A rocket-borne investigation of auroral electrodynamics within the auroral-ionosphere

Transcription

1 University of Iowa Iowa Research Online Theses and Dissertations Spring 2013 A rocket-borne investigation of auroral electrodynamics within the auroral-ionosphere Stephen Roland Kaeppler University of Iowa Copyright 2013 Stephen Kaeppler This dissertation is available at Iowa Research Online: Recommended Citation Kaeppler, Stephen Roland. "A rocket-borne investigation of auroral electrodynamics within the auroral-ionosphere." PhD (Doctor of Philosophy) thesis, University of Iowa, Follow this and additional works at: Part of the Physics Commons

2 A ROCKET-BORNE INVESTIGATION OF AURORAL ELECTRODYNAMICS WITHIN THE AURORAL-IONOSPHERE by Stephen Roland Kaeppler An Abstract Of a thesis submitted in partial fulfillment of the requirements for the Doctor of Philosophy degree in Physics in the Graduate College of The University of Iowa May 2013 Thesis Supervisor: Professor Craig A. Kletzing

3 1 ABSTRACT This dissertation focuses on data analyzed from the Auroral Current and Electrodynamics Structure (ACES) sounding rocket mission. ACES consisted of two payloads launched nearly simultaneously in 2009 into a dynamic multiple-arc aurora. The mission was designed to observe the three-dimensional nature of an auroral arc current system. The payloads were flown along nearly conjugate magnetic field footpoints, separated in altitude with small temporal separation. The high altitude payload took in situ measurements of the plasma parameters above the current closure region to measure the input signature into the lower ionosphere. The low-altitude payload took similar observations within the current closure region, where perpendicular cross-field currents can flow. A detailed description of the experimental configuration is presented, including operational details of the fields and plasma instruments flown on both payloads. The methods used to process data from the electrostatic particle detectors and the fluxgate magnetometer on both payloads are presented. Data from the all-sky imager details the auroral configuration at the time of launch. In situ data are presented detailing observations of the electric fields, magnetic fields, and the electron differential energy flux, as the payloads crossed nearly conjugate magnetic field lines. Field-aligned currents were calculated from magnetometer observations on the high altitude payload. These data were combined with electron flux data to show that the high altitude payload traversed regions of upward and downward field-aligned current. The low altitude payload observed signatures in the residual magnetic field components consistent with perpendicular closure current. Ionospheric collisionality is investigated to determine if it is a significant mechanism to explain observed differences in the low energy electron flux between the high altitude and low altitude payload. As a result of increased ionospheric collisionality, the ionospheric conductivity is investigated to interpret the in situ electric field observations.

4 2 A model of auroral electrodynamics, that is under development, is discussed in the context of interpreting magnetometer data from the low altitude payload. The evolution of precipitating electron flux into the ionosphere and the effect this precipitation has on generating ionization is presented. The electron spectrum produced by the model were fit to the electron flux data observed by the low altitude payload. The height ionization profile, equilibrium electron density, and Hall and Pedersen conductivities were determined from the model electron spectrum incident to the ionosphere. It was shown that the low altitude payload flew just above the peak Hall and Pedersen conductivities, suggesting that the low altitude payload flew directly in the region where perpendicular closure currents were most significant. Abstract Approved: Thesis Supervisor Title and Department Date

5 A ROCKET-BORNE INVESTIGATION OF AURORAL ELECTRODYNAMICS WITHIN THE AURORAL-IONOSPHERE by Stephen Roland Kaeppler A thesis submitted in partial fulfillment of the requirements for the Doctor of Philosophy degree in Physics in the Graduate College of The University of Iowa May 2013 Thesis Supervisor: Professor Craig A. Kletzing

6 Copyright by STEPHEN ROLAND KAEPPLER 2013 All Rights Reserved

7 Graduate College The University of Iowa Iowa City, Iowa CERTIFICATE OF APPROVAL PH.D. THESIS This is to certify that the Ph.D. thesis of Stephen Roland Kaeppler has been approved by the Examining Committee for the thesis requirement for the Doctor of Philosophy degree in Physics at the May 2013 graduation. Thesis Committee: Craig A. Kletzing, Thesis Supervisor Donald Gurnett Steven Spangler Gregory Howes James LaBelle

8 This dissertation is dedicated to: Richard and Carol Kaeppler, and John Kasprowski, all of whom cultivated my passion for physics and encouraged me to pursue my dreams. ii

9 ACKNOWLEDGMENTS First and foremost, I would like to thank Prof. Craig Kletzing for providing me with the opportunity to pursue scientific research in space physics. I am grateful that I had the opportunity to work on two sounding rocket missions, and the valuable instrumentation and data analysis experience I gained through these missions. Moreover, I deeply appreciate Craig s guidance in directing my scientific pursuits, along with his honesty, and the straight-forward manner in dealing with the professional aspects of being a scientist. I would like to thank Dr. Scott Bounds for all of his support and guidance, particularly in the technical aspects of hardware work and data processing. Scott s lousy memory will never ceased to amaze me. I would also like to thank the members of my thesis committee: Prof. Jim LaBelle, Prof. Donald Gurnett, Prof. Steven Spangler, and Prof. Gregory Howes. I especially want to thank Prof. LaBelle, for writing letters of recommendation on my behalf, and Prof. Howes for the constructive conversations we had regarding numerical techniques that composed part of the modeling chapter of this dissertation. I would like to acknowledge a few people who assisted in various aspects of this dissertation. I am thankful for the useful conversations about field aligned coordinates which I had with Dr. Kristine Sigsbee. I am also grateful for the useful discussions I had with Dr. Matthew Zettergren at Embry-Riddle University and his work in modeling similar portions of the auroral-ionosphere. There are additional people I would like to thank. First, Prof. Robert Mathieu and Prof. Peter Timbie for the research experience and guidance you provided to me as an undergraduate. Dr. Andrew Kopf, for his undying love of anything Hawkeyes, and his study plan which got us through the qualifying examination. Chris Doran, for the late-night study sessions early in graduate school and the discussions we had over beer. I would especially like to thank Kris Klein, for challenging me to strive in plasma physics and for our ongoing discussions about politics, mead, and breadmaking. I also iii

10 want to acknowledge the many colleagues and friends I made through the sounding rocket program. I am grateful that you included me at various conferences, and I especially would like to thank Dr. Sarah Jones, Dr. Meghan Mella, Dr. Allison Jaynes, Dr. Nick Bunch, Dr. Jennifer Kissinger, Nathaniel Frissell, Christine Lin, Micah Dombrowski, Matthew Broughton, and Philip Fernandes. I want to thank my former and current officemates: Dr. Derek Theucks, Dr. Aaron Breneman, Mike Larson, and Richard Dvorsky. Rich, I appreciate how you kept things light in the office. I would also like to thank the members of our group including Dr. Joseph Howard, Dan Crawford, Carol Preston, Ryan Phillips, Tim Beckman, and Wayne Boynck. I especially thank Mr. Michael Fountain for machining various sounding rocket parts, help with dealing with the University, and for giving me the opportunity to do a few side projects. Last but not least, I would like to thank the Wednesday Night Dinner group, especially Dr. Justin Schulz and Dr. Elizabeth Stangl, who are very close friends. I am so thankful I met you all in early graduate school. I would like to thank my family for their love and support throughout graduate school. I especially want to thank my parents and grandparents for providing me with opportunities that I am so fortunate to have and instilling into me a strong work ethic. I would especially like to recognize (Uncle) John Kasprowski, whose stories about radios cultivate my interest in science at a young age. And most importantly, I would like to thank my wonderful and very understanding wife, Mary. Our lives changed forever on a warm September afternoon in 2010 when you decided to come to my office to give me a thank you card. iv

11 TABLE OF CONTENTS LIST OF TABLES vii LIST OF FIGURES viii CHAPTER 1 INTRODUCTION The Aurora Closure of Field-Aligned Current in the Ionosphere The ACES Sounding Rocket Mission OVERVIEW OF AURORAL PLASMAS AND ELECTRODYNAMICS The Early Years: Early Observations Early Theory The Evans 1974 Paper The Later Half of the 1970s: Observations of Currents and Electric Fields The S3-3 Satellite Theory The 1980s Observations Theory The 1990s- The Present Day FAST satellite Other Observations Auroral Source Region Recent Observations (2005-Present Day) Summary INSTRUMENTATION AND DATA PROCESSING Instrumentation Electrostatic Analyzer Electric and Magnetic Fields Electron Density and Temperature Data Processing EEPAA Processing High Frequency Electric Field Processing Magnetometer Processing Field-Aligned Currents Summary RESULTS AND ANALYSIS v

12 4.1 Flight Launch Conditions and Flight Performance All-Sky data and Conjugate Data Electron Flux DC Electric Fields Magnetic Fields Alfvén Wave Signatures Currents Analysis Ionospheric Collisionality and Conductivity Electric and Magnetic Fields in 2-D Arc Model Summary MODELING The Mallinckrodt Model The Calculation of Electron Flux Primary Electron Beam Ionospheric Response Validation with Evans [1974] Height-Ionization Profiles Electron Density Hall and Pedersen Conductivities Comparison with ACES Low Data Summary SUMMARY AND FUTURE WORK Future Work APPENDIX A HALL AND PEDERSEN CURRENTS B APPROXIMATE EXPRESSION FOR HALL CONDUCTIVITY C PARALLEL EQUIPOTENTIAL D ELECTROSTATIC ANALYZER BIBLIOGRAPHY vi

13 LIST OF TABLES 5.1 The Modeled Hall and Pedersen Conductances D.1 Radial Variable D.2 Effective gains vii

14 LIST OF FIGURES 1.1 A diagram from Kelley [2009] showing the whole magnetospheric system. The regions and subsystems associated with the nightside auroral zone are highlighted with colors. Precipitating electrons flow along the geomagnetic field and carry field aligned current into the auroral zone Figure 1 from Baumjohann [1982] of individual subsystems that form electrodynamic coupling between magnetospheric and the ionosphere. The arrows indicate the direction of flow and in most cases are bidirectional A diagram from Roach and Smith [1967] showing the energy levels of atomic oxygen which are responsible for red and green auroral light emission. It is noted that the transition lifetimes are shown for these forbidden transitions. The green light is observed at 5577Å with a life time of 0.74 s. The red light emission is at 6330Å or 6364Å, and has a lifetime of 110 s Figure 2.4 from Kelley [2009] that details the different cases of particles moving perpendicular across the geomagnetic field. Case (a), is the strong collisional case in which the plasma constituents would have many collisions with neutral atmosphere, resulting a low level of magnetization. Case (b), is when the plasma is strongly magnetized. This situation would result in E B drift motion, which would not set up a perpendicular current. Case (c), is the situation that happens at the peak of the conductivity in the ionosphere where there is a balance between collisional effects and the plasma remaining tied to the magnetic field lines. This case results in the most significant perpendicular drifts Schematic diagram of the ACES mission configuration including the magnetic field geometry and the currents to be measured Figure 5 from Evans [1968] showing the detector response versus the measured electron flux. The detector response is the solid line with large circles, the observation are the small circles. There is clearly good agreement between the modeled Dirac-function response with the observational data An example of inverted V features that were observed by the ACES Low sounding rocket. The white arrows highlight the edges of the inverted V emission. The characteristic increase in flux to a peak energy followed by a decrease in flux can be clearly seen in both of the inverted Vs viii

15 2.3 The polarization electric field within the 2-D auroral arc. The electric fields are divided based on their direction into the zonal (east-west) and meridional (north-south) components. The convective electric field is labeled by a superscript C, likewise, the auroral electric field is labeled by a superscript A. The polarization electric field is an electric field which is created because of the increased ionospheric conductivity Two magnetospheric-ionospheric configurations put forth in Boström [1964] that drive the auroral arc. In the first case, a large closure current is set up in the zonal direction (East-West) through the enhanced conductivity within the arc. This first case is associated with significant polarization electric fields. The second configuration has significant field aligned current sheets located at the equatorward and poleward edges of the auroral arc, with a closure current maintained by the Hall and Pedersen currents Figure 10 from Gurnett [1972] demonstrating how observed spiky electric fields represented in the lower right hand corner were found to be observed in the same spatial location as inverted V precipitation, as shown in the upper right hand corner. These observations of converging electric fields were consistent with a U-shaped electrostatic potential that was traversed by the Injun 5 satellite. The magnitude of the electrostatic potential drop below the satellite could be determined by integrating through the region of converging electric field crossed by the satellite Figure 7 from Evans [1974] showing a comparison between the backscatter model with a 400 ev electrostatic potential drop along magnetic field, a Maxwellian distribution with a density of 5 cm 3 and temperature of 800 ev, represented as the thick line. The dots are data from the electron detector on Injun 5 Frank and Ackerson [1971] Figure 13 from Iijima and Potemra [1978] showing the location in MLT and invariant latitude of Region 1 (R1) and Region 2 (R2) field aligned current system Figure from Mozer et al. [1977] detailing how the S3-3 satellite observed the high altitude U-shaped potential drop associated with auroral electrons. S3-3 observed the electrostatic shocks, which were the strong inward directed electric fields that could be generated by the U-shaped potential structure Figure 2 from Mizera and Fennell [1977] showing simultaneous distributions of both ions and electrons. There is a clear peak in the contours indicating an upflow of ions. A loss cone signature and trough in the electron contours is observed at 180 o pitch angle and a general depletion of electrons is observed around 90 o pitch angle ix

16 2.10 Figure 1 from Chiu and Schulz [1978] detailing the phase space diagram of the different populations for the electrons. Emphasis has been added by the author to label each of the regions. It is important to note that the precipitating electrons of magnetospheric, ionospheric, and backscatter that are above a given energy and pitch angle will populate the loss cone The evolution of a suprathermal electron burst from sounding rocket data provided by McFadden et al. [1986]. One can see the sharp field aligned peak evolve as the rocket passes. It is further emphasized how narrow the beam width is in perpendicular velocity Summary of electrodynamic parameters in invariant latitude and magnetic local time provided in the review paper by Baumjohann [1982]. Upper left is the conductivity, upper right is the electric field direction, lower left is the electrojet structure for upward/downward field aligned current, lower right is the field aligned current structure with closure current direction. It is emphasized that these represent the large scale electrodynamic configuration The electric field configuration based from Baumjohann [1982] for the morning side and evening side. Panel A shows the ambient, convective electric field. Panel B details the electric field within the ideal 2-D arc. Panel C is the combination of the convective electric field with the ideal field within the arc. Panel D shows the enhancement or dearth of electron density associated with the electric field The 2-D current closure configuration, in red, from Mallinckrodt [1985] based on different electric field or current boundary conditions. Panel A is the current configuration based on a boundary electric field that maps through the ionosphere and the conductivities that are generated from accelerated, precipitating electrons carrying the upward field aligned current. This configuration is most consistent with a polarization arc. Panel B is the current configuration for an upward-downward field aligned current pair and is most consistent with a Birkeland type arc. It is noted in panel B that the sheet field aligned current into the ionosphere equal the sheet field aligned current out of the ionosphere. Panel C is a combination of both a boundary electric field and field aligned currents Figure from Marklund et al. [1997] demonstrating the connection between both the upward directed current region with inverted V aurora and the downward current region with black aurora A summary figure of the upward and downward current region, corresponding to visible and black aurora, respectively. Please see the text for an explanation x

17 2.17 A downward view of the 2-D arc model and the association with an auroral arc and the black aurora regions. The upward directed field aligned current resides within the visible auroral arc and the downward field aligned current is associated with the black aurora regions. The field aligned current closes through the Hall and Pedersen currents that are based on the perpendicular electric field direction. There are conductivity enhancements within the auroral arc because of the deposition of precipitating electrons. The electric fields and residual magnetic fields are associated with two directions relative to the arc: tangential to the arc and normal to the arc The instrument configuration on both ACES High and Low. Please see the text for details Cross section diagram of the EEPAA detector flown on ACES High and Low. The inner electrode is swept in voltage, while the outer electrode is at spacecraft ground. A particle trajectory is shown for a particle that is selected by the electric field created between the inner and outer electrodes The magnetometer can be envisioned as a rotating coordinate system that samples the Earth s magnetic field. The primary rotational frequency is the spin (ω s ) frequency and there is a longer coning frequency (ω c ) nutation There was a slight misalignment between the gyroscope axes and the magnetometer axes. A small Euler rotation was applied to the magnetometer axes to properly align to the gyroscope axes to correct for the small angular difference. The angles that were used in the rotation were determined using a 2 grid search that minimized the power at the coning and spin frequencies The field-aligned coordinate system that was defined by Eriksson et al. [2005]. The spacecraft is shown moving along a dipolar field line and the radial unit vector is defined to point outward at the equator. In the auroral zone, field-aligned unit vector will be downward, radial unit vector will be in the meridional (northward) direction, and the zonal unit vector will be in the eastward direction The top panel shows the residual magnetic field component in the zonal direction in black and the coning offset in red. The bottom panel shows the result after the coning correction has been subtracted off the time series data. There is still significant spin frequency modulation on the signal, but a Butterworth filter was used to the spin component further An angular rotation applied to the field-aligned coordinate system in calculating the field aligned currents. This rotation was about the ˆp axis. This rotation was applied so the calculation of the field aligned current would not diverge xi

18 4.1 This is the time series data showing the ground-based magnetometer observations from Fort Yukon, Alaska. The H-component of the magnetometer is associated with the electrojet current systems. Large gradients in the H-component correspond to large-scale currents ACES High and Low trajectories plotted as functions of altitude and geographic latitude. Dashed lines are magnetic field lines mapped to footpoints at 110 km. The times in the figure indicate when both payloads crossed the same magnetic field footpoint, respectively Left Column: ACES High Data; Right Column: ACES Low Data. Row 1: Electron Differential Energy Flux; Row 2-3: DC Electric Field Data; Row 4-6: Residual Magnetic Field Components. The electric field and residual magnetic field contain dashed lines at zero and the positive direction represented eastward (zonal), northward (meridional), and fieldaligned, respectively. Gray bands are regions where data are not available. The black line in the ACES Low differential electron energy flux represents the maximum energy observed by ACES High of 500 ev The images from the Fort Yukon all-sky imager showing the evolution of the auroral event on January 29, The footpoints for ACES High and Low after being mapped to 110 km are represented by a red square and blue dot, respectively An example of electron acceleration by Alfvén waves. The top panel is the differential energy flux observed by ACES High. It is clear that there is time-dispersion in the electron flux with high energy electrons arriving first, followed by low energy electrons. The middle panels are the residual magnetic field components showing perturbations in the magnetic field that correlate with the time-dispersed electrons. The final two panels show the electric field components with modulations in the electric field that correlate with the time-dispersed electrons Results from the calculation of field-aligned current using Ampére s Law. The top panel is the differential electron energy flux and the middle panels correspond to the zonal and meridional electric fields, respectively. The bottom panel illustrates the field aligned current configuration with upward and downward field-aligned currents represented as positive and negative, respectively. It can be clearly seen that intense and narrow downward field-aligned current regions correspond to a depletion of precipitating auroral electrons. The upward field-aligned current corresponds to regions of visible aurora and precipitating electrons The results from the stopping altitude calculation which show that precipitating electrons at 500 ev are scattered and become indistinguishable at about 170 km from background ionospheric electrons. The ACES Low apogee is located at approximately 130 km, as indicated by the red horizontal line xii

19 4.8 This diagram presents the results from the comparison between the data and the 2-D arc model. As shown in black, the orientation of the arc was determined using data from the all-sky imager. The tangential line was determined at the location where the payload entered the auroral arc. The results for the electric field and the residual magnetic field are shown in blue and red, respectively. The normal residual magnetic field component and the tangential electric field component were both independently minimized using the grid search Left: The electric field vectors, after having the convective flow removed, as ACES High traversed the quasi-static arc. The vectors are consistent with what would be expected for a U-shaped potential drop mapped down from high altitudes. Right: The residual magnetic field as ACES High traversed the quasi-static region. The field pattern is consistent with what would be expected for an upward field-aligned current A schematic diagram of the velocity and distribution space mapping is presented. The velocities are gridded at the ionosphere and mapped up to the magnetosphere where the distribution function is well defined. By Liouville s theorem the distribution function can be mapped in phase space from the magnetosphere to the ionosphere A schematic diagram of the evolution of a precipitating electron beam from Evans [1974]. The left-hand side is a schematic diagram showing the precipitating magnetospheric electrons that are accelerated by the parallel electric field. The mirror force then interacts with the velocity distribution, transferring parallel velocity to perpendicular velocity as the particles move toward the ionosphere. The right-hand side of the figure shows the evolution of the electron beam in velocity space. A discussion is given in the text of each panel on the right-hand side An overplot comparison between our model results in red versus the results from Evans [1974] Figure 5 in black. As can be seen, with respect to the primary beam there is excellent agreement. The ionospheric contribution from the model has slightly overestimated the flux near the peak energy of the primary beam,. However, there is good agreement of the model results with the results from Evans [1974] An overplot comparison of results between Semeter and Kamalabadi [2005], in black, to the model being developed, in color. The beams at each of the energy distributions was assumed to be a monoenergetic beam of precipitating electrons. As it can been seen, there is excellent agreement with the higher energy monoenergetic beams, especially above 10 kev. At lower energies, the energies between what was published versus our models are inconsistent xiii

