Analysis and Applications of Ionospheric Measurements from the Integrated Miniaturized Electrostatic Analyzer

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ANALYSIS AND APPLICATIONS OF IONOSPHERIC MEASUREMENTS FROM THE

INTEGRATEDMINIATURIZED ELECTROSTATIC ANALYZER

by

GABRIELRENNER WILSON

B.S. & B.A., University of Colorado at Boulder, 2007

A dissertation submitted to the Graduate Faulty of the University of Colorado Colorado Springs

in partial fulfillment of the requirements of the degree of

Doctor of Philosophy

Department of Physics & Energy Science 2020

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GABRIELRENNER WILSON

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This dissertation for the Doctor of Philosophy degree by Gabriel Renner Wilson

has been approved for the

Department of Physics & Energy Science by

Mathew G. McHarg, Chair

Zbigniew Celinski

Robert Camley

Anatoliy Glushchenko

Carlos A. Maldonado

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Wilson, Gabriel Renner (Ph.D., Applied Science - Physics)

Analysis and Applications of Ionospheric Measurement for the Integrated Miniaturized Electrostatic Analyzer

Dissertation directed by Professor M. Geoff McHarg, USAFA

Abstract

Since the beginning of the space age electrostatic instruments have aided us in

understanding the near Earth space environment. Measurements of the ionosphere are valuable in understanding geomagnetic phenomena and can be used to improve space weather forecasting in order to reduce the societal impact of extreme space weather. The Integrated Miniaturized Electrostatic Analyzer (iMESA) was a satellite based parallel plate electrostatic analyzer that characterized the ion density and ion temperature in the vicinity of the spacecraft and quantified the electric potential of the spacecraft with respect to the background plasma. The instrument directly measured the ion current through the sensor head as a result of the motion of the spacecraft through the relatively stationary plasma. The current was amplified, measured, digitized, and stored by the instrument electronics before transmission to the ground. The transmitted data were post processed and analyzed to provide the quantities describing the environment near the spacecraft. The ultimate goal of this research is to demonstrate that the ion density measurements provided by iMESA can improve the accuracy of a space weather model and can, by extension, aid in space weather forecasting. The initial milestones of the project were the development of procedures to calibrate the instrument using simulations and process the raw instrument data. The calibrated and processed data had to be

validated against another ionospheric instrument to ensure the quality of the iMESA data products. The International Reference Ionosphere (IRI) was used to convert ionosonde measurements to electron density and temperature at the location of the spacecraft from

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derived from the calibration simulations. The modeled anode current agrees with the current measured by iMESA to within a Pearson’s coefficient of 0.848. A direct

comparison of the plasma densities and ion temperatures from IRI and iMESA produced a determined Pearson’s coefficient r = 0.549. While a direction comparison of measured iMESA ion temperature and modeled ion temperature from IRI produced a Pearson’s coefficient of r = 0.061. The validated ion density measurements were assimilated into the Global Positioning System Ionospheric Inversion (GPSII) model ionospheric program and predicted ionograms were generated. The inclusion of iMESA data into the GPSII improved the linearity of the modeled data when compared to ionosonde measurements but failed to improve the skill score of the model for the height and frequency of the F2 peak.

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Dedication

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Acknowledgments

I would like to thank the Air Force Office of Scientific Research, the University of Colorado at Colorado Springs Mentored Doctoral Fellowship program, and Defense Advanced Research Projects Agency for the funding and support that allowed for the suc-cess of this research. Additionally, I would like to thank the USAFA Cadets and Person-nel who worked on this instrument especially Dr. Geoff McHarg, Dr. Richard Balthazor, Dr. Carlos Maldonado, Dr. Parris Neal, and LtC Jake Harley. Thanks is also due to the research groups who’s data and collaboration made this research possible, the Global Iono-sphere Radio Observatory for their ionosonde data, NorthWest Research Associates for use of the GPSII software, and the Community Coordinated Modeling Center for use of their online IRI suite. I would also like to thank my parents, Dave and Linda Wilson, for all their support and encouragement and my high-school physics teacher and very close friend Mr. C. E. Flock.

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List of Tables

1 Ionospheric parameters used to predict the Chapman functions shown in

Figure 3. . . 21

2 Dimensions of the ESA plates. . . 25

3 The geometric factors of the iMESA instrument calculated from SIMION simulations. . . 32

4 The geometric parameters of the iMESA instrument calculated from SIMION simulations. . . 35

5 The iMESA IRF constants as a function of deflection plate voltage. . . 40

6 The NASA published standards for Earth observing data processing. . . 49

7 The standards to which iMESA data was processed to at each Level. . . 50

8 The Format of the data packet transmitted from the satellite. . . 51

9 STPSat-3 TLE point for November 17, 2017 taken at 21:35:07 UTC. . . 53

10 The standards to which iMESA data was processed to at each Level. . . 54

11 The inputs options to IRI2016 and the reasoning behind the decision. . . 71

12 The range and magnitude of the spacecraft charging in comparisons with the seed values used to derive the modeled drifted Maxwell-Boltzmann distributions. . . 80

13 The range and magnitude of the difference between seed ion temperature used to derive the modeled drifted Maxwell-Boltzmann distributions and the resulting fit ion temperature. . . 83

14 The range and magnitude of the difference between seed ion temperature used to derive the modeled drifted Maxwell-Boltzmann distributions and the resulting fit ion temperature. . . 85

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16 The calculated Pearson’s coefficient for GPSII modeled values when com-pared to ionosonde measurements. . . 103 17 The difference between the GPSII model outputs and the ionosonde

mea-surements before and after iMESA data assimilation. . . 104 18 A list of future research topics for the iMESA data and the procedures

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List of Figures

1 The iMESA instrument. . . 3 2 The structure of the Ionosphere. . . 17 3 Example Chapman density profiles derived from measurements over Jeju,

Korea. . . 20 4 The iMESA instrument prior to integration with the STPSat-3 satellite.

The coordinate system is along the dimensions defined in Figure 5 and are also displayed in Figure 6 . . . 23 5 The design drawing of a filter plate. Dimensions shown are in millimeters. . 24 6 A model of a single ESA channel showing the alignment of the apertures,

created in SIMION. . . 24 7 A schematic drawing of the STPSat-3 iMESA instrument detector head

electronics. . . 26 8 The relationship between the anode current and the TIA output voltage. . . 27 9 The deflection plate voltage driver circuitry. . . 28 10 The deflection plate voltage driver circuitry. . . 29 11 The results of the SIMION simulation. . . 31 12 The instrument’s efficiency response to particles with velocities across the

narrow dimension of the aperture. . . 33 13 The instrument’s efficiency response to particles with velocities along the

narrow dimension of the aperture. . . 34 14 A sample sweep displaying the mean (blue), full width half at half

maxi-mum (black) and amplitude of the distribution. . . 41 15 The difference in density between 350 km and 500 km at both day and night. 46 16 A visualization of Level 2 data. . . 55 17 A visualization of Level 3 data. . . 58

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18 Anode Current spectra with uncertainties (blue) captured by iMESA and

fitted Maxwell-Boltzmann distributions with 95% confidence bounds (red). 59 19 The Percent of Sweeps that provided enough signal to generate plasma

parameters. . . 60

20 Histograms depicting the range of the recorded ion density (A), ion tem-perature (B), and spacecraft potential (C). . . 61

21 Diagram depicting an ionosonde sounding the bottom-side ionosphere. . . . 65

22 An example ionogram capture on November 27, 2013, at the Wuhan Digisonde station. . . 66

23 The potential Digisonde overflights for March 20th, 2015. . . 67

24 The structure of the Ionosphere. . . 69

25 A comparison between distribution functions. . . 74

26 The relative shape of the functions involved in the convolution. . . 75

27 The measured and modeled anode current for a sweep. . . 76

28 The measured current in nA against the modeled current in nA. . . 78

29 The Pearson’s Coefficient between the measured sweep and the modeled sweep after varying the temperature and density. . . 79

