1.21 ×10−4Te)(Te−T0) (2.12)
LO2
elast = 1.29 ×10−43NeNO2(1 −3.6×10−2pTe)(Te−T0) (2.13)
LN2
rot = 4.65 ×10−39NeNN2
Te−T0
√Te
(2.14)
LO2
rot = 1.11 ×10−38NeNO2
Te−T0
√Te
(2.15)

CHAPTER 2. ELF/VLF GENERATION AND PROPAGATION PHYSICS 41
LN2
vib = 4.79 ×10−37NeNN2efN2(Te−2000)/(2000Te)[1 −e−g(Te−T0)/(TeT0)] (2.16)
LO2
vib = 8.32 ×10−38NeNO2efO2(Te−700)/(700Te)[1 −e−2700(Te−T0)/(TeT0)] (2.17)
where T0is the ambient temperature, NN2and NO2are the number densities of
molecular nitrogen and oxygen, respectively, and fN2,fO2and gare dimensionless
quantities given by
fN2= 1.06 ×104+ 7.51 ×103tanh[0.0011(Te−1800)] (2.18)
fO2= 3300 −839 sin[0.000191(Te−2700)] (2.19)
g= 3300 + 1.233(Te−1000) −2.056 ×10−4(Te−1000)(Te−4000) (2.20)
2.2.2 Modified ionosphere
Although we now have the ability to track the changing electron temperature, our
actual objective is to deduce the modified electrical properties of the ionosphere, and
the induced modulated currents in the presence of the auroral electrojet system, so the
electron temperature must be related to ionospheric conductivity. We first calculate
the modified collision frequency as a result of the changing electron temperature (as
in Rodriguez [1994, pg.176]) as a sum of the average collision rates with O2and N2
νN2
eff =5
3νN2
av =5
3·2.33 ×10−17NN2(1 −1.25 ×10−4)Te)Te(2.21)
νO2
eff =5
3νO2
av =5
3·1.82 ×10−16NN2(1 −3.60 ×10−2)pTe)pTe(2.22)
For the purpose of calculating the ionospheric conductivity, the average collision rate
νav, is multiplied by an additional factor of 5
3, because Equation 2.9 assumes a velocity-
dependent collision frequency. The factor 5
3, derived by Sen and Wyller [1960], yields
an effective collision frequency, νeff, which, for quasi-transverse propagation, may be

CHAPTER 2. ELF/VLF GENERATION AND PROPAGATION PHYSICS 42
−15
0
15
95 km
Conductivity Modification (∆σ, dB)
−15
0
15
90 km
−15
0
15
85 km
−15
0
15
80 km
−15
0
15
75 km
−15
0
15
70 km
500 1000 1500 2000 2500
−15
0
15
65 km
Temperature(K)
−10 −8 −6 −4
65
70
75
80
85
90
95
log10(σ)
Altitude (km)
Ambient Conductivity
Hall
Pedersen
Parallel
Figure 2.3: Variations of ionospheric conductivities as a function of temperature
used in Equation 2.9 when |ω±ωce|  νav, as is the case for altitudes above 65 km
or so.
The ionospheric conductivity components as in Equation 2.5 are derived in Tomko
[1981, pg. 137] from kinetic calculations, and are given as a function of the driving
frequency. However, since the auroral electrojet is treated here as constant, we can
rewrite those expressions as

CHAPTER 2. ELF/VLF GENERATION AND PROPAGATION PHYSICS 43
σP=4πq2
3meZνavv3
e
ν2
av +ω2
ce
∂fe
∂ve
dve(2.23)
σH=4πq2
3meZωcev3
e
ν2
av +ω2
ce
∂fe
∂ve
dve(2.24)
σk=4πq2
3meZv3
e
νav
∂fe
∂ve
dve(2.25)
where feis the electron distribution function (the number density of electrons as a
function of energy).
Figure 2.3 shows the relationship between temperature and ionospheric conduc-
tivity. The left panel shows the ambient ionospheric conductivities, based on the
nighttime ionosphere shown in Figure 2.2. Due to the high conductivity of a magne-
tized plasma along the magnetic field, σkis the highest conductivity at all altitudes,
especially at higher altitudes where collisions are very low. At an altitude of ∼70 km,
σH=σP, and above this altitude, σHincreasingly dominates over σP.
The right hand panels of Figure 2.3 show the relationship between increasing
temperature and the three ionospheric conductivities (the dB values are in comparison
to Te=200 K), at several different altitudes. At all altitudes shown, σHand σkdecrease
with electron heating, by as much as 30 dB at 65 km and 3000 K. This decrease is
due to the heated electrons colliding much more often and therefore having a lower
mobility. The Hall conductivity, however, changes very little with temperature at the
highest altitudes.
The changes to σPare quite different in character. Below ∼80 km, σPis decreased
by as much as 15 dB, but above 80 km, σPis enhanced as a result of electron heat-
ing. The fundamental reason is that the higher collisions impede the electrons from
gyrotating around the magnetic field line, so the Pedersen conductivity, which has a
component in the direction of the electric field, is boosted (at the expense of less Hall
conductivity). This behavior is one of the reasons that modulation of σPis believed
to be less important in the context of ELF/VLF generation, since the regions above
and below 80 km have opposite reactions to electron heating in terms of σP, which
means the generation effects may counteract and tend to cancel one another.