20 5.5 An example of the total integrated response for the height ionization profiles. Three individual Gaussian beams at energies of 500 ev, 2 kev, and 10 kev (in color) are summed together to get the total ionospheric response (in black). This figure was shown as a check of our numerical integration routine The top panel presents the location that was chosen in the differential energy flux spectrogram observed by ACES Low. The bottom panel is a comparison between the differential number flux observed by ACES in red versus the model beam and ionospheric response, in black. The ionospheric response was slightly underestimated relative to the observed differential number flux. Overall, there is good agreement between the modeled flux and the flux observed by ACES The results from the model. Panel A shows the parallel differential number flux incident to the ionosphere. Panel B is the height ionization profile from the parallel differential number flux, plotted as a function of altitude. Panel C shows the equilibrium number density plotted as a function of altitude. Panel D are the Hall and Pedersen conductivities as a function of altitude. The location of the ACES Low payload is plotted in panels C and D to indicate the location of the payload for these data The top panel shows the direct comparison of the modeled Hall and Pedersen conductances (over the full altitude range) using data presented in Figure (5.7) at 09:55:57 UT versus the data over the full flight presented in Marklund et al. [1982]. The lower panel is a similar comparison between the model height-integrated currents at a single time versus the full flight data from Marklund et al. [1982]. As it can be seen, in both cases the ACES data are lower than what was observed by Marklund et al. [1982], because of the incident electron flux observed by Marklund et al. [1982] was two orders of magnitude larger than what was observed by the ACES Low payload xiv

21 1 CHAPTER 1 INTRODUCTION The Earth s magnetosphere is a complex plasma physics system driven by the solar wind. Figure (1.1) shows a schematic diagram detailing the major regions and systems that form the Earth s magnetosphere. The regions highlighted with colors in Figure (1.1) are associated with the nightside auroral zone. Electric fields, currents, and plasma trapped on magnetic field lines within the magnetosphere, form the fundamental nonlinear feedback mechanisms that control the dynamics within the magnetospheric system. A systems approach can be used to study individual subsystems and the interaction between different interconnected regions of the magnetosphere with the ionosphere. Figure (1.2) illustrates the subsystems that form the electrodynamic coupling between the magnetosphere and the ionosphere. A key subsystem in the magnetospheric-ionospheric system is field aligned current. As shown in Figure (1.1), field aligned current (in red) connects plasma from the plasmasheet (in blue) in the distant magnetosphere to the auroral oval (in green) at ionospheric altitudes. Currents flowing perpendicular to the mean magnetic field within the ionosphere close the magnetospheric-ionospheric (MI) circuit by connecting the upward and downward field aligned currents. Energy from the magnetosphere is dissipated into the ionosphere through Joule heating (J E ), collisional ionization, and heating, that can be significantly enhanced by auroral particle precipitation. Energy dissipation in the ionosphere is an important function within the whole magnetospheric system. 1.1 The Aurora The aurora is an important subsystem within the magnetosphere-ionosphere system. Visible light is a key observable associated with the aurora and is emitted through atomic de-excitation, at visible or sub-visual intensities. Visible light commonly observed in an

22 2 Nightside Auroral Zone Figure 1.1: A diagram from Kelley [2009] showing the whole magnetospheric system. The regions and subsystems associated with the nightside auroral zone are highlighted with colors. Precipitating electrons flow along the geomagnetic field and carry field aligned current into the auroral zone. auroral display is at red or green wavelengths, and results from forbidden transitions of atomic oxygen molecules. Figure (1.3) from Roach and Smith [1967] shows the energy levels and transition times for atomic oxygen. These forbidden transitions have excited life-times of the order of seconds, rather than atomic transition that obey the selection rules with life-times of the order of micro- or nano-second. The green line at 5577Å is typically associated with auroral displays and has a metastable 1 S 1 D transition with a life-time of 0.74 seconds. The light associated with this transition will be seen at altitudes above 100 km, because the excited atom is more likely to collide before it emits light at lower altitudes [Paschmann et al., 2002]. The red line is associated with auroral displays at higher altitudes and corresponds to the 1 D 3 P transition that has wavelengths of 6330Å or 6364Å, depending on which orbital the electron transitions to. The red light exhibits

23 3 Magnetospheric Electric Fields Magnetospheric Currents Magnetospheric Plasma Frozen-in Fields Field Aligned Currents Particle Precipitation Aurora Ionospheric Electric Fields Ionospheric Currents Ionospheric Conductivity Figure 1.2: Figure 1 from Baumjohann [1982] of individual subsystems that form electrodynamic coupling between magnetospheric and the ionosphere. The arrows indicate the direction of flow and in most cases are bi-directional. less structure because of the longer transition time of approximately 110 s and is observed at altitudes above 200 km [Paschmann et al., 2002]. This long transition time allows the excited species to be influenced by plasma drifts, that can further diffuse structure. Aurorae are generally divided into two major classes based on the particle acceleration mechanism: discrete aurora and diffuse aurora. Diffuse aurora is typically not associated with an acceleration mechanism, rather plasmasheet ions and electrons are pitch angle scattered into the loss cone [Kennel and Petschek, 1966]. Although the mechanisms which cause diffuse aurora are important in the context of magnetospheric physics, the focus of this dissertation will be on discrete aurora (for a current review of diffuse aurora, see Lessard [2012]). Discrete aurora is caused by a parallel electric field at altitudes of

24 4 Figure 1.3: A diagram from Roach and Smith [1967] showing the energy levels of atomic oxygen which are responsible for red and green auroral light emission. It is noted that the transition lifetimes are shown for these forbidden transitions. The green light is observed at 5577Å with a life time of 0.74 s. The red light emission is at 6330Å or 6364Å, and has a lifetime of 110 s km above the ionosphere that accelerate plasmasheet electrons. These precipitating plasmasheet electrons reside on closed magnetic field lines. U-shaped electrostatic potential structures have been found to be consistent with electric field observations. Visually, discrete aurora are comprised of structures such as auroral arcs, sheets, and rays. An emission feature in the electron spectrograms called the inverted-v is a characteristic upside-down V shape that has been associated with U-shaped electrostatic potentials and visible aurora. There are other types of discrete aurora with differing acceleration mechanisms; most notably, aurora produced by electron acceleration through parallel electric fields generated by inertial Alfvén waves. There are also other electron

25 5 spectral features such as suprathermal bursts which are strongly field-aligned precipitation at energies typically below 1 kev. Discrete aurora are also typically associated with upward field-aligned currents and these currents are carried by precipitating, accelerated, plasmasheet electrons. Black aurora, or regions devoid of visible light and electron flux have been associated with the return, downward field-aligned current. The auroral region still has many open questions, with one of chief the questions regarding the mechanism(s) that are responsible for the generation of parallel electric fields. Despite many theories presented in the literature, at the current time this question remains unresolved [Borovsky, 1993; Karlsson, 2012]. 1.2 Closure of Field-Aligned Current in the Ionosphere A connection exists between ionospheric currents, ionospheric conductivity, that can be significantly enhanced by particle precipitation, and electric fields. The effect of these interconnected elements is expressed through Ohm s law, as shown in the lower portion of Figure (1.2). The current closure region is located where field aligned current from the magnetosphere closes because plasma collisions with neutral atoms become sufficiently significant to allow particles to drift across magnetic field lines, thereby breaking the frozen-in approximation. Ohm s law can be used to describe plasma drift perpendicular to the mean magnetic field. The perpendicular current can be related to the electric field by, j (z) = q i n i (z)u i q e n e (z)u e = j P (z) + j H (z) (1.1) = σ P (z)e σ H (z)(e ˆB) where U s is the perpendicular bulk velocity for ions or electrons, E is the electric field perpendicular to the mean magnetic field, and ˆB is the magnetic field unit vector

26 6 [Paschmann et al., 2002]. A derivation of the Hall and Pedersen current is presented in Appendix A. The Pedersen conductivity is defined as, ( ) σ P (z) = e 2 ν in n e m i (νin 2 + Ω2 i ) + ν en m e (νen 2 + Ω 2 e) and the Hall conductivity, σ H (z) = e 2 n e ( Ω i m i (ν 2 in + Ω2 i ) ) Ω e m e (νen 2 + Ω 2 e) (1.2) (1.3) where Ω i and Ω e are the ion and electron cyclotron frequency, respectively [Paschmann et al., 2002]. The Hall and Pedersen conductivities are altitude dependent. A key point to note from equation (1.1) is that the perpendicular electric field determines the direction of the Hall and Pedersen current. Pederson currents (j P in eq. 1.1) flow parallel to E ; whereas, Hall currents (j H in eq. 1.1) flow perpendicular to both E and ˆB. Over an auroral arc, the enhancement of electrons deposition by particle precipitation can increase the local electron density by orders of magnitude compared to the background electron density; this effect can significantly increase the Hall and Pedersen conductivities within an arc. To quantify how collisions with atmospheric neutral atoms allows electrons and ions to break off their orbits in the auroral ionosphere, the variable κ can be defined as the ratio of the cyclotron frequency over the collisional frequency, that is, κ i = Ω i /ν in and κ e = Ω e /ν en for the ions and electrons, respectively [Kelley, 2009]. As shown in Figure (1.4a), when κ i, κ e 1 the ions and electrons will experience strong collisions and effectively be decoupled from the magnetic field. In this limiting case, the Hall and Pedersen conductivities will asymptote to the strongly collisional limit, σ e 2 n e /ν in m i. In the limit that the plasma is strongly magnetized, κ i, κ e 1, then the Hall and Pedersen conductivities go to zero. This situation is consistent with ions and electron traveling on E B drift orbits, as shown in Figure (1.4b). No perpendicular current is set up because the E B drifts are independent of charge; therefore, the ions and electrons move in the

27 7 Figure 1.4: Figure 2.4 from Kelley [2009] that details the different cases of particles moving perpendicular across the geomagnetic field. Case (a), is the strong collisional case in which the plasma constituents would have many collisions with neutral atmosphere, resulting a low level of magnetization. Case (b), is when the plasma is strongly magnetized. This situation would result in E B drift motion, which would not set up a perpendicular current. Case (c), is the situation that happens at the peak of the conductivity in the ionosphere where there is a balance between collisional effects and the plasma remaining tied to the magnetic field lines. This case results in the most significant perpendicular drifts. same direction with no bulk velocity difference. The final case is the situation where κ 1 and is schematically represented in Figure (1.4c). In this situation, there is a balance between collisions and the E B drift motion for the ions and the electrons. This sets up significant perpendicular drifts of the ions relative to the electrons, which translates into a significant perpendicular closure current. It can be shown that the conductivities peak when the condition that κ = 1 is satisfied for the ions and the electrons, respectively. This situation can be interpreted as the largest drift between ions and electrons.

28 8 The key equation that connects the field aligned current with the perpendicular closure current is the continuity of charge equation, ρ t + j = ρ t + j (z) + j (z) = 0 (1.4) z In a steady state current configuration ( ρ/ t = 0), the current continuity equation can be solved to yield, j (z) z = j (z) (1.5) which connections the divergence of the perpendicular current to vertical gradients in the field aligned current. Equations (1.2), (1.3), and (1.5) are explicit functions of altitude (z). A simplifying assumption that is commonly invoked is to integrate out the altitude dependence in the conductivities [Fejer, 1953], yielding the height integrated conductivities or conductance, Σ i = σ i (z)dz (1.6) where i corresponds to either the Hall or Pedersen conductivity. The current continuity equation, (equation 1.4) can be integrated to get an expression for the field-aligned current in terms of the divergence of the electric fields and the conductances. If it is assumed that the perpendicular electric fields independent of altitude, then the continuity of current equation can be simplified to, j = (Σ P E ) ( ) Σ H (E ˆB) (1.7) where Σ H and Σ P are the height integrated Hall and Pederson conductivities, respectively. If E = 0 is further assumed, then equation (1.7) can be simplified to, j = ( Σ P ) E + Σ P ( E ) ( Σ H ) ( ) E ˆB (1.8) and if the perpendicular gradients in the Hall or Pedersen conductances equal zero, then

29 9 the closure current is solely composed of the Pedersen current [Paschmann et al., 2002]. Equations (1.7) is the key equation that dictates the closure of field-aligned current within the ionosphere for a steady-state situation. One key assumption in the derivation of the Hall and Pedersen currents is that electric fields map down from the magnetosphere into the ionosphere. That electric fields can be mapped is because it is often assumed that magnetic field lines are equipotentials. This condition is supported by the very high parallel conductivity (σ ) that exists along the magnetic field. As shown in Appendix C, the continuity of current equation can be solved to obtain a condition that E σ = 1 [Kelley, 2009]. The consequences of this equation are two fold. First, as Kelley [2009] suggests if the conductivity is infinite along the field line, then the potential drop between two altitudes is zero, and the potential difference between two field lines is a constant. The second consequence is a result of the limit of nearly infinite conductivity that is generally valid between the magnetosphere into the ionosphere because the plasma along the field lines is collisionless. However, as will be discussed in the Chapter 2, the idea of parallel electric fields causing auroral electron acceleration was contentious because it suggested there were regions of finite parallel conductivity, that contradicted the plasma being collisionless between the magnetosphere and the ionosphere. Discrete aurora exist because of the generation of a parallel electric field. In the auroralionosphere, if the frozen-in condition is violated by collisions, it would be expected that the electric field equipotential contours would also break at these altitudes. Therefore, it is significant to assume E maps through the ionosphere. However, in some situations magnetospheric electric fields have been observed at altitudes below the ionosphere [Kelley, 2009; Mozer and Serlin, 1969]. Many questions still remain regarding the structure of the current closure region and the effects this region has within the magnetospheric-ionospheric system as a whole. One of the key questions that is not well understood: what is the configuration of the

30 10 current structure in the region where field aligned current closes? Closely related is the question: what is the fraction of Hall or Pedersen current that closes the field-aligned current? Based on observed or inferred closure configuration, what are the consequences for the dissipation of energy within the ionosphere through the Pedersen current? In a model of the auroral ionosphere by Mallinckrodt [1985], it was shown that the altitudinal and latitudinal structure of the current closure region strongly depended on the boundary electric fields, currents, and conductivities. Observationally there have been few in situ observations within the low altitude auroral ionosphere. Incoherent scatter radar observations can be made of the current closure region; however, such observations have limited capability particularly in deducing the current structure within this region. To the author s knowledge, the only recent in situ observation that has focused on the low altitude ionosphere have been from the JOULE II sounding rocket missions [Sangalli et al., 2009]. Additional multi-point in situ observations can better enable our ability to deduce the current closure structure in the ionosphere. 1.3 The ACES Sounding Rocket Mission The Auroral Current and Electrodynamics Structure (ACES) sounding rocket mission was devised to make new observations that would examine the current structure, energy transfer and the electrodynamics within the current closure region. Figure (1.5) is a schematic diagram detailing the design of the mission to investigate the current structure of the upward and downward field aligned currents, along with cross field perpendicular closure current. Two payloads containing similar instrument packages were flown along nearly conjugate magnetic footpoints. A high altitude payload (hereafter referred to as ACES High) was designed to fly at a higher altitude to measure the input electrodynamic and plasma parameters onto the current closure region. A low altitude payload (hereafter referred to as ACES Low) was designed to fly through the current closure region to make in-situ observations of the plasma parameters and electrodynamics within this region. The

31 11 400km ACES High j j PFISR Radar Altitude (Not to scale) Pedersen Conductivity B? Electrodynamics and Current Geometry? Geomagnetic Field 120 km j Hall Conductivity ACES Low Latitude (Not to scale) Figure 1.5: Schematic diagram of the ACES mission configuration including the magnetic field geometry and the currents to be measured. longitudinal dimension (out of the plane of the Figure (1.5)) was kept small so that a thin sheet approximation could be applied and the payloads crossed magnetic field lines mapped to similar footpoints nearly simultaneously to constrain the spatial-temporal ambiguity inherent of in situ observation. Data obtained from these payloads, for conjugate footpoints, allows for comparison between observations at different altitudes. This dissertation will examine plasma and electrodynamic observations above and within the current region using data from the ACES sounding rocket mission. Chapter 2 is a review of auroral physics and field-aligned currents, with an emphasis on auroral zone electric field measurements and precipitating electrons. The experimental configuration that was flown on the ACES mission and processing of that data are presented in Chapter

32 12 3. The main results and scientific analyses are contained in Chapter 4, which follow very closely to results that were presented in Kaeppler et al. [2012]. The development of a model of the auroral ionosphere that was used to assist in the interpretation of the results is discussed in Chapter 5. Finally, a summary and some potential directions for future research in this topic are presented in Chapter 6.

33 13 CHAPTER 2 OVERVIEW OF AURORAL PLASMAS AND ELECTRODYNAMICS The early 20th century brought some of the first scientific inquiries into the mechanisms surrounding the aurora. Birkeland [1908] deduced that magnetic compass deflections by auroral forms were caused by large scale electric currents flowing overhead. Birkeland [1908] further proposed two components of these currents, one current flowed parallel to the geomagnetic field, called field-aligned current. The other current component formed perpendicular to the mean magnetic field creating the current closure mechanism in the ionosphere, called the auroral electrojet. Many other pioneers moved the field of auroral physics forward after Birkeland, including Chapman, Davis, and Dungey. With respect to in situ observations of space plasma, the advent of the space age in the late 1950s with the work of Van Allen is the most logical starting point. It is emphasized that the review presented will focus primarily on quasi-static aurora and will include background about electron populations, electric fields, and field aligned currents. 2.1 The Early Years: Early Observations Some of the first in-situ observations of auroral forms used sounding rockets and satellites. McIlwain [1960] used a variety of high energy ion and electron detectors on a sounding rocket that was launched into a discrete auroral arc. It was discovered that electrons with energies < 10 KeV were responsible for producing auroral light emission. These results were the first published observations that electrons caused discrete aurora, contrary to the dominant idea at that time that ions were responsible for auroral forms. Satellites made similar observations to those of McIlwain [1960]. On the Injun 3 satellite, Gurnett [1966] made an observation correlating auroral light emission with a peak in the observed electron flux, for electrons with energies < 10 KeV.

34 14 McIlwain [1960] further suggested that an electrostatic field parallel to the geomagnetic field could explain the observed KeV energy associated with in situ auroral electron observations. The idea that parallel electric fields cause auroral particle acceleration was very controversial in early auroral physics. To understand why, a short argument will be presented or refer to Appendix C. If one considers the generalized Ohm s law written into its parallel component, and perpendicular component, J σ = E (2.1) J σ = E + (U B) (2.2) Magnetospheric plasma, well above the ionosphere, is a collisionless plasma and therefore the collisional frequency is effectively zero. The conductivities σ and σ which are inversely related to the collisional frequency (σ 1/ν) and asymptote to infinity as the collisionality goes to zero. As a result, the left hand side of both equations (2.1) and (2.2) equals zero, thus E 0. The perpendicular velocity component can be solved for the usual E B drift motion. O Brien [1970] put forth additional arguments disputing the existence of parallel electric fields. Most significantly, if a population of electrons is accelerated by a parallel electric field, all electrons observed should gain energy equal to the magnitude of the parallel electrostatic potential drop. It was found in early observations that lower energy electrons (below the inferred magnitude of the electrostatic potential drop) were also observed along with the KeV electrons that fell through the potential drop ([O Brien, 1970], and references therein). This presented a contradiction between observational data and the theory surrounding the acceleration mechanism. Early observations of auroral electrons with better energy resolution, pitch angle (PA) coverage, along with in situ measurements of currents, refined the observations first

35 15 made by McIlwain [1960]. Evans [1968] used an electrostatic particle detector that included an energy sweep from KeV on a sounding rocket flown over a discrete auroral arc. As shown in Figure (2.1), the electron differential energy flux over the arc is represented by dots. The solid line in the figure is the convolution of the theoretical detector response with a δ-function in energy at 3.8 KeV. The narrow peak in electron flux data showed strong correlation with the single energy detector response, thus being termed the monoenergetic peak. Evans [1968] found that the mechanism accelerating electrons must be narrow in energy and suggested the accelerating mechanism was simply due to a parallel electric field. Armstrong and Zmuda [1970] made early satellite observations of the current system above the ionosphere. Observations of depressions in magnetic field strength called bays, combined with the direction of the satellite motion and the assumption of a sheet geometry, were used to estimate the magnitude of the field aligned current. Equation (2.3) was used to calculate the field aligned current magnitude, J = B(γ) 4πL (2.3) where L was chosen to be the latitudinal distance of 1 o at 1100 km and the change in magnetic field strength B was measured in terms of bays, γ (1γ = Gauss). Estimates were additionally made of the electron particle flux based on the measured current and the magnitude of the parallel electric field, assuming a nominal parallel conductivity. Albert and Lindstrom [1970] used sounding rocket data to describe two observational effects in the electron pitch angle distributions that resulted from parallel electric fields. Since energy is conserved in the system, the presence of the parallel electric field is an additional term that needs to be considered in the total energy (W) of the system, W above + Φ = W below (2.4) where Φ is the energy associated with the parallel electrostatic potential drop and the

36 16 Figure 2.1: Figure 5 from Evans [1968] showing the detector response versus the measured electron flux. The detector response is the solid line with large circles, the observation are the small circles. There is clearly good agreement between the modeled Dirac-function response with the observational data. subscripts above and below correspond to the magnetosphere and ionosphere, respectively. The first adiabatic invariant is also conserved, µ above = µ below = W B = W sin2 α B (2.5) where α is the pitch angle. The parallel potential (Φ ) will cause the magnetic mirror point to move deeper into the ionosphere, allowing precipitating plasma to penetration to lower altitudes. This deeper penetration of precipitating electrons is also realized through a sharpening of pitch angle because the electron gains parallel energy associated with the

37 17 electrostatic potential drop. The second observed effect is a quasi-trapped population of electrons. Substituting equation (2.4) into equation (2.5) for populations above and below the potential drop yields, ( B below 1 Φ ) sin 2 α above = sin 2 α below (2.6) B above W below If α above = 90 o then α below, the observed pitch angle will gain parallel energy because of the potential drop and form a population of particles that are trapped with pitch angles α below α 90. The magnetic mirror force causes electrons to move upward, away from the ionosphere. However, these upgoing electrons do not have sufficient energy to overcome the parallel electric field above. Therefore, the electrons will be reflected and move back toward the ionosphere. This interaction creates an electron population that is trapped between the magnetic mirror point in the ionosphere and the electrostatic potential above. The pitch angle distribution of this population is centered around 90 o. Data from sounding rocket observations by Albert and Lindstrom [1970] validated this prediction by observing a trough in the electron flux centered at a pitch angle of Inverted-V Inverted V emission was described by Frank and Ackerson [1971] and was one of the most significant observational discoveries in the early 1970s. Data from the ion and electron detectors on the Injun 5 satellite were plotted on time-energy spectrograms (xaxis: time, y-axis: energy, z-axis: flux intensity). As the satellite moved through time (varying invariant latitude), the particle flux showed a characteristic increase to a peak energy, that was followed by a decrease in energy and flux. This characteristic shape was first described as an up-side down V, but with higher resolution measurements is better described as an upside-down U. Nonetheless, the name inverted V has remained in use.