30 Fitted spacecraft potential as a result of varying the temperature and den-sity. Ideally this should be constant. . . 81

31 The fitted temperature as a result of varying the temperature and density. . . 81

32 The fitted temperature at a constant density, 3.072 m−3_{, and variable input} temperature. . . 82

33 The fitted temperature at a constant density, 3.072 m−3_{, and variable input} temperature. . . 82

34 Fit density as a result of varying the temperature and density. . . 83

35 The fit density at a constant temperature, 3.072 m−3_{, and variable input} temperature. . . 84

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36 The fitted density at a constant temperature, 3.072 m−3_{, and variable input}

temperature. . . 84 37 Derived ion density current in m−3_{against the modeled electron density,}

in m−3_{. . . 86}

38 Derived ion temperature current in K against the modeled ion temperature in K. . . 88 39 Modeled anode current sweep with numerical fit and 95% confidence

bounds. . . 89 40 Modeled anode current sweep with simulated noise and numerical fit and

95% confidence bounds. . . 89 41 The position of the good iMESA data points for the week 28-March, 2016

to 3-April, 2016. . . 92 42 The position of the good iMESA data points used in the GPSII simulation

and the ionosondes in the area 28-March, 2016 to 3-April, 2016. . . 93 43 The GPSII startup tab setting used in this analysis, displaying the time

frame of the simulation. . . 95 44 The GPSII grid tab setting used in this analysis, displaying the region

simulated. . . 95 45 The settings used by GPSII for IRI-2016. . . 96 46 A sample of the iMESA data used as an input for GPSII. . . 98 47 GPSII data files tab, where the location of the list of files to assimilate is

dictated. . . 98 48 The GPSII GUI representation the list of files to be assimilated. . . 99 49 Example of ionosondes generated from GPSII and an α-Chapman

func-tion derived from ionosonde measurements. . . 100 50 The critical frequency of the ionosphere with STPSat-3 position showing

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51 A point-by-point comparison of the height of the F2 peak as measured by

the Ionosondes and the GPSII prediction before assimilation of iMESA data. 101 52 A point-by-point comparison of the height of the F2 peak as measured by

the Ionosondes and the GPSII prediction after assimilation of iMESA data. 102 53 A point-by-point comparison of the frequency of the F2 peak as measured

by the Ionosondes and the GPSII prediction before assimilation of iMESA data. . . 102 54 A point-by-point comparison of the frequency of the F2 peak as measured

by the Ionosondes and the GPSII prediction after assimilation of iMESA

data. . . 103 55 The frequency of the F2 Peak above Jeju Island, Korea. . . 105 56 The height of the F2 Peak above Jeju Island, Korea. . . 106 57 Frequency of the F2 Peak for all points where the GPSII output was

al-tered after assimilation of the iMESA data. . . 106 58 Height of the F2 Peak for all points where the GPSII output was altered

after assimilation of the iMESA data. . . 107 59 Point-by-point comparison of the height of the F2 peak for all points

where the GPSII output was altered after assimilation of the iMESA data. . 108 60 Point-by-point comparison of the frequency of the F2 peak for all points

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Nomenclature and Abbreviations

ADC = Analog to Digital Converter

CCMC = Commuunity Coordinated Modeling Center CME = Coronal Mass Ejection

DAC = Digital to Analog Converter

DARPA = Defense Advanced Research Projects Agency

EOSDIS = Earth Observing System Data and Information System ESA = Electrostatic Analyzer

GIRO = Global Ionosonde Radio Network GPSII = GPS Ionospheric Inversion GUI = Graphical User Interface

iMESA = Integrated Miniaturized Electrostatic Analyzer iMESA = Interplanetary Magnetic Field

IRF = Instrument Response Function IRI = International Reference Ionosphere ISS = International Space Station

LLA = Longitude, Latitude, and Altitude

NaN = Not a Number

NASA = National Aeronautics and Space Administration NetCDF = Network Common Data File

NOAA = National Oceanic and Atmospheric Administration

NPOESS= National Polar-orbiting Operational Environmental Satellite System RMS = Root Mean Square deviation

SNR = Signal to Noise Ration SOH = State of Health

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STK = Satellite Tool Kit STP = Space Test Program SWaP = Size, Weight, and Power

SWPC = Space Weather Prediciton Center TEC = Total Electron Count

TIA = Trans-Impedance Amplifier TLE = Two Line Element

UCCS = University of Colorado at Colorado Springs USAFA = United States Air Force Academy

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Section 1 Introduction

Space weather phenomena has the ability to severely impact the regular functions of a technological society [1]. Geomagnetic storms have affected Global Position System (GPS) navigation [2], satellite based and terrestrial communications [3], and the terrestrial electrical grid [4]. Forecasting the conditions in the near Earth

environment can reduce the impact of such events[5] but the ability to predict the future geomagnetic conditions is far behind that of terrestrial weather[6]. Space weather forecasting models require input from environmental sensors in order to improve the accuracy and timeliness of predictions[7].

Space weather is primarily driven by the sun. Variations in the solar activity and eruptions from the solar atmosphere in the form of prominences or Coronal Mass

Ejections (CME) can cause extreme events. Historically, the Carrington event in 1859 was the first major storm recorded when massive CME hit the Earth’s magnetosphere[1]. The storm affected telegraph communications, even causing some sites to operate without any power sources and started fires in telegraph offices[8]. A smaller storm in March 1989 caused, among many other things, an overload of the power grid throughout most of Quebec causing power outages for up to nine hours [9]. It is theorized that a Carrington level event today would cause a great deal of damage to electronic systems.

Accurate prediction of the impact of extreme space weather can reduce the impact of future storms. The Space Weather Prediction Center (SWPC), a part of the National Oceanic and Atmospheric Administration (NOAA), is the foremost group focused on space weather forecasting [10]. They use data collected on the solar activity to predict the related geomagnetic conditions up to 24 hours in advance. Many models regarding the behavior of particular parts of the Earth-sun system are cataloged at NASA’s

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Community Coordinated Modeling Center (CCMC) [11][12]. The Defense Advanced Research Projects Agency (DARPA) started the Space Environment Exploitation (SEE) program in an effort to extend all space weather prediction capabilities from 24 hours to 72 hours [13].

Ionospheric models can use plasma density, as well as other ionospheric measurements, to bound forecasts of environmental conditions[14]. Simulated iMESA ion density has been shown to improve the accuracy of ionospheric models[15]. The more measurements incorporated into a model the closer the output of the model becomes to describing the real environmental conditions[16]. There is a need for more accurate and timely forecasting of space weather conditions[17]. Direct measurements of the plasma density within the ionosphere are difficult to collect due to the obstacles associated with access to space[18]. Preparing and evaluating one such plasma density sensor for use in space weather modeling and forecasting, the Improved Miniaturized Electrostatic Analyzer (iMESA), is the focus of this research.