CHAPTER 2. ELF/VLF GENERATION AND PROPAGATION PHYSICS 44
2.2.3 HF wave propagation
One final complication arises from the fact that HF waves propagating in the iono-
sphere do not in general travel in a straight line at the speed of light. Moore [2007,
pp. 22-26] discusses the main principles, which we briefly review here. There are
two main sources of bending of the HF wave. Assume that the HF wave is incident
on a sharp boundary from a medium with refractive index n1into a medium with
refractive index n2. Assume the wave normal is incident at an angle θ1with respect
to the boundary normal, and is refracted into the second medium at an angle θ2. The
first source of wave bending is from Snell’s law, which causes the HF ray to bend
according to
Re(n1) sin(θ1) = Re(n2) sin(θ2) (2.26)
However, the anisotropy of the ionosphere also causes the HF energy to travel in
a different direction from the wave normal, and this angular separation is governed
by
tan(∆Θ) = 1
n
∂n
∂Θ(2.27)
where Θ is the angle between the wave normal and the Earth’s magnetic field line,
and ∆Θ is the deflection of that angle away from the magnetic field. For HF waves
in the D-region, the ionosphere can be divided into a series of horizontal layers, and
the propagation of the HF energy through each boundary is a good approximation of
the propagation through the more smoothly varying ionosphere, a technique known
as ray tracing [Budden, 1985, ch.14]. At each boundary, the HF energy is refracted
according to the above two laws. Finally, we must also keep track of the group velocity
(vg) of the HF energy, which is derived by [Budden, 1985, pg.130] and given as
vg=c∂ω
∂(ωn)
1
cos(∆Θ) (2.28)
In practice, the bending and slowing of HF energy as it encounters an increasingly
dense ionosphere has a rather small effect on our theoretical results, since most of the

CHAPTER 2. ELF/VLF GENERATION AND PROPAGATION PHYSICS 45
bending and slowing of the HF wave occurs above the altitude where most of the HF
energy is absorbed. However, it is worth noting that the ray tracing properties do not
change appreciably during the HF heating process, since the real part of nis largely
unchanged by HF heating. Hence, tracking the ray tracing properties requires just
one set of calculations for a given ionosphere, and does not have to be recalculated
at each time step. Given the meager computational resources required, in the HF
heating model described here we nevertheless choose to fully track the bending and
slowing of the HF energy.
2.3 Model construction
The difficulty with constructing a model to predict the ionospheric response to HF
heating from the ground is that the energy balance equation (defined by Equation
2.11) is nonlinear and time-variant, so that an analytical solution is difficult, if not
impossible. We can, however, break up these nonlinearities into two separate pieces,
and describe each one separately.
2.3.1 Energy balance at one altitude
First, consider the three terms of the electron energy balance (Equation 2.11). It can
be seen that both the left hand term, and the right hand term (reflected in Equations
2.13-2.17) are proportional to the electron density Ne. However, as can be seen from
Figure 2.2, the absorption coefficient χ=−Im(n) is also approximately proportional
to Nefor the range of electron densities and collision frequencies considered here.
Therefore, the dependence on Necan be effectively removed from Equation 2.11,
yielding an equation dependent only on νav and the HF wave power density S.
It can also be seen that Equation 2.22 which converts electron temperature to
collision frequency, is not dependent on Ne, but rather is only dependent upon the
neutral densities of molecular nitrogen and oxygen, and the electron temperature.
And finally, the expression for ionospheric conductivity (Equations 2.25) is strictly
proportional to Ne(via the term ∂fe/∂ve), so that the dependence of conductivity

