A Study of the Ionosphere During the Onset of Spread F in Kwajalein

A STUDY OF THE IONOSPHERE DURING THE ONSET OF SPREAD F IN KWAJALEIN

A Thesis Presented to the Faculty of the Graduate School

of Cornell University in Partial Fulﬁllment of the Requirements for the Degree of M.S.

A study of plasma instabilities in the F-region of the equatorial ionosphere termed equatorial spread F (ESF) is undertaken considering data from recent experiments. ALTAIR radar scans from WINDY (2017) and Too WINDY (2019) and sounding rocket data from Too WINDY are analysed in an attempt to identify characteristic ionospheric conditions during the onset of ESF. A review of recent research and relevant linear plasma theory is followed by a study of experimental data. ALTAIR scans collected during WINDY are studied to identify electron density signatures that may serve as indicative signs of instability. A quantitative analysis of the same radar data led to the discovery of a characteristic spectral distribution in the small to medium scale irregularities present during the onset of ESF activity. This distribution was studied during quiet and active nights to compare the structuring of the ionosphere when stable and unstable. ESF in the moderate solar ﬂux conditions during WINDY followed a familiar pattern beginning with small scale instability in the lower altitude bottom side and evolving into large scale instabilities in the top side of the F-region.

Observations of ESF proved more elusive during Too WINDY owing to the low solar ﬂux conditions in June of 2019. Post-sunset ESF was observed on a sin- gular night, a much lower rate of occurrence than that during WINDY. ALTAIR data from the night of the rocket launch of Too WINDY showed the presence of post-midnight ESF over Kwajalein. Sounding rocket data conﬁrmed the electron density measurements and revealed the presence of whistler mode hiss and ELF waves in the F-region plasma. The Cornell ionospheric simulation was used to try and reproduce the observations of post-sunset ESF from WINDY by seeding with pink noised produced using characteristics derived from the spectral analysis. Gravity waves and meridional winds were used to seed the simulation attempting to reproduce the observations of post-midnight ESF from

Too WINDY but these methods showed limited success. The relevance of these experiments is ﬁnally discussed in light of other research in the ﬁeld. BIOGRAPHICAL SKETCH

Siddhant Rao was born on 26 March, 1996 in Mumbai, India. After attending school in Mumbai, Siddhant studied Physics at Cornell, graduating with a Bach- elor of Arts in 2018. Following that, Siddhant has been a graduate student in Atmospheric Science at Cornell and does research with professor David Hysell in ionospheric plasma physics.

iii ACKNOWLEDGEMENTS

I would like to thank the chairperson of my special committee, Professor David

Hysell for giving me the opportunity to be involved with the WINDY and Too WINDY experiments and introducing me to this ﬁeld. Thanks goes to Professor Peter Hitchcock on my special committee as well, for providing his expertise despite taking this role on short notice.

I am indebted to Steven Powell, whose contribution was vital to the success of the Too WINDY sounding rockets and also to my learning. Our co-investigators during the WINDY and Too WINDY experiments, Dr. Miguel Larsen, Dr. Keith Groves and Dr. Don Hampton also deserve thanks for their roles in the success of these experiments. I would also like to thank the staff at NASA Sounding Rockets Contract (NSROC) and at ALTAIR without whom procuring the data for this thesis would not have been possible.

I must thank the entire Earth and Atmospheric Science department at Cornell for providing help and support when needed and the Space Plasma Physics group in 3154 Snee, especially Sevag Derghazarian and Dr. Enrique Rojas- Vilalba who were ever willing to share their knowledge.

iv TABLE OF CONTENTS

1 Introduction 1 1.1 Background ...... 3 1.2 Linear theory of the plasma interchange instability ...... 10 1.3 Recent studies in the ﬁeld ...... 17

2 Radar investigations during project WINDY (2017) 23 2.1 ALTAIR radar operations and data Processing ...... 24 2.2 Presentation and discussion of ALTAIR scans ...... 31 2.3 Spectral analysis of irregularities ...... 38

3 Rocket and radar investigation during project Too WINDY (2019) 42 3.1 Radar observations during Too WINDY ...... 43 3.2 Rocket operations and data processing methods ...... 49 3.3 Presentation of sounding rocket data ...... 54

4 Numerical simulation of ESF 64 4.1 Description of the Cornell ionospheric simulation ...... 65 4.2 Simulation of post-sunset ESF during WINDY ...... 71 4.3 Simulation of post-midnight ESF during Too WINDY ...... 75

5 Post-midnight Equatorial Spread F 80 5.1 Observations of post-midnight ESF over Jicamarca during Too WINDY ...... 81 5.2 Observations of post-midnight ESF by the C/NOFS satellite . . . 84 5.3 Relevant literature from the Asian and South American longitudes 86

6 Conclusion 89 6.1 Relevance of WINDY and Too WINDY in ESF studies ...... 89 6.2 Explanation of observations and theories ...... 91 6.3 Limitation of experimentation and analyses during WINDY and Too WINDY ...... 94

A Experiment electronics integration at wallops ﬂight facility 96 A.1 General safety measures ...... 97 A.2 Mechanical installation and alignment ...... 99 A.3 Pre-vibration telemetry and sequence test ...... 104 A.4 Vibration test ...... 109 A.5 Nose cone deploy ...... 113 A.6 Magnetic calibration ...... 114 A.7 Mechanical tests and GPS roll-out ...... 116 A.8 Photos of the facility ...... 116

Bibliography 119

v LIST OF FIGURES

2.1 a) VHF scans of the first observed irregularities showing log10 electron density (cm−3). b) UHF scans preceding panel a by 10 minutes ...... 33 2.2 a) VHF scans of the first observed irregularities showing log10 electron density (cm−3). b) UHF scans preceding panel a by 10 minutes ...... 34 2.3 Scans from different radar modes on August 31st 2017 showing the evolution of the instabilities through the evening. a) VHF scans perpendicular to the magnetic field of log10 electron density (cm−3). b) UHF scans oblique (6◦off-perpendicular) to the −3 magnetic field of log10 electron density (cm ). c) Signal to noise ratio...... 36 2.4 Scans from different radar modes on September 4th 2017 showing the evolution of the instabilities through the evening. a) VHF scans perpendicular to the magnetic field of log10 electron density (cm−3). b) UHF scans oblique (6◦off-perpendicular) to the −3 magnetic field of log10 electron density (cm ). c) Signal to noise ratio...... 37 2.5 Amplitude function superimposed over the frequency distribution of small and intermediate-scale irregularities ...... 40 2.6 Amplitude function superimposed over the frequency distribution of small and intermediate-scale irregularities ...... 41

3.1 ALTAIR scans at the onset of ESF ...... 44 3.2 ALTAIR scans at the onset of ESF ...... 45 3.3 ALTAIR VHF scans from the rocket launch ...... 47 3.4 ALTAIR UHF scans from the rocket launch ...... 48 3.5 Electric field vector data from the rocket flight upleg ...... 55 3.6 Electric field vector data from the rocket flight downleg . . . . . 56 3.7 Measured magnetic field compared to the IGRF model field . . . 57 3.8 Magnetic field fluctuations perpendicular to the Earth’s magnetic field ...... 59 3.9 Spectra from the electric field data ...... 61 −3 3.10 Log10 electron density (cm ) measurements from the Langmuir probe ...... 62

4.1 Plasma density proﬁles of the numerically simulated ionosphere for 31 August 2017 using white noise as a seed. Densities are shown here for three different species: molecular ions (red), atomic oxygen ions (green) and hydrogen ions (blue) in MKS units (m−3)...... 72 4.2 Plasma density proﬁles (m−3) of the numerically simulated ionosphere for 31 August 2017 using pink noise as a seed...... 73

vi 4.3 Numerical simulation of instabilities of the ionosphere in Kwa- jalein during the summer of 2019. Ion densities (m−3) are shown here for three different species: molecular ions (red), atomic oxygen ions (green) and hydrogen ions (blue)...... 76 4.4 Numerical simulation of instabilities of the ionosphere in Kwa- jalein during the summer of 2019 with the addition of gravity waves and meridional winds. Ion densities (m−3) are shown here for three different species: molecular ions (red), atomic oxygen ions (green) and hydrogen ions (blue)...... 78

5.1 Aperture synthesis radar images of irregularities above Jica- marca between 00:30 and 01:12 ...... 82 5.2 Aperture synthesis radar images of irregularities above Jica- marca between 01:24 and 02:45 ...... 83

A.1 Angular values for alignment in reference to the rockets body . . 99 A.2 Magnetometer placement on axis plane ...... 100 A.3 Stacer boom in the retracted position (gold sphere) aligned in such a way that it can extend below the metal skeleton...... 101 A.4 Magnetometer (black cuboid) aligned against the rocket axes. The nosecone of the rocket is pointing up in this image...... 102 A.5 2 booms are pictured, the first pointing out of the page and the second pointing upwards. To the left of the Stacer booms is the telemetry circuit box connected to the boom instruments by the white wires...... 102 A.6 The entire instrument section of the rocket body is visible. The Langmuir probe is installed at the end of the green rod towards the top of the image. Here it is covered by bubble wrap and an orange cone to prevent accidental damage when the rocket is aligned flat...... 103 A.7 The correct way to make the connection to the voltage sensors on the stacer booms. The metal strip taped to the sensor is connected through conducting clips to a resistor in series which can either be connected to ground or a signal generator during the telemetry tests...... 105 A.8 several different resistors in combination connected to the Lang- muir probe. To the bottom left of the image you can see the red terminal from the coaxial cable from the signal generator connected to the 10k resistor...... 106 A.9 Telemetry screen showing different readings from rocket components. The left half of the screen shows the readings from the science instruments...... 107 A.10 The remove before flight labels ...... 110

vii A.11 The remove before flight screw, label attached in the form of a plastic tag with black marker writing ...... 110 A.12 The pin attached to the remove before flight tag in fig A.10 . . . . 111 A.13 The clamp with the screw that must be removed before flight. . . 111 A.14 The boom after the clamp in fig A13 has been removed...... 112 A.15 Tags used to record and date the measured extension of the boom after removal of the safety items. The red arrows show the space where the extension should be measured...... 112 A.16 (L) The rocket body in the nose cone deploy test space. (R) Post- nose cone deploy...... 113 A.17 The rocket payload with nosecone in the mechanical testing area 116 A.18 The rocket payload installed on the vibration table for the vibration test ...... 117 A.19 (L) The payload without the nosecone in the electronics testing area where the telemetry and sequencing tests take place. . . . . 117 A.20 Movement of the rocket payload using cranes and a rolling table between different testing areas...... 118 A.21 Positioning of the rocket payload in the magnetic calibration chamber ...... 118

viii CHAPTER 1 INTRODUCTION

The NASA WINDY (2017) and the Too WINDY (2019) radar and sounding rocket experiments were investigations aimed at studying the stability of the post-sunset ionosphere in the equatorial paciﬁc. The purpose of these experiments was to study the plasma instabilities occurring in the equatorial F-region ionosphere known as equatorial spread F (ESF). The campaign took place on the island of Roi-Namur in the Kwajalein Atoll, part of the Republic of the Marshall Islands. The ionosphere was primarily studied using the ARPA Long Range Tracking and Instrumentation Radar (ALTAIR) during both experiments and

NASA sounding rockets during project Too WINDY. In addition, an ionosonde and a Fabry-Perot interferometer were used to probe ionospheric conditions.

This thesis provides a background in ESF research and then details the results of the WINDY and Too WINDY experiments. The first chapter provides a review of key discoveries in the field, beginning with the first experiments at the

Jicamarca Radio Observatory in Peru up through the 2004 Equis II campaign in Kwajalein which was the latest sounding rocket experiment in the equatorial paciﬁc. This is followed by a brief derivation of the plasma interchange instability, one of the key instability mechanisms associated with equatorial ESF. The chapter ends with a review of the recent literature in the ﬁeld which provides context to the questions asked in this thesis.

The second chapter details the methods used to process the signals from AL- TAIR before showing the scans of the ionosphere it produces. These scans are studied and their main features are discussed. A spectral analysis of the elec-

1 tron density data from ALTAIR is done to include a quantitative discussion of the data. The third chapter presents radar scans and sounding rocket data from project Too WINDY. ALTAIR scans are shown and discussed in a manner similar to the previous chapter with a focus on the new and interesting features observed. The sounding rocket data are presented in the form of scalar and vector state parameters along with their spectra and the main features from this data set are discussed in light of relevant literature.

The fourth chapter contains details of the Cornell ionospheric simulation beginning with its computational methods and key basis equations. The simulation is run to reproduce the experimental observations presented in the previous chapters and the results of this are shown and discussed. The ﬁfth chapter provides a review of recent literature on the topic of post-midnight ESF which is relevant to the ﬁndings in the previous chapter, comparing data from Jicamarca with that from Kwajalein.

The ﬁnal conclusive chapter evaluates the theories and ideas postulated in previous chapters and discusses the overall signiﬁcance of the two experiments in the grand scheme of ESF research, ending with unanswered questions that require further investigation. The ideas and methods in this thesis are supported by two main publications Radar Investigation of Postsunset Equatorial Ionospheric

Instability Over Kwajalein During Project WINDY [24] and Equatorial F-Region Plasma Waves and Instabilities Observed Near Midnight at Solar Minimum During the NASA Too WINDY Sounding Rocket Experiment [25].

2 1.1 Background

Plasma instabilities in the Earth’s equatorial ionosphere termed ’equatorial spread F’ (ESF) have been an area of interest for researchers since the early part of the 20th century. The term ’equatorial spread F’ comes from its location and the nature of high frequency echoes associated with it. This phenomenon is typically observed in the F-region of the ionosphere, which comprises the altitudes between 150 km and 800 km, and speciﬁcally in the equatorial regions. The echoes received are ’spread’ in range and also in frequency. Ionospheric research initially focused on studying chemistry, energetics, and transport in the plasma formed by the electron and ion species in the D, E, and F-region. Inter- est in the stability of the F region stemmed from high frequency (HF) ionosonde (sounder) experiments starting in the 1920s. These experiments showed that disturbances in the F-region were affecting radio-wave propagation in some characteristic ways. Scientists found that communications were not as reliable at equatorial latitudes, and radar signals cannot be used effectively during ESF activity [43].

Contemporary research has primarily focused on predicting ESF activity by studying ionospheric conditions before and during the onset of this phenomenon. The investigations in this ﬁeld are primarily done with two broad methodologies – in-situ measurements provided by satellites and sounding rockets and ex-situ measurements provided by ionosondes and radars. While radar investigation of the ionosphere has been continuous, leading to several interesting climatological data sets, episodic sounding rocket experiments such as those described later in this document have provided key insights into micro-

3 physical and intermittent processes. In this section, a brief qualitative description of ESF will be followed by a review of review of relevant research. This will include a brief history, highlighting the important breakthroughs in our understanding and referencing key investigations in the ﬁeld.

We consider the lower boundary of the postsunset F-region where the density gradient 5n is normal to the background ionospheric currents. In the valley of the F-region ionosphere, currents are driven by electric fields, winds, and gravity. At the equator, the magnetic field is perpendicular to this boundary and the plane in which it lies. When the plasma boundary is distorted in the direction of the gradient, ion drifts and currents arise perpendicular to it. The charge separation from these currents causes a vertical E × B drift which am- plifies the initial distortion. Therefore the initial plasma rarefaction leads to depletions or ’bubbles’ rising into the topside and to density enhancements de- scending into the vacuum which distort the boundary. An important feature of the waves produced by the interchange instability is that their wavevectors lie almost completely in the plane perpendicular to the magnetic field, k · B = 0. This allows for a two-dimensional treatment of the ionosphere to provide a fairly complete picture of the waves and instabilities. We have just described the electrostatic Rayleigh-Taylor instability at work in the ionosphere and it is the key mechanism through which perturbations in the plasma density can develop into plasma instabilities in the ionosphere.

Decades of investigations into ESF allowed researchers to have a detailed understanding of the morphology and chronology associated with these plasma structures. Data sets sourced from different longitudinal sectors over the world

4 have painted a consistent picture of the observed ionospheric events to some extent. The irregularities at the lowest altitudes are known as the bottom-type layers, seen in the lower F-region between 150 and 250 km in range. These structures are usually conﬁned to this narrow range of altitudes. While ESF at higher altitudes is considered a specialised variant of the Rayleigh-Taylor instability, these irregularities are believed to be brought about by neutral wind driven gradient instabilities [22]. They are generally smaller in scale relative to the structures in the other scattering layers, but the wave structures can extend several tens of kilometres in both altitude and horizontally. Bottom-type layers are usually the ﬁrst to appear during an ESF event.