Electrostatic Analyzers (ESA) are not unique for space weather data collection, and other instruments are capable of collecting data from which the ionospheric density can be derived. ESA have flown on Earth orbiting satellites like the National

Polar-orbiting Operational Environmental Satellite System (NPOESS)[19], planetary missions like Cassini [20] and New Horizons[21], and even solar missions like the Parker Solar Probe [22]. Typically these ESAs have a design called a top-hat [23], in which they exploit cylindrical symmetry to gain a wide field of view and large energy range. While effective and accurate, top-hat ESA are complicated to design and manufacture [24].

iMESA, Figure 1, was a parallel plate ESA designed and constructed by the Space Physics and Atmospheric Research Center (SPARC) at the U.S. Air Force

Academy (USAFA)[25]. The iMESA instrument was designed to have a small envelope and require a small amount of low power to capture measurements. iMESA weighed

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620g, occupied on a 10.16 × 10.16 × 3.45 cm3_{enclosure, consumed 882 mW average}

orbital power and has been call by SPARC a low Size, Weight, and Power (SWaP) unit. The low SWaP and easy integration make iMESA a plausible candidate for flight on many satellites, therefore providing a large coverage of accurate ionospheric data for space weather prediction. It can easily be integrated onto a spacecraft, as has been shown in the 5 operating follow-on missions[26, 27]. The analysis performed on iMESA can be applied to later generation iMESA instruments to create a constellation of units able to supply ionospheric data for space weather modeling and prediction. The instrument must be well understood and characterized before integration into a model.

Figure 1: The iMESA instrument.

iMESA was launched on-board the DoD’s Space Test Program’s (STP)

experimental satellite, called STPSat-3, on 20 November, 2013. The satellite was inserted into an orbit with 0.00046 eccentricity and an inclination of 40o_{. The spacecraft initially}

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were first taken on 24 November, 2013 and the instrument operated nearly continuously until the end of mission on 1 July, 2019. iMESA measured the flux of ions through a kinetic energy band pass filter which produced a quantifiable electrical current. Analysis of the measured current resulted in values for ion density and temperature in the vicinity of the spacecraft and the spacecraft potential with respect to the background plasma.

iMESA fundamentally measures an electric current produced by ionospheric ions incident on a collection plate, called the instrument anode. The motion of the spacecraft through the, relatively, stationary ionospheric plasma produced an ion flux through the instrument sensor head inducing a current on the instrument electronics. The current, on the scale of nanoamps, was amplified and converted to a voltage using a Trans-Impedance Amplified (TIA). The behavior of the sensor electronics was quantified using traditional circuit analysis and was verified by models in LTSpice[28]. The output voltage of the TIA was scaled to the input of an Analog to Digital Controller (ADC), which digitized the measurement for data processing. The output of the ADC was recorded by the instrument processor and stored in an on-board SD-card until it could be transferred to the satellite. The raw instrument ADC was serialized into data packets and transmitted to the ground where the scientific information could be extracted.

Derivation of the environmental values from the raw instrument data was accomplished in three steps. Initially the instrument science packets were removed from the satellite data transmission and the scientific information was further extracted from the instrument packets. Then the location and orbital velocity of the satellite, in the form of Longitude, Latitude, and Altitude (LLA), was determined from published Two Line Elements (TLEs) using the Systems (Satellite) Tool Kit (STK) software suite[29]. Lastly, the raw instrument data was processed from values recorded by the instrument’s ADC to the current measured at the anode. Once derived, the anode current spectra were fit to drifted Maxwell-Boltzmann distribution functions for energy. To conclude the third

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processing step, the instrument geometric parameters, determined from instrument simulations, were used to calculate the local ion density, ion temperature, and spacecraft potential.

Deriving the environmental information form the measured values requires knowledge of the effect the instrument has on the plasma before it is quantified. These effects are related to the geometry of the instrument and are therefore labeled, as a group, the geometric parameters. The plate factor, fp, is a geometry specific quantity that relates

the voltage applied to the deflection plates to the most probable ion kinetic energy in the instrument pass band, E. The width of the instrument pass band is called the energy resolution, ∆E, and scales with the deflection voltage so it is typically reported as the ratio of the width of pass band to the most probable energy in the pass band, ∆E/E. The ratio of ions that enter the instrument sensor head with kinetic energy within the instrument energy resolution for a given deflection plate voltage that interact with the instrument anode is called the instrument efficiency, ε. The angular resolution is the quantification of how instrument efficiency is attenuated when the direction of the incident ion stream is not coincident with the instrument normal. Lastly the instrument geometric factor, FG, is

the accumulation of all of the instrument geometric parameters into a function which converts the number of particles detected to flux of the ambient plasma[30]. The accumulation of these quantities can also be used to define the Instrument Response Function (IRF) which was used to validate the instrument calibration. Quantification of an instrument geometric parameters is most easily determined from simulation because the distribution of the incident particles can be precisely known.

SIMON is an ion optics simulation program that was used to model one of the 176 total channels of the iMESA electrostatic analyzer[31]. Single ions were injected into the initial aperture of the ESA across the height of the channel. After each raster across the channel height the kinetic energy of the particles was incremented until the entire pass

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bad of the instrument was captured. Ions that traversed the ESA channel and exited the final aperture plate were marked as counted and used to generate a function relating the instrument efficiency with respect to initial ion kinetic energy. This function was fit the the sum of two Gaussian distributions and used to derive the instrument geometric parameters and the instrument response function.

In order to validate the accuracy of the calibration derived from simulation, ion density and temperature data was gathered for another set of instruments for comparison. The Global Ionosonde Radio Network (GIRO) is a globally spanning group of

ionospheric sounders[32] that can be used with the International Reference Ionosphere 2016 update (IRI-2016)[33] to model the ionospheric properties at the location of the iMESA instrument [34]. The environmental data generated by IRI was used, along with the measured spacecraft potential, to create a distribution function of the ambient

ionosphere in the vicinity of the spacecraft. The distribution function was then convolved with the instrument response function (IRF) and integrated over the energy resolution of the instrument to model the electric current measured at the anode. These modeled

currents were compared to the measured currents to generate a statistical representation of the accuracy of the instrument, taking into account the accuracy of the measurements under comparison. The electron density and ion temperature computed by IRI were also compared to the ion density and ion temperature, respectively, derived from the iMESA measurements.

The validated iMESA data product was then input into an ionospheric model. The ionospheric data assimilation algorithm called GPS Ionospheric Inversion (GPSII; pronounced “gypsy”) is a space weather model capable of generating predicted ionosonde data[35]. The accuracy of the predicted ionosondes were evaluated both before and after the model was given iMESA ion density data. The ionosondes generated by this model were evaluated to produce the height and frequency of the peak ionospheric density,

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which were compared against actual ionosonde measurements taken by the Digisonde network.

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Section 2 Scientific Background

2.1 Plasma Physics

2.1.1 Introduction

Plasma is the fourth state of matter in which ionized atoms and free electrons exist in a gaseous state. It is defined as a quasi-neutral gas of charged and neutral particles which exhibits collective behavior[36]. In order for an ionized gas to be a plasma its density must be such that the Debye length, Equation 1, is much smaller than the scale of the system. Commonly encountered types of plasmas are the discharge of a spark, like a lightening bolt, and the auroras; however a plasma is more likely to occur when the density of gases is lower than that encountered on the surface of the Earth. In space, where the densities of gases are much lower, nearly all free particles are ionized into some form of plasma.

2.1.2 Basics

The most fundamental aspect of a plasma is the density. The densities can vary between populations but the number of ions is typically similar to the number of electrons in a neutral plasma. In addition to density, the temperature of each population within the plasma can describe much of the behavior of the system. The temperature of each population are typically not equal because temperature is related to the mean kinetic energy, which is mass dependent.

Particles in a three dimensional plasma with have a average kinetic energy equal to hEi = 3/2kBT. A two population plasma, made up of electrons and ions will have to

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collision rate between particles in the same population than in different populations. The electrons are highly mobile within a plasma and respond to changes in the electric field more quickly than the other species.

Electrons in a plasma will move to shield out applied electric potentials. A fundamental characteristic of plasmas is how well it shields electric fields. The distance within a plasma that an electric can exist before it is eliminated by the shielding effect is called the Debye Length,

λD=

s ε0kBTe

neq2e

. (1)

Which depends on the temperature of the electrons, Te, the density, ne, and the charge of

the electrons, qe. Electric field gradients in a plasma will perturbed electrons from a

neutral position. Plasma have a primary frequency at which they are most easily excited to oscillation called the Plasma frequency,

ωp=

s neq2e

ε0me

, (2)

which depends on the density, ne, the charge of the oscillation particle, qe, and the mass of

the particle, me. Electromagnetic radiation with frequencies below the plasma frequency

that encounter the plasma is reflected. Radiation with higher frequencies can pass through the plasma.