CHAPTER 2. ELF/VLF GENERATION AND PROPAGATION PHYSICS 46
changes on electron density is linear and straightforward.
This important result implies that the nonlinear dynamics of heating and cooling
at a given altitude do not depend on the highly variable electron density conditions
at that altitude, but only on HF power density and collision frequency. In the larger
context, the amount of HF power that reaches a certain altitude is dependent on the
absorption below that altitude, which is a strong function of the ionospheric electron
densities, but this aspect can be separately treated later. For now, we can begin by
exploring the ionospheric modification independently of the ambient ionosphere, as
long as we consider one altitude and input HF power level at a time. One might
consider this a zero-dimensional simulation.
Let us consider the response of the ionosphere to an HF heating input, at one
isolated point. We calculate the relevant parameters forward in small time increments,
and at each time step, Equation 2.11 is discretized, and an incremental temperature
change is calculated. We can then update the electron temperature from time point
mto m+ 1 according to
Tm+1
e=Tm
e+ ∆tdTe
dt (2.29)
The time step ∆Tmust be chosen small enough that the linearization of Equation
2.11 is a valid approximation. In the simulations performed throughout this thesis,
∆T= 1 µs is found to be sufficiently short. Simulations repeated with ∆T= 0.5 µs
confirm that results do not change as a result of numerical inaccuracies.
At each time step, the value of Tedetermines the modified values of νav,σH,σP,
and σk. It is also crucial that the modified value of νeff be used as input into the next
time step, since the amount of HF energy absorbed is affected by νeff.
Figure 2.4 shows an example of the ionospheric response to modulated HF heating.
In this example, we consider the ionosphere at 75 km with an HF input power (S) at
3.25 MHz sinusoidally varying between 0 and 3 mW/m2, as shown in the top panel.
In this first simulation, the magnetic field is assumed to be vertically oriented, and
the HF power arrives vertically.
The remaining four panels of Figure 2.4 show the electron temperature, collision

CHAPTER 2. ELF/VLF GENERATION AND PROPAGATION PHYSICS 47
0
2
4
S (mW/m2)
0
1000
2000
Te (K)
0
15
30
νeff (MHz)
0
10
20
σH (nS)
0 1 2 3 4
0
10
20
Number of ELF/VLF Periods
σP (nS)
CW Heat
Ambient
2 kHz
4 kHz
Figure 2.4: Heating and cooling dynamics at 75 km altitude

CHAPTER 2. ELF/VLF GENERATION AND PROPAGATION PHYSICS 48
frequency, Hall conductivity, and Pedersen conductivity, respectively, as a function
of time. The blue lines show the ambient levels, and red line shows the level that
results from continuous wave (CW) heating. Results for periodic modulated heating
at both 2 kHz and 4 kHz are also shown. An electron density of 10 cm−3is assumed,
although we stress again that the plot data are independent of this electron density,
except for a linear scaling of the conductivities. The simulation requires at least a
few ELF/VLF periods in order for a sinusoidal steady state to be reached.
For the purpose of ELF/VLF generation, temporal development of the ionospheric
conductivity is most important, since it is this parameter which modulates the auroral
electrojet currents. Ideally, to maximize the HF to ELF/VLF conversion efficiency,
σHand σPwould vary between the red line and the blue line, utilizing the maximum
possible conductivity depth. Clearly this is not the case, in fact σHchanges by
only about one fourth of the available conductivity depth. Although the electrons
recover much closer to the ambient values, σHchanges most drastically at the lower
temperatures, as can be seen in Figure 2.3.
The nonlinearities inherent in the energy balance equation dictate that the con-
ductivity modulation function is not in general sinusoidal, so that higher harmonics of
the modulation frequency are also be generated, even though the HF power envelope
contains only one frequency.
Comparison between the 2 kHz and 4 kHz traces show that the heating and
cooling dynamics do depend on frequency. In both cases, the ionospheric parameters
reach the CW level, which is the strongest possible ionospheric modification for this
particular situation. However, heating at 2 kHz allows more time for the ionosphere
to recover closer to its ambient state. In neither case does it fully recover, hence for
both frequencies, some fraction of the HF power is wasted on sustained heating of
the electrons, which does not contribute to periodic modulation of the ionospheric
conductivity. Since this waste appears to be smaller at 2 kHz compared to 4 kHz, we
have a hint that the ionospheric response to HF heating at this altitude may function
as a lowpass filter within the ELF/VLF range, as higher frequencies are too fast for
the electron recovery rates.
To illustrate this, we can repeat the single-point simulation at many different

CHAPTER 2. ELF/VLF GENERATION AND PROPAGATION PHYSICS 49
Altitude (km)
60
70
80
90
100
Altitude (km)
30 mW/m2
2 4 6 8 10
60
70
80
90
100
|σH| (For Ne = 1000 cm−3)
Frequency (kHz)
3 mW/m2
2 4 6 8 10
300 µW/m2
2 4 6 8 10
dB−nS/m
0
20
40
60
30 µW/m2
dB−rel
2 4 6 8 10 −40
−30
−20
−10
0
Figure 2.5: Hall conductivity modulation vs. height, frequency, and HF power