The second type of layer looks similar in structure to the first and is known as a bottom-side layer, so named because of its confinement to the bottomside of the F-region, well below the F-peak, usually around 200 - 300 kilometres in altitude. The irregularities here are larger in scale, with scale sizes extending to over a hundred kilometres. In addition to the larger size, the bottomside structures show more development in time. The primary mechanism that generates these layers is believed to be the shear flow in the bottom-side F-region where the plasma drifts are opposite to the direction of the neutral winds. Initially, shear flow instabilities were thought to be damped by the collision, but a numerical investigation by [22] discovered that a certain branch of the collisional shear flow could be destabilising for wave structures in both the bottomside and bottom-type layers.

These layers can show vertical development in time and, when driven by vertical currents, can evolve into the the third class of scattering structures known as

5 topside layers or plumes. Low altitude irregularities are seen as seeds for irregularities at higher altitudes. Topside echoes are the signature indication of ESF activity and can be attributed to several causes including the development of the bottom-type and bottomside irregularities [43]. The interchange instability takes different forms in the inertial and collisional regime; in the inertial regime it is essentially the electrostatic Rayleigh-Taylor instability which is a source of turbulence in the F-region. However, in practice, the inertial regime is not as relevant for ESF studies as collisions are seldom negligible. In the collisional regime, background winds and currents drive the instability.

The main different between the collisional regime and the inertial regime is the relative importance of the source of momentum change. In the collisional regime, the time between ion-neutral collisions is much less than the time scale of the dynamics. This is primarily in the lower F-region between 200 km and 400 km, at altitudes where the neutral density is high. In the inertial regime, above approximately 600 km, the neutral density decreases, and ion inertia becomes signiﬁcant. Here, the time between collisions is comparable to the time scales of the observed dynamics. A large part of ESF research is focused on determining the conditions that precede ESF with the aim of predicting these events. There is a great deal of interest in studying the wave-like nature of bottom-type scattering layers as these are viewed as precursors to more emphatic ESF phenomena and are seen consistently in the hours before the topside plumes develop. [23].

In 1976, a new digital processing method allowed Woodman and La Hoz [43] to acquire two dimensional maps of backscatter power and samples of the frequency spectra as a function of altitude and time. The backscatter technique

6 was an important development in ESF studies because it could provide a continuous chronology of ESF events with exact measurements of the altitudes at which the irregularities are present while also measuring physical parameters like the background electron density and drifts. This data set from the Jicamarca radar showed that ESF could occur in the valley region between the E and F layers, the bottomside and the topside. The key experimental result here was the spatial connection between the topside and bottomside irregularities by plume- like structures. This was seen as evidence for the Rayleigh-Taylor instability in action. These fundamental observations have been reproduced several times in the last few decades in investigations not only at Jicamarca but also in Kwa- jalein.

In 1989, Zargham and Seyler [45] considered analytical and computational treat- ments of the ionospheric interchange instability in the collisional and inertial regime. The aim of the investigation was to follow the evolution of the plasma structures in the ionosphere. A numerical analysis using a two-dimensional ﬂuid model showed that in the nonlinear stages, there is a difference between these two regimes. In the inertial regime, the instability is essentially the electrostatic Rayleigh-Taylor instability, and in the collisional regime, it resembles the E × B instability with gravity. The key difference found in this study was the deformation of the rising plasma bubbles in the collisional regime would result in an oval structure while in the inertial regime it would transform into a folded circular cap proﬁle. Analysis and nonlinear simulations showed that the growth was dominated by certain horizontal wavelengths in both the collisional and inertial regimes, leading to similar qualitative properties in some respects.

7 Several researchers had investigated the role of the shear flow in the bottom- side F region and its effect on the growth of the interchange instability. Previous investigations [20], [12] were primarily to determine the stabilizing properties of the shear flow but did not tell the whole story. Hysell and Kudeki [22] investigated the destabilizing effect of the shear flow. They considered a two- dimensional fluid model and came the following conclusions regarding the role of the shear flow. As the density gradient in the F-region valley increases, the shear flow may destabilize the plasma in the ionosphere. This collisional shear instability could be several times faster than the Generalized Rayleigh-Taylor

(GRT) instability that operates in this region given certain conducive conditions such as an intensification of the shear flow around twilight. The shear flow also begins to act several hours before sunset and so may be responsible for the creation of seed instabilities required by the GRT instability.

Kudeki and Bhattacharya [28] demonstrated that the neutral wind could be driving a gradient instability. They argued that the vortical flows in the bottom- side could create a mixing effect in the steep electron density gradient, causing density gradients in the zonal direction. These would then be susceptible to the vertical currents arising from the shear flow. The current is sensitive to small variations in the plasma density leading to large polarization fields in the irregularities [28]. They presented data from Jicamarca showing that observations of the vortex are accompanied by irregularities in the bottom-side; the structures that routinely precede ESF plumes in the topside.

In 2004, the EQUIS II sounding rocket and radar investigation provided experimental evidence for the role of the shear ﬂow in the evolution of the plasma

8 instabilities [23]. The data from the sounding rockets showed the location of the bottom-type layers to be in the valley region where the retrograde plasma drifts are the fastest. The experiments supported the idea that neutral winds [28] drive these instabilities by finding that the perturbed vertical fields are stronger than the zonal electrical fields in this region, while there are strong zonal plasma density gradients. The regular spacing of the bottom-type layers seen in the AL-

TAIR data was also seen in the topside plumes suggesting that these layers are precursors to more vigorous ESF activity and behave like seed instabilities for the GRT mechanism.

9 1.2 Linear theory of the plasma interchange instability

In this section, we consider a linear treatment of the plasma interchange instability, a ﬂuid instability akin to the Rayleigh-Taylor instability for charged particles. The linear theory should provide us with a basic understanding of the major driving forces for the instability mechanism, derived from the growth rate of the plasma waves. We follow the derivation of Zhargam and Seyler [45], beginning with the continuity and momentum conservation equations for electrons and ions. ∂N j + 5 · (N u~ ) = 0 (1.1) ∂t j

−eN (E~ + u~e × B) − 5P − Nm νeu~e = 0 (1.2)

! ∂ NM + u~ · 5 u~ ∂t i i

= eN (E~ + u~i × B~) − 5P − NM νi u~i + NM~g (1.3)

where N is the total plasma density, ν j is the collision frequency and j = i for ions and j = e for electrons. The other symbols denote the conventional symbols for the electric field (E~), the magnetic field (B~), pressure (P), velocity of the particles (~u), mass of the ions (M), mass of the electrons (m) and acceleration due to gravity (~g). These equations are in the frame of the neutral wind velocity. Col- lisions with neutrals are the only collisions considered because the momentum transfer between Coulomb collisions is negligible. We define a new coordinate system at the equator in order to contextualise this instability to ESF where xˆ points towards the east, yˆ points in the direction of the magnetic field (north) and zˆ points vertically upwards from the surface of the earth. In this treatment, the variations along the magnetic field are not taken into account, and only the

10 x − z plane is studied. Quasi-neutrality is imposed such that

5 · J~ = 0 (1.4) where J~ is the current density. In the F region, the drifts of the electrons and ions can be calculated as follows 1 T u~ = E~ × ~y + 5 ln N × yˆ e B e B νe 1 νe T − E~ − + 5 ln N (1.5) Ωe B Ωe e B 1 T g u~i = E~ × yˆ − 5 ln N × yˆ + × yˆ (1.6) B e B Ωi where (Ω j) is the species gyrofrequency and T is the temperature of the electrons and ions (Te = Ti = T in the nighttime ionosphere). Using the conservation of momentum, we can combine the ion drifts, density and electric ﬁeld into one equation. Taking the curl of this expression and imposing the quasi-neutrality condition gives ∂ 5 ×(N u~ ) + 5 × [u~ · 5N u~ )] = ∂t i i i m − ν 5 × (Nu~ ) + ν 5 ×(Nu~ ) + 5 × (N ~g) (1.7) i i M e e

It is important to note that while we have assumed the collision frequencies to be constant in the zˆ direction while deriving these equations; in reality they decrease exponentially with altitude. This is one of the reasons that the delineation between the collisional and inertial regime becomes important for ESF studies. Eq 1.7 relates the electric field and the plasma density. The electric field can be split into a background field plus a potential term, E~ = E0 − 5φ. A stream function can be defined with 5ψ = (1/B) 5 φ + (T/eB) 5 ln N. Substituting these quantities, we get the following equations describing the plasma dynamics in the F region. ! dN νe E 2T νe = 0 · 5 + 52 N − ρ (1.8) dt Ωe B eB Ωe

11 dρ 1 + (ˆy × 5| 5 ψ|2) · 5N = dt 2 " !# E0 g − νiρ + ~g × yˆ + νi + · 5 N (1.9) B Ωi

5 · (N 5 ψ) = ρ (1.10) where the new variable ρ is a the curl of momentum. The time derivative here is deﬁned as d ∂ = + (ˆy × 5ψ) · 5 (1.11) dt ∂t The E~ × B~ drifts of the magnetized electrons and ions are much larger than the other drifts and the electric ﬁeld is determined from the electron and ion currents. Still following the derivation in [45], we non-dimensionalize the variables in equations 1.8 - 1.10 in the following way

t = rt0

5 λ−1 = 50

0 N = N0 (1 + n )

−1 −1 ρ = τ N0 ρ

ψ = λ2 τ−1ψ0

ν = τ−1ν0

g = λτ−2g0

−1 0 (E0/B) = λτ (E0/B) where τ is a characteristic time scale and λ is a characteristic length scale. Equa- tions 1.8 - 1.10 now look like

∂n 2 + (ˆy × 5ψ) · 5n = D∗ 5 n (1.12) ∂t

∂ρ 2 + (ˆy × 5ψ) · 5ρ = (g × yˆ + νE /B) · 5n − νρ + µ∗ 5 ρ (1.13) ∂t 0

12 52ψ = ρ (1.14)

Where we have dropped the primes and only retained the quadratic nonlinear terms. This assumption is valid if we assume density ﬂuctuations that are small compared to the average density. The new terms in this expression D∗ and µ∗ are the diffusion coefﬁcient and viscosity, respectively. We can now use these equations to solve for a linear growth rate by using perturbations

i [(kx x−kzz) +γt] i [(kx x−kzz) +γt] of the form n0(x, z, t) = n0(z) + δn e , ρ0(x, z, t) = δρ e and

i [(kx x−kzz) +γt] ψ0(x, z, t) = δψ e in equations 1.12 - 1.14 to get the following results for γ.  r  k2 1  2 2 2 x  γ = − (D∗k + ν + µ∗k) − (D∗k − ν − µ∗k ) + 4γ  (1.15) 2  0 k2  2 0 where γ0 = (1/Ln)(g + νE0/B and Ln is a scale deﬁned by n0(z) = 1/Ln. To solve for the fastest growing eigenmodes we set D∗ = µ∗ = 0 and only look at the horizontal modes so kz = 0. In the collisional regime we have

1 E g γ(ν) = 0 + (1.16) Ln B ν and in the inertial regime

!1/2 g νE γ(ν) = + 0 (1.17) Ln LnB

The key takeaway from this result is that in the collisional regime, the electric ﬁeld term dominates the growth rate while in the inertial regime, the prime driver is gravity. While the linear theory does not completely describe the picture of the GRT dynamics in the F-region, it does give us an idea of how the growth rates might be expected to behave as a function of the driving forces.

The local treatment used to derive these expressions is a good description of the interchange instability when we are considering modes where the wavelength is much less than the scale length Ln. In order to study modes where

13 these two quantities are comparable, we must use a non-local analysis. Fol- lowing the analysis of Zhargam and Seyler [45], We use the perturbations

(γt+i kx) (γt+i kx) n(x, z, t) = n0(z) + nk(x, t) e and ψ(x, z, t) = ψk(x, t) e in equations 1.12 - 1.14 and get 2 ! 0 d 2 γn = ikn ψ D∗ − k n (1.18) k 0 k dz2 k 2 ! νE0 d 2 γρ = ik g + n − νρ + µ∗ − k ρ (1.19) k B k k dz2 k ! d2 − k2 ψ = ρ (1.20) dz2 k k

We assumes that nk and ρk are smooth function of z and since D∗, µ∗ << 1, we can ignore the second derivative terms and simplify to

2 " 0 # d ψ (g + νE0B)n k 0 − ψ 2 + 2 2 1 k = 0 (1.21) dz (γ + D∗k )(γ + ν + µ∗k )

0 0 2 2 Expanding n0 about its maximum at z = 0 gives us n0(z) = (1/Ln)(1 − z /d ) where d is a quantity that represents the localization of the gradient of the initial density proﬁle. This allows us to reframe Eq 1.21 into the quantum harmonic oscillator equation 2 2 ! d ψk ξ + E − ψ = 0 (1.22) dξ2 4 k Solving for the ﬁrst eigenmode of this equation gives us the largest nonlocal growth rate.

1 γ = − [(D k2 + ν + µ) ∗ k2) 2 ∗ q 2 2 2 2 − (D∗k − ν − µ∗k ) + 4 γ0 fnt(kd)] (1.23)

To this point, the dimension in the direction of the magnetic field has been ignored. A common approach to reintroducing it involves calculating flux tube integrated quantities and growth rates. Using this method allows us to calculate the contributions from the entire magnetic flux tube. We follow the calculations

14 of Sultan [37] and begin by introducing a new coordinate system for the equations relevant to this analysis. L is the geocentric distance, measured in units of

RE, pointing upward and φ is the geomagnetic longitude of the magnetic ﬁeld line of interest. These form a two-dimensional polar coordinate system. We begin with equations 1.1 - 1.4 and write the components of current density and ion velocity that are transverse to the magnetic ﬁeld. g jφ = σP(Eφ − B uL) + σH (EL − B uφ) − n e (1.24) Ωi

jL = σP(EL + B uφ) − (Eφ − B uL) (1.25)

jL EL v = − (1.26) φ n e B jL Eφ v = + (1.27) L n e B

Here, σP and σH are the Pedersen and Hall conductivities of the ionosphere and the other symbols have been defined before (here the plasma density is n). These quantities must be integrated along the magnetic field and the assumption is made these are electric equipotentials. The equations for the ion flux, F, and integrated current, J, are B B g J E − 0 UP E 0 UH − 0 e L N φ = ΣP φ 3 L + ΣH L + 3 φ (1.28) L L Ω0 B B J = Σ E + 0 UP − Σ E − 0 UH (1.29) L P L L3 φ H φ L3 L 1 L3 Fφ = Jφ − EL N (1.30) e B0 1 L3 FL = JL + Eφ N (1.31) e B0 P The new quantities N, ΣP, UL are defined as Z 2 3 N = RE L n(1 − ξ ) dξ Z 2 ΣP = RE L σP(1 + 3ξ ) dξ R L Z (1 + 3ξ2)1/2 UP E u σ dξ L = L P 2 3/2 ΣP (1 − ξ )

15 H P H ΣH, UL , Uφ and Uφ can be deﬁned similarly for the Hall conductivity and the ve- locities in the appropriate directions. These new quantities are the total electron content in the ﬂux tube N, the Pedersen conductivity ΣP, the Hall conductivity

P,H ΣH and the Pedersen or Hall conductivity weighted neutral wind UL,φ . These quantities together deﬁne the ﬂux tube. If we substitute these values into the continuity and conservation of current equations and introduce perturbations of the form ∝ ei(γt− kLL+ kφφ), the maximum growth rate can be found for purely horizontal waves (kL = 0).

4 2 −g0mi N0L ΣP,0 γRT = K (1.32) 2 2 ∂Σ 2 B0 ΣP,0 L H,0 2 m2 ∂L + ΣP,0 where 1 ∂ K L3N = 3 ( 0) (1.33) RE L N0 ∂L This represents the ﬂux tube integrated growth rate for the Rayleigh-Taylor instability without taking into consideration the effects of neutral winds or ambient electric ﬁelds.

16 1.3 Recent studies in the ﬁeld

Most of the recent studies in the field of ESF have been concerned with forecasting this phenomenon by studying the characteristics of the ionosphere in the post-sunset sector. Several studies have attempted to find sufficient conditions to be able to forecast ESF activity consistently. The primary physical phenomena of interest have been seeding from gravity waves, precursor wave structures and the effects of the pre-reversal enhancement (PRE) in the vertical drift. In the daytime, the electric fields are towards the east and at the equator lead to an upward E × B plasma drift. At night the electric field direction changes to point west and that leads to a downward drift. Prior to this reversal, there is a strong enhancement in the eastward electric field. If we look back at the growth rates derived in the previous section, we see that 1 E g γ(ν) = 0 + (collisional) (1.34) Ln B ν !1/2 g νE γ(ν) = + 0 (inertial) (1.35) Ln LnB In the collisional and inertial regimes, the growth rates depend strongly on the electric field and gravity respectively, where the relative effect of the latter compared to the former increases with increasing altitude due to the reduction in ion-neutral collisions where the neutral atmosphere is thinner. Hence the effects of the enhancement in electric fields during the PRE can affect the growth rate of the GRT and cause rapid vertical development post-sunset. The PRE also affects another important paramater and that is the F layer height. The enhancement in eastward electric fields causes a rapid ascent of the F layer, leading to a larger plasma density gradient where the GRT mechanism can develop. Fur- thermore, the height of the F layer determines whether the GRT mechanism is operation in the collisional or inertial regime. Gravity waves prove to be an im-

17 portant concept because the GRT requires some initial perturbation in order to develop; these waves have been proposed as a seeding mechanism, causing the undulations in plasma density that then evolve into the ESF instability.