38 18 Inverted-V Inverted-V Figure 2.2: An example of inverted V features that were observed by the ACES Low sounding rocket. The white arrows highlight the edges of the inverted V emission. The characteristic increase in flux to a peak energy followed by a decrease in flux can be clearly seen in both of the inverted Vs. Data from the ACES Low sounding rocket show clear examples in Figure (2.2), highlighting two inverted V events with the up-side down U shape in the electron differential energy flux. Ackerson and Frank [1972] extended upon this work by directly correlating all sky images of aurora to Injun 5 conjunctions. The authors concluded that inverted V emission was responsible for the energy flux required to create discrete aurora as observed by all-sky imagers Early Theory The basic models of field aligned currents and auroral electrojets had been developed by the early 1960s ([Boström, 1964], and references therein). One of the most fundamental models for the auroral system was developed by Boström [1964] who took into account a variety of physics lacking in previous models. A 2-D model was put forth in which an auroral arc was considered an infinitely long conducting strip in the zonal direction. The electric fields and current directions within the arc were in two directions: normal and

39 19 tangential to the arc. It was further assumed, via the Maxwell boundary conditions, that the tangential electric field outside the arc and the tangential electric field within the arc were continuous across the arc boundary (E CON ˆn = E ARC ˆn where ˆn is normal to the arc, nominally in the meridional direction). The altitude dependence of the Hall and Pedersen conductivities was accounted for by this model and it was found that both conductivities peaked in magnitude at an altitude of approximately 100 km. The result suggested that the auroral arc was a region of significantly enhanced conductivity relative to the background conductivity. One of the consequences of enhanced conductivity is the polarization electric field within the arc [Boström, 1964]. Figure (2.3) shows the basic configuration of the polarization electric field within the 2-D arc model. The convective electric fields in the zonal and meridional direction, labeled with the superscript C, are imposed onto the arc. The zonal components are continuous between the region outside of the arc, that is dominated by the convective electric field, and within the arc. The convective meridional component will map within the arc, but the increased arc conductivity allows charges to easily flow in response to the imposed electric field. As a result, a positive space charge is found at the northward edge of the arc, while a negative space charge is found at the southward edge of the arc (in the case of an eveningside arc), thus generating a polarization electric field. This southward polarization field, labeled in red in Figure (2.3) opposes the convective electric field. The total observed electric field is the sum of the convective and polarization electric field and is northward with a reduced magnitude. The polarization effect is a secondary effect that occurs within the auroral ionosphere and is important for understanding electric field observations in the vicinity of an auroral arc, particularly for observations made in the late 1970s and early 1980s. An altitude layer of enhanced conductivity also suggested that there was a region in the ionosphere where cross field currents are significant. This model further examined

40 20 A Σ Polarization Effect in 2-D Arc C E mer A E Pol C E mer A E Mer A E zone C E zone Meridional Zonal Figure 2.3: The polarization electric field within the 2-D auroral arc. The electric fields are divided based on their direction into the zonal (east-west) and meridional (north-south) components. The convective electric field is labeled by a superscript C, likewise, the auroral electric field is labeled by a superscript A. The polarization electric field is an electric field which is created because of the increased ionospheric conductivity. whether the cross field currents could be driven by ionospheric sources, such as neutral winds, or by magnetospheric sources through field aligned currents. It was concluded that ionospheric electrojets driven by neutral winds were not plausible because the neutral wind speed required needed to be three times larger than observed. As for the magnetospheric source, Boström [1964] examined two current configurations using a nominal current to test the validity of each model. Figure (2.4) schematically represents the two magnetospheric-ionospheric configuration that were put forth to drive the 2-D aurora and close the MI current circuit [Boström, 1964]. In the first configuration, a current circuit was set up along individual magnetic field lines at the eastward edge of the arc closing through the ionosphere to the westward edge of the arc, then returning to the magnetosphere. The second current configuration involved large collisionless current sheets that were magnetically field aligned flowing to the equatorward and poleward edges of the arc. The closure current in the ionosphere was maintained by Hall and Pedersen currents. From these results, it was concluded that

41 21 Bostrom, 1964 MI Configuration Case 1 Case 2 Figure 2.4: Two magnetospheric-ionospheric configurations put forth in Boström [1964] that drive the auroral arc. In the first case, a large closure current is set up in the zonal direction (East-West) through the enhanced conductivity within the arc. This first case is associated with significant polarization electric fields. The second configuration has significant field aligned current sheets located at the equatorward and poleward edges of the auroral arc, with a closure current maintained by the Hall and Pedersen currents. the magnetosphere, rather than the ionosphere, was the source driving the closure currents within the ionosphere. Later observations were able to verify that the large poleward and equatorward sheet current configuration was observed most frequently. The work of Boström was an important first step in modeling auroral electrodynamics while also considering magnetospheric-ionospheric coupling. Rees [1963] developed height ionization profiles that were caused by precipitating auroral electron flux onto the ionosphere. An empirically derived relationship called the range-energy function describes the penetration of energetic electrons within the ionosphere. Specifically, the range energy function describes the amount of material that is traversed by energetic electrons, rather than the exact path of the penetrating electron [Kivelson and Russell, 1995]. This range energy function was a power law relation that was determined experimentally by Grün [1957] through laboratory measurements and valid for

42 ev to 300 KeV electrons (and later updated by Barrett and Hays [1976]). Using four different distributions for incident electrons, Rees [1963] calculated the height ionization profiles. The most significant result was that the ionization peaked at lower altitudes as the characteristic energy increased of the incident electron flux. Satisfactory agreement was found between the ionization profiles when compared with nitrogen emission observed by photometers on sounding rockets. The peak ionization at lower altitudes with increasing energy explains why visible red auroral emission tends to be observed at higher altitudes while more energetic green and blue light emissions are observed at lower altitudes. Theorists developed a new class of models to relate current and voltage in a manner similar to Ohm s law; such models could create a direct link between field aligned current and parallel electric fields. An early model developed by Carlqvist and Boström [1970] described a mechanism for generating current from a voltage drop, similar to the currentvoltage relationship of a vacuum tube diode. In a vacuum tube diode, a charge cloud is formed when electrons are boiled off the cathode. The current is carried primarily by electrons. When the space charge surpasses a critical threshold between the cathode and anode a current will flow. The excess charge separation between the plates set up a potential difference; however, the magnitude of the potential is regulated by the current. A model was created, considering the ionosphere and magenetosphere as the boundary, further constraining the current only along the magnetic field lines. The electrostatic potential structure to support this mechanism was U-shaped. For nominal scale sizes (1-10 km) and potential drops based on observations of electron flux (1-100 KeV), this mechanism required magnetospheric plasma flows that were typical of the order of what was observed. This mechanism was suggested for small scale localized aurora and did not take into account large scale stable auroral structures. Nevertheless, this mechanism did produce a U-shaped electrostatic potential and was a first step toward future current-voltage relations.

43 23 Early observations by Gurnett [1972] from Injun 5 supported a U-shaped electrostatic potential. Gurnett [1972] showed that converging spiky electric fields were observed near the edges of inverted-v precipitation. This is schematically represented in the right hand side of Figure (2.5), it can be seen that the spiky perpendicular electric fields align with the edges of the inverted V emission. A U-shaped electrostatic potential was put forth as a configuration that could support the converging electric field observations, as shown in Figure (2.5). To estimate the magnitude of the electrostatic potential, the perpendicular electric fields were integrated over the length of the acceleration region (Φ s in Figure 2.5). It was found that the magnitude of the electrostatic potential below the payload was approximately 6 KeV. The maximum energy of precipitating particles observed was 15 KeV, so this result suggested that a substantial portion of the precipitating electrons were accelerated through a parallel electric field above the spacecraft location. Knight [1973] expanded on the work of Carlqvist and Boström [1970] through the development of a well known current-voltage relationship. If the plasmasheet electron population is assumed to be a Maxwellian distribution, and using nominal plasmasheet parameters, it can be shown that the loss cone has a half-angle width at the magnetic equator of approximately 1.1 [Paschmann et al., 2002]. The remaining downgoing electrons would end up mirroring at a higher altitude due to the lack of sufficient parallel velocity to reach ionospheric altitudes. Using the fluid equations for the parallel current density, Knight incorporated a parallel electrostatic potential into the exponential portion of the bi-maxwellian distribution describing the plasmasheet electron population, f(v, v ) exp( (v 2 + v2 + e Φ)/2kT e). Knight [1973] investigated how a parallel electrostatic potential drop could be used to overcome the mirror force, and enable electrons to carry field aligned current from the magnetosphere to ionosphere that closes the MI circuit. Using nominal electron temperatures, densities, along with current density data from Armstrong and Zmuda [1970], Knight estimated the magnitude of a parallel potential

44 24 Figure 2.5: Figure 10 from Gurnett [1972] demonstrating how observed spiky electric fields represented in the lower right hand corner were found to be observed in the same spatial location as inverted V precipitation, as shown in the upper right hand corner. These observations of converging electric fields were consistent with a U-shaped electrostatic potential that was traversed by the Injun 5 satellite. The magnitude of the electrostatic potential drop below the satellite could be determined by integrating through the region of converging electric field crossed by the satellite. drop to approximately 6 KeV that match well with field aligned current observations made by sounding rockets. The Knight relation provided a plausibility argument using fluid theory and based on data that directly coupled the field aligned current with a necessary parallel electrostatic potential drop.

45 The Evans 1974 Paper One of the most significant arguments in favor of parallel electric fields was made by Evans [1974] in which the effect that a parallel electric field would have on the energy spectrum of the observed electrons was investigated. The parallel electric field was assumed to be infinitely thin and reside at a high altitude above the ionosphere. A model for how low energy electrons from the ionosphere were generated from the precipitating auroral electrons was also included. The model demonstrated that a ev electron population, below the characteristic inverted-v energies of a few KeV, was created by degraded primary electrons or secondary electrons produced from collisions with neutrals. If a parallel electric field was present, the low energy electron component would not have enough energy to surpass the electrostatic potential drop, and would be reflected back toward the ionosphere appearing as low energy precipitating electrons. In addition, the lower energy distribution of electrons would experience the same quasi-trapping mechanism about 90 o pitch angle as described by Albert and Lindstrom [1970]. As a final test, this model was compared against electron flux data from Injun 5, as shown in Figure (2.6), which shows a strong agreement between the model and data. By simply assuming a parallel electric field was present, and including the ionospheric electron population, Evans [1974] was able to demonstrate that backscattered electrons were the source of the lower energy precipitating component of the observed electrons. The results of this paper defused one of the most significant arguments raised by O Brien [1970] against the existence of parallel electric fields. 2.2 The Later Half of the 1970s: Observations of Currents and Electric Fields The later half of the 1970s advanced observations in a variety of auroral physics phenomena, particularly in auroral electrodynamics. A deeper understanding of field aligned

46 26 Figure 2.6: Figure 7 from Evans [1974] showing a comparison between the backscatter model with a 400 ev electrostatic potential drop along magnetic field, a Maxwellian distribution with a density of 5 cm 3 and temperature of 800 ev, represented as the thick line. The dots are data from the electron detector on Injun 5 Frank and Ackerson [1971]. currents was gained through observation in the mid to late 1970s. An earlier review by Arnoldy [1974] suggested that electrons could be broken up into five populations. It was put forth that the electrons with energies < 1 KeV were responsible for carrying field aligned current. Through sounding rocket observations, Arnoldy [1977] found that the majority of field aligned current was carried by precipitating electrons of energies below the inverted-v. This observation indicated that electrons responsible for inverted V emissions were not the primary current carriers. Moreover, Arnoldy [1977] found that low energy current carrying electrons were located poleward and equatorward of the luminous discrete auroral arc. It is noted that these observations may have been some of the first observations of suprathermal bursts, which will be discussed later in this Chapter. The large scale structure of field aligned currents was investigated by Iijima and

47 27 R2 R2 R1 R1 R2 Figure 2.7: Figure 13 from Iijima and Potemra [1978] showing the location in MLT and invariant latitude of Region 1 (R1) and Region 2 (R2) field aligned current system. Potemra [1976], who examined data from a 3-axis magnetometer flown on the Triad satellite. The net eastward-westward magnetic perturbations were used to determine the magnitude and direction of the field aligned current for satellite crossings at various magnetic local times (MLT) and invariant latitudes. Iijima and Potemra [1976] defined Region 1 and Region 2 field aligned currents as shown in Figure (2.7). The poleward portion of the field aligned current is defined as Region 1 current (R1 in Figure 2.7). Region 1 current flow into the ionosphere from MLT (morning-noon sector) and out of the ionosphere from MLT (noon-night sector). Region 2 current (R2 in Figure 2.7) is defined as the equatorward portion of the field aligned current. Region 2 current is opposite of Region 1 current in orientation, that is, from MLT the field aligned current flows out of the ionosphere and between MLT the field aligned current flows into the ionosphere. Iijima and Potemra [1978] later expanded their study, as shown in Figure (2.7), by examining current structure at substorm conditions (AL 100γ) compared to the quiet time (AL 100γ) conditions.

48 28 Observations of electric field surrounding an auroral arc were an active area of research in the late 1970s, in part, due to differing observations between magnetic local time sectors (MLT). Many in situ and radar observations compared the electric field structure within an auroral arc to the electron precipitation, either using in situ observations or by measuring enhanced Hall and Pedersen conductances. Radar observations by de La Beaujardiere et al. [1977] showed that the electric field magnitude and both conductances decreased in an auroral arc in some MLT sectors. However, in other MLT sectors, the electric field within the arc increased in magnitude while both Hall and Pedersen conductivities decreased. From sounding rocket measurements over an auroral arc, Evans et al. [1977] used the differential number of the precipitating electrons to calculate the height integrated Hall and Pedersen conductivities. The calculations of the Hall and Pedersen conductance used the observed electron flux to determine the height ionization profiles using expressions from Rees [1963] and a model neutral atmosphere. The recombination rates and the relative concentrations of ions were used to deduce the background electron density. Over the arc, an anticorrelation between the reciprocal of the height integrated Pedersen conductivity (1/Σ P ), which is controlled by the auroral particle precipitation, versus the total electric was observed. Evans et al. [1977] also observed that the Joule heating was at a minimum over the auroral arc relative, but there was significant energy deposition through particle precipitation The S3-3 Satellite S3-3 was one of the most significant satellite missions in the history of auroral plasma physics. S3-3 made revolutionary observations that advanced understanding of the electric field structure above the auroral zone (< 8000 km), providing additional evidence in favor of particle acceleration by parallel electric fields. Mozer et al. [1977] discovered electrostatic shocks, large deviations in the transverse electric field (E ) of

49 29 the order of 100 mv/m, but as large as 1000 mv/m. These electrostatic shock observations were similar to observations made by Gurnett [1972]. The electrostatic shocks persisted for timescales of the order of 10 s, the same order of time as the 18 s rotation period of the satellite. As illustrated in Figure (2.8), the timescale of the electrostatic shocks along with the satellite velocity, suggested that the horizontal scale size was of order of 10s of km. Mozer et al. [1977] posited that electrostatic shocks were consistent with observations of the high altitude signature of the U-shaped electrostatic potential above the auroral zone. As shown in Figure (2.8), as S3-3 would traverse the inferred U-shaped electrostatic potential, such a potential distribution was consistent with converging electric fields (electrostatic shocks) that were observed by the satellite. S3-3 observed electrostatic shocks up to 8000 km [Mozer et al., 1977], which provided an observational constraint of the altitudinal scale size of the accelerating potential. Torbert and Mozer [1978] proposed seven arguments to connect electrostatic shocks and visible aurora, ranging from the similarity of geometry of the shock with inverted-v emission to the similar invariant latitude location of electrostatic shocks and the aurora. Mozer et al. [1977] additionally reported magnetic activity consistent with upward field aligned currents on the order of a few µa m 2, which are carried by downgoing electrons. Particle measurements on S3-3 also produced significant results. Shelley et al. [1976] observed two events, in the nighttime and morning MLT sectors, of strong upflowing ion beams (that peak at 180 pitch angle), while simultaneously observing electron loss cone troughs. Figure 1 from Shelley et al. [1976] showed the strong upward ion flow that were observed had narrow flux for both the O + and H + species (note: the pitch angle convention in Figure 1 from Shelley et al. [1976] is opposite the usual convention). In addition, there were also observations of loss cone electrons. If the satellite flew through the region containing the parallel electric field, there would likely be observations of both accelerated precipitating electrons and loss cone electrons. The simultaneous observations

50 30 S3-3 Figure 2.8: Figure from Mozer et al. [1977] detailing how the S3-3 satellite observed the high altitude U-shaped potential drop associated with auroral electrons. S3-3 observed the electrostatic shocks, which were the strong inward directed electric fields that could be generated by the U-shaped potential structure. of sharply peaked upward ions and loss cone electrons are both signatures consistent with the effects of a parallel electric field at an altitude below the satellite, in this case at 6000 km. Mizera and Fennell [1977] expanded on this work by examining distribution functions of both ions and electrons observed simultaneously for an electrostatic shock event on August 12, Figure (2.9) shows contours in the ion distribution indicative of a peak where ions are flowing away from the ionosphere at 600 km/s. The contours in the electron distribution indicate the presence of precipitating electrons at 0 pitch angle, along with a distinct loss cone signature that is symmetric about a pitch angle of 180. It was further found that the angular size of the loss cone and the parallel velocity of the upward ion beam were consistent, and both have magnitudes of approximately 2 kev which was interpreted as the potential drop below the satellite. It was also suggested that the precipitating electrons at 0 pitch angle had an energy of approximately 1 KeV. In Figure (2.9), there appears to be little flux in the electrons between the region bounded by the circle and

51 31 Figure 2.9: Figure 2 from Mizera and Fennell [1977] showing simultaneous distributions of both ions and electrons. There is a clear peak in the contours indicating an upflow of ions. A loss cone signature and trough in the electron contours is observed at 180 o pitch angle and a general depletion of electrons is observed around 90 o pitch angle. the hyperbola at 90 o pitch angle. This observation is consistent with the quasi-trapping of electrons by the electrostatic field above and the ionospheric mirror force below [Albert and Lindstrom, 1970] Theory Theorists were also active in the late 1970s extending models for auroral particle acceleration and current-voltage relationships. In the process of creating a model for auroral electron acceleration, Chiu and Schulz [1978] combined observations of magnetospheric and ionospheric ion and electron source populations. The first adiabatic invariant

52 32 was used to determine which regions of phase space each population occupied for an upward directed parallel electric field. Figure (2.10) shows the phase space for the electrons, in which, M stands for magnetospheric electrons, I is for ionospheric electrons, T is the trapped population around 90 o pitch angle [Albert and Lindstrom, 1970] and S are backscattered (degraded primary) electrons. Each circle or oval represents which source population dominates in that region. The dashed straight lines represent the demarcation between electrons that enter the loss cone and electrons that will be mirrored back up the magnetic field lines. From Figure (2.10), the electron population in the loss cone region (red added for emphasis) contains magnetospheric electrons, along with background ionospheric electrons and backscattered electrons. As one moves past the boundary between the loss cone entry criterion, the source populations are ionospheric or backscattered electrons. By moving up in v space, the trapped population exists between the magnetic mirror and the parallel electric field. Non-precipitating magnetospheric electrons are also represented as bouncing back and forth between their magnetic mirror. The results by Mizera and Fennell [1977] verified that ionospheric, magnetospheric, and trapped populations were consistent with the demarcations shown in Figure (2.10). Chiu and Schulz [1978] represents a summary that defined the sources and demarcations of the electron populations observed in the auroral zone. Motivated by the work of Knight [1973], Lyons et al. [1979] applied a currentvoltage relationship to data obtained from sounding rocket observations. It was assumed that the only electron populations present were of magnetospheric origin, having been accelerated by a parallel electric field and thermal ionospheric electron populations were ignored. It was further assumed that the potential drop was at a higher energy than the magnetospheric source population and that field aligned current was related to the net electron energy flux by ɛ = ev J. The linear form of the Knight relation states is that J = K ev, where K is a constant [Knight, 1973; Paschmann et al., 2002]. Lyons et al.