2.1.3 Kinetic Theory

A velocity distribution function, f (~r,~v,t)d~v, refers to the number of particles per cubic meter at time t and position~r, with velocities between ~v + d~v [36]. A normalized distribution function, ˆf, has the solution that,

Z ∞

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An unnormalized distribution function can be written as the product of a normalized distribution and a density function,

f(~r,~v,t)d~v = n(~r,t) ˆf(~r,~v,t). (4)

The distribution functions can be integrated over a number of function, each called an Nth

order moment. The zeroth order moment,

ns(~r,t) =

Z ∞

−∞fs(~r,~v,t)d~v, (5)

can be used to determine the number density of the population [37]. The first order moment is the average velocity, or bulk flow, of the distribution,

~u(~r,t) = R f(~r,~v,t)~vd~v R fs(~r,~v,t)d~v . (6)

Higher order moments can be used to determine the mean kinetic energy, pressure, and many others. Collisionless, low density neutral plasma is described by the normalized Maxwell-Boltzmann distribution function[37].

f(~v) = m 2πkBT 3₂ exp − mv 2 2kBT d3v. (7)

In the presence of a bulk flow, ~v0, this can be written as a drifted Maxwell-Boltzmann

distribution function, f(~v) = m 2πkBT 3₂ exp −m(~v −~v0) 2 2kBT d3v. (8)

The drifted Maxwell-Boltzmann distribution function for velocity can be converted to a function for energy by converting, E = 1/2mv2_{. The differential in this}

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case becomes

dv=r 2 m

r 1

4EdE (9)

in each dimension. Converting to kinetic energy, the distribution function can be written as f(~v) = ₁ 4πkBT E 3₂ exp " − √E₋√E02 kBT # , (10)

where E0= 1/2mv2₀. Since the temperature and density of a system can be determined

from the distribution function, knowledge of the distribution function greatly aids in describing a plasma.

2.2 Space Physics

2.2.1 Introduction

Space Physics is the study of everything in the solar atmosphere including the plasmas in the Earth’s ionosphere and solar wind. Plasmas in space are typically low density to the point where they can be assumed to be collisionless. The driving force behind space physics and the source of a tremendous amount of plasma is the sun. Ionized matter streams from the surface of the sun as the solar wind, pulling the solar magnetic field with it. The extension of the solar magnetosphere into interplanetary space is called the Interplanetary Magnetic Field (IMF). The solar wind interacts with the Earth’s magnetic field which can influence the extent, density, and shape of the Ionosphere.

2.2.2 The Sun and the Solar Wind

The sun is made up of mostly plasma and has a very complex magnetic field that is affected by the differential rotational speeds at different solar latitudes [38]. Typically the solar material is convective, but sometimes the materiel gets caught on a complex field

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line and convection ceases. This plasma cools in comparison to the surrounding solar material and is seen as a dark spot, called a sun spot, by solar observers. Sun spots exist for up to 100 days, and can be seen throughout multiple, solar rotations. The number of sunspots follows an approximately 11 year solar cycle, after each of which the magnetic poles of the sun are reversed. The peak of each solar cycle is associated with many more sunspots and greater solar activity.

The plasma caught in magnetic field lines, indicated by sunspots, can be released in solar eruptions. The most familiar type of solar eruption is a prominence, when a great arc of solar material erupts from the sun. The trapped magnetic energy can also be released as an intense burst of radiation, called a solar flare. The most striking form of solar eruption is a Coronal Mass Ejection (CME), which is when the solar atmosphere violently ejects large amounts of plasma. These events travel outward from the sun with much greater speed and densities than the typical solar wind.

The solar wind is a flow of ionized solar plasma and a remnant of the solar magnetic fields that pervade interplanetary space. Pressure difference between the corona and interstellar space drives the plasma outward. It is a neutral ionized plasma with a density of 30 cm−3_{that travels outward from the sun at 450 km/s [37]. The solar wind}

due to a CME or solar flare can travel at over 1000 km/s [38] and have a much greater density [39].

The solar magnetic filed is locked into the solar wind. It carries the direction of the magnetic field along with the plasma. The "north-south" direction of the solar wind, as referenced form the Earth, can cause significant coupling with solar and terrestrial magnetic fields. When the two fields have opposite directions, particles from the solar wind can cross into the Earth’s magnetosphere.

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2.2.3 Magnetosphere

The solar wind is slowed significantly as it encounters the sun-ward edge of the Earth’s Magnetosphere. This creates a buildup of plasma at the interaction, called the Bow Shock. The Earth’s magnetic field points north at the bow shock and a northward pointing solar wind will compresses the magnetic field. As the plasma flows around the the plasma extends the magnetic field away from the sun, called the magnetotail.

When the solar wind points southward, the magnetic fields are able to link. As the plasma pulls the magnetic field with it the link field lines are also pulled anti-sunward. In the magnetotail, these field lines reconnect with the Earth’s magnetic field carrying with them a lot of energy, this is called reconnection. Reconnection can also pull particles from the solar wind which can influence the Earth’s atmosphere.

2.3 The Earth’s Atmosphere

2.3.1 Introduction

The Earth’s Atmosphere is the sea of gas that surrounds the planet extending from the surface to around 1000 km. It is characterized by the relationship between pressure, temperature, and altitude[40]. It is mostly characterized by the relationship between altitude and temperature, called the thermal profile. The structure of the thermal profile can be modeled using an exponential.

2.3.2 Mathematical Description

The relationships are complex but can be closely approximated by applying a few key concepts. Upper neutral atmosphere usually obeys a hydrostatic equation [37].

nn= noexp −(h − h o)

H

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To first order all atmospheres are in hydrostatic equilibrium [40] meaning the pressure is balanced by the density and gravitational force,

∆P = −gρ∆z (12)

Another way to say this is that the change in pressure, ∆P, is dependent on the

acceleration of gravity, g, the atmospheric density, ρ, and the change in height, ∆z. More particularly the change in pressure with respect to height within the atmosphere, dP

dz, is

dependent on the force of gravity, g(z) and the atmospheric density, ρ(z) as a function of altitude.

d p

dz = −g(z)ρ(z), (13)

where z is the altitude, g(z) is the gravity constant at the altitude, and ρ(z) is the atmospheric density at the altitude. The relationship between the temperature and pressure of any gas can be written as

P= NkBT = ρRgasT Ma = ρkBT µamamu . (14)

Recalling the ideal gas law, 14, where µais the mean molecular weight and

mamu= 1.67 × 10−24 is the conversion of atomic mass units (amu) to kilograms, the

atmospheric pressure the pressure at an altitude, z, can be expressed as Equation 15, where H(r) is called the Scale Height. The pressure as a function of altitude can be written as

P(z) = P(z0)e−

Rz

z0H(r)dr _. (15)

The Scale Height, typically denoted by the capitol letter H, is the height, z, above the initial height, z0at which the pressure decreases by a factor of e ≈ 2.7138. The

atmospheric density, ρ(z) follows the same law except it requires the atmospheric density scale height, H∗_{(r). The scale height is dependent on many factors within the atmosphere,}

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the first two terms are shown in Equation 16. H(z) = kBT(z) g(z)µa(z)mamu 1 H∗(z) =T1(z) dT(z) dz + g(z)µz(z kT(z) + O(∆µz, ∆g) (16)

One primary driver in both the density and pressure scale height is the Temperature at height z making the thermal structure of the atmosphere important to understanding the atmosphere as a whole.