Abdu et al [2] argued that the most important condition for ESF occurrence is the enhancement of the zonal electric ﬁeld. The increased vertical drift causes the rapid accent of the F-layer leading to a a large gradient in the bottom-side which is then susceptible to becoming unstable from the interchange instability mechanism. In an earlier study, [1] Abdu et al. state that planetary waves play a major role in the variability of the strength of the PRE which subsequently results in the variability in the vigour of ESF activity. They presented data from a SkiYmet meteor radar at Cachoeira Paulista and vertical plasma drifts measured by digisondes at Cachimbo and concluded that the mesospheric winds heavily affect the vertical coupling process in the E and F region dynamos through planetary-tidal wave interaction. In a 2009 investigation, Abdu et al [2] showed data from Sao Luis comparing the values of the PRE on quiet days and showed that downward drifts of 50-60 m/s corresponded to quiet nights in months where ESF was otherwise a common occurrence. The data also suggested that

ESF was triggered shortly following strong peaks in the drift velocity but did not necessarily subside with the transient decrease in drift values.

Eccles et al [11] explained the mechanisms behind this PRE. At sunset, the eastward electric ﬁeld is enhanced which causes the plasma drift, given by E~ × B~, to increase in the upward direction, causing the ionosphere to rise up to 100 km and creating free energy in the valley region where there is a strong density gradient that became unstable. The F region zonal neutral wind in the eastward

18 directions gives rise to vertical Pedersen currents. The divergence of this current in the F region dynamo causes the plasma to drift in the eastward direction as well, leading to the enhancement. Another mechanisms postulated [11] is related to the Hall conductivity which is approximately 20 times larger during the day than at night. The downward electric polarization electric fields generate a westward Hall current which is also much larger during the day. The negative divergence of this current leads to a eastward electric field before E-region sunset and then reverses into a westward field, which agrees with what we know about the movement of the plasma in this region.

Huang [14] linked the PRE mechanic to the generation of ESF by calculating threshold values that form necessary conditions to observe plasma instabilities using the data from several different investigations. The study cited evidence from the Jicamarca radar suggesting that no ESF occurred on nights when the PRE was less than 20 m/s. Evidence from Jicamarca, Ancon and Atofagasta measuring scintillation activity provided further evidence for the 20 m/s threshold value. Citing a study using over 20 years of Jicamarca data, Huang showed that the minimum threshold value increased with an increase in solar ﬂux conditions, going from 5-10 m/s near solar minimum to 50-60 m/s when f10.7 index was 250. In addition to the threshold value for PRE, there was also a direct relations between the onset height for ESF instabilities and the variation in solar ﬂux, with a higher onset height between 10-20 km producing stronger ESF. Observations from the C/NOFS satellite [16], however, suggested a relation between the probability of ESF occurrence and PRE values rather than a absolute threshold. The C/NOFS satellite took measurements over multiple geographic sectors while most of the evidence for the threshold values came from studies

19 at Jicamarca.

Seeding hypotheses are another popular ﬁeld of study in ESF research. Tsunoda

[40] argued that increased ESF activity did not necessarily have to depend on the growth rate of the Rayleigh-Taylor mechanism but rather on the amplitude of seed plasma perturbations that have a seasonal dependence. Tsunoda postu- lates that these perturbations could be directly linked to gravity waves which would explain ESF activity during solstices. The argument here is that a zon- ally propagating gravity wave whose wave fronts are aligned with the Earth’s magnetic ﬁeld can drive a divergent Pedersen current and therefore generate a zonal electric ﬁeld.

A related theory is the idea of large scale wave structures (LSWS) present in the bottom-side of the equatorial F layer. Tsunoda et al [40] postulate that the occurrence of ESF is related to the presence of these structures which come about by a modulation of isodensity contours in altitude. They argue that there is no requirement of a post-sunset rise of the F-region, contrary to what other theories might suggest. Presenting ionogram data from Kwajalein, they make the argument that the ESF activity signalled by the growth in virtual height of the F layer actually corresponds to an increase in the amplitude of an upwelling of the aforementioned LSWS. The absence of any kind of temporal oscillation in height only suggests that there was no zonal movement in the LSWS. Their conclusion in this case was that the LSWS are a sufﬁcient condition often aided by the post-sunset rise of the F-layer but not requiring it.

Huba and Krall [19] further investigated the role of meridional winds and the

20 role they play in ESF, pushing against the conventionally accepted theory that these winds have a stabilizing effect on the Rayleigh-Taylor instability. Exper- imental observations did not seem to conclusively support either argument so

Huba and Krall investigated this using the NRL simulation code SAMI3 [19]. The simulation was run with several different meridional wind profiles, and they found that the key feature of the wind was actually the gradient; a wind profile with a positive gradient was a stabilizing influence while one with a negative gradient was destabilizing, with the gradient being latitudinal. This investigation followed the first results of the aforementioned SAMI3 model which provided numerical evidence for some of the theories discussed earlier. The model showed that pre-sunset ionospheric density perturbations led to ESF activity and that zonal shear flows were observed across the plasma bubbles [17].

Anderson and Redmon [3] explicitly addressed the question of the role played by the virtual height of the F layer in ESF activity. They attempted to calculated a threshold value which would be able to successfully predict radio wave scintillation due to ESF bubbles. This theory is based on the premise that the rapid post-sunset rise of the F layer is the most important physical phenomenon in

ESF dynamics. Using the S4 index, a measure of the amplitude modiﬁcation of radio waves due to ESF bubbles, they measured the likelihood of scintillation activity for different values of h0F, the virtual height of the F layer. Using their

FIRST [3] forecasting technique in 5 longitudinal sectors they found h0F values successfully predicted scintillation activity 89% of the time. A real time forecasting system would require a network of digital sounders across the magnetic equator.

21 This section does not constitute an exhaustive list of all the research being done in ESF but aims to address the key areas of research. Some of these topics may be revisited later on while discussing the outcomes of the WINDY campaign, speciﬁcally the ideas of seeding from gravity waves and meridional winds.

22 CHAPTER 2 RADAR INVESTIGATIONS DURING PROJECT WINDY (2017)

Project WINDY (Waves and Instabilities from a Neutral DYnamo) was a radar experiment that took place on Roi-Namur in the Kwajalein Atoll between Au- gust 30th and September 10th, 2017. The experiment was centred around a sounding rocket investigation of the equatorial ionosphere and the conditions preceding ESF activity with the aim of being able to forecast the occurrence of this phenomenon. The ALTAIR radar was used to study the ionosphere every evening for 10 nights, providing an unbroken data set of ESF characteristics at the equator. Due to the failure of the rocket motors during launch, no in-situ data are available for this campaign, but the radar scans provide an excellent picture of ESF activity during moderate solar ﬂux conditions. The aim of project WINDY ultimately became the evaluation of the bootstrap theory of convective plasma instability [24].

23 2.1 ALTAIR radar operations and data Processing

The ARPA Long-Range Tracking and Instrumentation Radar (ALTAIR) is located on the island of Roi-Namur in the Kwajalein Atoll (9◦23’46”N,

167◦28’33”E). The radar is a fully steerable, large aperture dish that can oper- ate in two frequencies, UHF (422 MHz) and VHF (158 MHz) simultaneously and measures both incoherent and coherent back-scatter from plasma irregularities. The following operational details are collected from [24]. ALTAIR typically operates at a peak power of 6 MW with a 5% duty cycle but these parameters can differ slightly from mode to mode. The radar modes used during both the

WINDY and Too WINDY campaigns were the same as those developed for the 2004 Equis II campaign [23].

Mode PW (µs) BW (MHz) Resolution (km) PRF (Hz) Duty (%) VEP 1-300 300 cw 45 67 2.0 VEP 3-300 300 0.01 15 67 2.0 VEP 13-13 13 1 0.15 200 0.26 UEP 1-300 300 cw 45 67 2.0 UEP 3-300 300 0.01 15 67 2.0 UEP 88-88 88 1 0.15 200 1.8 U0.25-400 400 0.25 0.6 120 4.8

Table 2.1: ALTAIR radar modes used during WINDY and Too WINDY

During the WINDY project, ALTAIR measured 10 consecutive days of post- sunset ionospheric activity, with scans beginning around 19:00 LT and contin- uing beyond 22:00. The purpose of the radar during this experiment was to identify the night and time at which to launch the sounding rockets. The main observation from the radar scatter was the structure and presence of plasma irregularities and the shape of the post-sunset ionosphere. The primary radar

24 modes employed were the UEP 3-300 and the VEP 3-300. This consisted of VHF and UHF scans approximately every 10 minutes from east to west aligned exactly perpendicular to the magnetic ﬁeld. The wave vectors of the instabilities of interest are aligned in the plane perpendicular to the magnetic ﬁeld, so the two dimensional scans paint the full picture of the plasma structures. Scans were also conducted in the UEP 1-300 and VEP 1-300 where the radar was steered

6◦off the perpendicular plane and are referred to as oblique scans. The perpendicular scans provide the conditions required to detect coherent scattering structures and the oblique scans provide ideal ionosphere density proﬁles for viewing ESF activity in the form of density irregularities.

The primary purpose of ALTAIR is the tracking of spacecraft and ballistic mis- siles, and ALTAIR is therefore a highly sensitive instrument. It can perform incoherent and coherent scatter experiments using the UEP and VEP modes mentioned above. This sections will focus on how ALTAIR is used for ionospheric studies using four important data processing methods. The ﬁrst is the calibration of the system to go from backscatter power to electron density. We begin with the radar equation

Ae f f P (W) = P (2.1) rx scat 4πR2 where Prx and Pscat are the power received by the radar dish and the power scattered by by the target respectively. Ae f f is the effective area of the radar dish. The scattered power can further be represented as

Dtx P = P σ (2.2) scat tx 4πR2 radar

Where Dtx is the directivity of the radar beam and the σ is the radar scattering

25 cross section of the target. This gives us an expression for the power received

Dtx Ae f f P (W) = P σ (2.3) rx tx 4πR2 radar 4πR2 For any given radar experiment, the quantities of interest in this expression are the directivity of the radar beam, Dtx and the effective area Ae f f . While in theory both these quantities can be calculated, the ALTAIR radar is a calibrated system, using a falling metal sphere with a known radar cross section to perform the calibration. The same calibration constant can be used to calculate volume scatter from the electrons in the F-region, which is done by using the following equations from [26].

dPinc = σv dV (2.4)

Dtx Ae f f dP (W) = P σ dV (2.5) rx tx 4πR2 4πR2 v

Where σv is the scattering cross section per volume of the soft target and Pinc is the incident power. The scattering volume can be calculated–it’s just the volume of the radar pulse in a particular range gate

dV = ∆rr2dΩ (2.6) where r and Ω are polar coordinates. Integrating this over all solid angles leaves us with an expression Z D(θ, φ) Ae f f (θ, φ) cτ P = P r2 sinθ dθ dφ (2.7) rx tx 4πR2 4πR2 2 Using the same calibration constant from the hard target case to calculate the received power, the electron density can be calculated from the following equation

σv = ne σe (2.8)

Where σe is the scattering cross section of an electron, which has been calculated. The constant used by ALTAIR for going from backscatter power to electron number density is 47.

26 Matched filtering is typically the first step in the receiver process which determines which part of the signal is processed. The filter characteristics are designed to ’match’ to the expected received signal and the function usually attempts to optimise the signal to noise ratio, though it may be designed perform other functions as well. We follow the calculations in [26] to explain how this process works. For a given input x(t) = f (t)+n(t), where f (t) is the incoming signal and n(t) is the noise. The output is y(t) = y f (t) + yn(t) which are the signal and noise components respectively. The aim is to maximise the ratio R which is just the ratio of the signal power to the noise power

| y (t ) |2 R f o = 2 (2.9) E | yn(to) |

The expectation of the noise power can be approximated with a time average since we assume the noise to be statistically stationary. We consider our linear ﬁlters H(ω) in the frequency domain and h(t) in the time domain which are Fourier transform pairs. Similarly we can consider our input signal F(ω) and noise N(ω) in the frequency domain. In the frequency domain the outputs are just the products of the ﬁlter and the signal components F(ω)H(ω) and

N(ω)H(ω). To convert to the time domain, we must Fourier transform this quantity. 1 Z y (t) = F −1(N(ω)H(ω)) = N(ω)H(ω) e jωt dω (2.10) n 2π The output noise power then being

!2 Z Z 1 0 y (t)y∗(t) = N(ω)H(ω) e jωt dω N∗(ω0)H∗(ω0) e jω t dω0 (2.11) n n 2π

27 The time average of this expression over an interval T is

!2 Z 1 1 0 hy (t) y∗(t)i = N(ω)N∗(ω0) H(ω)H(ω0) e j(ω−ω )t dω dω0 dt n n T 2π 1 Z = S (ω)|H(ω)|2dω (2.12) 2π n where the new term S n is the power spectrum of the noise in power per Hz. If the noise is white, the spectrum is ﬂat and this quantity is a constant S 0. Using these results in the expression for R for a given instant in time t0. R | 1 jωt0 |2 2π F(ω) H(ω)e R|t0 = R (2.13) S 0 | |2 2π H(ω) dω Making use of the Schwartz inequality to calculate the upper limit, the maximum signal to noise ratio follows when the expression is equal. With f = F, g = H e jωt and |g|2 = |H|2

Z b 2 Z b Z b 2 2 f (x)g(x) dx = | f (x)| dx |g(x)| dx (2.14) a a a

When we use these results in the time domain, we see the physical meaning of the matched ﬁlter theorem.

∗ ( H(ω) = AF (ω) e − jωt0) (2.15) 1 Z h(t) = AF∗(ω)e− jωt0 e jωtdω 2π 1 Z = AF∗(ω)e− jω(t−t0)dω 2π !∗ 1 Z = AF∗(ω)e− jω(t−t0)dω 2π

∗ = A f (t0 − t)

Therefore we see that the ideal ﬁlter is the complex conjugate of the time reverse of the signal itself.

Related to the concept of matched ﬁltering is that of pulse compression. Pulse

28 compression is a technique used in order to to balance the range resolution (related to the width of the pulse) and sensitivity (related to the power in the pulse). In doing so, we can also optimize the usage of the transmitter’s duty cycle which would otherwise be limited by constraints to avoid range and frequency aliasing. The fundamental principle behind pulse compression is that the range resolution of the pulse is not related to the transmitted pulse width itself, but rather the width of the matched ﬁlter output that determines this. A suitably modulated long pulse can appear ’compressed’ when received through the matched ﬁlter and increase the signal to noise ratio.

Pulse compression is primarily done in two different ways: The ﬁrst is phase coding and the second is frequency chirping. In phase coding, the original pulse is split into several divisions, each with a phase of 0◦or 180◦. This is known as binary coded pulse since there are two possible phases; for different series of binary codes, different outcomes can be achieved such as compressing pulses, suppressing side-lobes etc. Frequency chirping is equivalent to phase coding in result but performed differently. Instead of modulating the phase of the pulse, the frequency of the pulse is changed. This has the same desired physical result of broadening the bandwidth of the pulse.

The method of Hildrebrand and Sekhon [13] is used to estimate the noise levels in the radar signals. A brief description of the method is given below following calculations in the paper. The signal and noise are both gaussians in nature but while the signal has a frequency distribution, the noise is white. The variance of a white spectrum is given by F2 σ 2 = (2.16) N 12

29 for a frequency span F and for Gaussian signals, spectral densities are indepen-

2 dent and var(S n) = hS ni . where S n = S (Fn). For white noise, S (Fn) can be calculated by averaging S n over n. The variance is calculated using a running average of p points 2 hS ni var (S ) = (2.17) n p Now given the Doppler spectra of the signal, new spectra can be created by ignoring frequencies above some arbitrary threshold value. This can be done repeatedly until the only signal left resembles white noise. The threshold of frequencies ignored forms the noise threshold of the signal. The equations used to then test for white noise are as follows

2 2 σ = (Σ fn2 S n/ΣS n) − (Σ fnS n/ΣS n) (2.18)

F2 σ 2 = (2.19) N 12

P = ΣS n/N (2.20)

2 Q = Σ(S n2 /N) − P (2.21)

2 R1 = σN2 /σ (2.22)

2 R2 = P /QP (2.23)

For white noise, R1 and R2 should be unity. For a radar signal it is expected that

R1 > 1 and R2 < 1.