53 33 Mirrored Trapped Loss Cone upgoing downgoing Figure 2.10: Figure 1 from Chiu and Schulz [1978] detailing the phase space diagram of the different populations for the electrons. Emphasis has been added by the author to label each of the regions. It is important to note that the precipitating electrons of magnetospheric, ionospheric, and backscatter that are above a given energy and pitch angle will populate the loss cone. [1979] obtained energy flux data from three sounding rocket flights. The parameter ev, the magnitude of the potential drop, was inferred from the energy flux data. The parameter K was then chosen to produce the best fit to ɛ = ev J = KV 2 (where e has been absorbed into K) for each of the rockets. Generally good agreement was found between the electron energy flux data and ev J. The model validated the linear relationship between current and parallel potential, and the relation between energy flux to the ɛ KV 2. It was additionally concluded that the particle precipitation and changes in parallel potential drop will equally affect the energy flux into an auroral arc.

54 Kinetic Alfén Waves A new mechanism involving Alfvén waves to explain magnetospheric-ionospheric coupling and the creation of quasi-static parallel electric fields was developed in the latter half of the 1970s. Ideal MHD, which is valid for collisionless plasmas, assumes E = 0. Hasegawa and Chen [1976] modified the theory of Alfvén wave propagation in a collisionless plasma by including particle kinetic effects and extending to the regime where k 0. With this modification it was possible to generate an electric field parallel to the direction of the propagating Alfvén wave. Kinetic Alfvén waves were used by Mallinckrodt and Carlson [1978] as a means by which to maintain a field aligned current that coupled the magenetosphere and ionosphere. Mallinckrodt and Carlson [1978] examined a magnetospheric source of transverse electric fields which propagated along the geomagnetic field lines by means of kinetic Alfvén waves. The waves were then reflected at the interface of the ionosphere, setting up a steady-state configuration. Simulations of this configuration matched electric field observations by Mozer et al. [1977] and the observed field aligned current magnitudes by S3-3 ([Mallinckrodt and Carlson, 1978], and references therein). It was also determined that within the ionosphere J E > 0, so the ionosphere acted like an electrical load to the magnetospheric current. It was concluded that the model was not sufficient to create a time independent, quasi-static, mechanism for parallel particle acceleration. This was due to the configuration of the converging perpendicular electric fields, which were oriented parallel to the ionosphere that was treated as an infinite conducting sheet. This electric field configuration was maintained as the wave propagated toward the ionosphere and there was no electric field component parallel to the mean magnetic field that could accelerate electrons. One of the key papers regarding kinetic Alfvén waves was by Goertz and Boswell [1979] and included the full plasma solution for a time-dependent propagating kinetic

55 35 Alfvén wave. The ideas used in the model by Mallinckrodt and Carlson [1978] were used and significantly expanded upon by Goertz and Boswell [1979]. More significantly, Goertz and Boswell [1979] solved the full set of equations to come to an analytical solution for the propagation of kinetic Alfvén waves. It was found that oblique fronts of an advancing kinetic Alfvén wave would create an electric field component parallel to the magnetic field. The analytic solution also indicated an explicit time dependence to maintain parallel electric fields. Goertz and Boswell [1979] compared results to Mozer et al. [1977] finding generally good agreement between the predicted magnitude of perpendicular electric fields and observations of electrostatic shocks on S3-3. The work of Goertz and Boswell [1979] formed the foundation for many of the simulations and models of kinetic Alfvén waves put forth by later authors, especially Lysak. To further summarize and contextualize the work of Goertz and Boswell [1979], the authors derived two cases of Alfvén waves that took into account particle kinetics: kinetic Alfvén waves and inertial Alfvén waves. Inertial Alfvén waves are in the limit V A V the, where V the and V A are the electron thermal velocity and Alfvén speed, respectively. Kinetic Alfvén waves are in the opposite limit, V A V the. The inertial Alfvén wave dispersion depends on k, the perpendicular wavenumber, such that ω 2 = (k V A ) 2 /(1 + k 2 λ2 e), where λ e = ω pe /c is the electron inertial length [Stasiewicz et al., 2000]. For finite k the wave has an electric field parallel to the mean magnetic field, E = k k λ 2 e E 1 + k 2 (2.7) λ2 e and when k λ e = 1 the parallel electric field is at its maximum magnitude [Stasiewicz et al., 2000]. Inertial Alfvén waves have been considered an important mechanism that is responsible for dynamic MI coupling, which will be discussed further in Section , and a generation mechanism of parallel electric fields that can accelerate electrons (Stasiewicz et al. [2000] and references therein).

56 The 1980s By the 1980s the idea of the quasi-static, parallel electric field in the form of a U-shaped potential structure was beginning to take root as the mechanism responsible for discrete aurora. The 1980s advanced understanding of electrostatic shocks, but also extended studies into other regions and observed features Observations Kletzing et al. [1983] followed up on the supposition made by Torbert and Mozer [1978] regarding the connection between electrostatic shocks observed on S3-3 and discrete aurora. Their observation examined conjunctions of S3-3 with all sky images from ground based imagers. By examining electric field data and electron flux data from S3-3, a direct link was established between electrostatic shock structures and visible discrete auroral arcs. It was suggested that the aurora resulted from electrons that were accelerated by parallel electric fields that corresponded to converging electric field structures that magnetically mapped down to ionospheric altitudes. Results from the S3-3 satellite also made some of the first observations of the effects of downward directed electric fields and further suggested a connection between electron beams and ion conics. Gorney et al. [1985] put forth observations of upward directed electrons beams and simultaneous observations of ion conics. Ion conics are flux distributions that are peaked at pitch angles between and the distribution has a conical shape in phase space. It was suggested that these observations could be explained by the presence of a downward-directed parallel electric field. The ion conics were a quasi-trapped population between the mirror force in the ionosphere and the downward directed parallel electric field at higher altitudes. Wave-particle interactions were suggested as a heating source which could affect the ion population. These wave-particle interactions would have enough time to affect the conic distribution because of the multiple bounces between the

57 37 mirror point and the electric field. After a sufficient amount of energy was attained the ions would be able to overcome the parallel electric field, which was verified through testparticle simulations. This quasi-trapped heating mechanism has been more colloquially referred to as the pressure cooker and in some aspects is analogous to the quasi-trapped electrons that were put forth by Albert and Lindstrom [1970] Suprathermal Bursts The 1980s also brought a great deal of attention to a new spectral feature in electron flux data called suprathermal bursts. This spectral feature was originally discovered independently by Burch et al. [1979] and Lin and Hoffman [1979] (and incidentally by Arnoldy [1977]). Suprathermal electrons are characterized by intense, highly field aligned, low energy electron (< 1 KeV) flux found at the equatorward or poleward edge of inverted-v emission. Suprathermal bursts were further examined using data from the ISIS 2 satellite and many of their properties were discussed in Johnstone and Winningham [1982] and through a sounding rocket study by Arnoldy et al. [1985]. Johnstone and Winningham [1982] noted suprathermal electrons primarily with pitch angles < 30 ; however, Robinson et al. [1989] found suprathermal bursts occurred at all pitch angles. Arnoldy et al. [1985] noted that the bursty nature, also observed by Johnstone and Winningham [1982], of suprathermal electrons could be due to a lack of pitch angle or temporal resolution. Arnoldy et al. [1985] and Johnstone and Winningham [1982] suggested that the latitudinal size of suprathermal burst events was of the order of a few kilometers or a few seconds, if these features were in fact temporal. Sounding rocket observations by McFadden et al. [1986] took high resolution observations at the edge of a discrete auroral arc through a suprathermal burst event. As shown in Figure (2.11), the evolution of the electron distribution was observed as the payload traversed the edge of the arc. A sharp field-aligned plateau feature was observed, as the parallel electron energy increased from 100 ev ev over the distance of 2.3 km, with a nearly constant, very narrow,

58 38 Figure 2.11: The evolution of a suprathermal electron burst from sounding rocket data provided by McFadden et al. [1986]. One can see the sharp field aligned peak evolve as the rocket passes. It is further emphasized how narrow the beam width is in perpendicular velocity. perpendicular temperature of 1.2 ev. Suprathermal electrons presented a significant discrepancy to the theory of quasi-static parallel electric fields: how could a parallel electric field explain these observations at energies below the potential drop? Auroral Electrodynamics Baumjohann [1982] reviewed currents, conductivities, and electric fields associated with an auroral arc, which summarized many of the advances in auroral electrodynamics. Figure (2.12) summarized invariant latitude and magnetic local time (MLT) data of the large-scale auroral conductivity, auroral electric fields, Pedersen and Hall currents (which form the auroral electrojet), and field aligned currents. Baumjohann [1982] presented a summary of the dichotomy between electric fields observed in the aurora in the evening

59 39 and morning sectors, which were consistent with many observations to date, including Evans et al. [1977] and de La Beaujardiere et al. [1977]. Figure (2.13) from Baumjohann [1982] summarized electric field observations in the morning and evening side. In the evening sector, the left hand side of Figure (2.13), panel A shows the ambient, convective electric field and the panel D shows the location of the auroral zone with an increased conductivity because of particle precipitation. Panel B shows the electric field associated with the auroral arc, in which a northward directed meridional electric field peaks in magnitude south of an arc and the electric field is southward within the arc, which may be accounted for by the polarization electric field. The resulting electric field that would be observed by a spacecraft is shown in the panel C, labeled as measured el. field, which is a combination of the arc associated field and the ambient electric field. The zonal electric field was constant across the arc, due to the tangential Maxwell boundary conditions at the interface of the arc. An oppositely oriented configuration would occur in the morning sector. The convective meridional electric field would be in the southward direction. A southward-directed meridional arc electric field would be located south of the arc, with a northward directed meridional field within the arc. The observed electric field would tend to be southward with within the arc and have an increased southward magnitude north of the arc. Again, the zonal electric field remains nearly constant in the westward direction. To summarize, Baumjohann [1982] suggested that evening sector arc will experience an anticorrelation between the electric field and the height integrated conductivities, whereas, morning sector arcs will experience a correlation between electric field and height integrated conductivities. Marklund et al. [1982] presented ground-based imager and magnetometer data, combined with in-situ rocket observations that advanced knowledge of auroral electrodynamics. A rocket payload instrumented with electrostatic particle detectors and electric

60 40 Figure 2.12: Summary of electrodynamic parameters in invariant latitude and magnetic local time provided in the review paper by Baumjohann [1982]. Upper left is the conductivity, upper right is the electric field direction, lower left is the electrojet structure for upward/downward field aligned current, lower right is the field aligned current structure with closure current direction. It is emphasized that these represent the large scale electrodynamic configuration. field instruments, but not a magnetometer, was launched into a stable auroral arc. By coincidence, the northward track velocity of the payload approximately matched the northward motion of the arc toward the later half of the arc crossing. This allowed for an extended

61 41 Auroral Electric Field Configuration Baumjohann, 1982 A E N E S E C E C E N E S B E pol E pol C E ARC = E C + E pol E ARC = E C + E pol D ARC ARC Figure 2.13: The electric field configuration based from Baumjohann [1982] for the morning side and evening side. Panel A shows the ambient, convective electric field. Panel B details the electric field within the ideal 2-D arc. Panel C is the combination of the convective electric field with the ideal field within the arc. Panel D shows the enhancement or dearth of electron density associated with the electric field. period of time for the payload to make observations within the arc. Electrojet currents were observed by ground-based magnetometer arrays, as the rocket moved through the arc. The most significant result was the strong anticorrelation observed between the electron energy flux and the electric field, over the auroral arc. At the equatorward edge of the

62 42 arc, the northward electric field was of the order of 100 mv/m, but abruptly decreased to approximately 20 mv/m in magnitude after passing into the arc. The authors suggested the presence of a southward directed polarization electric field and it was further suggested that the arc was consistent with an asymmetric electric field configuration as defined by de La Beaujardiére et al. [1981] (and later classified in Marklund [1984]). Marklund et al. [1982] also presented calculations of the horizontal current and inferred current structures within the arc. Using the electron flux data the Hall and Pedersen conductances were calculated in a fashion similar to Evans et al. [1977]. It was found that the ratio Σ H /Σ P was approximately 1.4 over the arc, and had a value of 1 near the arc edges. The northward and eastward horizontal sheet currents were also calculated. In the equatorward and center region of the arc, the horizontal currents had a magnitude of the order of 1 A/m. At the equatorward edge of the arc, a significant decrease in the electric field was observed and the northward directed current had a sharp increase in magnitude to a maximal magnitude of 1.2 A/m. While the payload did not carry a magnetometer, another method that calculated J = 0 from the horizontal currents concluded that a narrow (6 km) downward field aligned current with a magnitude of 10 µam 2 was present at the same time as the significant northward current. A model of east-west directed groundbased currents was set up to correlate the rocket observations with ground-based observations. As a final note, Marklund et al. [1982] presented an analytic solution of the time dependent continuity equation that neglected ionization motion. It was shown that the time dependent solution modeled the observed density slightly better than the equilibrium solution and it was suggested that the time scales of ionization must be taken into account. Marklund [1984] put forth a classification system based on auroral electric field observations and the mechanism that maintains current continuity across the arc. It was suggested that there were two mechanisms which could maintain current continuity ( J = 0) through the arc: a polarization electric field and field aligned current. The

63 43 polarization electric field would be able to regulate the movement of charge carriers across the arc, by adjusting the electric field through enhanced arc conductivity. Field aligned currents regulate charge carriers within an arc in a different way, by allowing the charges to move away from the arc into the magnetosphere. Solving the current continuity equation over the arc can be represented by equation 5 from Marklund [1984] for these two situations, E A m = E pol + J /Σ A P (2.8) where E pol is the polarization electric field, E A m is the meridional electric field observed within the arc, and Σ A P is the Pedersen conductance within the arc. Observationally a polarization type arc is typically observed to have E A m E pol ; whereas, in the field-aligned current arc, J /Σ A P is significant. Marklund [1984] comprehensively summarized observations at the time of publication and categorizes the observations into either polarization type arcs, field-aligned current arcs, or a combination of both mechanisms. It was put forth that whenever the electric field surrounding the arc was significant it was likely that it was a polarization type arc. Furthermore, it was emphasized that the continuity of the tangential electric field across the arc has a significant impact on the polarization electric field within the arc. This point is true because the higher ratio of Σ H /Σ P is typically observed in an auroral arc, which controls the contribution from the tangential electric field The Mallinckrodt Papers Two papers in the mid 1980s by Mallinckrodt were particularly important for the ACES mission. Mallinckrodt and Carlson [1985] made rocket observations finding an anticorrelation similar to observations by Evans et al. [1977]. It was found that the magnitude of the auroral electric field was anticorrelated with the peak electron energy flux. To explain this observation, Mallinckrodt and Carlson [1985] extended the model put forth by Evans et al. [1977] to include the additional effects of neutral winds and arc motion.

64 44 These effects were used to compute the ionization rates, the height integrated Hall and Pedersen conductivities, and then compared to the observed electric fields within the arc. The effects of the plasma motion relative to the arc predicted that a smearing effect would occur in the Hall and Pedersen conductivities which blotted out the small scale structure observed in the electron flux at the peak energy. As the strength of the electric field perpendicular to the arc decreased, and the velocity of the arc motion increased, the height integrated Hall and Pedersen conductivities show less variation. This prediction was not consistent with observation; the plasma velocity required relative to the arc was three times higher than the observed limit. The relationship between both Hall and Pedersen height integrated conductivities and energy of auroral electrons was further examined with the model, by varying the electron source temperature. A nearly linear relationship was found between both height integrated conductivities up to a potential drop of 3-4 KeV at all source electron temperatures. To further analyze the results of Mallinckrodt and Carlson [1985], a model of the ionosphere below the payload was developed by Mallinckrodt [1985]. The latitudinal and altitudinal current structure was modeled, which depended on boundary value currents and electric fields. The model included other significant effects such as height-ionization profiles from precipitating electrons and neutral winds in the electric field frame. Boundary conditions based on observations by Mallinckrodt and Carlson [1985] were also used in the model. In panel A of Figure (2.14) a nominally observed electric field was applied in the northward (+X) direction and mapped through the ionosphere. An altitudinal and latitudinal conductivity profile was generated from accelerated, precipitating auroral electrons; these precipitating electrons will carry the upward field aligned current. The electric field was then mapped latitudinally using the condition that the divergence of the current was equal to zero. With the electric field solution and the 2-D map of the conductivities, the latitudinal and altitudinal current structure was determined which is what is presented

65 45 in panel A of Figure (2.14). This situation is most consistent with a polarization arc. The current structure which forms from this configuration shows a vortex at 110 km, which results in a significant Hall current to form. Figure (2.14) Panel B demonstrates the type of closure current that will form if the northward directed electric field electric field is zero (no polarization electric field forms), but there is applied field aligned currents in an upward-downward pair. It is important to note in this case that the field aligned current entering the system is equal to the field aligned current exiting this system. This situation is consistent with a Birkeland arc. As shown by the red arrows in panel B, the result of this configuration is a U-shaped closure current that forms well within the lower ionosphere, with zones of rather strong magnitude currents at an altitude of 130 km. Panel C is a combination of panel A and B, both the northward electric field and field aligned currents are specified. As can be seen by the red arrows, the result is a combination of the two cases, in which there is a smaller current vortex which forms within a generally U-shaped current structure. As can be seen in Figure (2.14), different current closure geometries strongly depend on the boundary condition electric fields and currents. In summary, the goal of the ACES sounding rocket mission was to constrain this kind of model with much needed measurements to understand how current closes in the ionosphere Ionization Regions of localized electron density enhancement, sometimes referred to as plasma blobs, had been observed on a variety of sounding rocket missions and incoherent scatter radar (LaBelle et al. [1989], and references therein). A variety of theories existed on the formation of these blobby regions, however, LaBelle et al. [1989] demonstrated that these enhancements of density were likely the result of increased localized ionization due to electron precipitation. From sounding rocket data, six separate density enhancement

66 46 Altitude(km) A E (0) X J B J E (x)=0 X C J J E (0) X J North Latitudinal Distance(km) South Figure 2.14: The 2-D current closure configuration, in red, from Mallinckrodt [1985] based on different electric field or current boundary conditions. Panel A is the current configuration based on a boundary electric field that maps through the ionosphere and the conductivities that are generated from accelerated, precipitating electrons carrying the upward field aligned current. This configuration is most consistent with a polarization arc. Panel B is the current configuration for an upward-downward field aligned current pair and is most consistent with a Birkeland type arc. It is noted in panel B that the sheet field aligned current into the ionosphere equal the sheet field aligned current out of the ionosphere. Panel C is a combination of both a boundary electric field and field aligned currents. events were correlated with enhancements in the electron energy flux. The electron distributions were used to determine the peak energy of the electrons, and in all events, this energy was less than < 500 ev. The ionization rate for the background and regions of the low energy flux enhancements were determined using data inputs from observation. It was found that low energy electrons significantly enhanced the ionization rate. LaBelle et al. [1989] found that ionization could explain localized electron density enhancements if soft electron precipitation could be sustained for a time period of s. Such a time frame is not uncommon for a stable auroral arc. This key result suggested that observed electron density features require a finite amount of time to reach steady-state.

67 Theory Robinson et al. [1987] presented an empirically based formula that allowed for estimation of the Hall and Pedersen conductances within the auroral ionosphere, that followed from the work of Harel et al. [1981]. The key equations are, Σ P = 40Ē Φ1/2 E (2.9) 16 + Ē2 Σ H Σ P = 0.45Ē0.85 (2.10) where Φ E is the energy flux in units of ergscm 2 s 1. Ē is the average energy and is defined in the following way, E max EF (E)dE E Ē = min E max F (E)dE E min (2.11) where E min and E max correspond to the detector minimum and maximum observable energy, respectively. The reason that the average energy is explicitly defined is to account for the difference between the characteristic energy of various distributions. As an example, a Maxwellian distribution, defined as f(e) = AE exp( E/E o ) has an average energy of 2E o, but a power law exponential, defined as f(e) = A exp( E/E o ) has a characteristic energy of E o [Robinson et al., 1987]. Furthermore, it was shown that these relations produced consistent results for various input distributions, such as, a Maxwellian, an accelerated Maxwellian through a potential drop, and an exponential distribution. Good agreement was found between these empirical relations with data from the HILAT satellite and incoherent scatter radar observations. These results present a rapid means for estimating the Hall and Pedersen conductances based on the energy flux and average energy for a detector. However, it is important to note that these relations are time stationary.