The thermal structure of the atmosphere is primarily governed by energy transport between atmospheric components. Planetary atmospheres, like Earth’s, consist of molecular gasses and are primarily heated from above[40]. Some major process to consider, in rough order of importance, when evaluating the thermal properties of an atmosphere are:

(1) The temperature profile is defined by solar radiation heating offset by radiative processes and conduction.

(2) Internal heat sources and re-radiated energy modify the temperature profile.

(3) Chemical reactions change the composition of the atmosphere and therefore alter the thermal structure.

(4) Clouds and other atmospheric debris affect the composition of the atmosphere and alter the thermal structure.

(5) Volcanoes can modify the atmosphere substantially.

(6) Interaction between the atmosphere and the crust, or ocean, influence the atmosphere.

(7) Earth’s atmosphere is affected by biochemistry and anthropogenic processes [40].

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2.3.3 Thermal Structure

The thermal structure of Earth’s atmosphere allows it to be easily divided into regions based on how the temperature changes with height.

2.3.3.1 Troposphere

The Troposphere is characterized by decreasing temperature with height, on Earth it ranges from the surface, 0 km to about 20 km [40], the end of the troposphere and the beginning the Stratosphere is designated the Tropopause.

2.3.3.2 Stratosphere

In the Stratosphere the temperature increases with due to more solar UV being absorbed. It ranges from 20 km to 50 km on Earth.

2.3.3.3 Mesosphere

The next higher region is call the Mesosphere, the boundary between it and the Stratosphere is called the Stratopause. The Mesosphere is another region with

temperature decreases with height and ranges from 50 km to 90 km. The Mesosphere ends and the Thermosphere begins at the Mesopause.

2.3.3.4 Thermosphere

The Thermosphere is the highest region of the Earth’s atmosphere ranging from 90km to 1000km. It is characterized by increased heating with altitude primarily because the density is low enough that particle collisions do not occur and therefore energy is transferred in that manner.

2.3.3.5 Exosphere

The Exosphere is considered the final portion of Earth’s atmospheric envelope. In this region the atmosphere is more a collection of free particles and the density

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gradually decreases until it blends in to the interplanetary medium.

2.4 The Earth’s Ionosphere

2.4.1 Introduction

The ionosphere begins at an altitude where the neutral density is low enough that free electrons can survive for a reasonable long time period, 80 km [38]. Ionization occurs primarily through interaction with solar photons but is also attributed to extra solar

photons and micrometeorite interactions[37]. The ionosphere is differentiated by the density of the electrons, or plasma frequency using Equation 2, as a function of height and ion composition, Figure 2. The critical frequency of the ionosphere the is highest

frequency at which electromagnetic waves are reflected, above which the waves penetrate the system[41].

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2.4.2 Density Structure 2.4.2.1 D-Region

The D-region is the lowest portion of the ionosphere below 90 km [37]. This region is difficult to study because it is higher than maximum altitude of scientific balloons and lower than than a satellite can orbit. The majority of ions are created due to photoionization of NO molecules [40].

NO_{+ hν −→ NO}++ e−, λ < 1220Å.

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The density in direct sunlight can be as height as 104_cm−3 _{but virtually disappears at}

night [42] through dissociative recombination

NO+ e− _{−→ N + O,} (18)

The D-region has a lower density compared to the higher region but does have a huge effect on radio waves, absorbing AM radio signals during the day.

2.4.2.2 E-Region

The E-region ranges from 90 km to 130 km [37] and can reach a maximum, daylight density, on the order of 105_cm−3_{. It is composed not only of photoionized NO}

molecules but also molecular oxygen in about equal proportions,

O2+ hν −→ O+₂ + e−,

λ < 1027Å.

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Like the D-region, the E-region typically vanishes at night and is reduced by dissociative recombination,

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2.4.2.3 F-Region

The F-region is the densest portion of the ionosphere ranging from 130km to the point of maximum density around 300 km [37]. The densities in this region range from 105_{ion per cubic centimeter up to nearly 10}7_cm−3_{. It typically has a large peak called}

the F2-peak but can occasionally have a second, less dense peak called the F1-peak. The F regions consist primarily of photoionized atomic oxygen [40],

O+ hν_{−→ O}++ e−, λ < 911Å

. (21)

The F1 region is also populated by molecular nitrogen and atomic oxygen. Photodissociation of N2

N2+ hν−→ N₂++ e−,

λ < 796Å.

(22)

Recombination of atomic oxygen occurs through a two step process, charge exchange,

O++ O2−→ O+₂ + O, (23)

then dissociative recombination shown in the reaction in Equation 20. This process is slow for and allows the F2-region to persist through the night without constant photoexcitation.

2.4.2.4 Upper Ionosphere

The upper ionosphere is the portion of the ionosphere above the F2 peak and is composed almost exclusively of atomic oxygen. It is composed of ionoized atomic oxygen in the lower portion and transition to Hydrogen at high altitudes. The ionosphere extends to approximately 1000 km. STPSat-3, at an altitude of 500 km orbited within this ionospheric10e6; region.

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2.4.3 Theα-Chapman Model 0 1 2 3 4 5 6 7 8 1011 0 100 200 300 400 500 600 700 800

Figure 3: Example Chapman density profiles derived from measurements over Jeju, Ko-rea.

The plasma density of the ionosphere can be be modeled simply with the α-Chapman function[34], N(h) = Nmexp ₁ 2 1 − z − e−z (24)

where Nmis is the electron density at the F2 peak and z is

z= h− hmF2 Hs

. (25)

This equation assumes that the scale height, Hs, is constant with altitude. The electron

density of the F2 peak can be calculated from the frequency of the peak, f0F2, using

Nm=

ε0me

q2_e (2π f0F2)

2

, (26)

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the F2 peak, hmF2, is taken from an ionospheric sounder. Refinements the α-Chapman

function have varied the scale height with altitude, other approaches were not investigated as part of this research[43].

Parameters used in Chapman Demonstration foF2 hmF2 Scale Height

Distribution 1 10.688 235.2 44.3 Distribution 2 7.925 245.9 48.4 Distribution 3 3.900 344.9 80.5 Distribution 4 3.850 314.7 47.3

Table 1: Ionospheric parameters used to predict the Chapman functions shown in Figure 3.

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Section 3 The iMESA Instrument

3.1 Introduction

iMESA, Figure 4, was a proof of concept for a satellite-based parallel plate plasma environment sensor[44]. The instrument flew aboard the Space Test Program’s (STP) STPSat-3 satellite, which launched on 20-November, 2013. The spacecraft was inserted into a near-circular orbit at an inclination of 40 degrees and an altitude of 500 km, which had decayed to an altitude of 455 km by the end of the mission on 1-July, 2019. iMESA first operated on 24-November, 2013, and continued data collection for the duration of STPSat-3’s operational lifetime totaling five years, seven months, and eleven days of operation. The instrument’s scientific objective was to (1) measure the plasma density in low Earth Orbit, (2) measure the plasma temperature in low Earth Orbit, and (3) quantify the spacecraft potential with respect to the ambient plasma potential in the ionosphere.