CHAPTER 2. ELF/VLF GENERATION AND PROPAGATION PHYSICS 50
frequencies and altitudes. Figure 2.5 shows the results, with the frequency on the
horizontal axis, the altitude on the vertical axis, for four different HF power densities
(all sinusoidally varying in time), and at 3.25 MHz. We note here that the maximum
possible ERP with HAARP at 3.25 MHz and 9.50 MHz is currently ∼575 MW and
∼3.8 GW, respectively, which implies a power density of S=9.3 mW/m2and 61.7
mW/m2, respectively, at an altitude of 70 km, in the absence of absorption below
that altitude.
The quantity shown in color in the top plots is the magnitude of the Hall con-
ductivity modulation (for Ne= 100cm−3, after Fourier-extraction at the fundamental
frequency once sinusoidal steady state has been reached, on a decibel (dB) scale with
respect to 1 nS/m. Since we have assumed Ne, the quantity plotted is independent
of the ionospheric variation, and represents the conductivity modulation induced per
1000 cm3of electrons. There is a strong dependence on height, frequency, and HF
power density, of the amount of conductivity modulation achieved with HF heat-
ing. The highest altitudes (above 85 km) have increasing conductivity modulation
as the HF power increases, at least through 30 mW/m2at 3.25 MHz. However, at
the altitudes between 70 and 85, the normalized conductivity modulation appears to
saturate between 300 µW/m2and 3 mW/m2. The lowest altitudes (below 70 km)
also saturate but at a higher HF power level.
In the bottom plots of Figure 2.5, the values at each altitude (for horizontal row)
from the top plots have been normalized to the maximum possible conductivity depth
(i.e., the difference between σAmbient and σCW). This normalization brings out the ef-
ficiency, or full utilization of the maximum possible conductivity modulation. The
lower altitudes generally contribute more to ELF/VLF generation. Additionally, in-
creasing the HF power density yields increasingly inefficient conductivity modulation.
2.3.2 Vertical structure
Having described the dynamics of HF heating at a single point, we extend our zero-
dimensional model to cover a one-dimensional line extending vertically through the
ionosphere. In other words, we are now considering the HF energy to enter the lowest

CHAPTER 2. ELF/VLF GENERATION AND PROPAGATION PHYSICS 51
60
68
76
84
92
100
Altitude (km)
Winter Night Summer Night
0 0.25 0.5 0.75 1
60
68
76
84
92
100
Altitude (km)
Time (ms)
Winter Day
0 0.25 0.5 0.75 1
Time (ms)
Summer Day
Figure 2.6: Power density reaching higher altitudes
altitudes and propagate upward in small vertical steps through the ionosphere. At
each step, some of energy is absorbed, and the remaining HF energy is passed on
to the higher altitude. Although we are restricting our consideration here to a one-
dimensional structure, we must also account for the r−2spreading of the HF energy
at each altitude step, which decreases the HF power density at higher altitudes even
in the absence of absorption.
In determining the HF power density at various altitudes, we are integrating the
absorption upward from the ground (or the lowest relevant altitude), and subtracting
the integral from the initial power density. The upward steps of this integration
through the ionosphere are separated by an altitude difference ∆h, which must be
small enough that the absorptive properties do not drastically change over that length.

CHAPTER 2. ELF/VLF GENERATION AND PROPAGATION PHYSICS 52
However, as is shown later, the absorption rate in the ionosphere can change sharply
over a few km altitude. Thus, in order to preserve the accuracy and stability of this
vertical integration without using excessively small values of ∆h, a classic 4th order
Runge-Kutta method is applied between each upward step. In this dissertation, we
find that ∆h=1 km is adequately small to produce accurate results. Accuracy is
verified by repeating identical simulations, with ∆h=0.5 km, to ensure that results
do not significantly change. We must also ensure that the vertical extent spanned
by the model includes the entire altitude span over which significant HF absorption
occurs. As before, we must track the effects of the changing ionosphere between time
steps, so that the vertical distribution of the HF power density must also be tracked
as a function of time.
Since our previous formulation takes into account the ionospheric dynamics at
a given altitude, we focus first on the evolution of the HF power absorption as it
propagates through the ionosphere. Since the previous section dealt with ionosphere-
independent dynamics, here we are considering the only aspect of HF heating and
cooling that is largely responsive to ionosphere conditions, i.e., the vertical structure
of absorbed HF power.
Figure 2.6 shows the importance of the HF absorption as a function of both
altitude and time. The four panels plot the shape of the HF power density as a
function of time received at altitudes between 60 km and 100 km, for the four different
ionospheres in Figure 1.1. The plots are shown in altitude increments of 4 km,
although the simulation is performed with 1 km increments. In this case, the HF
power applied at the bottom is 12.7 mW/m2, at 3.25 MHz, and it is modulated with
a 100% depth, 50% duty cycle square wave, and modulation frequency of 2 kHz. The
curves here are normalized to show the qualitative changes, and the delay of the HF
power propagating upward (which is substantial compared to the ELF/VLF period)
is also removed for the sake of visual clarity. The temporal shape of the square wave is
morphed as it propagates through the ionosphere, an effect known as self-absorption,
discussed in detail by [Moore, 2007].
For instance, in the winter nighttime ionosphere, the power density at the highest
altitude (100 km) decreases during the ON portion of the HF heating (whereas it