68 The Lysak Papers Three papers by Lysak advanced the picture of MI coupling by means of Alfvén waves and also further investigated mechanisms that could generate quasi-static U-shaped potentials. Lysak and Carlson [1981] suggested that weak turbulence could account for the creation of an anomalous resistivity. The anomalous resistivity is defined as η = σ 1 is supported by a mechanism that would create an effective resistance parallel to the magnetic field line, thereby supporting a parallel electric field for a collisionless plasma. Lysak and Carlson [1981] modified the Vlasov equation into a quasi-linear form to include the effects of turbulence; an effective collisional frequency was derived which was constant. A shear Alfvén wave was then launched and the effect of the turbulence was included in the propagation of the Alfvén wave. It was found that turbulence would damp and slow the propagation of the Alfvén wave, and through turbulence it was possible to support parallel electric fields that would be set up on a single reflection with the ionosphere having time scales of the order of minutes. Lysak and Dum [1983] expanded this model even further with a numerical simulation that included the effect of excitation of local current driven instabilities in the effective collisional frequency. Lysak and Dum [1983] derived the equations for Alfvén wave propagation, including the effective collisional frequency and the ionospheric boundary conditions. The simulation included a current driven magnetospheric source, or current generator and a voltage driven magnetospheric source or voltage generator. It was found that in the current generator case, it was possible to create U-shaped electrostatic structures with the inclusion of turbulence, in five Alfvén bounce times. However, it was also found that similar structures appeared in the voltage generator case, although the solution was not electrostatic because of the presence of magnetic diffusion. Lysak [1985] examined the magnetospheric sources in more detail by including a driving function and the effects these sources have on MI coupling. Unlike the earlier models by Lysak, the and

69 49 dipolar nature of the Earth s magnetic field was included in this model. Lysak [1985] found, that in general, smaller scale auroral features, such as inverted V structures, tended to be current driven, whereas, the large scale auroral current system were voltage driven. It was also found that in the regions of non-linear resistivity, such as the results of Lysak and Dum [1983], that it was possible for ionospheric currents to become decoupled from the magnetospheric generator. These three papers formed the basis for much of the work done involving Alfvén waves with regards to MI coupling and auroral particle acceleration. Reflections of Alfvén waves with the ionosphere sets up the ionospheric Alfvén resonator [Lysak, 1990]. The idea that Alfvén waves can produce quasi-static U-shaped potential structures which is an area of active research to this day [Chaston et al., 2010]. 2.4 The 1990s- The Present Day By the 1990s much of the ground work had been developed in the realm of auroral physics, particularly with inverted-v aurora associated with upward directed field aligned current and converging electric fields (electrostatic shocks). Advances in higher resolution and more complete measurements on satellites and rockets along with more powerful computers moved the field forward by offering much better observations and modeling of phenomena first discovered in the 1970s and 1980s. The Freja and FAST satellites from this era have significantly advanced knowledge regarding the structure of the auroral zone in the downward field aligned current region Freja Satellite The Freja satellite mission, launched in 1992, brought many new observations which extended and advanced observations that were made on S3-3; particularly, regarding the electric field configuration in the auroral zone and electron measurements. S3-3 observed intense converging (inward pointing) perpendicular electric fields, termed electrostatic

70 50 shocks, at high altitudes ( km) that were associated with upward field aligned current and precipitating electrons. The parallel electric field from this configuration was inferred to be upward-directed. Marklund et al. [1994] observed a different configuration on Freja; similar intense electrostatic fields were found to be diverging (outward pointing) at lower altitudes (< 1760 km) that were associated with downward field aligned currents and a lack of precipitating electrons. Marklund et al. [1994] termed these regions black aurora due to the lack of precipitating electrons. These aurora were first associated with dark vortex structures [Marklund et al., 1994] and later with long dark east-west bands [Marklund et al., 1997]. These observations suggested a downward directed parallel electric field. A statistical study of these diverging electric field structures was undertaken by Karlsson and Marklund [1996] in which it was found that most of the diverging electric fields occurred in the pre-midnight to post-midnight MLT sector and that the majority of these structures were < 5 km in size. Karlsson and Marklund [1996] also compared the height integrated conductivity that was determined by solar radiance. It was found that the majority of the diverging electrostatic potentials were anticorrelated with the height integrated conductivities, which Karlsson and Marklund [1996] suggested established a connection between these events and the ionosphere. Boehm et al. [1995] provided observations from Freja of upward directed electron beams which were correlated with downward directed field aligned currents. Upgoing electron beams had been observed infrequently on other satellites, including S3-3 ([Boehm et al., 1995; Gorney et al., 1985], and references therein). Observations from Freja indicated that upgoing electron beams occurred more frequently than previously thought. Boehm et al. [1995] highlighted one event in which a significant result was the low perpendicular temperature of ev associated with the upstreaming electrons. The low electron perpendicular temperature suggested that the electron source was the ionosphere, although Boehm et al. [1995] also pointed out an ionospheric cooling source could have

71 51 Figure 2.15: Figure from Marklund et al. [1997] demonstrating the connection between both the upward directed current region with inverted V aurora and the downward current region with black aurora. affected the electrons. Boehm et al. [1995] also observed a local decrease in the electron density in the region of electron upflow. Marklund et al. [1997] later pointed out that the upgoing electron beam events appeared in the same local time sector as the black aurora. Figure (2.15) illustrates the updated picture of the auroral zone based on observations of upflowing electrons that carry downward directed field aligned currents along with diverging electric fields, which formed a connection to the black aurora FAST satellite The Fast Auroral SnapshoT (FAST) satellite has been one of the most successful satellite missions since its launch in August, The results from the FAST mission have solidified current understanding of a stable auroral arc. The FAST satellite was

72 52 launched into an elliptical orbit with an 83 inclination [Carlson et al., 1998a], making the satellite nearly a polar orbiter. The apogee and perigee of the spacecraft was 4175 km and 350 km, respectively [Carlson et al., 1998a]. Details regarding the instrumentation and mission goals can be found in [Carlson et al., 1998a]. One of the key aspects that lead to high quality data from FAST was the high temporal resolution of the observations. Results from FAST expanded upon the observations from Freja in the downward current region. Results from Carlson et al. [1998b] summarize many satellite passes in which the upward current region has precipitating inverted-v electrons and also includes ion beams at a pitch angle of 180. The ion beams had energies of the order of a few KeV, further suggesting that these ions were accelerated by a parallel electrostatic field. The downward current region had intense electron fluxes with energies less than 1 KeV, small perpendicular temperatures of less than 1 ev, but number fluxes 100 times greater than inverted-v fluxes. Ion conics and broadband extremely low frequency (ELF) waves were observed in association with the downward current region. These combined observations were further confirmation that the plasmasheet is the source distribution for the upward-current region; whereas, the cold ionosphere is the source region for the downward current region that can be determined from the temperature of the distribution. It was also shown that the upgoing electron beams were associated with a diverging electric field configuration, which correlates the electric fields with the black auroral regions. Carlson et al. [1998b] also made key observations regarding the distribution of the upward- and downward-current region, along with the location of the parallel electric field. It was shown that of the 670 orbits used in the data set, 78% observed upgoing electron beams (downward-current region), while the ion beams (upward current region) were observed 70% of the time. Furthermore, it was shown at altitudes less than 2000 km for ions and 1500 km for electrons, that beam events were observed with an occurrence rate of less than 5%. These observations placed a lower boundary on the parallel electric field location

73 53 to be at or above altitudes of km. Elphic et al. [1998] used data from FAST to examine the field aligned current structure surrounding an auroral arc. One of the key observations was the size difference between the two current regions. In the case study presented in Elphic et al. [1998], the upward field aligned current region traversed by FAST had a latitudinal scale length of 360 km and a low magnitude of a few µam 2. To contrast, multiple downward current regions were observed, of the order of 10s of km, located at the edges of inverted-v precipitation, and containing significant downward field-aligned current. In this case study, the upward and downward field aligned current balanced out. This case study was an example of a typical observation of many quiet-time satellite passes made by FAST. The current voltage relation [Knight, 1973; Lyons et al., 1979] was found to be linear in the upward current region and non-linear in the downward current region. Elphic et al. [1998] further suggested that the FAST observations were more consistent with a current generator as the source mechanism, that is to say, that the electric fields would change to keep the current into the ionosphere regulated. Peria et al. [2000] presented a statistical study of field aligned current characteristics observed by FAST using an automated search algorithm. The key results from this study were that the field-aligned currents tended to be of the order of 10s of km in size, with over half of the sample size being less than 50 km. Within the sample, only 20% of the observed currents were found to be in a configuration consistent with the Region 1 and Region 2 currents [Iijima and Potemra, 1978]. From this study, it was suggested that finer-scale currents play a significant role in the global current system, not just the large scale field aligned currents. This study also found that the closure of field-aligned current occurred at altitudes below 300 km. As suggested by the author, this observation may have been one of the first observational verifications the current closure region resides below 300 km.

74 Other Observations A sounding rocket paper by Kletzing et al. [1996b] presented another thorough study of auroral arc electrodynamics, following in the same vein as Evans et al. [1977]. The mission consisted of two successful sounding rocket payloads launched from the polar cap (74 invariant latitude, from Sondrestrom, Greenland) toward the south into two sundirected auroral arcs. The data from the rockets were rotated into an arc frame using data from the all sky imagers. The data showed inverted-v electron flux, as well as, lower energy superthermal type bursts. As the author noted, near textbook examples of electric and magnetic field observations were made with respect to the 2-D arc model [Boström, 1964]. The tangential electric field component and the normal residual magnetic field component showed very low levels of variation over the arc crossings. However, the normal (nominally meridional) electric field and the tangential (nominally zonal) residual magnetic field components showed significant variation. The tangential residual magnetic field observations were consistent with upward directed field aligned currents that were collocated with inverted V aurora. The electric field observations over most of the inverted V crossing showed a decrease in the electric field magnitude, consistent with an anticorrelation type arc [Evans et al., 1977; Marklund, 1984]. Furthermore, electric field observations showed that regions of electron precipitation were associated with negative space charge, as deduced from the electric field observations ( E). Finally, field-aligned currents were calculated from the electron flux and from the magnetometer with good agreement being found between the data from both instruments. The authors noted that a key limitation in using the electron detectors was the inability to integrate over the cold electron population at energies below the minimum detector energy. Kletzing et al. [1996a] presented one of the most complete studies of sunward-directed aurora, and one of the cleanest data sets of auroral arc electrodynamics to date.

75 Auroral Source Region More recently, Kletzing et al. [2003] have characterized the source population of auroral electrons that come from the high-latitude plasmasheet. Winningham et al. [1975] used observations from the ISIS 1 and 2 satellites to map electron precipitation into various regions within the magnetotail. These results were some of the first that suggested that the source region of auroral electrons was on high latitude magnetic field lines connected to the plasmasheet. Electron and ion flux data were used to derive the characteristic density and temperature of the source population that mapped to POLAR satellite crossings. From this high-latitude data set, it was found that the equatorward and poleward boundary of the electron flux mapped down to auroral zone invariant latitudes. This observation suggested that the electrons observed in the auroral zone mapped to the plasmasheet. Moreover, the characteristics of the source electron populations were deduced from these observations. Most significantly, statistically the electron population fits best to a κ-distribution, with a κ 10. The κ-distribution is particularly advantageous for modeling a high-energy tail in a distribution. In a statistical study of the dataset it was found that the κ-distribution could be fit for 45% of the events; whereas, the Maxwellian distribution (when κ ) could only be fit in 23% of the events. At the equatorward boundary, the electron density had a range of values from cm 3 and a characteristic energy (corresponding to the temperature) of ev. At the poleward boundary, the electron density was lower, ranging from cm 3 and a similar characteristic energy of ev Auroral Ionospheric Cavities Since Mallinckrodt [1985], there have been two modeling efforts that have examined the auroral ionosphere. Both of these models were interested in understanding auroral ionospheric cavities, which are a phenomena in which electron density cavities or evacuations form in the ionosphere. Doe et al. [1993] undertook a statistical study of observations

76 56 of depletions of auroral ionospheric electrons using data from the Sondrestrom radar. It was found that these features were < 100 km in size and that the electron densities decreased in these regions by 20-70%. Doe et al. [1995] proposed four possible mechanisms that could produce auroral density cavities; however, two of these mechanisms were not feasible on the time scales of an auroral arc. Of the remaining two mechanisms, one was properly modeled by Doe, but this mechanism failed to explain the connection between density depletions and the aurora ([Doe et al., 1995], and references therein). The fourth and final mechanism proposed was that downward directed field aligned currents could carry ionospheric electrons, thus creating the regions of depleted electrons. To test this theory, a model was developed by Doe et al. [1995] in which a 2-D current system was formed over an ionospheric region that included the upward and downward directed field aligned currents along with a closure current. The steady-state divergence of current was used to connect field aligned current to the cross-field current. The electrostatic potential structure also mapped down into the ionosphere. With the full current structure included, the electron density continuity equation was solved including the additional effects of diffusion, recombination rates, and production rates. Different values of field aligned current were used as inputs, ranging from µa m 2, and the fieldaligned currents had length scales of the order of 100s of km. From these currents it was shown that densities cavities could form by the downward directed field aligned current on timescales of 30-64s. These simulations also showed an increase in the current density in the region of the density cavity. It was also noted that the altitude at which the large density depletion was modeled corresponded to the region where the Pedersen conductivity peaked (140 km). The result of this model suggested that the most plausible mechanism for the formation of electron density cavities in the ionosphere was a result of downward directed field aligned current. Karlsson and Marklund [1998] expanded upon the model by Doe et al. [1995] to

77 57 examine the diverging electric field configurations in the context of the downward current region observed by Freja and FAST. Doe et al. [1995] examined the case of large scale field-aligned currents and applied an electrostatic potential at the top boundary of the simulation; that is, Dirichlet boundary conditions were used. Karlsson and Marklund [1998] instead examined small size currents, of the order of 10s of km, and used Neumann boundary conditions at the top of the simulation consistent with a field-aligned current into the simulation region. It was shown for field-aligned currents with magnitudes that peaked at 30 µa m 2 that an amplification of the diverging electric fields would be observed at altitudes of 500 km on timescales of the order of minutes. In addition, small scale (2 km length scale) evacuations of ionospheric electrons would be observed at the center of the downward current region, again, on the timescales of the order of minutes. While this model had promising results that could be applied to FAST or Freja results, there is one key point in this model that is questionable. This model predicts strong, up to 30 mv/m parallel electric fields at altitudes of approximately 100 km. The electric field magnitudes associated with parallel electric fields accelerating auroral electrons are thought to be of the order of 1 mv/m [Gorney et al., 1985] over ranges of s of km, making these fields difficult to directly observe. However, 30 mv/m would be more easily observed at ionospheric altitudes. The author of this dissertation is unaware of any observations of parallel electric fields with this magnitude within the ionosphere Recent Observations (2005-Present Day) In 2007, the JOULE II sounding rocket mission successfully launched to examine the low altitude auroral ionosphere and neutral atmosphere. The mission focused on making observations of the interaction between the neutral wind and the demagnetization of ions [Sangalli et al., 2009]. Sangalli et al. [2009] presented in situ ion flow velocities, the E B drift velocities, the electron density, and direct calculations of the Hall and Pedersen conductivities from these observed parameters. The JOULE II rocket mission also

78 58 included additional chemical release payloads to measure neutral wind velocities for altitudes between 90 to 130 km. It was found that the ions remained magnetized at altitudes above 150 km, but at altitudes between km the ions moved with the neutral wind. Sangalli et al. [2009] found that the in situ Joule heating rate peaked at approximately 114 km. When the effects of neutral winds were included, Joule heating rates decreased by 28%. The reduction in the Joule heating rate suggested that some of the energy was dissipated through ion-neutral frictional drag. It was also found that the altitude κ = 1 for the ions was at approximately 118 km, which correlates very well with the peak rate of the Joule heating, and the peak of the Pedersen conductivity when κ = 1. The results from the JOULE II mission are one of the few in-situ observations within the auroral ionosphere of neutral wind coupling with the plasma. 2.5 Summary A review has been presented of the major advances in auroral physics over the last 50 years with particular emphasis placed on electric fields, precipitating electrons, and field aligned currents. To conclude this section, a review of the configuration of the quasistatic auroral arc is presented. The presentation will follow from Carlson et al. [1998a] and Marklund and Karlsson [2001], which separates the auroral zone based on current direction, as illustrated in Figure (2.16). The region of upward field aligned current is carried by hot magnetospheric electrons from the plasmasheet that have been accelerated by a parallel electric field at altitudes of approximately km. The electric field configuration at high altitudes would likely observe converging perpendicular electric fields, that have been called electrostatic shocks. A U-shaped (or less frequently S-shaped) electrostatic potential structure is most consistent with the observations of converging perpendicular fields and associated with a parallel electric field. The precipitating electron flux would appear as an inverted-v signature that would map down to the auroral arc at ionospheric altitudes. Above the

79 59 Inverted-V Diagram Altitude (Not to scale) U or S-shaped Quasi-Static Potential E (other mechanisms) E Altitude (Not to scale) Black Aurora E Ions (Beams) E km E Electrons E U-shaped Potential?? km Earth B-field Ions (Beams) Earth B-field J Electrons (Beams) Ions (Trapped) J Spacecraft Altitude km 100 km Energy Auroral Ionosphere Increased Ionospheric n e Density Spacecraft motion Inverted-V (Electron Flux) Latitude (Not to scale) Spacecraft Altitude km 100 km Evacuated Ionospheric Density Black Aurora Auroral Ionosphere Spacecraft motion Latitude (Not to scale) Figure 2.16: A summary figure of the upward and downward current region, corresponding to visible and black aurora, respectively. Please see the text for an explanation. parallel electric field, ion beams would be observed having been accelerated by the parallel electric field. At ionospheric altitudes, the deposition of precipitating electrons causes a local increase in the electron density, that further enhances ionospheric conductivity. The downward field aligned current region is associated with a lack of precipitating electron flux and visually these regions have been termed black or inverse aurora. The downward field aligned current is carried by cold ionospheric electrons and these currents are typically narrow in latitudinal extend and intense in magnitude. These regions have a diverging electric field configuration, with a downward directed parallel electric field. At high altitudes, electron beams can be observed that are consistent with cold ionospheric electrons being accelerated by the parallel electric field. The ion population is composed of two components: ion conics and ion beams. The conics are ion distributions with pitch angles between and are typically trapped between the electrostatic field at high

80 60 2-D Auroral Arc Looking toward Ionosphere E mer Auroral Arc Σ H J H E X - Latitude J J J P Σ P E zone Black Aurora J Y - Longitude X Meridional B-Earth δb-n min Y-Zonal δb-t max E-N max J E-T min Auroral Arc E Ambient Electric Field Figure 2.17: A downward view of the 2-D arc model and the association with an auroral arc and the black aurora regions. The upward directed field aligned current resides within the visible auroral arc and the downward field aligned current is associated with the black aurora regions. The field aligned current closes through the Hall and Pedersen currents that are based on the perpendicular electric field direction. There are conductivity enhancements within the auroral arc because of the deposition of precipitating electrons. The electric fields and residual magnetic fields are associated with two directions relative to the arc: tangential to the arc and normal to the arc. altitudes and the magnetic mirror at ionospheric altitudes. Although, conics have also been observed at altitudes above the acceleration region. The ions that have gained energy through the pressure cooker mechanism can overcome the parallel electric field. As shown in Figure (2.17), within the ionosphere the upward and downward field aligned currents are closed through Hall and Pedersen currents. The closure current is driven by field aligned currents. In the stationary 2-D model configuration, for a long arc

81 61 with significant zonal extent, the tangential magnetic field component relative to the arc will exhibit maximal variation, but the component normal to the arc will have minimal variation. This is indicated by the coordinate axes in Figure (2.17). The residual magnetic field components will exhibit maximum variation in the tangential direction and minimum variation in the normal direction. The residual electric field tangent to the arc will have minimal variation and will match with the ambient, exterior electric field across the boundary of the arc. The continuity of the electric and magnetic fields across the arc boundary are enforced by the Maxwell boundary conditions.

82 62 CHAPTER 3 INSTRUMENTATION AND DATA PROCESSING Having presented the relevant scientific background surrounding the discrete aurora, a discussion of the detection techniques and data processing is in order. How measurements are made to determine relevant scientific parameters is of key importance to the experimentalist. A discussion will be given of the basic operation of the instruments used on the rocket payloads and the physical quantities they were designed to measure. Data processing will be presented on two of the data sets that are most relevant for understanding current closure: the electron flux and the magnetometer data. 3.1 Instrumentation The ACES mission utilized two well-instrumented payloads that measured key electrodynamic and plasma parameters. Figure (3.1) illustrates the layout of the instrumentation on both the ACES High and Low payloads. Two instruments were provided by the University of Iowa on the forward section of the payload: swept and fixed biased Langmuir probes to measure the electron density and the Electrostatic Electron Pitch-Angle Analyzer (EEPAA) to measure the electron differential energy flux. Two magnetometers were located on the forward section of the payload, the science magnetometer (Sci Mag in Figure 3.1) was provided by John Hopkins University Applied Physics Laboratory and the attitude control system (ACS) magnetometer (ACS Mag in Figure 3.1) provided by NASA Wallops. The NASA Goddard Space Flight Center (GSFC) provided perpendicular DC electric field measurements that were made by probes on four booms located on the forward section of the payload using the double probe technique (DC E-field in Figure 3.1). High frequency (HF) AC electric field measurements were also made using the double probe technique. This instrument was provided by Dartmouth College and located on the aft section of the payload (HF E-field in Figure 3.1). The University of New Hampshire provided the electron retarding potential analyzer (ERPA) located on a boom on the

83 63 Figure 3.1: The instrument configuration on both ACES High and Low. Please see the text for details. aft section of the payload that measured the cold electron population. NASA GSFC also provided an impedance probe on the forward section of the payload (Z-probe in Figure 3.1) to provide absolute measurements of electron density. An AC magnetic field coil was provided by collaborates at LPC2E/CNRS in France (AC B-field in Figure 3.1); however, these data will not be used in the present study.