Ionospheric measurements were collected by quantifying the ion current at the instrument anode as a result of the spacecraft’s relative motion through the plasma. The current measurements were analyzed to determine the local ion density, ion temperature, and the spacecraft potential with respect to the background plasma. iMESA is the

predecessor to six similar instruments, designated iMESA-R, which are currently on orbit, and ÉPÉE[45], which is in the design phase. All the iMESA and iMESA-R instruments employ a flat plate architecture to sample the ionosphere[44]. Each instrument in the iMESA family is designed as low Size, Weight, and Power (SWaP) solutions for

ionospheric data collection. The subsequent iMESA-R instruments are aboard STPSat-4, STPSat-5, the Orbital Test Bed, the Green Propellant Infusion Mission, and the ISS through STP-H6. ÉPÉE has yet to be officially manifested but is target to fly aboard the

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Figure 4: The iMESA instrument prior to integration with the STPSat-3 satellite. The coordinate system is along the dimensions defined in Figure 5 and are also displayed in Figure 6

ISS through STP-H9

3.2 Mechanical Design

The iMESA on STPSat-3 was developed to consume low power and to occupy a small envelope while also being designed and constructed by advanced undergraduates. When the iMESA was delivered for integration with the spacecraft it was measured to have occupied a 10.16 × 10.16 × 3.45 cm3_{aluminum housing, weighed 620 g, and}

consumed 882 mW while under normal operations. The sensor head was constructed from a stack of five stainless steel plates alternating between filter plates and deflection plates. Each of the parallel plates were 86 × 86 mm2and had 176 apertures cut through each using electrical discharge machining. The apertures were arranged in sixteen groups of eleven, Figure 5, in order to fit around the instrument’s mechanical frame, as can be seen in Figure 4.

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Figure 5: The design drawing of a filter plate. Dimensions shown are in millimeters.

ions could not follow a straight trajectory to the anode. Apertures in the first filter plate were offset such that one edge was in line with the edge of an aperture in the first

deflection plate (Figure 6). The second filter plate aperture was aligned along the opposite edge of the deflection plate aperture so that ions would need to trace an "S" shape to pass into the second filter plate aperture. This arrangement was then reversed and the ions would need trace a second "S" shape as they passed through the second filter plate, second deflection plate, and third filter plate to the instrument anode.

Figure 6: A model of a single ESA channel showing the alignment of the apertures, cre-ated in SIMION.

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dictated the behavior of the instrument. Figure 6 show an example cross-section of an iMESA ESA channel generated using SIMION [31]. In this figure, the ESA filter plates and deflection plates (as labeled) were held at spacecraft ground and 10V respectively. The saddle shape in the equipotentials (blue) within the deflection plate aperture focuses the ions (red) through the instrument. The light blue coordinate axis (bottom-left) defines the x-direction as the direction of the ion current, the y-direction along the narrow

dimension of the filter plate aperture (Figure 5) and the z-direction along the wide direction in the filter plate aperture, completing the right-hand coordinate system. Ions with kinetic energy in the range of the instrument pass-band would navigate both s-bends and could then interact with the instrument anode, inducing a current in the electronics.

The three filter plates were 0.635 mm thick stainless steel plates with 0.15 ± 0.02 mm by 14.90 ± 0.02 mm apertures. The first filter plate made up the face of the

instrument, thus presenting a total area of 393 ± 4 mm2for the ion current to enter the sensor. The two deflection plates were placed between each adjacent pair of filter plates and were 1.140 ± 0.02 mm t with 0.58 ± 0.02 mm by 14.90 ± 0.02 mm apertures. All plates were separated by 0.255 mm insulating Teflon spacers placed outside the path of the ESAs. The filter and deflection plate dimensions as well as the apertures cut into them are listed in Table 2.

Plate Dimensions

Plate Plate Aperture Aperture Manufacturing

Name Thickness Height Width Tolerance

Filter 0.635 mm 0.15 mm 14.90 mm _±0.02mm Deflection 1.140 mm 0.58 mm 14.90 mm _±0.02mm

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3.3 Electronics

3.3.1 Anode Current Sensor

The velocity of the spacecraft through the ionospheric plasma created a flow of ions onto the instrument face and through the apertures of the first filter plate. The band pass filter for ion kinetic energy was created by applying a voltage to the deflection plates relative to the filter plates, which were held at instrument ground [46]. Ions with the selected energies were focused through the ESA, creating a current in the instrument electronics (Figure 7). The deflection plate bias voltage was stepped from −2.1 ± 0.4 V to 25.9 ± 0.6 V in 1 V steps, sampling the anode current at each step after waiting 2 ms for the voltage to settle. The current on the anode was measured at each deflection plate voltage value. The entire collection of current measurements at each deflection plate voltage, along with the instrument time when the first deflection plate voltage was set, is called a sweep.

Figure 7: A schematic drawing of the STPSat-3 iMESA instrument detector head elec-tronics.

The anode current was amplified and converted to a voltage by a

trans-impedance amplifier (TIA) with a gain of −1.02 ± 0.01 × 106_V_{/A. The output of}

the TIA was biased at 1.330 ± 0.003V so that the quiescent output voltage was near the center of the dynamic range of the ADC (0 to 2.50 ± 0.02V). The behavior of the sensor

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head electronics was modeled using LTSpice, a freeware analog circuit modeling

application provided by Analog Devices[28]. The simulation modeled how the output of the Trans-Impedance Amplifier (TIA) was related to a range of anode currents, Figure 8. The TIA was scaled to convert the anode current to a voltage within the input range of the ADC, 0 and 2.5 volts.

Figure 8: The relationship between the anode current and the TIA output voltage.

The ADC had a twelve bit resolution, an uncertainty ±1 bits, and a minimum detectable voltage of 610.4 ± 0.9µ V. This correlated to a minimum measurable anode current of 598 ± 6 pA. The output of the ADC, NADC, was left bit shifted by one bit before

it was transmitted to the instrument processor, the bit shift is represented by increasing with value by a factor of 2. The conversion from anode current, IT IA, to ADC output is

NADC = 2

IT IART IA+VBIAS

2.5

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VBIAS= 1.33 ± 0.003V. The ADC values were read by the instrument processor and saved

in on-board storage before being packaged and transmitted to the ground where the anode current was revealed during post processing. The anode current as a function of deflection plate voltage was then curve fit to a drifted Maxwell-Boltzmann distribution from which the plasma parameters could be derived using the instrument geometric parameters.

3.3.2 Deflection Plate Voltage Driver

The electronics used to control the deflection plate voltage are shown in Figure 9. The voltage was set by digital commands sent to a Digital to Analog Converter (DAC)

Figure 9: The deflection plate voltage driver circuitry.

with ten bit resolution and ±3 bit uncertainty. Byte values starting at 999 and sweeping down to 131 in −31 count steps were sent to the DAC. Evaluating the plate electronics provided the commanded plate voltages along with their associated uncertainties using

V_plate= −Rf R1 " Vre fNDAC 210 +VBIAS 1 2R1 R4+1₂R1 !# . (28)

The feedback resistor was Rf = 1 × 106Ωand the biasing resistors were R1= 100 × 103Ω

and R4= 33 × 103Ω. The reference voltage was Vre f = 3.3 V and the bias voltage was

VBIAS= −5 V. This results in voltages applied to the deflection plates ranging from

−2.1 ± 0.4 V to 25.9 ± 0.6 V in 0.990 ± .005 V steps. A simulation of the the

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LTSpice, the resulting Voltage-Voltage Curve is shown in Figure 10.

Figure 10: The deflection plate voltage driver circuitry.

3.4 Simulation

3.4.1 Instrument Geometric Parameters

Deriving the plasma parameters from the anode current and deflection plate bias voltage required knowledge of the instrument geometric parameters that govern the instrument response[47]. The primary instrument geometric parameters are the analyzer constant ( fp), instrument efficiency (ε), energy resolution (∆E/E), response to spacecraft

(47)

define as the percentage of ions that enter the instrument with kinetic energy within the energy band that are measured at the anode. The energy resolution is the range in kinetic energies that were detected at a single deflection plate voltage.