CHAPTER 2. ELF/VLF GENERATION AND PROPAGATION PHYSICS 53
60
70
80
90
100
Altitude (km)
Winter night
Ambient
Maximum
Minimum
Summer night
Local
Integrated
1/r2
0 20% 40% 60% 80%
60
70
80
90
100
Altitude (km)
Absorption (% loss per km), or Power Density (% remaining)
Winter day
0 20% 40% 60% 80%
Summer day
Figure 2.7: Absorption of HF energy at 3.25 MHz
is constant at the bottom of the ionosphere). As a result of the change in collision
frequency at the lower altitude, more absorption takes place and less power becomes
available at the highest altitudes. On the other hand, the strongly ionized summer
daytime ionosphere shows quite a different character, with the HF power density at
higher altitudes increasing during the ON portion, so the absorption at lower altitudes
decreases as a result of HF heating.
A more quantitative description of the HF absorption can be found in Figure 2.7,
for the same HF heating conditions. For the four ionospheres, the dashed lines show
the HF power density as a function of altitude, as a percentage of the power at the
bottom of the ionosphere (in this case, 12.7 mW/m2). The gray dashed line shows
the power density that would result from strictly 1/r2reduction in the power density

CHAPTER 2. ELF/VLF GENERATION AND PROPAGATION PHYSICS 54
(which would be the case for free space propagation). The red and green dashed
curves show the maximum and minimum HF power densities (respectively) during
the ELF/VLF cycle. The solid curves show the absorption rate of the ionosphere per
kilometer (i.e., the derivative of the total absorption, or (1 −e−2kχS)), for the same
maximum and minimum points (red and green, respectively) as well as the ambient
ionosphere. At the altitude where the absorption rate becomes substantial, the power
density falls below the free space curve.
It can be seen here that the absorptive part of the ionosphere changes significantly
over small altitude differences (a few km). For this reason, the upward integration
is achieved with fourth-order Runge-Kutta technique, so the propagation of the HF
energy to the next higher altitude slab requires four steps. We can also see that the
altitude where the HF energy is deposited varies significantly as a function of the
ionosphere. In general, the more ionized is the ionosphere, the lower is the altitude
at which the bulk of the HF energy is deposited. At 3.25 MHz, most of the HF
energy is absorbed, though at higher frequencies (where the ionospheric parameter Z
is smaller), a higher fraction of the power escapes the Dregion entirely.
Figure 2.8 shows the ionospheric modification at five different altitudes between
70 and 90 km, resulting from the winter daytime ionosphere HF heating case shown
in Figure 2.7, from which we can see the altitude dependence of the key ionospheric
modification panels. The top left panel of Figure 2.8 shows the temperature variation
in time. The lag of the rising portion of the temperature waveform at the highest
altitude is simply due to the delay of the HF power propagating upward from the
ground. The electrons are heated to the highest temperature at an altitude near 80
km, even though the highest absorption rate, as can be seen in Figure 2.7, occurs
closer to 85-90 km. This difference is because at 80 km, there are fewer electrons,
so the power absorbed is concentrated on a smaller number of particles, in addition
to the fact that there is simply less HF power density at 90 km compared to 80 km,
so if the fractional absorption were the same between 80 km and 90 km, that would
means less power absorbed at 90 km.
The top right panel of Figure 2.8 shows the collision frequency as a function of
time. Although 85-90 km is the peak power absorption rate altitude, and 80 km

CHAPTER 2. ELF/VLF GENERATION AND PROPAGATION PHYSICS 55
0
1000
2000
3000
Te (K) 0
1
log10(ν) (MHz)
0
2
4
Hall (all harmonics)
log10(σ) (nS/m)
Ped (all harmonics)
1.00 1.25 1.50 1.75
−200
−100
0
100
200
Time (ms)
Hall (1st Harmonic)
σ (nS/m)
1.00 1.25 1.50 1.75 2.00
Time (ms)
Ped (1st Harmonic)
70 km
75 km
80 km
85 km
90 km
Figure 2.8: Ionospheric modification at varying altitudes