30 2.2 Presentation and discussion of ALTAIR scans

The ALTAIR radar scans show 10 nights of ESF climatology over Roi-Namur in the Kwajalein Atoll (9◦23’ 46” N, 167◦28’ 33” E). The radar scans began at roughly sunset every day with each scan taking approximately 10 minutes. The occurrence of topside plumes was common during this period of moderate solar ﬂux (f10.7 ≈ 100). As is typical, the topside activity was preceded by patchy bottom-type irregularities that showed vertical development through to the topside in the post-sunset hours. 9 of the 10 nights displayed moderate to strong ESF activity, manifesting in large plasma depletion bubbles observed by AL-

TAIR preceded by scattering layers in the bottom-side. These scans be used to identify the irregularities in plasma density which act as the required perturbations for the GRT and also the developed plumes in the topside. The ﬁgures in this section plot the base-10 logarithm of the electron density.

Fig 2.1 details the scans during the onset of the plasma instabilities. While AL-

TAIR ran for several hours each night, the scans presented here show the earliest observations of the irregularities. In panel ‘a’ on the left, VHF scans of the ﬁrst irregularities observed on a given evening are show. We see the perturbations at the F region boundary in the VHF scans that are required for instabilities to develop by the GRT mechanism. On the right, panel ‘b’ shows the UHF scans from 10 minutes prior. The VHF VEP 3-300 mode is the most sensitive to coherent scatter and is therefore used to probe for bottom-type layers. The UHF scan shows the structure of the F-region clearly. The objective in displaying the data in such a manner is to provide the opportunity to identify any features in the ionospheric density proﬁle that can foreshadow the eventual onset of ESF.

31 The phenomenology is consistent from night to night. Bottom-type irregularities form in the valley region before large ESF plumes appear in the topside of the F-region. On some nights, the ionosphere shows moderate structuring, but these undulations do not seem to cause the formation of the scattering structures that are inevitably seen later.

32 Figure 2.1: a) VHF scans of the ﬁrst observed irregularities showing log10 electron density (cm−3). b) UHF scans preceding panel a by 10 minutes

33 Fig 2.2 shows similar scans but because of the unpredictable nature of the event, there were no scans available of the ionosphere before irregularities appeared. ALTAIR began recording scans at roughly 19:15 - 19:30 local time every- day, so if irregularities developed before the ﬁrst scan, then the data for that time is not available. In the panel on the right here, bottom-type patchy irregularities are already present

Figure 2.2: a) VHF scans of the ﬁrst observed irregularities showing log10 electron density (cm−3). b) UHF scans preceding panel a by 10 minutes

34 Fig 2.3 and 2.4 show the different radar modes of ALTAIR in action during a night of vigorous ESF activity. The panels labelled ‘a’ are the familiar VEP 3-300 VHF mode used to identify irregularities and the development of the plumes are clearly visible in this mode as well. The panels labelled ‘b’ are the oblique modes, where scans are made 6◦off perpendicular to the magnetic ﬁeld. There is no coherent scatter from plasma structures in this mode and the depletions of electron density in the ionosphere are clear. The panels labelled ’c’ plot signal to noise ratio rather than showing log10 electron density; the plumes in the topside are clearly visible in this mode.

Presenting the scans in this manner allows us to also identify any potential seed structures such as large scale wave structures from gravity waves that may appear as undulations in the plasma density preceding ESF activity. During the WINDY project, no such signatures were seen in the ALTAIR data. The main takeaway from this data is the formation of bottom-type scattering from the shear instability which appears to seed the GRT.

35 Figure 2.3: Scans from different radar modes on August 31st 2017 showing the evolution of the instabilities through the evening. a) VHF scans perpendicu- −3 lar to the magnetic ﬁeld of log10 electron density (cm ). b) UHF scans oblique ◦ −3 (6 off-perpendicular) to the magnetic ﬁeld of log10 electron density (cm ). c) Signal to noise ratio.

36 Figure 2.4: Scans from different radar modes on September 4th 2017 showing the evolution of the instabilities through the evening. a) VHF scans perpendic- −3 ular to the magnetic ﬁeld of log10 electron density (cm ). b) UHF scans oblique ◦ −3 (6 off-perpendicular) to the magnetic ﬁeld of log10 electron density (cm ). c) Signal to noise ratio.

37 2.3 Spectral analysis of irregularities

A quantitative analysis can be done for the dataset from the WINDY missions, analysing the intermediate-scale irregularities that exist in the ionosphere before the coherent scattering structures appear. The aim of this analysis is to identify any periodic structures in the plasma density that may suggest the presence of seed waves and to evaluate their effect on the development of ESF. While these were not visible to the eye, a spectral analysis may reveal density undulations for amplitudes that cannot be detected by looking at the scans. For this analysis, the ﬁrst VHF scan of the night was used. In both cases, there were no detected coherent structures at this time and no irregularities were visible in the scans. The easiest way to perform this analysis would be in two-dimensional Cartesian coordinates, but the ALTAIR radar acquires data in polar coordinates as seen in the scans. In this format each row contained data from different ranges for a given azimuthal angle measured from the horizontal. For this analysis, we used the values of electron density stored at each location. Since we are interested in the spectral properties in a Cartesian system with East-West being x and Up- Down being y, the data must be converted to a Cartesian grid. This can be done using bilinear interpolation by deﬁning a map function for each location in the Cartesian grid as a function of locations in the polar grid governed by the equations: x = r cos φ (2.24)

y = r cos φ (2.25)

The analysis could now be done quite simply in the horizontal and vertical directions.

38 The Cartesian array was filtered using a median filter of order 5 to remove any spurious signals that would interfere with then analysis. The quantity δn was calculated which is defined as the difference in the unfiltered and filtered ar- rays. This quantity was used as the estimate for the noise to be studied. The array was then truncated to exclude the columns on the edges because of edge effects from the coordinate transformation. Only altitudes above 150 km were considered by further truncating the array to exclude clutter from the E-region, giving us a grid of 600 km by 600 km in the horizontal and vertical directions which we will call x and y. The dominant frequencies in the ambient noise were identified by taking a two-dimensional Fourier transform of the quantity δn/n where n is the filtered density profile.

The analysis revealed that the noise followed a two-dimensional power law, corresponding to the two dimensions of the array δn. In order to generate the pink noise, the two-dimensional spectral power density was ﬁt to a function of

m n the form P0/(1 + (kx/k0x) + (ky/k0y) ) where P0, k0x, k0y, m and n were the parameters to be fit. The parameters m and n were iterated manually while the k0x, k0y and P0 were fit numerically. Fig. 2.5 and Fig. 2.6 show the functional form as a contour plot superimposed on the colour plot of the computed frequency distribution. The table below contains the values identified by the curve fitting. These values are for m = n = 2

−5 −1 −5 −1 6 2 Date k0x (10 m ) k0y (10 m ) P0(10 m ) 31-08-2017 2.106 1.612 5.61 08-09-2017 1.550 2.251 5.62

Table 2.2: Parameters describing the spectral distribution of irregularities

The k0x value corresponds to horizontal wavelengths of 200 km on August

39 31st and wavelengths of 150 km on September 8th. The spectral analysis shows that there are certain preferred wavelengths in the density ﬂuctuations in the ionosphere. However, there doesn’t seem to be any evidence that this structure is only present during or before ESF activity. Similar results are found for 31st August and 9th September; vigorous ESF was observed on 31st August and no instabilities were observed on 9th September.

Figure 2.5: Amplitude function superimposed over the frequency distribution of small and intermediate-scale irregularities

40 Figure 2.6: Amplitude function superimposed over the frequency distribution of small and intermediate-scale irregularities

41 CHAPTER 3 ROCKET AND RADAR INVESTIGATION DURING PROJECT TOO WINDY (2019)

Project Too WINDY took place two years after WINDY with the aim of successfully completing the sounding rocket investigation that had been planned earlier. This experiment took place with a return to Roi-Namur in the Kwajalein atoll. The ALTAIR radar was in operation, used to monitor ionospheric conditions and to decide whether the physics was ideal for a rocket investigation. The launch window for this investigation was between June 9th and June 19th, 2019. The data from the sounding rockets would complete the picture that was partially covered by project WINDY by acquiring in-situ data of the F region to study the shear ﬂow mechanism. The Too WINDY datasets provided sounding rocket data of the F-region in addition to another ALTAIR dataset. The space weather climate was slightly different during this campaign, leading to different observations from WINDY but still providing an excellent picture of ESF in the Paciﬁc sector.

42 3.1 Radar observations during Too WINDY

During Too WINDY, radar scans similar to those from WINDY were also acquired by running ALTAIR for 10 nights during the launch window. Like during WINDY, the role of ALTAIR was to monitor ionospheric conditions and the development of small-scale irregularities in the bottomside layers which would prompt the launch of the rocket. However, unlike during WINDY this did not always result in a systematic run beginning every day post-sunset and continu- ing for roughly 4 hours. The optical conditions on several nights of project Too WINDY ruled out any rocket launches which made the use of ALTAIR purely academic after the opportunity to launch had passed. Apart from certain technical difﬁculties, this allowed us to procure another dataset of radar scans. The biggest difference in the space weather climate was the low solar ﬂux in June,

2019, averaging around 70, as opposed to 100 or more in September, 2019. Due to this, most nights were unremarkable regarding ESF activity, the scans from the rocket launch and one single night where plumes were observed have been presented.

On June 12 2019, 1 week before the rockets were launched, ESF was observed with similar phenomenology to the WINDY data. Unfortunately due to poor optical conditions, the rockets could not be launched. However it is interesting to note that ESF did occur despite the low solar flux conditions. Fig. 3.1 details the scans from that evening. They are presented similarly to the WINDY data discussed earlier. One of the features of note right away is that the density if the F region is much lower than during WINDY owing to the low solar flux and reduced ionisation. The first panel shows the VEP 3-300 mode when irreg-

43 Figure 3.1: ALTAIR scans at the onset of ESF ularities were ﬁrst detected. The lower panel then shows the UEP 3-300 mode scanned 10 minutes prior. There are some undulations observed in the bottom- side east of center in the scan. The irregularities in the ﬁrst panel seem to appear in the density trough of this undulation after. These perturbations at the boundary showed vertical development into the topside later that night. Undulations similar to these were observed on other nights during the Too WINDY campaign but scattering layers did not necessarily develop, suggesting that, by itself, ionospheric structuring is not indicative of ESF. Fig 3.2 shows the evolution of post-sunset ESF through the night. Interestingly there are also sporadic E-

44 Figure 3.2: ALTAIR scans at the onset of ESF layers observed at low altitudes. This data was not typical for the observations during Too WINDY but ﬁts in well with what we expect to see on an active ESF night as demonstrated by the data from WINDY.

45 On June 19 at a roughly 23:30 local time, the presence of some coherent scattering structures in the topside and structuring in the bottom-side layers prompted the launch of the rocket [25]. Fig 3.3 shows the VHF scans; being the more sensitive mode, coherent structures are clearly visible in the topside even before the rocket launch. In panel c, the signature at an altitude of ≈ 350 km and at -350 horizontally is the presence of the rocket being observed by ALTAIR as a scattering structure. The other signatures are all plasma structures in the topside. The less sensitive UHF mode in Fig 3.4 paints a similar picture to the VHF mode, while detecting less coherent scatter. The features of interest are the same, with panel c showing scatter of the sounding rocket and panel g showing topside irregularities.

This was not a typical ESF event. This variety of ESF, known as post-midnight ESF (PMSF) is commonly observed during periods of low solar ﬂux. It has been often been observed at Jicamarca but the phenomenology has typically followed that of post-sunset ESF, beginning with the bottom-type patchy layers that develop into topside plumes. However, the data from the launch night suggest that some other factors may be at play, since no bottom-type echoes were observed before the plasma bubbles in the topside appeared. Theories for why this plume appeared in the topside with no warning are discussed in subsequent sections while considering other research considering this and postulat- ing theories to help understand this.

46 Figure 3.3: ALTAIR VHF scans from the rocket launch

47 Figure 3.4: ALTAIR UHF scans from the rocket launch

48 3.2 Rocket operations and data processing methods

The rocket launches took place on 19 June, 2019, at 23:28 local time (22:36 SLT) and 23:33 (22:41 SLT) from the island of Roi-Namur, part of the Kwajalein Atoll in the Marshall Islands. The ﬁrst rocket launched carried the chemical payload containing tri-methylaluminium and lithium. The TMA would be released at 100 km and the lithium would be released at higher altitudes in the F-region.

The chemicals would be used as tracers in order to measure neutral winds in the mesosphere-lower-thermosphere and thermosphere regions [25]. An ex- tensive ground camera system at three locations would be used to triangulate the motion of the tracer chemicals once launched. An aircraft would also be photographing the chemical ignitions in order to bypass the low-level cumulus which were obstructing the view of the ground cameras. The aircraft’s view could have been potentially obstructed by cirrus structures overhead and me- teorological conditions were closely monitored in order to ensure maximum visibility. This was the primary reason why the rocket launches could not take place on 12 June 2019 during the ESF event.

The second sounding rocket was launched 5 minutes after and carried the instrument payload. The payload included four stacer booms installed at 90◦to one another with a separation of 6 feet between spheres. The two sets of parallel booms measured voltage differences across from one another, and those quantities were used to calculate electric ﬁelds. A Langmuir probe boom was mounted forward, perpendicular the electric ﬁeld booms, to measure the in situ currents from which electron density estimates could be made. A 3-axis Flux- gate magnetometer was the third instrument on the instrument rocket. The data

49 acquired were scalar electric fields, currents and vector magnetic fields against time after launch and the altitude of the rocket. The magnetic attitude controls system kept the body of the rocket aligned with the earth’s geomagnetic field while the electric field booms spun in the plane perpendicular to the field [25].

Sounding rocket data underwent data processing in order to ﬁnd the relevant quantities. This section will focus on the methods use to convert the raw data from the rocket to values of interest. The electric ﬁeld data was acquired as a vector quantity, measured in the plane perpendicular to the length of the rocket.

The rocket was spinning, in order to maintain attitude, and also gyrating about the lengthwise axis. This motion produced an oscillatory component into the electric ﬁeld data that had to be removed computationally. This was done using the data from the horizon crossing indicator (HCI) installed on the rocket.

The HCI functions as a horizon sensor for any planetary body of interest, in this case Earth. In a passive scanning set-up, the camera sweeps its field of view along with the gyrating motion of the rocket, measuring the infrared radiation in its current field of view. As its field of view crosses the Earth’s horizon and points towards space, there is a noticeable gradient in the infrared radiation. The time between each crossing and the velocity data can be used to estimate the rotational motion of the vehicle. The electric field data has another unwanted component originating from the ~v × B~ field generated by the rockets propagation through the Earth’s magnetic field. Both these artifacts must be taken into consideration while processing the data.

The GPS position and velocity data of the rocket were acquired in ECEF (Earth-

50 centred, earth-ﬁxed) coordinates and had to be converted to ENU (East-North- Up) coordinates using the following transformation where Φ is the geocentric latitude in radians and Ψ is the longitude in radians.              − sin Ψ cos Φ 0  vx  veast              − cos Ψ sin Φ − sin Ψ sin Φ − cos Φ vy = vnorth (3.1)              cos Ψ cos Φ sin Ψ cos Φ sin Φ  vz  vup 

The ~v × B~ ﬁeld can now be calculate using the velocity in ENU coordinates.

The values for the Earth’s magnetic ﬁeld were taken from the International Ge- omagnetic Reference Field (IGRF) model in ENU coordinates rather than the instrument on the rocket because of its superior precision. As described earlier, the electric ﬁeld data had an oscillatory component due to the spinning of the rocket about its axis. In order to extract the mean and amplitudes of the electric

2πt ﬁelds, the data was ﬁt to a function of the form A sin( T + φ) + E0 for the parameters A, T, φ and E0; the amplitude, period, initial phase angle and DC offset respectively.

This was done for both the ﬁelds from parallel sets of Stacer booms 1, 2 and booms 3, 4. This quantity can be further converted to another convenient coordinate system known as the eccentric dipole coordinate system with axes along the earth’s magnetic ﬁeld, perpendicular to plane containing the magnetic dipole axis and earth’s rotation vector and the third completing the right handed system. At the equator, these axes can be termed ‘parallel’, ‘vertical’ and

‘horizontal’ corresponding to the parallel to the earth’s magnetic ﬁeld, vertical with respect to the ground and horizontal with respect to the ground, pointing towards the east. This transformation can be done using the following matrix, where δ is the angle of magnetic declination and θ is the angle of magnetic incli-

51 nation.             − sin δ − cos δ sin θ cos δ cos θ  veast   vvertical               cos δ − sin δ sin θ sin δ cos θ vnorth = vhorizontal (3.2)              0 cos θ sin θ   vup   vparallel 

In order to correct for the gyrating motion of the rocket, data from the HCI was used. By calculating the difference in the time between the upper and lower peaks of the HCI, corresponding to the sensor pointing towards Earth and space. The period of the gyration was not constant and the trend was fit to a polynomial of degree 2. This polynomial was then used to calculate the frequency of the gyration against time of flight and therefore the angle of rotation at any point during the flight. These measurements can then be converted into eccentric dipole coordinates using the following equations where α is the rotation angle that was just calculated.