84 64 Top-Hat Style Electrostatic Energy Analyzer Charged Particle Trajectory Light Baffles FOV (+/- 6) Outer Electrode Inner Electrode Micro-channel Plates Anodes Axis of Symmetry Figure 3.2: Cross section diagram of the EEPAA detector flown on ACES High and Low. The inner electrode is swept in voltage, while the outer electrode is at spacecraft ground. A particle trajectory is shown for a particle that is selected by the electric field created between the inner and outer electrodes Electrostatic Analyzer The EEPAA detectors were used to measure the electron differential energy flux, which can be used to determine the electron distribution function. The EEPAA detector flown on the ACES payloads was a tophat style, full pitch angle electrostatic analyzer, which was first designed by Carlson et al. [1982]. Figure 3.2 shows a cut-away diagram detailing the EEPAA detectors used on the ACES payloads. How the electrostatic analyzer selects an electron with given energy can be shown through a simple derivation. After a particle enters into the detector, the electrostatic force, that is provided by the voltage drop between the electrodes, will provide a centripetal force onto the particle. The solid line in Figure (3.2) shows a particle that has been guided on a circular trajectory by the electric field created by the potential drop between the two electrodes. For simplicity, if it is assumed that particles move on circular orbits and that

85 65 the plates are cylindrically symmetric then the force balance can be written as, mv 2 r o = qe o (3.1) where q is the charge, r o is the equilibrium trajectory of the particle along the circular orbit, and E o is the electric field set up between the plates. The electric field can be approximately written as E o Φ/ r where Φ is the voltage of the inner electric and r = r out r in is the separation between the inner and outer electrode (Please refer to Appendix D for an exact boundary value solution for the electric field). After some manipulation, this can be solved to get an expression, E = qφr o 2 r (3.2) where E corresponds to the energy of the particle. If the particle energy is too high or low the particle will instead be absorbed by the outer or inner hemisphere, respectively. The voltage between the electrodes is swept to create a time-varying electric field that selects electrons or ions with energies between KeV. The separation between the potential difference acts as an effective gain factor of the applied voltage. A particle with the correct energy will strike the microchannel plates which are similar to a photomultiplier tube; when the electron strikes the plate a small cascade of tertiary electrons are created. The small charge is collected by an anode and transmitted down to a charge sensitive amplifier that creates a 5V TTL pulse that is accumulated by a counter controlled by a digital signal processor. The number of counts are integrated over an 860µs time period (t acquistion ) for each energy increment. The energy sweep (voltage sweep) is accomplished in 1 ms logarithmic steps over a 48 ms time period, which allows for full plasma (electron or ion) distributions to be measured every 48 ms. The EEPAA detector is cylindrical symmetry about its symmetric axis that ideally has the entrance aperture well-aligned with the mean magnetic field. There are 24 anode pads covering 15 o pitch angle bins to obtain full o particle distributions about the symmetry axis.

86 66 One other key factor is that the energy resolution of the tophat electrostatic detector remains constant, E/E = γ [Pfaff, 1996]. In the simplified picture presented above, if the limiting cases are particles moving along the inner and outer electrode hemisphere at radius, r in and r out, then equation (3.2) becomes, This equation can be solved such that, E(in[outer]) = qφ 2 r r in[out] (3.3) γ = E E = E(r out) E(r in ) E = r r o (3.4) which shows that γ depends upon the distance between the inner and outer electrodes, which is fixed based on the physical dimensions of the detector. The key data obtained by the electrostatic analyzers are the electron or ion distribution functions, that can be derived from the differential energy flux. To gain insight into how the electrostatic analyzers can measure the electron distribution function, the following derivation is presented which follows from Kletzing and Torbert [1994]. The total number flux of the distribution function in velocity space is defined as [Reif, 1965], Φ = dω f(v)v 3 dv (3.5) where dω is the solid angle and Φ has units of cm 2 s 1. The total number of particles, or the number of counts, can be found by integrating the distribution function, C = dt da dω f(v)v 3 dv (3.6) where da would be integrated over the collecting area of the sensor and dt is integrated over the acquisition interval of the sensor. A change of variables can be made from velocity space into energy space so that equation (3.6) becomes, C = dt da 2Ef(E) dω de = m 2 dt da dω j(e, α)de (3.7)

87 67 where j(e, α) is the differential number flux, in units of cm 2 s 1 ster 1 ev 1. In this case the velocity components can be related to the pitch angle by, v = v cos(α), v = v sin(α) (3.8) where α is the pitch angle. The geometric factor of the detector, takes into account the angular and physical response of the detector and is defined as, [ ] G(E) = da dω = [A Ω] sensor (3.9) sensor In an analog to light optics, the geometric factor is the term which represents the physical collection area of the detector, similar to the aperture and focal length in optics. The geometric factor in Equation (3.9) is energy dependent, but it can be simplified by virtue of the energy independence of the tophat analyzer, G(E) E = G(E)γE = GE (3.10) where E is the integration variable and G = G(E)γ is the total geometric factor that is not dependent on the energy [private communication C.A. Kletzing, 2008]. A nominal geometric factor for an individual channel on the EEPAA detectors has been determined through computer modeling. The nominal geometric factor magnitude for the ACES detectors was between and units of ster cm 2. The pre-flight calibration procedure confirmed the actual response of each channel pad relative to the nominal single channel model. The count rate observed by the detectors can be obtained by integrating over the acquisition interval. The differential number flux can be solved in terms of the number of counts, C = dt da dω j(e, α)de = J(E)t acq GE (3.11)

88 68 which can be simplified using the count rate, J(E) = Ċ GE (3.12) for a single pitch angle channel. The count rate, Ċ, is the total number of counts that has been divided by the acquisition interval, Ċ = C t aquistion C t deadtime (3.13) where the dead time corresponds to the time after a count during which the charge amplifier does not respond to new counts. The dead time was calibrated in the laboratory before flight for each charge amplifier, along with, the charge amplifier sensitivity threshold. A nominal deadtime value was of the order of 100s of ns. It was also verified that each amplifier would produce a 5V TTL pulse for a threshold amount of charge. To complete the derivation, differential energy flux is related to the differential number flux by, ρ(e) = EJ(E) = Ċ G (3.14) in units of evcm 2 s 1 ster 1 ev 1. The differential energy flux has the advantage that it is only dependent upon the geometric factor and the count rate, both quantities which can be calibrated in the laboratory. To summarize, the differential energy flux can be related back to the differential number flux and the distribution function (in energy space), through the following key relation, ρ(e) = EJ(E) = 2E2 f(e) m 2 e = (Ċ) G (3.15)

89 Electric and Magnetic Fields The double probe technique was used to measure both AC and DC electric fields. The double probe technique utilizes a differential voltage measurement ( Φ) between the two probes (typically spheres) separated on a boom by a fixed distance. The electric field can be determined through the following relation, Φ = E d (3.16) where Φ is the voltage difference between the probes and d is the vector distance between the probes. Coupling and sheath effects, as well as instrumental gains and offsets, and the frame-dependent electric field (E = U sc B) need to be properly accounted for with this technique. The payload attitude is also crucial in determining the correct geophysical orientation of the distance vector (d) between the probes while in flight, considering that the payload is undergoing spin and coning motion. DC electric field double probe measurements were made perpendicular to the geomagnetic field, covering a bandwidth of 0 3 KHz. HF AC double probe measurements were obtained parallel to the spin axis of the payload, covering a bandwidth of 0 5 MHz. The data from the perpendicular DC double probes were processed at NASA Goddard. Two fluxgate magnetometers were included to measure the DC magnetic fields. A high precision scientific fluxgate magnetometer and a commercially available fluxgate magnetometer for feedback into the attitude control system (ACS). These magnetometers were used to measure the magnetic field direction during flight and perturbations of the background magnetic field indicative of current structures. To understand how a fluxgate is able to measure magnetic field an idealized situation for detection is described, which is used for simplicity. Fluxgate magnetometers typically use two coils wrapped around a core of magnetically permeable material. A large AC current drives the magnetically permeable primary core into a state of oscillating saturation.

90 70 The alternating saturation is measured by the sensing coil. If the sensing coil was plotted against the drive coil, the curve would show the hysteresis curve of the magnetically permeable material being driven into oscillating saturation, provided no external magnetic field was applied. In this case, there would be a 50% duty cycle of the hysteresis curve, which would appear essentially as a square wave due to the hard driving into saturation. However, if an external magnetic field is present and it is pointing in the same direction as the symmetry axis of the magnetometer, the approximately square wave will no longer be symmetric. For example, the top portion of the square wave may show a skew due to the presence of the external magnetic field. Since square wave forms can be decomposed into an odd infinite Fourier series, the even infinite Fourier series can be used as a proxy for the asymmetry that is observed in the square waveform. The first even term in the even Fourier series is used for detection of the externally applied magnetic field. The sense coil can also be used as a nulling coil. The amount of current in the sense coil required to null the even harmonics of the Fourier series, along with the geometry of the coil, can be used to determine the magnitude of the external magnetic field. Like DC double probes, use of magnetometer data depends crucially on the rocket attitude solution (i.e., the true alignment of the symmetry axis of the magnetically permeable core) to properly align into a geophysical coordinate system, and additionally on the proper calibration of instrumental gains and offsets Electron Density and Temperature Fixed biased and swept biased Langmuir probe measurements were obtained to determine the relative and absolute electron density. Langmuir probes use the current-voltage characteristic of the probe within the plasma to measure plasma parameters, such as electron density, temperature, and plasma potential. At the most fundamental level, density

91 71 measured by the probe can be related back to, I = 1 4 n eeav (3.17) where n e is the electron density, A is the surface area of the probe and v is the electron thermal speed [Schott, 1968]. It is found that equation (3.17) is similar to the amount of flux that would hit a planar surface, as derived in section 7.11 of Reif [1965]. The electrical current in the Langmuir probe is created by an incident particle flux ( 1n 4 ev) onto a probe surface (A) that has been voltage biased relative to the spacecraft (effectively ground). If the plasma distribution function is assumed, such as a Maxwellian distribution, measurements of parameters such as temperature (T ) and plasma potential (Φ p ) can be determined by fitting to the current-voltage characteristic. These measurements can be related back to the density of the plasma that is assumed to be a Maxwellian distribution through equation (3.18), n e = n 0 exp ( ) eφp kt (3.18) where n 0 is the mean density measurement. Deriving plasma parameters from Langmuir probe data are non-trivial and the data are strongly dependent upon a variety of assumptions, such as, probe collecting area, the magnetization of the plasma and, most significantly, sheath effects surrounding the probe. For example, Mozer et al. [1979] stated at least ten assumptions that were used to calculate the electron density from the Langmuir probe on the S3-3 satellite. The University of New Hampshire provided an electron retarding potential analyzer (ERPA) to measure low energy (0-3 ev) background electrons. The ERPA used a swept voltage which rejects all electrons of energies lower than the bias potential. A low-noise anode collects the precipitating electrons which sets up a small current that is measured. Although all electrons above a given energy are collected, the higher energy precipitating auroral electrons form a negligible fraction compared to the colder background electron

92 72 population. As illustrated in Figure (3.1), the ERPA detectors were aligned parallel to the spin axis of the payload to measure the field-aligned bulk flows of background electrons that carry field-aligned current. It is noted that the ERPA detectors are commonly used to determine the electron temperature of the cold plasma because the temperature can be fit to the slope of the distribution function, that is to say, ln [f(v)] ev/kt. 3.2 Data Processing EEPAA Processing Further data processing were required to improve the calculation of the differential energy flux. A cross calibration routine of in-flight EEPAA data was applied to improve the accuracy of the charge amplifier response. Warming of the charge sensitive amplifiers during the calibration procedure causes somewhat degraded performance away from the nominal response. This is not a pronounced issue on a fifteen minute rocket flight; however, the calibration routine for the detectors lasts up to ten hours. As such, it is useful to check the in-flight data against calibration data for individual counter channels. In flight, it was assumed that the plasma distribution is the similar for a given pitch angle bin, so two channels at the same pitch angle bin should observe the same differential energy flux. However, as a result of differing values of the geometric factor and varying sensitivity between charge amplifiers, the same count rate is not necessarily observed. The in-flight cross calibration routine uses a chi-squared grid search method to improve the response between two channels. The basic idea was to use a multiplicative factor that would match two counter channels. The cross calibration routine is defined in the following equation, χ 2 = 1 N (A i c i A j c j ) 2 (3.19) c i + c j ij where A i and A j are the multiplicative factors that are applied to the i-th and j-th channel

93 73 pads, N is the total number of overlap occurrences when pad i and j observe the same pitch angle bin. One channel pad was chosen that had an accurate response and set as the model channel pad that the others were cross calibrated against. For example, channel 0 was chosen as the ideal response, then A 0 was set equal to 1. Due to the coning and spinning motion of the payload, two adjacent channels often observed the same pitch angle bin. For example, channel c 0 would observe overlaps with the adjacent channels c 1 and c 23 ; channel c 1 would observe overlaps with the adjacent channels c 0 and c 2 ; channel c 3 would observe overlaps with the adjacent channels c 2 and c 4 ; etc, etc. By the cylindrical symmetry of the detector, two opposite channel pads also observed the same pitch angle bin. For example, if c 0 observed 0 o pitch angle; channel pad c 1 and c 23 would observe the 15 o pitch angle bin; channel pad c 2 and c 22 would observe the 30 o pitch angle bin; etc etc. These connections between the adjacent and opposite channels allowed for the relation back to the model channel pad (A 0, in this case). A grid search was then performed in which A i and A j were varied between values of , over seven pads (with one fixed counter pad) in a run to ensure a lower computational time. The connection between adjacent channels allowed for later runs to be subsequently connected to each other. The lowest value of χ 2 that was found from the grid search represented the best fit connecting multiple detectors. Due to the large coning angle on ACES Low, there was much overlapping between multiple neighboring counters, which allowed for the cross calibration scheme to be applied. ACES High, having a smaller coning half angle, did not have as many overlap occurrences correlating back to a single channel. Consequently, the average geometric factors over all channels from the calibrations of all 24 pads were used for the data from ACES High High Frequency Electric Field Processing High frequency (HF) AC electric field data were provided by Dartmouth College. The primary interest in these data for this study was to determine electron densities based

94 74 on cut-offs of plasma frequency (f pe, when f pe >> Ω e ). The HF electric field data were transmitted over a baseband signal and sampled on the ground with a different time base relative to the other payload instruments. A time correction was applied to align the HF electric field data with the other instruments. This correction was accomplished by using a nominal time sampling ( t cadence ) provided by colleagues at Dartmouth College and finding the start location in the raw waveform data of a calibration event which occurs every 60s. The raw wave form calibration events were compared against the same event in the automatic gain control data, which were sampled on the same time frame as other payload instruments. A linear fit was used to correct the times, t = t cadence N points + t offset (3.20) in which the t cadence is the time cadence, N points are the number of points to the start of a calibration in a raw waveform and t offset was empirically found to be about 5 ms. The second portion of processing the HF AC electric field data was to obtain the power spectrum. Determining the power spectrum was important for generating spectrograms of the AC electric field measurements. However, the same procedure will be used with the magnetometer data to determine the power at the spin and coning frequency. In the process of taking the fast Fourier transforms (FFT) to obtain the power spectrum, the sampling rate becomes important for determining the temporal scale of phenomena that can be observed. The lowest frequency is determined by the sample interval for the Fourier transform, and the highest frequency is the Nyquist frequency, f crit = 1/2 = f sample /2, where is the sample interval [Press et al., 2007]. The sampling rate of the AC electric field data was 10 MHz and had a corresponding Nyquist frequency of 5 MHz. That is to say that frequencies above 5 MHz would not be properly sampled and will suffer from aliasing. By design, the receiver incorporated strong filtering that rolled off at frequencies of approximately 4 MHz to prevent aliasing. For processing the data, an interval size of 50,000 points was chosen which corresponded to 5 ms and the

95 75 Nyquist time was 50 ns. This 5 ms sample interval also defines the frequency resolution after applying the Fourier transform, which in this case is 200 Hz (1/5ms = 200). The Fourier transform is then applied using a Hanning window, f N (ω) = F[g N f N (t)] (3.21) where g N corresponds to a Hanning window of size N points, f N (t) corresponds to the time series AC electric field data, and f N (ω) is the complex Fourier transform. The Hanning window, or other windows, are used to guarantee that the raw waveform will have a value of zero at the end points. This will ensure that the Fourier transform does not contain specious elements in the transformed spectrum. The Fourier transform generates a symmetric frequency spectrum of positive and negative frequencies that are centered at the point N/2, where N is the total number of points. In the example, from would be the positive frequencies and from would be the negative frequency component. The power spectrum is obtained by taking the absolute value, P N/2 (ω) = f N/2 (ω)f N/2 (ω) (3.22) where f(ω) is the complex conjugate of f(ω). When applying the frequency resolution of 200 Hz to the sample size of points, the bandwidth is 5 MHz. An averaging and summing can be applied to the power spectrum to generate lower time resolution spectrograms. This is especially useful for overview type spectrograms. For this type of reduction, the power is summed together and averaged with respect to time. As an example, the AC electric field data were averaged over 10 points in frequency space, which reduced the number of points from to 2500 and changed the frequency resolution from 200 Hz to 2 KHz. These data points were then averaged over four, 5 ms time intervals, to generate a temporal resolution of 20 ms.