CHAPTER 2. ELF/VLF GENERATION AND PROPAGATION PHYSICS 56
is the altitude of peak temperature modulation, the strongest effect on the collision
frequency occurs at 70 km (the lowest of the four altitudes), due largely to the fact
that the ambient collision frequency is higher to begin with.
The middle panels of Figure 2.8 show the temporal development of the Hall (left)
and Pedersen (right) conductivities in the ionosphere, plotted on a logarithmic scale.
Proportionally, the strongest change in conductivity occurs at the lowest altitude
(70 km), whose Hall conductivity rises by about an order of magnitude. On the
other hand, at 90 km, the modulation of the conductivity can barely be seen. These
plots again show that the conductivity modulation in general has a harmonic content
different from the harmonic content of the HF heating envelope (a square wave in
this case).
The bottom plots of Figure 2.8 show the Fourier-extracted first harmonic of the
curves in the middle plots, and plotted now on a linear scale. The strongest conduc-
tivity modulation, for both the Hall and Pedersen conductivities, occurs at 90 km,
even though the proportional change in the conductivity is small, since the conduc-
tivity at 90 km is so much higher to begin with. The phases of the extracted sinusoid
shift later in part due to the group delay of the HF signal, but they are also affected
by the slower rise time and fall time evident in the upper panels, which causes the
phase of the first harmonic to additionally lag at 90 km.
It should be emphasized, however, that the comparative role of different iono-
spheric altitudes in ELF/VLF wave injection cannot be determined strictly on the
basis of the amplitude of the conductivity modulation. Thus, even though 90 km
appears to be the altitude of highest conductivity modulation (and therefore, gener-
ate the highest ELF/VLF currents for a homogeneous electrojet field), the ELF/VLF
signal on the ground or in space may be dominantly due to the conductivity modu-
lation at a different altitude, due to nontrivial propagation effects of the ELF/VLF
signal through the ionospheric plasma. This propagation aspect is considered later in
this chapter. For instance, the generated signals observed on the ground may appear
to be originating from an effective (or dominant) altitude, which may be different for
magnetospheric injection.

CHAPTER 2. ELF/VLF GENERATION AND PROPAGATION PHYSICS 57
Narrow
3.25 MHz
y (km)
−50 0 50
−50
0
50
Narrow
9.50 MHz
x (km)
−50 0 50
Broad−NS
3.25 MHz
−50 0 50
Broad
3.25 MHz dB−rel
−50 0 50 −30
−20
−10
0
Figure 2.9: HF power at 60 km from HAARP
2.3.3 Extension to 3D
Now that we have described the vertical distribution of the HF energy deposition,
our remaining task is to extend the model to three-dimensions. For this purpose, the
horizontal space at each altitude is divided into segments of equal length ∆x, which
must be small enough to capture the structure of the input radiated pattern from
HAARP, as well as any small scale structures induced in the ionosphere.
Let us first describe the input HF power from the HAARP phased-array HF
heating facility, since the experiments conducted here take place with HAARP. The
HF frequency can vary between 2.75 MHz and 9.9 MHz. At a given frequency,
HAARP can operate in a number of modes of operation, a few of which are shown in
Figure 2.9. The power density arriving at 60 km altitude is plotted on a logarithmic
scale, where the center of the horizontal region shown is directly above the location of
HAARP on the ground. The most straightforward mode of operation involves driving
all the HF antennas in phase, shown in the left two panels (for 3.25 MHz and 9.50
MHz, respectively), which maximizes the vertical beam focusing and therefore the
ERP. However, since the HF array is finite in size, some of the power also leaks into
the sidelobes which can be seen forming a ‘+’ shape around the main beam. The ‘+’
shape is oriented 14◦East of geographic North, which is the orientation of the rows
and columns of HF transmitters at HAARP.
The sidelobe power density delivers no more than −15 dB power density compared