These values were quantified using SIMION simulations which tracked the path of singly ionized atomic oxygen ions with known kinetic energy through an ESA channel. The simulation was performed with the deflection plate bias held at ten volts. A total of 71,000 ions were simulated with kinetic energies from 7 eV to 19 eV in 284 increments of 0.0423 eV. At each kinetic energy value, 250 ions were simulated with initial positions spread vertically across the height of the first filter plate aperture (0.15 mm) in 0.5 µm steps. The simulated ions were tracked individually through the instrument until they either impacted into the instrument walls or passed through the third filter plate aperture. Figure 11 shows the analyzed results of the simulation depicting the efficiency of the ESA against the ratio of ion kinetic energy to the deflection plate voltage.

The results of the simulation were numerically fit to a double Gaussian function for the number of ions detected with respect to the kinetic energy,

N(E) = A1e− _E −µ1 σ1 2 + A2e− _E −µ2 σ2 2 . (29)

The means of the two Gaussian functions, µ_1,2, along with the respective amplitudes, A_1,2, were used to calculate the peak ion kinetic energy at the simulated plate voltage using

Epeak= A1_(Aµ1₁+A_+A₂2₎µ2. (30)

Considering the total number of ions simulated, Nsim, at the peak energy, Epeak, and the

(48)

instrument efficiency can be derived using

ε= N(Epeak)

Nsim . (31)

The analyzer constant,

fp= Epeak

Vsim,

(32) is the ratio of the peak ion kinetic energy, E_peak, to the plate voltage, Vsim. The instrument

energy resolution (∆E/E) is calculated as the ratio of the Full Width at Half the Maximum (FWHM) of the fitted curve and the peak energy, Figure 11.

1.4

1.5

1.6

1.7

1.8

0

0.2

0.4

0.6

0.8

1

Figure 11: The results of the SIMION simulation.

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confidence interval (red). The peak instrument efficiency (dark green) was taken as the instrument analyzer constant, fp. The energy resolution, ∆E/E (teal) was determined as

the width of the curve where the efficiency is half the peak instrument efficiency. The total efficiency of the instrument, ε, is taken as the ratio of the number of particles flown with energy within the instrument energy resolution to the number of ions detected in that same range. The values derived for each of these quantities are shown in Table 3. A separate set of simulations were performed to quantify the instrument’s response to satellite rotation.

iMESA Instrument Geometric Parameters

Name Symbol Values Units

Analyzer Constant fp 1.52 ± 0.08 eV_V

Energy Resolution ∆E_E _{0.131 ± 0.009} ∆eV_eV Peak Instrument Efficiency ε 0.608 ± 0.007 Nout

Nin

Table 3: The geometric factors of the iMESA instrument calculated from SIMION simu-lations.

3.4.2 Response to Satellite Rotations

Changes in spacecraft pitch and yaw modify the instrument efficiency. These rotations can be interpreted as introducing components of the ion velocity perpendicular to the instrument normal. The two axes of the rectangular aperture produce a different angular response to ions with velocity along the height of the aperture, θythe y-axis in

Figure 6, and those with velocity along the width of the aperture, θz the z-axis. Ions

receive an apparent velocity across the sensor face when the satellite performs both pitch and yaw maneuvers. Two sets of SIMION simulations were performed over a range of incidence angles for ions with velocity components in either the y-direction or the z-direction. The simulation used to determine the instrument geometric parameters was modified to give the incident ions perpendicular velocity components, v_⊥. Perpendicular velocity was added to each ion at each energy step to create incidence angles

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θI = cos−1 v_⊥/v_k

for θI ∈ (−45o, 45o) in half degree steps. The instrument efficiency

was determined for a range of incident velocities in the same manner as the peak instrument efficiency was determined.

Figures 12 and 13 depicts the angular response along both axes with fit curves tracing the lowest order Fourier series that could be fit to the data with a coefficient of determination, R2value, greater than 0.9. The instrument response to satellite rotation at each angle simulated is shown in blue. Numerical fits of Fourier series with 95%

confidence bounds are shown in red. The black line indicates the range where the

efficiency is half the peak value. The points where this line intersects the curve were taken as the maximum range for rotations in ±y plane.

-10

-5

0

5

10

0

0.2

0.4

0.6

Simulation Results

Half Peak Efficiency

Fourier Series Fit

Fit Bounds

Figure 12: The instrument’s efficiency response to particles with velocities across the nar-row dimension of the aperture.

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-40

-20

0

20

40

0

0.1

0.2

0.3

0.4

0.5

Simulation Results

Half Peak Efficiency

Fourier Series Fit

Fit Bounds

Figure 13: The instrument’s efficiency response to particles with velocities along the nar-row dimension of the aperture.

Figure 12 is a depiction of the response to a rotation that produces ions with velocity in the y-direction as indicated by the coordinate system defined in Figure 6. The shallower slope at negative incidence angels is attributed to the asymmetry of the ESA channel, which allows incoming ions from the negative y direction to be focused more easily through the ESA. Figure 13 depicts the angular response of the instrument in the Z direction along the width of the aperture. The efficiency peaks at the extreme angles are an interesting feature and may be due to the energy resolution becoming very small at these angles. The exact cause of the peaks is an area of future research. The maximum angular range (black) in each direction is the angle in which the calculated efficiency is equal to half of the peak instrument efficiency, Epeak. The numerical values for the

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iMESA Angular Response Characteristics Angular Range

Name Symbol Values Units

Y Angular Range Θ _{(−7.97 ± 0.07, 5.1 ± 0.1)} Deg

Z Angular Range Φ _{(−29.2 ± 0.1, 29.2 ± 0.1)} Deg Angular Fourier Coefficients

ε(θ ) = a0+ ∑i[aicos(iωθ ) + bisin(iωθ )] Y Coefficients: ω 0.2 Y Coefficients: ai [14.8, 133.7, 71.9, 0.7, -133.3] Y Coefficients: bi [ -15.4, 94.5, 13.9, -33.7] Z Coefficients: ω 0.04 Z Coefficients: ai [-2.7, 4.9, -3.4, 1.9, -7.7, 2.2, -4.2, 3.8] Z Coefficients: bi [ 0.0, 0.0, 0.0, 0.0, 0.0, 3.0, -3.6]

Table 4: The geometric parameters of the iMESA instrument calculated from SIMION simulations.

Ideally, the Fourier series which detail the correction to the instrument efficiency would be used to modify the peak instrument efficiency to give more accurate values for the ion density spectra. However, comprehensive satellite attitude data has not been made available. Fortunately, STPSat-3’s avionics had a pointing accuracy 0.01o_{and other}

experiments on the satellite required accurate and consistent pointing. Therefore, the efficiency modification due to orthogonal ion velocity is assumed to be unity.

3.5 Instrument Response

A more detailed analysis can produce a closed form function that can predicts the number of ions incident on the anode for any kinetic energy and plate voltage. This function is called the Instrument Response Function (IRF). The IRF is useful for predicting the flow of ions through the instrument due to a real-world plasma

environment. This can be used to design and calibrate electronics or, as is the case with iMESA, compare the measurements of other instruments to the quantity actually measured by the instrument. The IRF for iMESA was derived by analyzing simulations

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voltages.

3.5.1 Deriving an Instrument Response Function

The measured distribution in the simulations, seen at the anode, can be

interpreted as the convolution of the incident distribution with the instrument response. Discrete convolution of two distributions, f (E) and h(E), is defined as

y_{(E) ≡ [ f (E) ∗ h(E)]}_k=

∞

∑

k=−∞

f_{(k)h(E − k).} (33)

Taking f (E) as the incident distribution in the simulation, seen at the instrument face, the energy is stepped across all possible values of the response function, h(E). The resulting distribution, y(E), will then be the the result of the simulation with respect to initial kinetic energy.

y_{(E) ≡ f (E) ∗ h(E) =}

Z ∞

−∞ f(τ)h(E− τ)dτ =

Z ∞

−∞ f(E − τ)h(τ)dτ.