Ehorizontal(t) = E12(t) cos(α(t)) + E34(t) sin(α(t)) (3.3)

Evertical(t) = −E12(t) sin(α(t)) + E34(t) cos(α(t)) (3.4)

After filtering these quantities using a Butterworth lowpass filter to remove any high frequency instrument noise. the ~v × B~ field bias can then be subtracted to give the DC electric fields. The transverse electric fields here imply transverse E~ × B~ drift and these drift are converted to the stationary frame of the radar.

Electron density measurements were made by the Langmuir probe mounted on the instrument payload. The Langmuir probe is used to measure a scalar current in the plasma medium through which it travelling. This is done by using an internal circuit to introduce a voltage bias on the probe. If the voltage of the probe Vp is much less than the voltage in space Vs then an ion current is collected. Following this, there exists a voltage and a corresponding current

52 where all the electrons have been repelled known as the Ion Saturation current. This value can be used to calculate the electron density but in order to do so, the electron temperature and plasma potential need to be calculated ﬁrst.

The transition region for the Langmuir prove is the region in the I-V relation- ship between the ion saturation current and the electron saturation current. For a Maxwellian distribution

Ie = Ies exp[e(Vp − Vs)/kbTe] (3.5) and ! kbTe I = eA n v¯/4 = en A (3.6) es s e e s 2πm where Ie is the electron current, Ies is the electron saturation current and As is the area of the probe sheath. The semi-logarithmic curve of the current and the probe potential should then be a straight line which is exactly 1/kbTe and is a robust measurement of the electron temperature. In order to ﬁnd the plasma potential, straight lines are drawn through the I − V curves in the electron saturation region and the transition region. The intersection of these lines then occurs at the values V = Vs and I = Ies.

Knowing the electron temperature and ion saturation current allows us to use the following equation to calculate ne ! r 1 kbTe I = A exp qn (3.7) sat s 2 e M which gives r Isat M ne = (3.8) qAs exp (−1/2) kbTe

53 3.3 Presentation of sounding rocket data

The purpose of the sounding rocket data is to acquire measurements of the electric field, magnetic field, plasma density and neutral winds in the bottom-side of the F region where the irregularities first develop. The study of these quantities will provide evidence of the shear flow mechanism which is responsible for the bottom-type scattering layers. Despite the successful launch of the rocket, neutral wind measurements are unavailable and this specific analysis could not be completed. However, the data from the instrumented sounding rocket is presented below with comments on interesting features. However, this data did not provide a tremendous insight into the planned study of ESF.

The processed data gives vector electric fields in the X and Y directions. These are plotted in Fig 3.5 and Fig 3.6 on the upleg and downleg of the flight respectively. Electric field measurements began around 250 km in altitude when the stacer booms deployed. It is clear that the upleg and downleg data mainly agree with each other and that irregularities can be seen in the zonal drifts as fluctuations in the field data. These are mainly present between 300-325 km and above 350 km altitude [25]. The most noteworthy feature of these data is the shift in

ﬂow from eastward to westward at 350 km.

54 Figure 3.5: Electric ﬁeld vector data from the rocket ﬂight upleg

55 Figure 3.6: Electric ﬁeld vector data from the rocket ﬂight downleg

56 Fig 3.7 shows the magnitude of the magnetic ﬁeld data as measured by the magnetometer on the rocket and it is plotted against the magnetic ﬁeld from the IGRF model [38]. IGRF stands for the International Geomagnetic Reference

Field. This model is calculated through a collaborative effort of modellers and institutions collecting magnetic field data and aims to reproduce the field generated by the Earth’s core without any external sources. The measured field was calibrated using the values from IGRF. In all calculations requiring the magnetic field components, such as the computation of the ~v × B~ bias in the D.C. electric fields, IGRF values are used.

Figure 3.7: Measured magnetic ﬁeld compared to the IGRF model ﬁeld

57 Fig 3.8 shows the magnetic field fluctuations perpendicular to the Earth’s field. The plot in Fig 3.4 was created by using the following equations involving the measured magnetic field.

q 2 2 2 B f luc = |Bmeasured| − Bx + By + Bz (3.9) where the last term in the equation uses values from the IGRF model. This was done in order to remove the Bz component of the measured magnetic field. The IGRF magnetic field at this latitude is primarily the Earth’s magnetic field in the zˆ direction. An attempt to further reduce noise was made by calculating and subtracting an oscillatory polynomial from the difference. However, data processing methods were not sufficient enough to reduce the noise to a point where fluctuations could be meaningfully observed. The fluctuations in the magnetic

field perpendicular to the Earth’s magnetic field are of interest to us because they are indicators for the presence of electromagnetic waves. The expected magnetic field deviations for this experiment were in the range of 1-3 nT which also happens to be the amount of instrument noise present. The fluctuations in the magnetic field imply fluctuations in current density which are statistically insignificant at this magnitude. The late launch time for the rockets and the low solar flux probably reduced the ionospheric conductivity to a much lower level than anticipated.

58 Figure 3.8: Magnetic field fluctuations perpendicular to the Earth’s magnetic field

59 Data from individual channels of the electric field booms were used to create periodograms of frequency measurements. These data were passed through a low pass hardware filter prior to sampling [25]. Spectra were computed by taking 1-dimensional Fourier transform of the samples multiplied by a Han- ning window. This value was then divided by the bin width to provide a power density that could be represented in a density plot. Fig 3.9 displays the measurements against flight time. Strong signatures between 100 Hz - 400 Hz suggest the presence of ELF hiss between the first gyroharmonic frequencies for helium and hydrogen [25]. ELF hiss is an extremely low frequency electromagnetic wave that has been observed in the ionosphere during ESF events by satellites such as DEMETER [33]. This phenomenon is relevant to ESF studies because these signatures have been found to disappear where plasma irregularities are present in the topside F region. [25] also calculated ELF spectrograms for the Langmuir probe and magnetometer data but found no features of interest in either of the instruments. As discussed earlier, the instrument noise levels of the magnetometer prevented any observation of the electromagnetic waves seen in the electric field data.

Hysell et al [25] made the connection between the ELF emissions seen in the electric ﬁeld spectra in Fig 3.9 at frequencies between 100 Hz - 1 KHz to the low-frequency whistler mode hiss that was observed by the Communication

Navigation Outage Forecast System (C/NOFS) satellite in the equatorial and low latitude regions [7]. Whistler-mode waves are very low frequency waves that have been shown to excite plasma density irregularities such as those seen during ESF events [29]. The characteristic harmonic frequency emissions and absorption can be used to identify ion composition in the ionosphere. Chen et

60 al [8] had investigated the dependence of low-altitude hiss on magnetic latitude. Their model showed that the observed hiss propagates downward and can leak from the magnetosphere into the ionosphere with a narrow frequency range at the equator [8]. T

In a later publication, they presented data showing signatures of multiple ion species in the ELF wave spectra at low latitudes [7]. They found minima in power spectral density at ion gyrofrequencies and their harmonics including those for O+, He+, H+ and N+. The values of the harmonics for O+ and the bi-ion

(H+ and O+) match the observations made by the sounding rocket during Too WINDY.

Figure 3.9: Spectra from the electric ﬁeld data

61 Fig. 3.10 displays the log of electron density as measured by the Langmuir probe as a function of altitude. This agrees with the measurements made by the ALTAIR radar. Panel c in Fig 3.4 can be used as a reference for that measurement. The electron density is plotted as a function of altitude to the right of the scans and the values agree between 150 and 400 km where the rocket measurements are available.

−3 Figure 3.10: Log10 electron density (cm ) measurements from the Langmuir probe

The sounding rockets were the main focus of the Too WINDY experiments but due to the unpredictable weather conditions and the timing of the launch, the rockets were unable to acquire data during the onset of a typical ESF event.

Instead, the instrument rocket was able to acquire ﬁeld data during the post-

62 midnight ESF event. While these data certainly had some interesting features that were highlighted in this section, they are incomplete without the neutral wind measurements. The failure of the other ground instruments such as the ionosonde and the Fabry-Perot interferometer further compounded the limitations on the sounding rocket data. ALTAIR was better equipped in this case to study such an event, as its measurements provided a broad picture of the ionosphere while the function of the rockets was far more speciﬁc.

63 CHAPTER 4 NUMERICAL SIMULATION OF ESF

The Cornell ionospheric simulation can be used in an attempt to reproduce the results observed by the experimental instruments during the WINDY and Too

WINDY experiments. The simulation has been used previously to simulate the collision shear instability [4], in the Pacific sector [5] and the Peruvian sector [21]. It attempts to recreate the plasma dynamics in the equatorial ionosphere by numerically calculating the self-consistent electric fields and the plasma density in three dimensions. When compared with the experimental data acquired, results from the simulation can shed light on the validity and limitations of the theories discussed previously. For this chapter, the simulation was run to accomplish two goals. The first was to accommodate the calculated spectral distribution of irregularities from the WINDY radar data. The second was to attempt to reproduce the post-midnight ESF observed during TOO Windy. A description of the algorithm and the results are presented below.

64 4.1 Description of the Cornell ionospheric simulation

The numerical simulation evolves the equatorial ionosphere in three dimensions by updating the electrostatic potential and plasma density [4]. Compared to other similar simulations, there are two key differences. The first is the three dimensional computations rather than assuming equipotential field lines. This condition deteriorates near the bottom of the E-region and the plasma is decou- pled. The second is the emphasis on the valley region on which the collision shear instability depends. Aveiro et al [4] suggest that other models may indi- cate that this region is more rarefied than it is. The self consistent initial vortex

ﬂow generated by the simulation in this region matches sounding rocket electric ﬁeld measurements in Jicamarca and at ALTAIR [4].

To initialize the simulation we use the SAMI2 model [18] which populates the ionosphere density profile. The SAMI2 model takes various parameters such as geographic and geomagnetic locations, solar flux and dates to accurately produce an ionospheric density profile for the specific days and times required to initialise the simulation. For the neutral winds, the Horizontal Wind Model (HWM-15) [10] is used. To generate the zonal electric fields we use the Fejer-

Scherliess vertical drift model [35]. The simulation is run in a 139 × 189 × 109 points wide rectangular grid. In the scans, cuts through the equatorial plane are shown, which spans 600 km in longitude and 100-600 km in altitude. Cuts through one plane perpendicular to the Earth’s magnetic field are representative of ESF activity along different planes. The irregularities observed and simulated are field aligned and therefore consistent along the magnetic field lines.

65 A brief review of the key equations and concepts is provided below following

+ + + + [21]. The densities of the ion species O , NO , O2 and H are simulated in time starting from the initial conditions provided by the SAMI2 model. The equations that govern the dynamics of these species are given below. The ﬁrst is the force-ﬂuid equation without inertia

0 = qs(E~ + v~s × B~) − KBT 5 ns X X 0 ~0 ˆ ˆ − νsnms(v~s − ~u) − νss ms(v~s − vs) · bb + ms~g (4.1) n s0,s

where qs, ns, ms and v~s are the number density, charge, mass and velocity of the species s. E~, B~,~g and ~u are the electric, magnetic, gravitational and neutral wind fields, Ts = Tn is the temperature, bˆ is the direction of the magnetic field vector and ν is the collision frequency between species. Coulomb collisions are only considered in the direction parallel to the magnetic field. From Eq 4.1, we can explicitly solve for the velocity of a given species

v~s = µs · (E~ + ~u × B~) − Ds · 5ns/ns + Ts · ~g (4.2)

where the new quantities µs, Ds and Ts are the tensor mobility, diffusivity and gravitational coefﬁcient for each species. These quantities can be calculated using empirical values from the NRLMSISE-00 model [34]. The current density can then be written as

X J~ = (qsnsv~s) s X = σ · (E~ + ~u × B~) − qsDs · 5ns + Ξ · ~g (4.3) s

There are two important computations performed by this simulation. The ﬁrst is a three-dimensional potential solver that calculates the self-consistent

66 electric ﬁeld by imposing quasi-neutrality using the equation    X  5 · · 5 5 ·  · ~ × ~ − · 5 ·  (σ φ) = σ (E + ~u B qsDs ns + Ξ ~g (4.4) s where Σ is the conductivity tensor, D is the diffusivity tensor, E is the background electric ﬁeld, ~u is the neutral wind, n is the number density, Ξg is the gravity driven current density and φ is the electrostatic potential that is being solved for. This elliptical partial differential equation is solved in three dimensions using a preconditioned biconjugate gradient method. Tilted magnetic dipole coordinates are used to match the magnetic declination at the geogra- phy where the simulation is being run.

The second is the advancing the number density in time using the continuity equation. ∂n + 5 · (nv~ ) = −β n (4.5) ∂t s The methods used to solve the ion continuity equation is a combination of upwind difference schemes, second-order total variance diminishing schemes [?] and ﬂux limiting [41] implemented in three dimensions using a dimension splitting technique [36].

A brief overview of some of the numerical methods is given below. Full details can be found in the corresponding citations. The potential equation is solved using a pre-conditioned biconjugate gradient method. Given an equation of the form A x = b (4.6)

∗ ∗ We can choose an initial guess x0, two other vectors x0 and b and a precondi-

67 tioner M. Then

r0 ← b − A x0

∗ ∗ r0 ← b − x ∗0 A

−1 p0 ← M r0

∗ ∗ −1 p0 ← r0 M and can be iterated

∗ −1 rk M rk αk ← ∗ pk Apk

xk+1 ← xk + αk · pk

∗ ∗ xk+1 ← xk + α¯k · pk

rk+1 ← rk − αk · Apk

∗ ∗ rk+1 ← rk − α¯k · Apk ∗ −1 r M rk+1 β ← k+1 k ∗ −1 rk M rk −1 pk+1 ← M rk+1 + βK · pk

∗ −1 ∗ −1 ¯ ∗ pk+1 ← M rk+1 M + βK · pk

The residuals can be computed as

rk = b − A k

∗ ∗ ∗ rk = b − xk A where the ∗ denotes the adjoint and the ¯ denotes the complex conjugate.

For the ion continuity equation, a combination of several different methods are used. A general overview of upwind difference schemes, total variation and second-order total variance schemes are given below, following the ideas in a

68 review paper of difference methods for computational ﬂuid dynamics [39]. We consider an equation of the form

∂u ∂ F(u) + = 0 (4.7) ∂t ∂x where u is the quantity to be conserved and F(u) is the flux term. These methods assign flux by accounting for the physical nature of the flow. For example, if the

ﬂow is towards the right, the ﬂux at the boundary of a cell xn+1/2 would be taken

t from cell n where Fn = v un. The CFL condition for this scheme is vδt/δx ≤ 1. This scheme is only ﬁrst order accurate and therefore highly diffusive. However, it does not produce any spurious oscillations. Nonlinear schemes are required for higher order accuracy. Harten [42] proposed the total variance diminishing condition, which is a nonlinear stability condition. The total variation for a solution, written in the discrete form of Eq 4.7 is

XN t t t TV(u ) = ui+1 − ui (4.8) i=1

The total variation is equivalent to the overall amount of small oscillations and can also be written as

t X X TV(u ) = 2 umax − umin (4.9)

The ﬂux assigment scheme is said to be TVD if

T(ut+δt) ≤ TV(ut) (4.10)

This equation means that the total number of oscillations is bounded. A second order accurate TVD scheme can be constructed by building upon the upwind scheme by adding second order corrections to the first order flux terms. Con- tinuing with the example above where the flux is positive and to the right. The

69 second order ﬂux corrects can be deﬁned as

Ft − Ft δFL,t = n n−1 n+1/2 2 t t F − Fn δFR,t = n+1 (4.11) n+1/2 2

Near extreme, the flux terms are reduced to first order and a flux limiter is used to determine the appropriate second order correction (positive or negative flow). A flux limiter is a function that takes the left and right flux terms as an argument and determined the correct flux to use. The Van Leer flux limited [41] is used here and can be defined as

2ab vanleer(L, R) = (4.12) a + b

The last method used to solve the continuity equation is a dimension splitting technique [36] which extends these methods to three dimensions.

70 4.2 Simulation of post-sunset ESF during WINDY

The numerical simulation was initialised using SAMI2 to represent the ionosphere during the WINDY experiment. This analysis aimed to use the spectral distributions calculated in section 2.3 as a seeding method and evaluate its effect on the development of the plasma instabilities. These simulations were run for 2 hours post-sunset and the ﬁgures show the evolution of the plasma instability at different times. The simulation is typically seeded with white noise; here the functional form of the power spectral density allows us to generate pink noise to correctly represent the seed irregularities in the ionosphere.