CHAPTER 2. ELF/VLF GENERATION AND PROPAGATION PHYSICS 58
to the main lobe. At higher frequencies, as the space between the HF transmitting
elements on the ground (some tens of meters) becomes a larger fraction of an HF
wavelength, the power becomes even more tightly focused into a smaller main beam
(hence the ERP at 9.5 MHz is ∼8.2 dB higher than at 3.25 MHz), although the side-
lobes are also more numerous at 9.50 MHz. HAARP also has the ability to broaden
the beam, as can be seen by the right two panels of Figure 2.9, and this broadening
can be performed in one direction, or in both directions. The broadening effectively
merges the main lobes with the sidelobes, spreading the beam power over a wider
area, thereby decreasing the ERP. This mode is achieved by varying the radiating
phases of the HF elements on the ground but is not utilized in the experiments of
this dissertation, though it has been used in a number of ELF/VLF wave genera-
tion experiments with HAARP. The ERPs and power densities into the ionosphere
for a variety of different HF frequencies, and beam broadening modes are given in
Appendix B.
Any of these modes can also be combined with beam tilting, where the center of
the main beam is not in the vertical direction, but is off by a zenith angle of up to
30◦from vertical, and any azimuth. This beam tilting ability is extensively used in
this dissertation.
The two-dimensional power density input into the bottom of the ionosphere con-
sists of a series of HF rays at each grid point. For this plane at the lowest altitude, the
propagation from the ground is assumed to be through free space, so that the group
delay at each location is simply the free space propagation delay from the HF array
location to the base of the ionosphere, and both ray direction and the wave normal
direction are equal to the free space arrival direction from the HF array to the grid
point at the bottom of the ionosphere. The power density is calculated using realistic
data of the HAARP array’s directional pattern, including the sidelobes, assuming
the HF energy spreads as 1/r2as it propagates to the base of the ionosphere. From
this input two-dimensional plane, the propagation upward through the ionosphere is
carried out in a series of vertical steps, separated by ∆h.
Figure 2.10 shows an interpolation method applied with each altitude step in the
upward integration. Each HF ray at the grid points (in red dots) is projected upward

CHAPTER 2. ELF/VLF GENERATION AND PROPAGATION PHYSICS 59
∆z
∆x
Interpolated Locations
HF Ray Path
Calculated Locations
Figure 2.10: 2D interpolation of HF parameters

CHAPTER 2. ELF/VLF GENERATION AND PROPAGATION PHYSICS 60
to the next altitude (shown with the green traces), intersecting that altitude at a
certain location offset from the grid (shown with blue dots). The HF densities at
the next altitude, however, are reduced by a 1/r2spreading factor, as well as the
calculated absorption in between the two altitude slabs, taking into account the fact
that the HF ray travels a distance ∆hcos θin between each altitude step, where θis
the ray angle from vertical.
A 2-D linear interpolation is then applied to calculate the values of the HF power
density at each of the grid points. The ray bending and slowing as a result of Snell’s
law and the magnetic field anisotropy is then calculated, and the HF ray directions
and group delay are updated accordingly.
The angle between the HF rays and the geomagnetic field must also be tracked,
and we utilize a realistic value and orientation of the geomagnetic field obtained from
the 10th generation International Geomagnetic Reference Field (IGRF-10) model
(values available from http://www.ngdc.noaa.gov/geomagmodels/IGRFWMM.jsp).
At 75 km altitude above HAARP, the geomagnetic field is ∼53.29 µT in the downward
direction, ∼12.57 µT to the North, and ∼4.99 µT to the East. These values vary by a
small amount (<1%) as a function of altitude between 50 and 100 km. The declination
(orientation of the horizontal component with respect to geographic north) is ∼21.65◦
to the East, and the inclination (or zenith tilting of the field from vertical) is ∼14.24◦.
The absorbed energy calculated in the horizontal slab is then applied as before
to a discretized form of Equation 2.11. Once the short HF pulse of duration ∆thas
been propagated through the ionosphere, the next time step integration is performed
using the ionosphere left behind by the previous time step. In the next time step,
the HF power input into the ionosphere may be different. Usually, the HF heating
model is run for several ELF/VLF periods, so that a periodic steady state of all the
ionospheric parameters is reached, typically after simulating a few milliseconds.
The calculation of the collision frequency enables the ionospheric conductivity to
be determined as a function of time, and this step is performed during the calcu-
lations. However, since we are interested in specific generated frequencies, we must
utilize Fourier extraction to withdraw the amplitudes and phases of individual fre-
quencies. Since the signal is periodic at a fundamental frequency, we can extract

CHAPTER 2. ELF/VLF GENERATION AND PROPAGATION PHYSICS 61
1.4 1.6 1.8
60
75
90
Altitude (km)
t (ms)
Te
Te (K)
−50 0 50
60
75
90
500
1000
1500
|σH|
x (km)
y (km)
h=70 km
−100 −50 0 50 100
−50
0
50
0
5
10
15
∠σH
x (km)h=70 km
−100 −50 0 50 100 0
100
200
300
nS/m
|σP|
x (km)
y (km)
h=83 km
−100 −50 0 50 100
−50
0
50
5
10
15
20
Deg
∠σP
x (km)h=83 km
−100 −50 0 50 100 0
100
200
300
Figure 2.11: Three-dimensional HF heating model results
these amplitudes and phases according to
AN=
T/∆t
X
m=1
σe−2πif m∆tN e−2πiftdN(2.30)
where fis the fundamental frequency, and Nis the harmonic of that frequency
we want to track, Tis the ELF/VLF period (or 1/f). The group delay tdof HF
energy from the ground, and σ, the conductivity tensor at each location (or, more
specifically, σH,σP, and σk) are stored for each location in the three-dimensional
grid. In this dissertation, we are primarily concerned with the amplitude and phase
of the fundamental frequency (i.e., N=1), calculated over the last ELF/VLF period
simulated (i.e., when steady state has been achieved). These quantities are the end
goal of this HF heating simulation.