96 76 Magnetometer Coordinates B z ω t c B o ω t s B B B y B x Figure 3.3: The magnetometer can be envisioned as a rotating coordinate system that samples the Earth s magnetic field. The primary rotational frequency is the spin (ω s ) frequency and there is a longer coning frequency (ω c ) nutation Magnetometer Processing The magnetometer data were the key data used to calculate the currents on both ACES High and Low. On ACES High, with the failure of the EEPAA energy sweep, it was not possible to obtain the field-aligned currents by integrating the distribution function, as was done in Kletzing et al. [1996b]. The magnetometer data processing included a multi-step process that properly calibrated the magnetic field observations and then transformed the data from a rocket-based XYZ frame into a geomagnetic field-aligned coordinate system. Similar steps were applied for both ACES High and Low; however, the ACES Low magnetometer required additional data processing because of the leak in the attitude control system. Basic theory will elucidate the reasons for applying in flight calibrations to the magnetometer data. The payload has two major motions that affect the magnetometer data:

97 77 the spacecraft spin and the slower coning nutation. During the flight, both payloads spun with a nominal frequency of 0.65 Hz and the spin-axis had a coning precession relative to the mean magnetic field. The magnetometer on the spinning and coning payload can be thought of as a rotating coordinate system that is sampling the Earth s magnetic field. Schematically this is represented in Figure (3.3), where X, Y, and Z are the magnetometer coordinates and the Earth s magnetic field vector, B o, is assumed to be fixed over the time interval of the spin and coning period. That is to say, it was assumed that the mean magnetic field did not vary significantly over the coning period, which had a period of 2 seconds. The projection of the magnetic field vector into spherical coordinates in the rotating coordinate system is, B X = G X B o cos(ω S t)sin(ω C t) + δb X (3.23) B Y = G Y B o sin(ω S t)sin(ω C t) + δb Y (3.24) B Z = G Z B o cos(ω C t) + δb Z (3.25) where B o is the magnitude of the Earth s magnetic field vector, G i and δb i are the instrumental gain and offset of the i-th component of the magnetometer, respectively. The Earth s magnetic vector remains invariant between any frame of measurement. In the rocket frame, the sum of the squares of the magnetic field components measured in the rocket frame will not equal the total magnetic field, B o, unless the instrumental gains and offsets are determined. If the total magnitude of the Earth s field is smoothly varying, the total magnitude measured on the payload must also be smoothly varying after correcting for the effects from payload spin and coning motion. The goal in processing the magnetometer data is to minimize or eliminate the effects of errors in the instrumental gains and offsets, before applying the attitude solution. The perpendicular component of the magnetic field, B, composed of B X and B Y sample the

98 78 perpendicular projection of the mean magnetic field at a cadence that is 90 out of phase with respect to each other. This configuration is advantageous for cross-calibrating, nearly simultaneously, between the two perpendicular components to resolve the instrumental offsets and gains of the magnetometer. An instrumental offset on either of the perpendicular components will result in a duty cycle in the time series data that is not 50%. Furthermore, as a figure of merit, if the gains and offsets have been properly accounted for, B will not have any residual spin signature. This can be seen by the quadrature some of equations (3.23) and (3.24). The power spectrum were used to determine the magnitude of the spin and coning frequency components of the magnetic field. The power at the spin frequency was used as a figure of merit to evaluate the effectiveness of the instrumental gain and offset determination for the B component. To summarize, the goal when determining the errors in the instrumental offsets and gains is to reduce the effects of payload spin and coning as much as possible before applying the attitude solution. There are a few methods used to determine the magnitude of the offsets in the perpendicular magnetic field components. The simplest is to use a running median or smoothing filter that has a window size that is approximately the same size as a spin period. As the window moves across the magnetic field component it will approximately cancel out the spin contribution leaving the DC offset. This method is fairly rudimentary, but if the payload does not have a significant payload half angle, this method can be implemented effectively. This was the case for the ACES High payload, where the coning half angle was 3 relative to the mean magnetic field. A median filter was applied to the magnetic time series data that significantly reduced the magnitude of the spin and coning effects. The residual DC magnetic field offset, post median filter, were fit using a third order polynomial fit to determine the offset in both of the perpendicular components over the duration of the flight. To quantify the effectiveness of the reduction in the spin and coning component,

99 79 hodograms can be used as an additional figure of merit. A hodogram plots B X versus B Y. If the gains and offsets have been properly applied, the hodogram of the perpendicular magnetic field components would appear as a perfect circle centered about the origin. If the offsets have not been accounted for properly, then the circle would be off center by the magnitude of the offset in either component. In addition, if the gains were not properly accounted for, the circle would instead be an ellipse. This method of offset and gain determination has been used on the ACE satellite [S.R. Bounds, private communication, 2012]. A higher-order method to determine the offsets is to use a low-pass filter routine. This method was specifically applied to the ACES Low magnetometer after various methods did not yield a satisfactory solution. In Fourier space, the zero frequency component of the power spectrum corresponds to the DC component of the time series data, which in this case is the magnetometer offset. A Butterworth filter was used as a low pass filter. This was implemented through the following method, δb i = F 1 [F(B i )B(O, f c )] (3.26) where F corresponds to a forward Fourier transform, B i is the i-th component of the magnetic field, and B(O, f c ) is the Butterworth filter of order O and critical frequency f c. One of the issues when using filters, such as a Butterworth filter, is the possibility of generating non-physical ripples on the signal of interest. To reduce this issue, the lowest order filter was used with the critical frequency set below the coning frequency of the payload. The calibration of the parallel gain and offset is more challenging. Returning to equations (3.23) - (3.25), the coning component of B should ideally cancel with the coning component in B, when the components are summed in quadrature. This fact can be used to guide the adjustment of gains and offsets in the parallel magnetic field component to balance with the perpendicular magnetic field component. The Fourier power spectrum at the coning frequency was used as a figure of merit. For both ACES High and ACES Low

100 80 the gains and offsets in the parallel component were manually adjusted in a chi-by-eye fashion to yield the minimum power at the coning frequency. After the gains and offsets have been applied to all three components of the magnetic field, the payload attitude solution was applied to transform the rocket-frame coordinates into an Earth-based inertial coordinate system. The attitude solution was obtained from a gyroscope flown on board both payloads and attitude data were provided by NASA Wallops. The application of the attitude solution can be represented by the matrix, B E B N B U A 11 A 12 A 13 B o cos(ω S t )sin(ω C t ) = A 21 A 22 A 23 B o sin(ω S t )sin(ω C t ) A 31 A 32 A 33 B o cos(ω C t ) (3.27) where the A-matrix corresponds to the attitude solution. The left-hand side of equation (3.27) are the East-North-Up magnetic field components in an Earth-centered Earth-fixed (ECEF) coordinate system that is commonly used for rocket and missile applications. The attitude A-matrix is a unitary transformation (AA 1 = A 1 A = I), which means that the application of the attitude solution should have no effect on the total magnetic field. The attitude solution serves two purposes. First, it effectively removes the remaining contribution of the spin and coning. Second, it properly weights and combines the contributions from the rocket-based axes into an Earth-based coordinate system. If the attitude solution is applied to a magnetic field component that has not had gains and offsets properly accounted for, an erroneous spin and coning signal will appear in the East-North-Up frame. In this case, the total magnetic field will not be a smoothly varying function. The scientific magnetometer Co-Is chose to sample their instrument on a different time-base than the attitude control system and the other instruments. In order to accurately apply the attitude solution, the science magnetometer data had to be adjusted to match with

101 81 the time-base of the payload. A linear fit was found to be sufficient to adjust the time-base between the science magnetometer and the payload instruments, t sci = X cad (t sci t offset ) + X offset (3.28) where t offset was a large timing offset determined by inspection and X corresponds to the linear fit parameters. The total magnetic field strength measured by the ACS magnetometer was matched with the total magnetic field strength measured by the science magnetometer. The ACS and science magnetometer both observed a clear minimum in the total magnetic field strength that was used to determine the bulk timing offset, t offset. A grid search routine was used to determine a fine time shift between individual spin periods of the ACS and science magnetometer. This fine offset was determined over two second time intervals that corresponds to approximately two spin periods. To determine the fine offset, the time interval was advanced at two second increments over the duration of the flight. The resulting fine offset over, for the flight duration, was then linearly fit to produce the coefficients X cad and X offset, which were the time cadence rate and the fine resolution offset, respectively. This method produced a magnetic field timing to better than 5 ms over the course of the flight. A small angular correction was also accounted for between the gyroscope and the magnetometer axes. As shown in Figure (3.4), there was a slight misalignment between the magnetometer and gyroscope that results from the magnetometer placement in the payload. Even a small misalignment of a few degrees will put power into the coning and spinning components of the magnetic field. To account for this effect, an Euler angle rotation matrix was applied to the magnetometer component before applying the attitude solution, [B ENU ] = [A] XY Z ENU [M 3D(γ, α, β)] [B (t ) XY Z ] (3.29)

102 82 Small Angular Rotation G z B z G y B x G x B y Payload skin Gyro Axes Magnetometer Axes Figure 3.4: There was a slight misalignment between the gyroscope axes and the magnetometer axes. A small Euler rotation was applied to the magnetometer axes to properly align to the gyroscope axes to correct for the small angular difference. The angles that were used in the rotation were determined using a 2 grid search that minimized the power at the coning and spin frequencies. where M 3D is defined using the following rotations, M 3D = R Z (γ)r Y (α)r X (β) (3.30) where X, Y, and Z are the magnetometer axes that are rotated about. After the attitude solution was applied, the Fourier power was calculated at the spin and cone frequencies. A grid search over the angles α, β, and γ was used to determine the location where both the spin and coning power was at a minimum magnitude. The grid search found solutions to α, β, and γ with magnitudes less than 0.5. After applying the attitude solution, the magnetometer data were rotated from a

103 83 rocket-based coordinate system into a field-aligned coordinate system. This process involved three steps. First, the ENU magnetometer data were rotated into the XYZ geodetic coordinate system (GEO) using the following transformation, B X B Y B Z GEO sin(φ) sin(λ)cos(φ) cos(λ)cos(φ) = cos(φ) sin(λ)sin(φ) cos(λ)sin(φ) 0 cos(λ) sin(λ) B E B N B U (3.31) where λ is the latitude from the geodetic equator and φ is the geodetic longitude. Next, B GEO was converted to B MAG which is a geomagnetic coordinate system [Kivelson and Russell, 1995]. This step was accomplished through routines in the IDL Geopack software package. The rotation from GEO into MAG coordinates is both a translation and rotation about the origin of the coordinate system. A key check of the routine can be performed by considering that the magnetic field vector should be unchanged. However, the projection of the magnetic field vector onto these different coordinate systems will vary. The MAG coordinate system is rotated into a field-aligned (FA) coordinate system, defined as: zonal, meridional, and field-aligned. Schematically, the field-aligned coordinate system is shown in Figure (3.5) and was based on the system defined in Eriksson et al. [2005] [K.M. Sigsbee, private communication, 2012]. Following this convention, the field-aligned coordinate is ˆp, the meridional direction is ˆr, and the zonal component is ê. The zonal direction is defined as, ê = (ˆp R sc) ˆp R sc (3.32) where R sc is the spacecraft location along a magnetic field line and is defined as, R sc = Xˆx MAG + Y ŷ MAG + Zẑ MAG (3.33)

104 84 Field-Aligned(FA) Coordinates Rear View sc Earth Side View Figure 3.5: The field-aligned coordinate system that was defined by Eriksson et al. [2005]. The spacecraft is shown moving along a dipolar field line and the radial unit vector is defined to point outward at the equator. In the auroral zone, field-aligned unit vector will be downward, radial unit vector will be in the meridional (northward) direction, and the zonal unit vector will be in the eastward direction. In the case of Figure (3.5), the spacecraft appears to be moving along a dipolar field line. The meridional component is defined to be pointed radially outward at the magnetic equator [Eriksson et al., 2005], ˆr = ê ˆp (3.34) and completes the right-handed coordinate system. In the auroral zone, field-aligned unit vector (ˆp) will be downward, the radial unit vector will be in the meridional (northward) direction (ˆr), and the zonal unit vector (ê) will be nominally eastward directed. The full transformation from MAG coordinates into the field-aligned system is accomplished

105 85 through the relation, B e B r B p F AC ê X ê Y ê Z = ˆr X ˆr Y ˆr Z ˆp X ˆp Y ˆp Z B X B Y B Z MAG (3.35) where each component within the matrix corresponds to the projection of that vector into the field-aligned system. The final step is to subtract off the Earth s mean magnetic field to obtain the residual magnetic field components. Two methods were used to determine the residual magnetic field component. First, the payload magnetic fields were subtracted from a mean field model, which was the International Geomagnetic Reference Field (IGRF) model provided by NASA Wallops at altitudes traversed by the payload. The second method was simply to fit a third order polynomial of the magnetic field components over the length of the flight and subtracting off the polynomial fit to get the residuals. There was good agreement between both methods and the polynomial fit was used for the remaining data analysis ACES Low Magnetometer The gas leak in the attitude control system on the ACES Low payload made processing the magnetometer data more challenging than for ACES High. Having attempted to adjust the offsets, gains, and the small rotation, the contribution from both spin and coning persisted in the despun, residual magnetic field components. The total magnetic field also contained oscillations that resulted from the payload spin and the coning motion. Additional steps were performed on the ACES Low magnetometer data to reduce the contribution of spin and coning that remained in the magnetic field components after the attitude solution had been applied.

106 86 Two additional adjustments were applied. First, to reduce the power at the coning frequency, a grid search was performed that subtracted a sine wave from the residual magnetic field component at approximately the coning frequency, δb i = δb i Asin(ω c t φ) (3.36) where δb i corresponds to the magnetic field residual, and the grid search was performed by varying ω c and A, the coning frequency and the amplitude of the coning, respectively. There was no DC offset that was applied to this solution as it would negate the parameter of interest. The top panel in Figure (3.6) shows an example of this subtraction on the residual zonal magnetic field component in black and the coning component in red. The bottom panel in Figure (3.6) is the result after the subtraction of the residual magnetic field component, where it can be seen that the majority of the power at the coning frequency has been minimized. The magnetic field remaining after this correction was the DC component of the residual magnetic field that still included spin effects. The second step was to reduce the remaining power at the spin frequency using a Butterworth low-pass filter. The critical frequency of the filter was set so it was below the spin frequency, but was not at a low enough frequency that the filter affected the DC component of the magnetic field. 3.3 Field-Aligned Currents The residual magnetic field components were used to calculate field-aligned current and also used as a proxy for the perpendicular closure current. Ampere s law can be used to calculate currents from gradients observed in the residual magnetic field observations. There are two key assumptions that are applied to calculate currents. First, when determining the field-aligned currents there is an assumption is that the current resides in an infinitely long 2-D sheet in the zonal-altitudinal plane (and is thin in the meridional direction). Armstrong and Zmuda [1970] was one of the first studies to apply the sheet approximation to calculate field-aligned currents. This assumption is valid because of the

107 Coning Correction δb E (nt) δb E (nt) A sin(ω t) c Time after T-0 (sec) Figure 3.6: The top panel shows the residual magnetic field component in the zonal direction in black and the coning offset in red. The bottom panel shows the result after the coning correction has been subtracted off the time series data. There is still significant spin frequency modulation on the signal, but a Butterworth filter was used to the spin component further. large difference in length scales between the zonal and meridional components. An auroral arc may span a length of the order of s of km in the zonal direction, while being less than 10 km in the meridional direction. In this respect, the zonal direction is effectively infinitely long. The second key assumption that can be invoked is the Taylor hypothesis that transform temporal variations into spatial variations [Taylor, 1938]. In the case of a steadystate auroral arc, where the arc is not changing rapidly with time, provided the spacecraft traverses the arc rapidly in the meridional direction, the approximation that temporal gradients can be converted to spatial gradients is reasonable. This can be validated by examining the all sky imager data of an auroral event. A payload has a typical track velocity of 1 km/s, and if an arc remains stable for longer than the time required for the payload to cross, the Taylor hypothesis can be applied. The Taylor hypothesis will be invoked in the

108 88 calculation of Ampere s Law to convert, j = jˆp = 1 ( ) Bê Bˆr = 1 ( ) Bê µ o Xˆr Xê µ o Vˆr t Bˆr Vê t (3.37) j = jˆrˆr + jêê = 1 ( Bˆp B ) ê ˆr + 1 ( ) Bˆr Bˆp ê µ o Xê Xˆp µ o Xˆp Xˆr = 1 ( Bˆp µ o Vê t B ) ê ˆr + 1 ( ) Bˆr Vˆp t µ o Vˆp t Bˆp ê Vˆr t (3.38) where Vî is the payload track velocity in the î direction and t is the time cadence. There were two methods that were used to calculate the gradient in the magnetic field component. The first method took a running difference between two consecutive data points, B = B n+1 B n. Eventhough this method is quite simple, the value of these differences were often very sharp and required the application of filters to significant smoothing the results. An alternative method designed to reduce some of the sharp edges involved a linear fit that was used over a small time interval to fit over the track velocity and the gradient in the residual magnetic field component. A running linear regression fit was used to calculate the gradient in the residual magnetic field, B nj, B nj = X Bj t n + X Boff (3.39) where n corresponds to the number of points over a given time interval and X Bj = B j / t is the parameter from the linear regression fit for the j-th component of the residual magnetic field. For the velocity component, the fit was slightly different, V AV = X V t n + X V off (3.40) where V AV corresponds to the average velocity over the time interval, t n. Magnetic

109 89 gradients can be derived directly for the j-th component, B j x k = X Bj V kav t = B j V kav t (3.41) where j corresponds to the magnetic field direction and k to the velocity component. A final rotation was applied to the residual magnetic field components to avoid numerical divergences (dividing by a very small number) when calculating the gradients. The initial rotation into the FA coordinate system caused the zonal track velocity to be very small that resulted in erroneously large field aligned currents. Moreover, the rotation from ENU into FA coordinates is not a significant rotation. The magnetic inclination angle at Fort Yukon, Alaska, the apogee location of the payload was approximately 11, which is nearly vertical. It is not unreasonable for the currents derived in ENU to be similar in magnitude to the currents in a FA coordinate system. Using this method for calculating currents, very large field-aligned currents were deduced as a result of small payload velocities that were transformed into spatial gradients. A final rotation about the parallel magnetic field component was applied and the currents were recalculated. This type of rotation is justifiable because it is rotating about the parallel magnetic field component, while keeping the other components orthogonal, but changing their relative direction. Figure (3.7) illustrates the rotation used is a standard 2-D rotation, ˆr cos(θ) sin(θ) ˆr = ê sin(θ) cos(θ) ê (3.42) where the nominal value of θ was determined in a chi-by-eye means that would agree well with the ENU system. It was found that 17 agreed very well.

110 90 Field-Aligned Current Rotation Top View Side View Figure 3.7: An angular rotation applied to the field-aligned coordinate system in calculating the field aligned currents. This rotation was about the ˆp axis. This rotation was applied so the calculation of the field aligned current would not diverge. 3.4 Summary A detailed description of the instruments were used on ACES High and ACES Low to obtain electrodynamic and plasma parameters were presented. The principles behind a top hat style particle detector were discussed. Aspects of how the data was processed from the ACES payloads were also discussed. In particular a significant discussion is put forth regarding the processing of the fluxgate magnetometer on both payloads. How the data were processed will be especially useful in the data presentation and analysis in Chapter 4. One other point is made with regard to the magnetometer processing on ACES Low. It has been suggested that there may be some additional effects that were not initially considered during the processing of the magnetometer data [S.R. Bounds, private communication, 2012]. This effect has to do with how the principle moments of inertia of the payload significantly differ from the alignment of the sensor, suggesting that there may be

111 91 a parallel magnetic field component that does not subtract out in a usual way. It would be useful to reprocess the magnetometer data to include these additional effects; however, that remains outside of the scope of this dissertation. Thus the data that will be presented in the following chapters is considered to be the best data product at the current time.

112 92 CHAPTER 4 RESULTS AND ANALYSIS This chapter forms the heart of this dissertation, the presentation of data obtained from the ACES sounding rocket mission. The data sets that will be presented are of importances for understanding the electrodynamic structure of the auroral ionosphere. The launch conditions and flight anomalies will be discussed to place into context the quality of the data obtained during the flights. The results from this chapter have been presented at a variety of American Geophysical Union meetings, Geospace Environment Model (GEM) workshops, and a Chapman Conference held in Fairbanks, Alaska in The data presentation in this chapter follows very closely from the Chapman Conference paper Kaeppler et al. [2012]. 4.1 Flight Launch Conditions and Flight Performance ACES High and Low successfully launched from Poker Flat Research Range, Alaska on January 29, 2009 at 09:49:40.0 UT and 09:51:10.0 UT, respectively. The overall geomagnetic conditions preceding the launch were very quiet as a result of the launch window being near the solar minimum. The payloads were launched into a dynamic multiple-arc aurora located north of Ft. Yukon, Alaska, which was the approximate apogee location of both payloads. Figure (4.1) shows the ground based magnetometer time series data that indicated a 100 nt deflection in the H-component observed at Ft. Yukon, which suggested that the event was likely a substorm with an electrojet. These observations suggested that a large-scale current system was present. The launch time of both payloads was approximately 2300 MLT which was in the evening-midnight MLT sector. The Altitude Adjusted Corrected Geomagnetic Model (AACGM) [Baker and Wing,

113 Fort Yukon Ground Magnetometer on 29 Jan 2009 nt nt nt H-Component D-Component Z-Component 08:00 08:30 09:00 09:30 10:00 10:30 11:00 11:30 12: ACES High/Low T-0 Figure 4.1: This is the time series data showing the ground-based magnetometer observations from Fort Yukon, Alaska. The H-component of the magnetometer is associated with the electrojet current systems. Large gradients in the H-component correspond to large-scale currents. 500 nt 500 nt 500 nt 1989] was used to produce the magnetic mapping presented in Figure (4.2) that shows the times when the payloads crossed conjugate magnetic field lines that map down to ionospheric footpoints at an altitude of 110 km. This magnetic field mapping between ACES High and ACES Low formed the means by which to compare observations between both payloads. ACES High reached an apogee of 360 km, and ACES Low attained an apogee of 130 km. The maximum longitudinal separation that mapped down to footpoints at 110 km between both payloads was 23 km at the end of the ACES Low flight. The mission was successful, although a few issues arose that affected the data gathered on each payload. The ACES High payload had good attitude control system performance and coned with a half angle of 3. However, due to a gas valve leak in the attitude control system, ACES Low coned at a much larger half angle of 13. The EEPAA on ACES High had a failure in the energy sweep electronics, that truncated the full sweep range to energies less than 500 ev rather than the planned 16 kev.

114 ACES High and Low Trajectory B-Field lines mapped to 110 km 9:54:13 9:55:40 Altitude(km) :51:58 9:53:00 9:57: :51:05 9:52:22 9:53:10 9:54:04 9:55:04 9:56: o Geographic Latitude( ) Figure 4.2: ACES High and Low trajectories plotted as functions of altitude and geographic latitude. Dashed lines are magnetic field lines mapped to footpoints at 110 km. The times in the figure indicate when both payloads crossed the same magnetic field footpoint, respectively. 4.2 All-Sky data and Conjugate Data The top row in Figure (4.3) are the spectrograms of the electron differential energy flux, with the x-axis being time, the y-axis is energy, and the z-axis is the flux intensity in color. The two middle rows in Figure (4.3) are the zonal (east-west) and meridional (north-south) DC electric fields after being transformed into a geomagnetic field-aligned coordinate system. The final three rows in Figure (4.3) present the residual DC magnetic field components in geomagnetic field-aligned coordinates after a third-order polynomial fit was applied to remove the Earth s mean magnetic field. The entire ACES Low data interval, in the right side of the Figure (4.3), is represented by the black line in the margin of the ACES High data, and this interval represents the conjugate magnetic field lines that

115 95 were eventually traversed by ACES Low. There was approximately 1 minute of conjugate data coverage between both payloads. Figure (4.4) presents a montage of six all-sky images, from the Fort Yukon all-sky imager, depicting the auroral evolution during the flights. These images show the magnetic footpoints of ACES High and ACES Low, especially during the time frame of conjugate data coverage between the payloads Electron Flux The spectrograms of the electron differential energy flux shown in the top panel of Figure (4.3) for both ACES High and Low cover the pitch angle range of This pitch angle range was selected because it was nearly field-aligned, while remaining relatively immune to pitch angle coverage gaps caused by payload coning motion. Although the full energy range was not observed on ACES High, the electron flux is ideal for an analysis focused on low energy precipitating auroral electrons. The data from the all-sky imager have been compared with the electron flux to gain insight into the auroral event ACES High traversed. ACES High had three auroral crossings over the course of the flight. As shown in Figure (4.4A), the payload entered a relatively stable auroral arc at 09:53:20 UT and exited the visible region at approximately 09:54:00 UT (hereafter, this event will be referred as the quasi-static arc ). There was a modest increase in the electron flux at approximately 09:53:20 UT which correlates well with the entry of the payload into the quasi-static arc. At 09:54:00 UT there was a depletion of low energy electron flux that correlates well with the time at which the payload entered the dark region adjacent to the poleward edge of the quasi-static arc, as shown in Figure (4.4B). At approximately 09:54:15 UT, ACES High passed over a faint rayed arc in the all-sky imager, as shown in Figure (4.4C), and a time-dispersed electron signature was observed in the electron flux.