The results of the simulation from Kwajalein using ionospheric parameters and empirical models from September 2017 are shown below. The simulations are initialized with the empirical models mentioned about with an addition of 12.5 m/s to the Fejer-Scherliess model, in order to increase the growth rate of the instabilities. This modiﬁcation reproduces the ascent of the F-layer and does not change the morphology of the plasma structures. The ﬁrst run uses white noise as a seed instability. The aim in doing this is to represent a spectrum of waves that are not restricted to the plasma convective instability but any mechanisms that affect the spatial variability in the background density [24]. The use of pink noise as a seed is to faithfully represent the spectrum of waves found in the AL- TAIR radar data in an effort to reproduce a morphology observed in the radar scans.

Fig 4.1A and 4.2A show scans of the ionosphere just after initialisation of the simulation. At this point in the simulation they are almost identical. Seeding the

71 simulation with white noise allows the solver to identify the frequencies with the highest growth rate while using pink noise identiﬁed from the radar data seeds the simulation with waves that exist preferentially in the natural ionosphere and evaluate whether this leads to a different result.

Figure 4.1: Plasma density proﬁles of the numerically simulated ionosphere for 31 August 2017 using white noise as a seed. Densities are shown here for three different species: molecular ions (red), atomic oxygen ions (green) and hydrogen ions (blue) in MKS units (m−3).

72 Figure 4.2: Plasma density proﬁles (m−3) of the numerically simulated ionosphere for 31 August 2017 using pink noise as a seed.

73 Panel B corresponds to times when, on most nights in the radar data, the initial irregularities are clearly visible as bottom-type scattering layers. There is more vertical development of the instabilities in Fig 4.2B and there is a wave- like structuring visible in the electron density in the ionosphere. While Fig 4.1B also shows vertical development, the growth rate seems to be lower in this case. There is a clear wave structure in Fig 4.2C and the instabilities have ascended further into the top side after 90 minutes. Topside plumes were typically visible in the ALTAIR data at this time. Fig 4.1C also shows topside activity as expected but there is a difference in the morphology of the plasma structures. The spacing between the major depletions in Fig 4.1C and 4.2C of 150-200 km are congruent with the fastest-growing modes of the shear ﬂow induced instability [24]. One of the key differences in seeding the simulation with white noise and pink noise is the clustering of the depletions observed in the ALTAIR data and reproduced in Fig 4.2. The depletions are uniformly distributed when using white noise in Fig 4.1 [24]. However it is important to note that there is ESF activity in both cases; instabilities developed even when the simulation was seeded with white noise, suggesting that the presence of a spectral distribution in the density is not a sufﬁcient condition for ESF activity.

74 4.3 Simulation of post-midnight ESF during Too WINDY

The key observations during Too WINDY portray the common characteristics of ESF activity during seasons of low solar ﬂux. The equatorial ionosphere was still susceptible to instabilities, though at a much lower frequency than during the moderate solar ﬂux conditions of project WINDY. Typical post-sunset ESF was only observed during one of the nights of the campaign, while post- midnight ESF was observed on the night of the rocket launch. The former has been successfully shown in simulations in the previous section. In this section, the simulations run by Hysell et al [25] are presented in an attempt to explain the presence of ESF plumes in the topside with no observable bottomside structuring or ESF activity in the pre-midnight hours.

There are 3 different scenarios that were postulated that could possibly lead to the observations during the rocket launch. The first is simply to assume that the low solar flux activity causes the same phenomenon to occur at a much slower rate, leading to ESF instabilities taking much longer to develop and irregularities therefore only manifesting themselves as the typical plumes in much later hours. This scenario was simulated, similarly to the simulations in the previous section but with low solar flux indices. The other two scenarios suggested by Otsuka (2018) [31] were the presence of gravity waves and the structuring of the ionosphere from background meridional winds. The details of the simulation are the same as presented in the previous chapter. Here, a 10 m/s vertical drift offset was added to the Fejer-Scherliess model.

75 Figure 4.3: Numerical simulation of instabilities of the ionosphere in Kwajalein during the summer of 2019. Ion densities (m−3) are shown here for three different species: molecular ions (red), atomic oxygen ions (green) and hydrogen ions (blue).

The first simulation run tests the hypothesis that the same mechanisms of post-sunset ESF are at work but due to the low solar flux, the lower density gradient means that it takes several times longer to develop. The numerical simulations in Fig 4.3 show what one would expect from the ionosphere during low solar flux conditions. The scans shown here correspond to the initialised ionosphere at 20:00 LT in panel A, 20:45 LT in panel B in order to compare the

76 structuring with simulations in the previous section and 23:30 LT in Panel C to correspond with the time that the rockets were launched and post-midnight ESF was observed in the radar data. There is some structuring in the bottom-side region suggesting the presence of scattering layers but this does not develop into the topside plumes observed in the radar data. They takeaway from this is that there is a possibility for ESF occurrence even during seasons of low solar activity, as was observed by ALTAIR on June 12 [25]. However, the overall morphology of the simulation do not resemble what was observed by ALTAIR on June 19 during the rocket launch. The presence of topside plumes without any bottom-type precursors in the radar data makes this hypothesis difﬁcult to ac- cept. The simulations in this section were run for 5 hours, which is much longer than those for the WINDY data in order to enter the post-midnight sector when the plumes were observed by ALTAIR.

The second simulation was conducted by adding two new features in order to test the theory that gravity waves provide forcing to the topside ionosphere in the post-midnight sector and these develop into the topside plumes without requiring the development of the bottom-type scattering layers. Internal forcing from gravity waves was added to the simulation by including waves propagating from the lower thermosphere and irregular meridional winds were added to test their destabilizing effect. In panel B we see the structuring is far less than in

Fig 4.1B and Fig 4.2B. In panel C, corresponding to 23:30 LT, the topside plumes are not visible as they were in the radar data, suggesting that by itself, forcing from gravity waves and meridional winds are not sufﬁcient to generate the ESF activity observed during Too WINDY. Hysell et al [25] found three main effects of this wave impulse on the ionosphere. The ﬁrst was the presence of sporadic

77 E layers and intermediate layers in the valley region. This was observed by AL- TAIR during the Too WINDY campaign on several occasions. The second was strong plasma ﬂows in the plane perpendicular to the magnetic ﬁeld and the third was the presence of intermediate scale irregularities in the bottom-side. However, this run was also unable to match the radar data from 19th June.

Figure 4.4: Numerical simulation of instabilities of the ionosphere in Kwajalein during the summer of 2019 with the addition of gravity waves and meridional winds. Ion densities (m−3) are shown here for three different species: molecular ions (red), atomic oxygen ions (green) and hydrogen ions (blue).

These conditions led to the generation of plasma instabilities in the bottom-

78 side as well but like the previous simulation, it does not seem to reproduce the observations during the rocket launch accurately. The necessity of the intermediate-scale irregularities in the bottom-side seem to suggest the initial conditions or forcing are not fully capturing the physics in play during these post-midnight ESF events. This incongruity seems to suggest that the convective instability is not the only force at work during these episodes of ESF.

79 CHAPTER 5 POST-MIDNIGHT EQUATORIAL SPREAD F

Post-midnight ESF is a phenomenon commonly observed during periods of low solar ﬂux in the equatorial region. As the name suggests, ESF activity manifests in the post-midnight sector as opposed to the post-sunset sector which is seen during periods of moderate and high solar ﬂux. It is unclear whether the same mechanisms are responsible for the generation of post-midnight ESF. Some of the key differences in the characteristics between post-midnight and post-sunset ESF are discussed in this chapter. While post-sunset ESF has been an area of study for several decades now, the discovery of post-midnight ESF is fairly recent. Data sets from the C/NOFS satellite have been important in this discovery as well as those from the JULIA radar at Jicamarca.

80 5.1 Observations of post-midnight ESF over Jicamarca during

Too WINDY

The Jicamarca unattended long term investigations of the ionosphere and atmosphere (JULIA) radar is a system designed to study plasma irregularities and waves for long periods of time. While making use of the main antenna array of the Jicamarca Radio Observatory radar, this system runs independently and does not make of the high power transmitters. This allows JULIA to run for long periods of time, unsupervised with minimal maintenance, making it especially useful for experiments such as WINDY and Too WINDY. It provides data from another longitudinal sector to compare with the observations from Kwajalein. JULIA was running on the night of the Too WINDY rocket launch campaign.

Comparing the observations of ESF in the Peruvian sector and the Paciﬁc sector is interesting. Low solar ﬂux observations of nighttime ESF at Jicamarca have been made for several years and these data sets give an idea of the phenomenology of these occurrences over a larger sample size. It has been found that during period of low solar activity, the occurrence of plasma instabilities is primarily in the post-midnight sector. During the Too WINDY campaign, pre-midnight ESF was only observed twice at Jicamarca [25].

Figures 5.1 - 5.2 show the chronology of the irregularities observed at Jicamarca beginning shortly after midnight local time and progressing to several hours after. There seem to be two phases of the ESF occurrence observed that night. Fig 5.1 shows one of the ﬁrst post-midnight scan. There doesn’t seem to be any ESF activity in the ﬁrst scan in Fig 4.1 at 00:30 local time. At this point, no structuring or irregularities are present in the bottomside. However, 18 minutes later

81 there seems to be some activity at an altitude of 350-360 km. In the bottom left panel, some bottom-type irregularities are observed at an altitude of 250 km. The spatial resolution at Jicamaraca is far superior to either mode at ALTAIR and therefore these small-scale irregularities are detectable here [25]. In the subsequent scans, spanning 24 minutes, there are vigorous ESF plumes observed briefly. In Fig 5.2, 12 minutes later, these signatures have more or less disap- peared in the first panel. Similar to the the first 4 scans, the ESF activity seems to increase after 2:00 LT and large plumes are observed again at 2:45 LT before disappearing; in the second instance however, the bottom-type layers are not observed.

Figure 5.1: Aperture synthesis radar images of irregularities above Jicamarca between 00:30 and 01:12

82 Figure 5.2: Aperture synthesis radar images of irregularities above Jicamarca between 01:24 and 02:45

In comparison to the observations at ALTAIR, the main difference seems to be the observation of a bottom type scattering layer during the stronger phases of the instability. A potential explanation could be the poor spatial resolution at ALTAIR was unable to detect any incoherent scatter from these structures.

If weak versions of bottom-type scattering layers were present during the topside activity observed in Kwajalein then that would ﬁt into what we expect of ESF occurrence during low solar ﬂux seasons. This could be an interesting result, suggesting that other methods of measurement are required in Kwajalein to capture the present of the bottom-type scattering layers.

83 5.2 Observations of post-midnight ESF by the C/NOFS satellite

The C/NOFS satellite, launched in April 2008 has been an invaluable tool in studying the F-region ionosphere. It contains a Planar Langmuir Probe as part of its payload which measures ion density, providing a large dataset of such measurements for the equatorial region. Dao et al [9] found that nighttime F- region is highly irregular during solar minimum. They calculated a ∆N/N quantity to track plasma irregularities while ignoring variance in the ambient plasma density, leading to the discovery that post-midnight irregularities are a common occurrence during solar minimum and barely seen during moderate to high solar ﬂux seasons. They then proceeded to analyze the dependence on longitude on this atypical ESF activity by comparing data from 10,000 orbits of C/NOFS. The highest activity was seen at the magnetic equator because as discussed earlier this is the prime location for the Rayleigh-Taylor instability to act. One sees activity in the South American sector year round [9] while the northern win- ter is when the paciﬁc sector (Kwajalein) is most active. In trying to explain this phenomenon, they found that there was a longitudinal correlation between meridional winds and nighttime density irregularities.

Huang et al [15] also studied C/NOFS data to come up with an explanation for the presence of plasma bubbles in the post-midnight sector. They presented data from C/NOFs showing a chain of plasma bubbles, separated by 800-1000 km each across a total length of 7000 km. The satellite took about 16 minutes to ﬂy through a local time range of 4 hours and the bubbles were observed in local time sectors between 22:00 and 5:00. These bubbles were still growing and showing upward development even post-midnight. The solar ﬂux during these

84 observations was an f 10.7 ≈ 70, identical to the values during Too WINDY. The theory postulated by Huang is the initiation of the Rayleigh-Taylor instability by gravity wave chains with wavelengths matching the periodicity of the bubbles observed. After the initial seeding, these waves play no roles and the bubbles are left to develop independently, driven by the R-T instability mechanism. While their model conﬁrmed the science, in reality the presence of an instantaneous gravity wave was considered implausible [15].

They proposed a second model, where the distance between bubbles was not due spatial seeding but rather from a periodic generation of bubbles at roughly the same location. The perturbation mechanism can be any variety of those discussed previously in this document. Given the rotational speed of the Earth to be 463 m/s and a zonal plasma drift of 130 m/s, the bubble would have drifted a distance of 600 km in 1000 s. With this model, their observations could be explained by a generation of plasma bubbles every 15-30 minutes and their eventual drift to other longitudes where no perturbation or seeding took place. This second theory has potential for explaining the presence of plumes in the topside without structuring in the bottom-side.

85 5.3 Relevant literature from the Asian and South American lon-

gitudes

Patra et al [32] presented observations from Gadanki in India of field aligned irregularities observed mainly in the post-midnight hours. They found that the occurrence and variability in these post-midnight ESF observations were strongly related to the midnight temperature maximum (MTM) phenomenon which has the potential to affect the growth rate of the Rayleigh-Taylor instability. The observations were made using an ionosonde and a mesosphere- stratosphere-troposphere radar and saw ESF every night in the months of July- August during solar minimum. Otsuka’s [31] statistical analysis showed that while the occurrence rate of pre-midnight irregularities increased with solar activity, the opposite was true for post-midnight phenomena, confirming that this trend was not limited to the South American or Pacific sectors.

The Equatorial Atmosphere Radar (EAR) in West Sumatra observed ionospheric irregularities and a comparison was made with the measurements of the C/NOFS satellite [44]. This was done by projecting observations onto the equatorial plane along magnetic ﬁeld lines. When weak irregularities were observed by C/NOFS post-midnight, EAR noticed disturbances and striations re- sembling medium-scale traveling ionospheric disturbances (MSTIDs) similar to those seen in higher latitudes. One of the more interesting observations from this experiment was the identiﬁcation of plasma depletions by the Langmuir probe on C/NOFS. During several orbits the irregularities were always observed in the post-midnight sector in local time, regardless of the Earth’s rotation. EAR observed strong E~ × B~ drift irregularities post-sunset local time and

86 these could be the source of the plumes seen later on by C/NOFS. They concluded that post-midnight ESF at the equator resembles the same phenomenon at higher latitudes quite closely. The post-midnight presence of the plumes was explained by the fact that the plumes rise to spacecraft altitude in the pre- midnight hours and are only detectable post-midnight. This doesn’t explain the observations from Kwajalein and Jicamarca where post-midnight ESF is observed without any activity seen in the preceding hours and no irregularities detected in the bottomside.

Nicolls et al (2018) [30] showed results from digisonde experiments in Brazil and Jicamarca showing the uplift of the F-region around midnight and found that it was a fairly common phenomenon near the magnetic equator. Through simulation, they showed that recombination plays an important role by driving the ionosphere upwards in conjunction with a weakening westward electric ﬁeld. The variability in the wind systems at the equator could be from MSTIDS or LSTIDS. They concluded that these may contribute to a secondary maximum, increasing the ESF occurrence rates in the post-midnight period. It is not mentioned whether ESF activity was observed earlier in the day or when the primary maximum in occurrence rate was–this might differentiate these observations slightly from those during Too WINDY.

The general trend of observations from Asia and South America, including Jica- marca, is that post-midnight plumes are seen during low solar ﬂux especially during the June solstice. In most of these observations, typical ESF activity is not observed whether it be ionospheric structuring or irregularities in the bottom-side. Therefore, it is difﬁcult to place where the observations from TOO

87 Windy lie in the larger map of post-midnight ESF research. There are some sim- ilarities in climatological conditions between observations elsewhere and those from Kwajalein in 2019 but the speciﬁc mechanism are difﬁcult to pin down due to the slight variation in the nature of the event.

88 CHAPTER 6 CONCLUSION

6.1 Relevance of WINDY and Too WINDY in ESF studies

The WINDY and Too WINDY campaigns are some of the latest in a long line of radar and sounding rocket investigations of the equatorial ionosphere. Such experiments in the South American and Asian longitudes are common, and investigations often involve data from ionosondes and observations from satellites.

Kwajalein is a unique location for ESF studies because it allows for the launch- ing of sounding rockets in conjunction with a radar experiment. The steering capabilities of ALTAIR also allow for scans sweeping several hundreds of kilo- meters, giving a spatial picture of the ionosphere that is rarely found in ESF research.

While the objectives of both these campaigns were the same at the outset, the signiﬁcance of the ﬁndings were vastly different. The WINDY project aimed to show the role of the convective instability in driving the vertical current that leads the plasma instabilities. Despite the failure of the rockets during this mis- sion, the rich radar data that was collected by ALTAIR provides further evidence for this plasma convective instability. The ionosphere was probed every night after sunset and it was clear from this data-set that no large scale wave structures existed before the emergence of the patchy bottom-type irregularities that have shown themselves to be precursors to more vigorous ESF activity.