CHAPTER 2. ELF/VLF GENERATION AND PROPAGATION PHYSICS 62
Figure 2.11 shows results from the three-dimensional simulation. The HF heat-
ing is taken to be at 3.25 MHz, with the beam oriented vertically, and amplitude
modulated at a frequency of 3 kHz, in the presence of a winter daytime ionosphere.
The top two panels show Te, on the left as a function of time, for points along the
center of the main beam (normalized to show the qualitative shape, as in Figure 2.7),
and on the right over a two-dimensional slice, vertically through the ionosphere. The
temperature slice is taken at the end of the period shown in the top left plot, so that
the values Terepresent the point in the ELF/VLF cycle where electron temperatures
have recovered closest to their ambient values (which is still as high as 1600 K, well
above the ambient value). The radiating pattern of the HAARP HF beam and its
two main sidelobes are evident in the plot.
The lower four panels of Figure 2.11 show horizontal slices of the ionosphere, with
the color indicating the amplitude (left) and phase (right) of the Fourier-extracted
Hall conductivity at the fundamental frequency (3 kHz). The middle plots are at 70
km altitude and show σH(a phasor quantity), whereas the bottom plots are at 83 km
altitude and show σP. The pattern of the HAARP beam and its sidelobes are again
visible.
At 70 km, the strongest (highest amplitude) values of σHoccur not in the center of
the mean beam, where the power density is strongest, but at the outside of the main
beam. This behavior is due to the effects of self absorption; in this case, higher power
densities are often needed in order to penetrate higher into the ionosphere. It is also
due in part to the fact that the HF energy at the outside of the main beam travels
slightly obliquely, so that it passes through longer length of ionosphere in between
each altitude slab, which also causes the HF energy to be deposited at lower altitudes.
The phase plot at 70 km shows the variable propagation delay from ground to the
ionosphere, with σHon the outside lagging in phase mainly due to a longer group
delay.
On the other hand, the character of σPat 83 km is markedly different. In particu-
lar, the strongest conductivity modulation occurs in two distinct regions: in a narrow
area in the center of the main beam, and then another thin ring of high conductivity
modulation at the edge of the main beam, with a null in between the two regions.

CHAPTER 2. ELF/VLF GENERATION AND PROPAGATION PHYSICS 63
The reason for these distinct regions can be seen in Figure 2.3. Between 80 and 85
km, as Teis increased, σPfirst rises, and then falls, thus depending on the maximum
and minimum temperature, the net change in σPmay be either positive or negative.
Since the maximum and minimum temperatures are dependent on the HF power
density, it is not surprising that there are two distinct regions of σPat this altitude.
Further evidence of this effect can be found in the bottom right panel of Figure 2.11,
which shows that the phase of the conductivity modulation changes by ∼180◦at the
boundary between the two regions of conductivity modulation, corresponding to a
transition between a regime where σPrises, and where it falls, with increasing Te. In
fact, this self-cancellation by the two regions of Pedersen conductivity modulation,
with opposite phase, is part of the reason that the Hall conductivity is believed to
be dominant in the generation of ELF/VLF signals radiated to longer distances by
HAARP.
Figure 2.12 shows the evolution of the modulated currents over an ELF/VLF
period (T), taking into account both the phase of the Fourier-extracted conductivity
waveform, and the delay from the HF propagation from the ground through the
ionosphere. The left hand six panels show a vertical slice (at y=0) of the Hall currents,
while the right panels show the Pedersen currents. The panels show frames spaced
out at six locations within the ELF/VLF period.
As a result of the delay in the HF signal, the conductivities at the highest altitudes
rise and fall slightly later than the conductivities at the lowest altitudes. As can be
seen in the left hand plots, the modulated Hall currents are phased in such a manner
so as to create an effective moving source in the vertical direction, at close to the
speed of light (since the HF is also traveling close to the speed of light). This vertical
phasing is intrinsically part of every modulated HF heating experiment, and likely
gives an advantage to modulated heating for magnetospheric injection that is not
present for injection via a ground-based transmitter. This effect may also play some
role in the formation of the so-called ‘column’ of radiation observed over HAARP
[Piddyachiy et al., 2008].
It can also be seen that the side lobes modulate the conductivity at a lower altitude
compared to the main lobe, another indication of the effect of HF power density on

CHAPTER 2. ELF/VLF GENERATION AND PROP