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Defines continuous convolution. It is both commutative

f_{(E) ∗ h(E) = h(E) ∗ f (E)} (35)

and distributive

f_{(E) ∗ (h}1(E) + h2(E)) = f (E) ∗ h1(E) + f (E) ∗ h2(E). (36)

Therefore, the convolution of an incident function, f (E), with linear superposition of a response function, h(E), is the linear superposition of the convolution of the incident function with each element of the response function, each of which generates the

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measured distribution, y(E). Thus, the measured distribution can be written as a series of convolutions, y(E) = N

∑

n=1 yn(E) = N

∑

n=1 Z ∞ −∞ f(τ)hn(E − τ)dτ. (37)

This means the measured distribution can be written as the linear superposition of a series of functions and can be treated as independent relations up to the point of the final

analysis.

y(E) =

N

∑

n=1

f_{(E) ∗ h}n(E) = f (E) ∗ N

∑

n=1

hn(E) (38)

Each term of the response function, hn(E), can be determined via the product of

a Fourier Transform of the incident function and the measured distribution,

F_k_{[ f (E)] ≡ F(k) =} _√1 2π Z ∞ −∞ f(E)e −ıkE_dE. ₍₃₉₎ and F_k_[y_n_{(E)] ≡ Y}_n_{(k) =} _√1 2π Z ∞ −∞

yn(E)e−ıkEdE, (40)

Convolution in phase space is multiplication,

Y(k) = F(k)H(k), (41)

and the response function in phase space, H(k), can be determine algebraically,

H(k) = Y (k)F−1(k). (42)

A reverse Fourier transform is needed to derive the calculated response function in E-space, h(E) = √1 2π Z ∞ −∞ Y(k)F−1(k)e2πikEdk. (43)

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3.5.2 iMESA’s Instrument Response Function

The simulated incident distribution, X(E), was made up of A ions with a single kinetic energy E and can be represented mathematically as the product of a constant and a Dirac delta distribution,

X(E) = Aδ (E). (44)

A simulation was performed for each ESA voltage from 1 V to 30 V in 1 steps. During each simulation, the energy of the incident distribution was shifted from a minimum energy, Ei, to a maximum energy, Ef, in 284 increments. The ion energy range, Ef to Ei,

was set such that the range of incident energies was well beyond the range of energies detectable by the instrument to ensure the entire response was captured.

Through inspection of previous instrument simulations, ion energy values of Ei= 0.7(ESA Voltage) eV and Ef = 1.9(ESA Voltage) eV in energy steps of

(Ef− Ei)/284 eV were satisfactory. At each kinetic energy value ions were stepped

across the height, y − axis, of the aperture in 610 nm steps, which is the smallest step the model could resolve, at the center of aperture width, z − axis. This resulted in A = 250 ions flown at each kinetic energy value. At each ESA voltage and ion energy value the number of ions that traversed the ESA were recorded. The recorded number of ions with respect to the initial kinetic energy was used to create the measured distribution.

Similar to the analysis performed to determine the instrument geometric parameters, the distribution was fitted to the sum of two Gaussian distributions,

X(E) = a1e− _E −u1 σ1 + a2e− _E −u2 σ2 . (45)

Each distribution was fit successfully, with a coefficient of determination of R2_{> 0.95. A}

fit was derived for each simulated ESA voltage to allow an instrument response to be calculated for the entire range of ESA voltages. The amplitudes, a_1,2, means, µ1,2, and

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standard deviations σ_1,2were linearly extrapolated t so that the measured distribution is applicable continuously across the energy range of the iMESA instrument.

The incident function used in the SIMON simulations can be represented as an impulse,

f(E) = Aδ (E), (46)

and the measured distribution is the sum of two Gaussian distributions, which are generally represented as yn(E) = ane− _E −µn σn 2 . (47)

The Fourier transform of the incident function is

F(k) = A (48)

and the general measured distribution becomes

Y(k) = √a 2σe

−k2σ2

4 +ıkµ_. (49)

The response function is then the product of Equation 49 and the inverse of Equation 48.

Hn(k) = a √ 2σe −k2σ2 4 +ıkµ ₁ A . (50)

The response function in k space is therefore

Hn(k) =

an

A√2σn

e−k2σ24 n+ıkµn_. (51)

Which, after an inverse Fourier transformation, is depicted in energy space as

hn(E) =

an

Ae

−µn−E_σn 2

(57)

Finally, the closed form of the Instrument Response Function, h(E), at each plate voltage, V, can be written as h(E) = a1 Ae −µ1( fpV)−E_{σ1( fpV)} 2 +a2 Ae −µ2( fpV)−E_{σ2( fpV)} 2 ₍₅₃₎

for the values of a_1,2, µ_1,2, and σ_1,2listed in Table 5, where fpV is the product of the plate

factor and the plate voltage and represents the peak energy at each plate voltage. IRF Constant Values

a₁ 134.5147 a2 151.6896 µ1( fpV) 0.967( fpV) − 0.003 µ2( fpV) 1.030( fpV) − 0.002 σ1( fpV) 0.031( fpV) + 0.002 σ1( fpV) 0.052( fpV) + 0.009

Table 5: The iMESA IRF constants as a function of deflection plate voltage.

3.6 Deriving the Environmental Data

The instrument measured the current on the anode with respect to deflection plate voltage, which was stepped from −2.1 ± 0.4 V to 25.9 ± 0.6 V in 1 V steps. Applying the derived plate factor, fp, this corresponds to a peak ion kinetic energy from

0 ± 0.7 eV to 39.4 ± 0.9 eV in 1.52 ± 0.08 eV steps. The measured current, Ianode, as a

function of plate voltage, V, is called a sweep and has the form of a drifted Maxwell-Boltzmann distribution function for energy,

Ianode(V ) = I0exp " − p fpV−√E0 2 kBTion # , (54)

with peak current I0, bulk kinetic energy E0, and ion temperature Tion. The spacecraft

potential, ion temperature, and ion density can be derived by analyzing the shape of the measured ion current as a function of plate voltage. Figure 14 shows a typical sweep with the associated numerical fit.

(58)

Figure 14: A sample sweep displaying the mean (blue), full width half at half maximum (black) and amplitude of the distribution.

3.6.1 Spacecraft Potential

Spacecraft can charge with respect to the background plasma due to the photoelectric effect, the charge and polarity of the solar panels, and interactions with ions[48]. STPSat-3 charged negatively with respect to the ambient plasma and therefore repelled the free electrons and attracted positively charged ions. The charge resulted in a sheath around the spacecraft. The sheath for a plasma with electron density, ne, and

electron temperature, Te, extends from one to several Debye lengths around the

spacecraft, Equation 1, where, ε0is the permittivity of free space, kBis the Boltzmann

constant, and qeis the charge of an electron[48].

Analysis and Applications of Ionospheric Measurements from the Integrated Miniaturized Electrostatic Analyzer

Abstract

Dedication

Acknowledgments

Table of Contents

List of Tables

List of Figures

Nomenclature and Abbreviations

Section 1

Introduction

Section 2

Scientific Background

2.1

Plasma Physics

2.2

Space Physics

2.3

The Earth’s Atmosphere

2.4

The Earth’s Ionosphere

Section 3

The iMESA Instrument

3.1

Introduction

3.2

Mechanical Design

3.3

Electronics

3.4

Simulation

1.4

1.5

1.6

1.7

1.8

0

0.2

0.4

0.6

0.8

1

-10

-5

0

5

10

0

0.2

0.4

0.6

Simulation Results

Half Peak Efficiency

Fourier Series Fit

Fit Bounds

-40

-20

0

20

40

0

0.1

0.2

0.3

0.4

0.5

Simulation Results

Half Peak Efficiency

Fourier Series Fit

Fit Bounds

3.5

Instrument Response

∑

∑

∑

∑

∑

3.6

Deriving the Environmental Data