Too WINDY set out to provide sounding rocket data of electric ﬁelds and a

89 chemical payload rocket to measure wind profiles to support this theory. How- ever, weather conditions controlled when the rockets could be launched, and the necessary measurements were not available. On the night of the rocket launch, typical post-sunset ESF did not manifest. The experimental data from the chemical payload rocket did not result in retrievable wind profiles, and therefore running any sort of simulation using these data was not possible. However the rocket did measure some small-scale plasma structures and ELF emissions in the lower F-region. The radar observations on the night of the launch showed a large plasma bubble in the upper F-region, an excellent example of post- midnight ESF which commonly occurs during low solar flux seasons. This observation highlights the need for more studies into this field. There have been very few explicit studies into the dynamics of post-midnight ESF. Most of the theories attempting explaining the mechanics seem to stem from observations made by the C/NOFS satellite. Several of these theories rely on the same fundamental science that explains post-sunset ESF without explicitly addressing the difference in phenomenology.

The lack of any scattering structures in the bottom-side during the ESF event during Too WINDY sets the observations of this campaign apart from other data. At Jicamarca, post-midnight ESF seems to follow the same rough chronology as its post-sunset counterpart where weak scattering layers in the bottom- side preceded topside plumes. The presence of these is seen as a necessary, if not sufﬁcient, precursor for topside plumes. However, with the topside activity in Kwajalein occurring without these scattering layers, there is a place for new science to explain this phenomenon.

90 6.2 Explanation of observations and theories

The observations from the WINDY campaign are excellent sources of evidence for the various instability mechanisms at play in the F-region of the ionosphere.

The data acquired is extremely interesting and will always be useful in the study of plasma instabilities during moderate solar ﬂux conditions. Even though there are various theories as to which mechanisms play the most important role in seeding these irregularities, the science behind this is fairly well understood. The same cannot be said about the observations for post-midnight ESF. Sev- eral researchers [44] [15] [31] [6] have postulated theories for these observations and Hysell et al [25] have attempted to simulate these conditions and compare the results to those from the experiment. None of these simulations seemed to match the phenomenology of the naturally occurring ESF activity but there are still three mains theories that might explain this observation.

The first theory is that post-midnight ESF is no different from the typical post- sunset ESF activity. The lower solar flux conditions lead to smaller density gradients in the valley regions of the ionosphere and that slows down the instability mechanism. The plasma dynamics are much slower and take several hours more to develop but eventually lead to the same phenomenon at a much later time. Here, we can assume that the bottom-type irregularities are present as scattering layers but are so weak that they cannot be detected by ALTAIR but can be seen at Jicamarca, thus the disparity in this key aspect of the data. Sim- ulation of this hypothesis (Fig 4.3) led to two results. 1) Under low solar flux conditions (f10.7 70), electric fields derived from the Fejer-Scherliess model and winds derived from the HWM14 model, the ionosphere was stable. 2) Adding

91 an offset to the electric ﬁelds to enhance their strength destabilised the ionosphere but it showed the same chronology of events as seen during WINDY, with the presence of the bottom-type irregularities showing vertical development into topside ESF.

The second, suggested by Otsuka [31] is the forcing from gravity waves or ionospheric structuring from meridional winds. Through simulation (Fig 4.4) Hy- sell et al [25] found that forcing from the neutral waves led to the creation of sporadic E layers and strong plasma flows in the plane perpendicular to the magnetic field. The introduction of the meridional winds cause slight structuring in the topside and further destabilised by zonal flows [25]. While the simulation did produce topside plumes, overall it did not reproduce the experimental observations from Too WINDY. The irregularities were not limited to the topside and even when structuring was observed at higher altitudes it was always accompanied by bottom-type irregularities. This theory could work in conjunction with the first. During low solar flux activity, forcing from meridional winds and gravity waves may be additional necessary conditions along with the presence of bottom-type scattering layers. The results from the simulation [25] certainly seem to show that they can occur together to produce topside plumes.

The third theory is that of fossil plumes that persist in the ionosphere and enter the view of the radar in the post-midnight sector. Krall et al [27] laid out this theory and examined the results using the SAMI3 [17] ESF model. Fossil plumes from earlier ESF activity could potentially explain their presence in the topside during the Too WINDY rocket launch. These plumes could originate at higher

92 latitudes and then travel along the ﬁeld lines till they are visible at the equator. Another explanation is that they originate at a different longitude and are then blown by a zonal wind to the paciﬁc sector; effects from such agents were not found to interrupt the development of these irregularities [27]. Numerical simulation was unable to reproduce this condition.

This idea, however, is problematic for two reasons. The first is that it assumes, without any proof, that there is topside ESF activity at some longitude which does not extend along field lines to the equator. Currently, we have not been able to verify that ESF at mid-latitudes translates to equatorial observations in this way. The ALTAIR scans also show the plumes appearing near the center of radar’s field of view suggesting that the theory of zonal movement is unlikely.

The second problem with this theory comes from the observation of bottom- type scattering layers at Jicamarca. These should not be visible if the plumes are remnants of earlier ESF activities. However, the phenomenology of post- midnight ESF at Kwajalein and at Jicamarca have been quite different so this may still apply to the observations from ALTAIR.

93 6.3 Limitation of experimentation and analyses during WINDY

and Too WINDY

Just as the findings from both these campaigns were different, the limitations to the experiments were also unique to the experimental methods, dates and space weather conditions during which they took place. During project WINDY, the solar flux conditions were moderate and ESF activity readily presented itself in the post-sunset hours on a consistent basis. However, the failure of the sounding rocket motors during this investigation meant that electric field measurements and neutral wind profiles were unavailable although the ALTAIR data was able to identify and observe plasma irregularities in the F-region clearly. The measurement of electric fields and neutral winds would have provided for a more robust simulation of the instabilities and perhaps enhanced our understanding of the key physics at play. This was not possible and the simulation had to be run using fields and winds derived from models, which were both successful in creating the desired result but lacking the scientific relevance of the experimental observations.

Rocket data was available during Too WINDY but the space weather conditions were less than ideal to observe ESF. The potential of rocket launches during this campaign were heavily controlled by cloud coverage in the lower atmosphere as maximum visibility was required for successful measurement of neutral winds by the ground and airplane camera systems in place. ESF activity was observed by ALTAIR on June 12th but the weather conditions prevented the rockets from being launched that night. The rockets were ﬁnally launched on June 19th after weak scattering layers were observed by ALTAIR. On the night, ESF activity

94 did not develop as expected. Bottom-type layers did not show vertical development into topside irregularities. Rather, a large ESF bubble was observed by ALTAIR that was seemingly disconnected from the irregularities at lower altitudes. However, the instrumented rocket did manage to acquire data and the radar data from the night was able to spark a discussion about the presence of post-midnight ESF in Kwajalein. One of the primary limitations of this experiment is the lack of data from the other instruments involved. Even though the chemical payload rocket launch was successful, neutral wind proﬁles could not be acquired from the data. Two ground instruments supported the radar and rocket investigation during this campaign. A Fabry-Perot interferometer was set up to measure thermospheric winds and an ionosonde was running every night in a similar role to ALTAIR. Due to technical difﬁculties, neither instrument could provide supporting data.

The observations during these campaigns did leave some unanswered questions that could potentially fuel future studies. Further rocket launches during ESF activity could provide numerical simulations with powerful experimental data that could reveal information that the models cannot. Explicit studies into post-midnight ESF are required to fully understand this phenomenon. Accurate ﬁeld measurements from the E and F-layers from instrumented sounding rockets, coupled with neutral winds could provide enough data for a numerical simulation to reproduce the observations from ALTAIR. A sounding rocket campaign designed to study post-midnight ESF, with the aim of measuring ﬁelds and neutral winds in the bottom-side could point to the presence of the shear instability mechanism, even if the bottom-type scattering layers produced by it are too weak to detect.

95 APPENDIX A EXPERIMENT ELECTRONICS INTEGRATION AT WALLOPS FLIGHT FACILITY

This chapter is dedicated to detailing the steps and procedures that go into electronics integration for the instrument rocket at the NASA’s Wallops Flight Facil- ity. The main steps in the integration schedule are listed below.

1. Mechanical installation and alignment of electronics

2. Pre-vibration telemetry test

3. Pre-vibration sequence test

4. Vibration test

5. Post-vibration telemetry test

6. Post-vibration sequence test

7. GPS roll-out test

8. Magnetic calibration test

9. Mass properties and balance test

While the ﬁrst 6 tests must take place in the order they are listed, the following 3 experiments can be performed any time after the post-vibration sequence test. Most of the scheduling will depend on the availability of the NASA engineers and therefore the entire process can take anywhere between a week and a month.

96 A.1 General safety measures

These are a few safety measures that apply to all the steps of the integration process and to any work being done on the rocket, the electronic components that are to be installed or any devices being used to perform tests such as signal generators or oscilloscopes.

• Make sure to always be wearing an ESD jacket when around the rocket to prevent electrostatic discharge from damaging the electronics of the

rocket. Electrostatic charge can easily be built up on the body and hands especially if wearing sweaters and jackets.

• As a further precautionary measure, use the grounding wrist strap whenever touching the electronics. The wristband is connected to a clip that should be clipped onto any grounding surfaces/wires either on or at-

tached to the rocket. During this process we brought our own wrist straps.

• Always monitor the current measurements whenever the experiment is

on. If the current exceeds the expected value by 10%, the experiment must be powered off immediately. (The expected value is judged by a combination of theoretical calculation and observation of the experiment when

its working normally.) The electronics can be inspected once the experiment is turned off and should only be turned on again once the problem is resolved.

• Make sure loose wire bundles are restrained with tape or ties before testing. There are several wires that need to be held in place especially during

the vibration tests so that their movement does not inadvertently damage adjacent electronics.

97 • Make sure all screws and bolts are tight before any mechanical tests. If working in a team, make sure each team member torques the screws and bolts so nothing is missed. This should be obvious.

• Any connections made the to the voltage sensors or the Langmuir probe should always be through a resistor. This includes connections to the sig-

nal generator and also when grounding the sensors. The values for the resistors are provided on the telemetry sheet attached with this document.

98 A.2 Mechanical installation and alignment

The electronics have to be installed at the front end of the rocket with a speciﬁc alignment to each other. The alignment of the axes of the electronics with the rocket does not need to be ﬁxed at one value as long as it is recorded, however, a perpendicular alignment is preferred to simplify matters. All four voltages sensing booms and the magnetometer have to be aligned during installation.

Figure A.1: Angular values for alignment in reference to the rockets body

In Figure A1, the rocket axes are shown. Looking in the direction of the ar- row in the top half of the diagram, gives you the cross-sectional view shown in the bottom half. In this case, boom 1 was aligned with the 0◦. Boom 2 must be aligned parallel and opposite to boom 1 as the voltage is measured across the two sensors. In this case that implies that boom 2 must be aligned with

99 the 180◦ axis on the rocket. Similar opposite and parallel alignment must follow for booms 3 and 4. The position of boom 3 with relation to boom 1 is not ﬁxed by convention but it is important to record the relative position. In this experiment, boom 3 was aligned with the 90◦rocket axis, implying boom 4 being aligned with the 270◦ axis.

The magnetometer must be mechanically installed on the front end of the rocket as shown in the following diagram.

Figure A.2: Magnetometer placement on axis plane

The top half of ﬁgure A2 shows additional mechanical details of the rocket.

The solid black lines are metal structures. The ﬁgure is symmetric about a 90◦ rotation. The booms must be aligned so that the are free to extend without

100 being obstructed by the metal skeleton. The magnetometer is installed on the circular plate on the left of the diagram. The cross-sectional view is shown in the bottom half of the ﬁgure. Again, a perpendicular orientation to the rocket axes and therefore the booms is preferred for convenience. The magnetometer used had axes labels printed on its exterior. In this installation, the X axis was aligned towards the front of the rocket (left in top diagram, out of the page in bottom diagram.). The Y axis was aligned with the 0◦ axis and the Z axis with the 90◦ axis. The NASA mechanical engineering technician will perform most of the installation in order to make sure it is positioned appropriately with respect to rocket electronics.

Camera photos of the installed electronics are included below for reference.

Figure A.3: Stacer boom in the retracted position (gold sphere) aligned in such a way that it can extend below the metal skeleton.

101 Figure A.4: Magnetometer (black cuboid) aligned against the rocket axes. The nosecone of the rocket is pointing up in this image.

Figure A.5: 2 booms are pictured, the ﬁrst pointing out of the page and the second pointing upwards. To the left of the Stacer booms is the telemetry circuit box connected to the boom instruments by the white wires.

102 The last instrument for installation is the Langmuir probe which is installed pointing towards the front of the rocket. While the orientation of the structure holding the probe is not important from an experiment perspective, it is aligned parallel to the front of the rocket for mechanical purposes.

Figure A.6: The entire instrument section of the rocket body is visible. The Lang- muir probe is installed at the end of the green rod towards the top of the image. Here it is covered by bubble wrap and an orange cone to prevent accidental damage when the rocket is aligned ﬂat.

103 A.3 Pre-vibration telemetry and sequence test

The purpose of the telemetry test is to determine whether the sensors are measuring and transmitting signals correctly. On the telemetry sheet at the end of this document is a comprehensive list of signal inputs that need to be tested and the theoretically calculated outputs that must be matched. The ﬁrst column tells you which data channel you should be seeing the signal on the display. Connec- tion to the boom 1 will give you signals V1s and V12 channels. The V1s is the static channel for boom 1 and the V12 is the differential channel across booms 1 and 2. Similarly for all the other channels. The cable is connected to the sensor across a resistor in series. The value of the resistor is provided along with the signal characteristics on the telemetry document. The Langmuir probe has 4 separate channels. For each channel there is a speciﬁc input voltage, expected gain and prescription for the resistance across which the signal generator is connected. These are all provided on the telemetry sheet.

Make sure to connect clip leads with resistors between each sensor and ground before beginning to connect to the signal generator. The value for these resistors should be 100 KΩ for the four electric ﬁeld boom sensors and a value of either

10 KΩ or 1 MΩ for the Langmuir probe sensor. The values of the resistors are documented on the telemetry sheet. One end of the coaxial cable is connected to the signal generator, at the other end, the red terminal is connected to the sensor (through a resistor) and the black terminal is connected to ground. The telemetry engineer should be able to provide a real time display of the output signals received in order to check the expected values from the sheet.

104 IMPORTANT: Never make a direct connection between any of the sensors to ground or to the signal generator, otherwise the experiment electronics may be damaged. Always place a resistor in line with the sensors as described above and on the telemetry sheet. (Note: Due to the temporal resolution of the display, some input frequencies had to be changed to 1 Hz to see the real time signals.)

Figure A.7: The correct way to make the connection to the voltage sensors on the stacer booms. The metal strip taped to the sensor is connected through conducting clips to a resistor in series which can either be connected to ground or a signal generator during the telemetry tests.

It is extremely important to monitor the current during this test and every other subsequent test. There is a theoretical current value calculated from the circuits provided on the telemetry sheet. Current fluctuations beyond 10% of this value may be a cause of concern. The experiment should be turned off immediately in case such fluctuations occur. Sometimes fluctuations in the region of 10% might be due to the signals on the sensors.

After the experiment is turned off, data from the voltage sensors and Lang- muir probe can be looked at in order to determine whether a higher current was drawn due to input signals at that time. While the current was calculated in mA, the display is in a differently scaled count. It is good to determine the nominal

105 Figure A.8: several different resistors in combination connected to the Langmuir probe. To the bottom left of the image you can see the red terminal from the coaxial cable from the signal generator connected to the 10k resistor. values of the current in the units they are displayed in so ﬂuctuations are easy to notice. The units during this series of tests was calculated to be 0.47 mA/count.

For the actual telemetry test, input the prescribed signals using the signal generator and monitor the output on the display. All the output measurements should be as expected and predicted on the telemetry sheet. The tests can be done both on external power and on battery power and it is best to check both and make sure the current is nominal.

The ﬁnal test is to check the deployment sensors on the booms. The sensor that connects the rotating spool to the boom is at 5V when in contact in the fully

106 retracted position corresponding to a binary state of 0. As the spool unwinds it momentarily loses contact during one full 360◦ rotation, changing the state brieﬂy to 1 (0 V). The boom deployment is determined by the number of cycles between 0 and 1 corresponding to the number of rotations as the spool unwinds. Around 20 cycles signals deployment in this case. These logic operators can be connected and disconnected to check that they are at the correct stage (5V).

Figure A.9: Telemetry screen showing different readings from rocket components. The left half of the screen shows the readings from the science instruments.

The purpose of the pre-vibration sequence test is to ﬁre all rocket systems in the same order as they would during ﬂight in order to test them working with each other. This test is not trivial with regards to the rocket system but for the experiment, only the signal outputs need be monitored. In the appendix of this document is attached a sheet that lists the sequence of events during

ﬂight. Several of these events are checked during the sequence test. Only one

107 channel for the voltage sensors needs to be connected during this test since one cannot keep changing the connections during the test. A backup power test will also take place where the external power is pulled to simulate external power failure and a backup system should switch the experiment to battery power. It is important to monitor the signals in this situation but more importantly make sure the current is still nominal.

The steps for the post-vibration telemetry and sequence test are the exact same as their pre-vibration counterparts and will not be repeated in this chapter.

108 A.4 Vibration test

This is the most important mechanical test for the rocket. Before this test certain steps need to be taken in order to prepare the rocket for the rigorous mechanical strain.

• Tightening of all wire bundles using plastic ties or tape.

• Checking screws and bolts on all installations and making sure they are

tightened.

• Checking the resistance of the pyrotechnics in the Stacer booms using a

specialized ammeter. These need to be checked so that they do not go off during the vibration test and deploy the booms.

After these general safety measures are taken, there are two key steps to ensure that the electronic components are being properly tested under mechanical strain.

1. Remove the “remove before ﬂight” items from the booms. These are safety items that prevent the boom being deployed by accident. However, in

order to test them in full ﬂight situations, these need to be removed. These items have tags that are bright red in colour.

2. Measure the extension of the booms once the safeties (remove before ﬂight items) have been removed. This must be done with a high precision measuring tool such as Vernier calipers. The extensions measured were in the

order of 0.01 inches.

109 During the vibration test, the sensors are unconnected. There are 3 phases of the vibration text and those are in the X, Y and Z axes of the rockets (in the direction of the 0◦, 90◦ and perpendicular to the face.) While the test proceeds, make sure current stays nominal, recording the values after each phase of the test. The expected signals are random because the rocket is vibrated randomly, however there should be a rough correlation between the amplitude of the output signals from the sensors and the amplitude of vibration which is announced as the test proceeds. Note that there is quite a long time between the X, Y and Z axis vibra- tions as the rocket needs to be realigned using a crane on the vibration table.

Figure A.10: The remove before ﬂight labels

Figure A.11: The remove before ﬂight screw, label attached in the form of a plastic tag with black marker writing

110 Figure A.12: The pin attached to the remove before ﬂight tag in ﬁg A.10

Figure A.13: The clamp with the screw that must be removed before ﬂight.

111 Figure A.14: The boom after the clamp in ﬁg A13 has been removed.

Figure A.15: Tags used to record and date the measured extension of the boom after removal of the safety items. The red arrows show the space where the extension should be measured.

112 A.5 Nose cone deploy

During this test the nose cone that is placed on the rocket covering the electronics is deployed. This can be a mechanically strenuous process for the components of the rocket and the shockwave sent from the deploy may damage electronics. During this test current must be monitored closely as always. After the nose cone deploys it is normal to see changes in the static voltage channels since the sensors are no longer shielded by the nose cone. During this integration there was a spike in current because of the spike in voltage during the instant of deployment. However, since the current values returned to normal immediately there was no cause for concern. Furthermore the spike could be explained by corresponding voltage data during the test. The DC channels can have an offset but the AC channels (VLF12 and VLF34) should be at 0.

Figure A.16: (L) The rocket body in the nose cone deploy test space. (R) Post- nose cone deploy.

113 A.6 Magnetic calibration

The magnetic calibration test takes place in a magnetically shielded facility several hundred yards away from F-10, the building where all the previous tests were done. There is a magnetic calibration test form that needs to be filled out during which specific tests can be requested. The facility will null all external magnetic fields and then create magnetic fields in the different axes of specified functions so that the output can be seen and the working of the magnetometer can be checked. The magnetic fields typically requested for experiment testing for a magnetometer whose saturation is at 60,000 nT are the following:

1. 50,000 nT in X, Y and Z directions.

2. Cosine functions with an amplitude of 50,000 nT in X, Y and Z direction.

3. Spherical shell test that is described by a vector of the following form:    A cos(γt)      B sin(γt) cos(ωt) (A.1)     B sin(γt) cos(ωt) subject to the constraint equations

γ ω (A.2)

0 6 γ 6 π (A.3)

A2 + 2 B2 = 50000 (A.4)

During the test the output signal from the magnetometer is clearly visible on the display and needs to be checked with the corresponding input signals

114 from the fields generated by the facility. For the last test, you should see the magnetic field along one axis slowly decreasing to 0 and then increasing and the other two oscillating in a sinusoidal manner and perfectly out of phase with each other but with amplitudes that increase and then decrease perfectly out of phase with the first field. The magnetic field vector should trace out a spherical shell by rotating about the x axis.

It is important to note that while the test is being announced, the ﬁelds will be announced in the coordinate system of the facility which is surely different from the way the magnetometer is aligned. It is important to note the alignment of the magnetometer axes with the facility axes before going ahead with the test in a table such as below.

Rocket payload Magnetometer Facility (Direction) Facility (Axis) Front X Up Z 0◦ Y North X 90 ◦ Z West −Y

Table A.1: Axis conversion table for magnetic calibration

115 A.7 Mechanical tests and GPS roll-out

These complete the tests important for the experiment electronics during integration. After this, the remaining safeties should be installed, after which boom extensions must be remeasured like in the previous steps. In order to reinstall the safeties, the boom might have to be pushed back into place slightly in order for the screws and pins to be installed in their original place. This is not a problem. This is also a good time for the resistance of the pyrotechnics in the booms to be checked. For the remaining tests, it is always good to monitor the currents and signals if possible and make sure there are no unexpected signals.

A.8 Photos of the facility

Figure A.17: The rocket payload with nosecone in the mechanical testing area

116 Figure A.18: The rocket payload installed on the vibration table for the vibration test

Figure A.19: (L) The payload without the nosecone in the electronics testing area where the telemetry and sequencing tests take place.

117 Figure A.20: Movement of the rocket payload using cranes and a rolling table between different testing areas.

Figure A.21: Positioning of the rocket payload in the magnetic calibration chamber

118 BIBLIOGRAPHY

[1] M. A. Abdu, P. P. Batista, I. S. Batista, C. G. M. Brum, A. J. Carrasco, and B. W. Reinisch. Planetary wave oscillations in mesospheric winds, equatorial evening prereversal electric ﬁeld and spread f. Geophysical Research Letters, 33(7), 2006.

[2] M. A. Abdu, E. A. Kherani, I. S. Batista, and J. H. A. Sobral. Equatorial evening prereversal vertical drift and spread f suppression by disturbance penetration electric ﬁelds. Geophysical Research Letters, 36(19), 2009.

[3] David N. Anderson and Robert J. Redmon. Forecasting scintillation activity and equatorial spread f. Space Weather, 15(3):495–502, 2017.

[4] H. C. Aveiro and D. L. Hysell. Three-dimensional numerical simulation of equatorial f region plasma irregularities with bottomside shear ﬂow. Jour- nal of Geophysical Research: Space Physics, 115(A11), 2010.

[5] H. C. Aveiro, D. L. Hysell, R. G. Caton, K. M. Groves, J. Klenzing, R. F. Pfaff, R. Stoneback, and R. A. Heelis. Three-dimensional numerical simulations of equatorial spread f: Results and observations in the paciﬁc sector. Journal of Geophysical Research: Space Physics, 117(A3), 2012.

[6] Ephrem Beshir, Melessew Nigussie, and Mark B. Moldwin. Characteristics of equatorial nighttime spread f – an analysis on season-longitude, solar activity and triggering causes. Advances in Space Research, 65(1):95 – 106, 2020.

[7] Lunjin Chen, Robert Pfaff, Roderick Heelis, Scott Boardsen, and Zhiyang Xia. Ion cyclotron resonant absorption lines in elf hiss power spectral density in the low-latitude ionosphere. Geophysical Research Letters, 47(2):e2019GL086315, 2020. e2019GL086315 10.1029/2019GL086315.

[8] Lunjin Chen, Ondrej Santol´ık, Mychajlo Hajos,ˇ Liheng Zheng, Zeren Zhima, Roderick Heelis, Miroslav Hanzelka, Richard B. Horne, and Michel Parrot. Source of the low-altitude hiss in the ionosphere. Geophysical Re- search Letters, 44(5):2060–2069, 2017.

[9] E. Dao, M. C. Kelley, P. Roddy, J. Retterer, J. O. Ballenthin, O. de La Beau- jardiere, and Y.-J. Su. Longitudinal and seasonal dependence of nighttime equatorial plasma density irregularities during solar minimum detected on the c/nofs satellite. Geophysical Research Letters, 38(10), 2011.

119 [10] Douglas P. Drob, John T. Emmert, John W. Meriwether, Jonathan J. Makela, Eelco Doornbos, Mark Conde, Gonzalo Hernandez, John Noto, Kather- ine A. Zawdie, Sarah E. McDonald, Joe D. Huba, and Jeff H. Klenzing. An update to the horizontal wind model (hwm): The quiet time thermosphere. Earth and Space Science, 2(7):301–319, 2015.

[11] J. V. Eccles, J. P. St. Maurice, and R. W. Schunk. Mechanisms underlying the prereversal enhancement of the vertical plasma drift in the low-latitude ionosphere. Journal of Geophysical Research: Space Physics, 120(6):4950–4970, 2015.

[12] P. N. Guzdar, P. Satyanarayana, J. D. Huba, and S. L. Ossakow. Inﬂuence of velocity shear on the rayleigh-taylor instability. Geophysical Research Letters, 9(5):547–550.

[13] Peter H. Hildebrand and R. S. Sekhon. Objective Determination of the Noise Level in Doppler Spectra. Journal of Applied Meteorology, 13(7):808– 811, 10 1974.

[14] Chao-Song Huang. Effects of the postsunset vertical plasma drift on the generation of equatorial spread f. Progress in Earth and Planetary Science, 5, 12 2018.

[15] Chao-Song Huang, O. de La Beaujardiere,` P. A. Roddy, D. E. Hunton, J. O. Ballenthin, M. R. Hairston, and R. F. Pfaff. Large-scale quasiperiodic plasma bubbles: C/nofs observations and causal mechanism. Journal of Geophysical Research: Space Physics, 118(6):3602–3612, 2013.

[16] Chao-Song Huang and Marc R. Hairston. The postsunset vertical plasma drift and its effects on the generation of equatorial plasma bubbles observed by the c/nofs satellite. Journal of Geophysical Research: Space Physics, 120(3):2263–2275, 2015.

[17] J. D. Huba and G. Joyce. Global modeling of equatorial plasma bubbles. Geophysical Research Letters, 37(17), 2010.

[18] J. D. Huba, G. Joyce, and J. A. Fedder. Sami2 is another model of the ionosphere (sami2): A new low-latitude ionosphere model. Journal of Geophysi- cal Research: Space Physics, 105(A10):23035–23053, 2000.

[19] J. D. Huba and J. Krall. Impact of meridional winds on equatorial spread f: Revisited. Geophysical Research Letters, 40(7):1268–1272, 2013.

120 [20] J. D. Huba and L. C. Lee. Short wavelength stabilization of the gradient drift instability due to velocity shear. Geophysical Research Letters, 10(4):357– 360, 1983.

[21] D. L. Hysell, R. Jafari, M. A. Milla, and J. W. Meriwether. Data-driven numerical simulations of equatorial spread f in the peruvian sector. Journal of Geophysical Research: Space Physics, 119(5):3815–3827, 2014.

[22] D. L. Hysell and E. Kudeki. Collisional shear instability in the equatorial f region ionosphere. Journal of Geophysical Research: Space Physics, 109(A11), 2004.

[23] D. L. Hysell, M. F. Larsen, C. M. Swenson, A. Barjatya, T. F. Wheeler, T. W. Bullett, M. F. Sarango, R. F. Woodman, J. L. Chau, and D. Sponseller. Rocket and radar investigation of background electrodynamics and bottom-type scattering layers at the onset of equatorial spread f. Annales Geophysicae, 24(5):1387–1400, 2006.

[24] D. L. Hysell, S. Rao, K. M. Groves, and M. F. Larsen. Radar investigation of postsunset equatorial ionospheric instability over kwajalein during projectwindy. Journal of Geophysical Research: Space Physics, n/a(n/a):e2020JA027997.

[25] D. L. Hysell, S. Rao, and M. F. Larsen. Equatorial f-region plasma waves and instabilities observed near midnight at solar minimum during the nasa too windy sounding rocket experiment. Journal of Geophys- ical Research: Space Physics, 125(9):e2020JA028408, 2020. e2020JA028408 10.1029/2020JA028408.

[26] David Hysell. Antennas and Radar for Environmental Scientists and Engineers. Cambridge University Press, 2018.

[27] Huba J. D. Ossakow S. L. Krall, J. and G. Joyce. Equatorial spread f fossil plumes. Ann. Geophys., 28(11):2059–2069, 2010.

[28] Erhan Kudeki and Santanu Bhattacharyya. Postsunset vortex in equatorial f-region plasma drifts and implications for bottomside spread-f. Journal of Geophysical Research: Space Physics, 104(A12):28163–28170, 1999.

[29] A. Labno, R. Pradipta, M. C. Lee, M. P. Sulzer, L. M. Burton, J. A. Cohen, S. P. Kuo, and D. L. Rokusek. Whistler-mode wave interactions with ionospheric plasmas over arecibo. Journal of Geophysical Research: Space Physics, 112(A3), 2007.

121 [30] M. Nicolls, M. Kelley, M. Vlasov, Yogeshwar Sahai, Jorge Chau, D. Hysell, P. Fagundes, F. Becker-Guedes, and W. Lima. Observations and modeling of post-midnight uplifts near the magnetic equator. Annales Geophysicae, 24, 07 2006.

[31] Y. Otsuka. Review of the generation mechanisms of post-midnight irregularities in the equatorial and low-latitude ionosphere. Prog Earth Planet Sci, 5(57), 2018.

[32] A. K. Patra, D. V. Phanikumar, and T. K. Pant. Gadanki radar observations of f region ﬁeld-aligned irregularities during june solstice of solar minimum: First results and preliminary analysis. Journal of Geophysical Research: Space Physics, 114(A12), 2009.

[33] Robert F. Pfaff Jr., Carmen Liebrecht, Jean-Jacques Berthelier, Michel Mal- ingre, Michel Parrot, and Jean-Pierre Lebreton. DEMETER Satellite Obser- vations of Plasma Irregularities in the Topside Ionosphere at Low, Middle, and Sub-Auroral Latitudes and their Dependence on Magnetic Storms, pages 297– 310. American Geophysical Union (AGU), 2008.

[34] J. M. Picone, A. E. Hedin, D. P. Drob, and A. C. Aikin. Nrlmsise-00 empirical model of the atmosphere: Statistical comparisons and scientiﬁc issues. Journal of Geophysical Research: Space Physics, 107(A12):SIA 15–1–SIA 15–16, 2002.

[35] L. Scherliess and B. G. Fejer. Radar and satellite global equatorial f region vertical drift model. Journal of Geophysical Research: Space Physics, 104(A4):6829–6842, 1999.

[36] Gilbert Strang. On the construction and comparison of difference schemes. SIAM Journal on Numerical Analysis, 5(3):506–517, 1968.

[37] P. J. Sultan. Linear theory and modeling of the rayleigh-taylor instability leading to the occurrence of equatorial spread f. Journal of Geophysical Re- search: Space Physics, 101(A12):26875–26891, 1996.

[38] Finlay C.C. Beggan C.D. et al. Thebault,´ E. International geomagnetic reference ﬁeld: the 12th generation. Earth Planet Sp, 67(79), 2015.

[39] Hy. Trac and Pen Ue-Li. A primer on eulerian computational ﬂuid dynamics for astrophysics. Publiciation of the Astronomical Society of the Paciﬁc, 15(805), 2002.

122 [40] Roland T. Tsunoda, David M. Bubenik, Smitha V. Thampi, and Mamoru Yamamoto. On large-scale wave structure and equatorial spread f without a post-sunset rise of the f layer. Geophysical Research Letters, 37(7), 2010.

[41] Bram van Leer. Towards the ultimate conservative difference scheme. v. a second-order sequel to godunov’s method. Journal of Computational Physics, 32(1):101–136, 1979.

[42] Bram van Leer. High resolution schemes for hyperbolic conservation laws. Journal of Computational Physics, 49(3):357–393, 1983.

[43] Ronald F. Woodman and Cesar´ La Hoz. Radar observations of f region equatorial irregularities. Journal of Geophysical Research (1896-1977), 81(31):5447–5466, 1976.

[44] T. Yokoyama, R. F. Pfaff, P. A. Roddy, M. Yamamoto, and Y. Otsuka. On postmidnight low-latitude ionospheric irregularities during solar minimum: 2. c/nofs observations and comparisons with the equatorial atmosphere radar. Journal of Geophysical Research: Space Physics, 116(A11), 2011.

[45] S. Zargham and C. E. Seyler. Collisional and inertial dynamics of the ionospheric interchange instability. Journal of Geophysical Research: Space Physics, 94(A7):9009–9027, 1989.

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