116 300. ev mv m-1 E-W DC E-Field FA ΔB-Field ACES Low Data 09:55: km 09:56: km 10 N-S DC E-Field 100. N-S ΔB-Field E-W ΔB-Field :54: km FA ΔB-Field 09:55: km ACES Low(21.139): Electron Flux E-W DC E-Field :57:00 UT: 295 km Alt: Up South Down West North East West East South North :55: km Up South Down West North East West East South North Figure 4.3: Left Column: ACES High Data; Right Column: ACES Low Data. Row 1: Electron Differential Energy Flux; Row 2-3: DC Electric Field Data; Row 4-6: Residual Magnetic Field Components. The electric field and residual magnetic field contain dashed lines at zero and the positive direction represented eastward (zonal), northward (meridional), and field-aligned, respectively. Gray bands are regions where data are not available. The black line in the ACES Low differential electron energy flux represents the maximum energy observed by ACES High of 500 ev. UT: 09:53:00 Alt: 308 km 09:54: km E-W ΔB-Field N-S ΔB-Field N-S DC E-Field ACES High(36.242): Electron Flux mv m-1 nt mv m-1 ev mv m-1-1 nt -1 nt -1 nt 2 ev cm ster s ev nt ev cm2 ster-1 s-1 ev-1 nt

117 Figure 4.4: The images from the Fort Yukon all-sky imager showing the evolution of the auroral event on January 29, The footpoints for ACES High and Low after being mapped to 110 km are represented by a red square and blue dot, respectively 97

118 98 The all-sky imager data in Figure (4.4D) indicate that ACES High skirted the westward edge of a large region of dynamic westward-moving aurora (hereafter, referred to as the westward-moving aurora). The electron data showed that there were moderate levels of low energy precipitation in this region along with embedded regions of more intense electron flux and isolated time-dispersed electron precipitation. By 09:55:15 UT ACES High had passed by the bulk of the westward-moving aurora and moved into a region that was devoid of visible aurora as shown in Figure (4.4E). Within this region, there were reduced levels of electron precipitation. At 09:56:15 UT the all-sky imager in Figure (4.4F) showed that ACES High encountered the final auroral crossing, into a very active poleward arc. After the payload passed through the region of reduced flux, intense time-dispersed electron precipitation was observed that correlate well with the active poleward arc. The electron flux for ACES Low indicated that the payload traversed two inverted- Vs that were located on magnetic field flux tubes that were similar to flux tubes previously crossed by ACES High. As shown in Figure (4.4B), ACES Low entered the quasi-static arc at 09:54:00 UT, 40 seconds after ACES High had previously passed through the same region. Figure (4.4C) shows that the visible arc remained relatively spatially stable. However, the arc began to fade in intensity after the ACES Low payload completed its passage through the arc, exiting at 09:54:25 UT. The correlation between the electron data observed by ACES Low and the all-sky images suggest that the quasi-static arc produced an inverted-v with a peak energy of 4 KeV. At 09:54:40 UT ACES Low began to enter the western edge of the westward-moving auroral form that ACES High had previously skirted, as shown by Figure (4.4D). ACES Low moved more centrally through the dynamic westward-moving region, as illustrated by Figure (4.4E). An inverted-v was observed in the electron flux with a similar peak energy of 4 kev that corresponded to the westwardmoving region.

119 DC Electric Fields The DC electric fields observed on ACES High and Low were generally southwesterly. For the midnight MLT sector, into which the payloads were launched, the electric fields observations on ACES High and Low were consistent with electric fields formed as the result of plasma convection around the Earth [Baumjohann, 1982]. Until 09:55:45 UT, ACES High observed DC electric field components that showed low levels of variation, although the meridional component exhibited more variability than the zonal component. After 09:55:45 UT, as the payload entered the region with multiple time-dispersed electron events associated with the poleward arc, the zonal and meridional electric field components reversed direction to more eastward and northward, respectively. Electric and magnetic field perturbations correlate with the time-dispersed arrival of electrons throughout the flight, especially at 09:54:15 UT and after 09:55:45 UT. These observations will be discussed further in Section (4.2.4). The DC electric fields on the ACES Low payload showed low levels of variation over the duration of the flight. The westward directed electric field exhibited a maximum variation of 15 mv m 1 ; whereas, the southward directed field had a maximum variation of 20 mv m 1. The oscillations at the beginning of the data, in both components of the electric field, were an artifact of the payload attitude solution. The total perpendicular electric field magnitude observed on ACES Low was typically half the magnitude of the total perpendicular electric field observed on ACES High Magnetic Fields The bottom three panels in Figure (4.3) present the residual magnetic field components for both ACES High and Low. On ACES High, before 09:56:00 UT, variations in the zonal and meridional residual magnetic field components suggest that field-aligned sheet currents were present. The most notable signature of field-aligned current occurred

120 100 at 09:56:00 UT, in which there was a 75 nt reversal from north to south in the meridional component; while simultaneously, there was a 100 nt reversal from west to east in the zonal magnetic field component. A dearth of precipitating electron flux was observed at the location of this magnetic reversal, which suggested a possible downward current region. As described in Section ( ), the ACES Low magnetometer required significant filtering to reduce the remaining effects of payload spin and cone in the residual magnetic field components. Gradients in the zonal and meridional residual magnetic field components correlate with a reduction in the electron flux at approximately 09:54:30 UT. This magnetic field gradient, combined with a lack of visible aurora in Figure (4.4D), and a reduction in the electron flux suggests that downward field-aligned current was present. Shortly thereafter, at 09:54:45 UT, gradients in the zonal and meridional residual magnetic field component correlate with precipitating electrons associated with the large westwardmoving auroral region. Even at lower altitudes, some component of field-aligned current may be penetrating down to the altitudes of ACES Low. One of the other notable differences between ACES High and Low resides in the magnitude of the residual field-aligned magnetic field component. From Ampére s Law, gradients in the residual zonal and meridional magnetic field components would only contribute to field-aligned currents. However, if cross field currents flow, large gradients in the residual field-aligned component would be present. This can be seen in equation (3.38) in which it is clear that the perpendicular current depends on gradients in the residual field-aligned component (ˆp), j 1 ( ) Bˆp ˆr 1 ( ) Bˆp ê (4.1) µ o Vê t µ o Vˆr t The maximum magnetic variation observed in the residual field-aligned component on ACES High was 25 nt; however, on ACES Low the maximum variation is approximately 145 nt. Moreover, the gradients observed in the residual field-aligned magnetic component

121 mv m mv m nt nt Energy(eV) Time(UT) ACES High (36.242) Differential Energy Flux Residual B-field Zonal Residual B-field Meridional E-field Zonal E-field Meridional 09:56:25 09:56:30 09:56:35 09:56:40 09:56: ev cm s ster ev 150 nt 150 nt Figure 4.5: An example of electron acceleration by Alfvén waves. The top panel is the differential energy flux observed by ACES High. It is clear that there is time-dispersion in the electron flux with high energy electrons arriving first, followed by low energy electrons. The middle panels are the residual magnetic field components showing perturbations in the magnetic field that correlate with the time-dispersed electrons. The final two panels show the electric field components with modulations in the electric field that correlate with the time-dispersed electrons. on ACES Low aligned well with the payload entering and exiting regions of precipitating auroral electrons. At 09:54:20 UT, as ACES Low exited the first arc, the residual fieldaligned component had a large gradient from negative to positive. Shortly thereafter, the residual field-aligned component reversed from large positive to negative values as the payload enters into the westward-moving auroral region. The larger magnitude gradients observed in the residual field-aligned component on ACES Low suggest the presence of closure current Alfvén Wave Signatures ACES High observed many time-dispersed electron events throughout the duration of the flight which result from electron acceleration by Alfvén waves. An example of the time-dispersed signatures associated with the poleward arc crossing is shown in Figure

122 102 (4.5) of the differential energy flux, the residual magnetic field components, and the electric field components. It can be clearly seen that there is time-dispersion in the electron flux in which higher energy electron flux arrives first, followed by intense lower energy flux. These time dispersed signatures line up well with perturbations in the residual magnetic fields (middle panels) and modulations in the electric field components (bottom panel). These time-dispersed electron events are similar in nature to the results of Kletzing and Hu [2001] who showed through simulation that electrons accelerated by Alfvén waves produce a time-dispersed signature. Chen et al. [2005] also showed through simulation that time-dispersed electrons can occur simultaneously with inverted-v precipitating electrons, which was more consistent with the observations made by the ACES payloads. The perturbations in the electric field and the residual magnetic field components further support the presence of Alfvén waves. To determine whether the Alfvén wave is propagating, the electromagnetic wave impedance µ 0 (δe/δb) was compared to the Alfvén impedance, µ 0 V A [Knudsen et al., 1992]. At altitudes of approximately 300 km O + was the dominant ion [Kelley, 2009], which was used in the calculation of the Alfvén speed. The ratio of δe/δb was found to be within a factor of two of the Alfvén speed for the event at 09:54:15 UT and later events after 09:56:00 UT. All of these observations strongly suggest that ACES High traversed multiple regions of aurora with associated Alfvén waves Currents As discussed in Section (3.3), field-aligned currents were calculated using a sheet approximation and gradients in the residual magnetic field components observed on ACES High. Figure (4.6) illustrates the result of this calculation, in which the differential electron flux and the DC electric fields are plotted with the field-aligned current for comparison. The current data presented has been smoothed to elucidate the large-scale features. ACES High observed modest regions of upward field-aligned current, indicative of precipitating electrons, that were mapped to inverted-v aurora as determined by ACES Low data and

123 103 the regions of visible aurora from the all-sky imagers. The most notable region is the quasi-static arc, with an extended region of low magnitude upward field aligned current is also associated with the westward-moving aurora, which ACES High skirted. A lack of narrow precipitating electron flux correlates well with regions of downward field-aligned current, which is consistent with upward moving electrons [Marklund et al., 1994, 1997; Elphic et al., 1998]. Moreover, the regions of downward field aligned current were narrow and intense, compared to the more spatially extended upward field aligned currents; these results were consistent with FAST observations [Elphic et al., 1998]. The region poleward of the quasi-static arc and the region poleward of the westward-moving aurora both have downward currents along with a reduction of electron flux. 4.3 Analysis Ionospheric Collisionality and Conductivity The lack of structure in the low energy electron flux was one of the most notable differences between observations made on ACES High versus ACES Low. Two explanations can account for these differences. First, the auroral configuration evolved during the time interval when ACES High first traversed a given region to the time when ACES Low passed through the same region. While the first auroral arc was quasi-static over the traversal time of both payloads, the larger westward-moving auroral region dynamically evolved over short time scales. This time variation could explain the difference in the observed signatures of the low energy electron between ACES High and ACES Low. The second explanation is that precipitating electrons colliding with atmospheric neutrals were significant at ACES Low altitudes. To determine the effect of ionospheric collisionality, the stopping altitude was determined, which is the altitude at which precipitating electrons have experienced enough scattering interactions to become indistinguishable from the background electron population. A procedure was used similar to that

124 ACES High Data ev eV cm ster s ev 10 East DC E-Field: Zonal 0-50 mv m West North DC E-Field: Meridional mv m South Up Field-Aligned Current ua m Down :56: km 09:55: km 09:54: km 09:53: km UT Altitude ACES Low Coverage Figure 4.6: Results from the calculation of field-aligned current using Ampére s Law. The top panel is the differential electron energy flux and the middle panels correspond to the zonal and meridional electric fields, respectively. The bottom panel illustrates the field aligned current configuration with upward and downward field-aligned currents represented as positive and negative, respectively. It can be clearly seen that intense and narrow downward field-aligned current regions correspond to a depletion of precipitating auroral electrons. The upward field-aligned current corresponds to regions of visible aurora and precipitating electrons.

125 Stopping Altitude Altitude (km) ACES Low Apogee Altitude 500 ev - Max Energy ACES High kev - Peak Energy ACES Low Beam Energy (kev) Figure 4.7: The results from the stopping altitude calculation which show that precipitating electrons at 500 ev are scattered and become indistinguishable at about 170 km from background ionospheric electrons. The ACES Low apogee is located at approximately 130 km, as indicated by the red horizontal line. described in Kivelson and Russell [1995] section 7.2.2, in which the following equation was solved iteratively to determine the stopping altitude, z s, R(E) = η(z s) ρ(z)dz (4.2) where R(E) is the range energy function defined in equation (5.13) in the Section (5.3) of this dissertation. The Mass Spectrometer Incoherent Scatter (MSIS) model [Hedin, 1991] was used to obtain the values of ρ(z), the total ionospheric mass density as a function of altitude (See Section (5.3) for a more in depth discussion of the MSIS model). Figure (4.7) presents the energy of peak ionization for the precipitating electrons versus altitude. As can be seen, it was determined from this calculation that electrons at 500 ev were typically scattered and became indistinguishable from the background plasma at approximately 170

126 106 km. This is 40 km above the apogee of ACES Low, which suggests that collisions are significant enough to diminish structure in the precipitating low energy electron flux. The low level of electric field variation observed on ACES Low is likely due to the inverse relationship between the electric field and ionospheric conductivity. As the conductivity in the ionosphere increases, it becomes significant enough to effectively short the electric fields in the lower ionosphere. The consequences of ionospheric conductivity are that the magnitude of the electric field is reduced and it effectively eliminates electric field structure at lower altitudes. An estimate was performed to understand the electric field observations from ACES Low by considering the ionosphere as a uniformly conductive slab ranging in altitude from km. From classical electrodynamics, the skin depth of a conducting slab is δ = 2/(ωµ 0 σ p ) [Jackson, 1998], where σ p is the Pedersen conductivity and the frequency was chosen to be 1 Hz. Using the magnitude difference between the observed electric fields from both payloads over both arc crossings, along with the altitude of ACES Low relative to the top side of the slab, the value for the Pedersen conductance (Σ p ) was determined. The height-integrated Pedersen conductivities were further calculated and found to be 2.9 mho for the quasi-static arc and 6.0 mho for the westward-moving aurora. These values are in good agreement with typical average values of 10 mho from Kelley [1989] and 5 mho using empirical relations from Robinson et al. [1987] Electric and Magnetic Fields in 2-D Arc Model The orientation of the observed fields within an auroral arc are important for making inferences regarding arc electrodynamics. A comparison between the electric and magnetic field data from the ACES payloads were compared with the 2-D arc model (see Section 2.5 for a summary of the 2-D arc). There were two basic questions that were investigated. First, does there exist a consistent direction of variation that is observed in both the electric and magnetic fields? This condition may not necessarily be fulfilled in

127 107 North Arc Boundary Arc norm B norm West East Arc Boundary E tan Arc tan E norm B tan South Figure 4.8: This diagram presents the results from the comparison between the data and the 2-D arc model. As shown in black, the orientation of the arc was determined using data from the all-sky imager. The tangential line was determined at the location where the payload entered the auroral arc. The results for the electric field and the residual magnetic field are shown in blue and red, respectively. The normal residual magnetic field component and the tangential electric field component were both independently minimized using the grid search. the data. Second, if there is a consistent direction, how well does the direction align with arc orientation and fit to the theory? A minimum variance technique [Sonnerup and Cahill, 1967] was used to determine how the orientation of the electric and magnetic fields compared with the 2-D arc model. The orientation of the normal and tangential components of the auroral arc were determined where the payload entered the arc based on data from the all sky images. The tangential component of the arc the all-sky images was done using a chi-by-eye analysis. An angular rotation was applied to the electric and magnetic field components to combine the rocket-based geophysical observations into an arc-based frame. As a check,

128 108 Quasi Stable Arc: Residual E Quasi Stable Arc: Residual B 10 mv/m nt 67.0 o Magnetic Latitude ( ) Auroral Arc o Magnetic Latitude ( ) Auroral Arc o Magnetic Longitude ( ) o Magnetic Longitude ( ) Figure 4.9: Left: The electric field vectors, after having the convective flow removed, as ACES High traversed the quasi-static arc. The vectors are consistent with what would be expected for a U-shaped potential drop mapped down from high altitudes. Right: The residual magnetic field as ACES High traversed the quasi-static region. The field pattern is consistent with what would be expected for an upward field-aligned current. a grid search was performed to find the angles that minimized the tangential electric field and the normal residual magnetic field, respectively. The angular rotation used was, ˆT arc ˆN arc sin(θ) cos(θ) Ẑ = cos(θ) sin(θ) ˆM (4.3) where Ẑ and ˆM corresponds to the zonal and meridional electric (magnetic) field component, respectively. The tangential and normal components within the arc frame of reference are denoted as ˆT and ˆN in equation (4.3), respectively. The chi-squared grid search used was of a similar form to equation 5 in Sonnerup and Cahill [1967], as shown to minimize tangential electric field component, χ 2 = (E T ĒT ) 2 (4.4)

129 109 and a similar form holds for the normal magnetic field component. ĒT is the mean value of the tangential electric field (or normal magnetic field) over the time interval that was selected. For the electric field component, the mean value corresponds to the electric field generated by plasma convection, which in the magnetic local time sector at the time of launch was south and westwardly Baumjohann [1982]. Figure (4.8) shows the results from the grid search that independently minimized the tangential electric field and the normal residual magnetic field. The directions of maximum variance are thickened to make it clearer to the reader. As it can be seen, there is good agreement between the normal direction of the arc and the normal direction of the residual magnetic field component. This result suggests that the current sheet and the arc were aligned closely. The results from the minimum variance procedure that were carried out on the fields of the quasi-static arc on ACES High. The results shown in Figure (4.9) are the components that exhibited maximum variation, the meridional electric field and the tangential residual magnetic field. The green region represents the arc location and orientation on a geomagnetic longitude and latitude grid. As seen in Figure (4.9), the residual magnetic fields have a significant tangential component that is well aligned to the arc, which is in good agreement with the 2-D model. This component points in the eastward direction on the equatorward side of the arc and westward on the poleward side of the arc, which is consistent with an upward directed field-aligned current that was observed in this region. The results for the residual electric field, are also shown in Figure (4.9). The electric fields are not as well aligned with the arc, but the fields do have a converging sense pointing toward the center of the arc. This electric field signature is consistent with electric fields associated with inverted-v type aurora [Marklund, 1984]. It worth noting that the all-sky imager observed some vorticity in arc that was occurring coincidently to the passage of ACES High through the quasi-static arc. In addition, the all sky imager observed some expansion of the arc width, which could be the result of E B plasma motion. These two

130 110 mechanisms could have affected the electric fields that mapped from the magnetosphere and explain the lack of alignment with the arc model of [Boström, 1964]. This analysis was also attempted on the westward-moving auroral region for ACES High and both of the auroral crossings on ACES Low. For both ACES High and ACES Low, the westward-moving auroral region dynamically evolved rapidly and the payloads appeared to have crossed different regions of the auroral event. The lack of a quasi-stable situation make application of the 2-D arc model difficult, at best. Unfortunately, there was no electric field data from ACES Low for a large portion of the quasi-stable arc crossing. This was caused by a gas leak in the attitude control system which disturbed the background plasma environment to such a level that the electric fields could not be determined. 4.4 Summary Results have been presented of from the all sky imagers and ground based magnetometers showing the evolution of the auroral event that ACES traversed. Conjugate data have been presented from both the ACES High and ACES Low spacecraft. The key data sets were the electron differential energy flux, the electric fields, and the residual magnetic field observations. Field aligned currents were derived for the ACES High payload from the residual magnetic field observations and these observations were found to be consistent with upward and downward directed field aligned currents. Inferences were made regarding the field aligned residual magnetic field component with respect a closure current over the auroral arc. Analysis was presented of the increased conductivity and ionospheric collisionality based on the precipitating electrons. Finally, the electric fields and residual magnetic fields were compared against the structure of a 2-D auroral arc. Good agreement was found between the model arc and the residual magnetic field measurements; although, the electric field measurements observed structure consistent with inverted V aurora, the fields appeared to be rotated relative to the arc.

131 111 CHAPTER 5 MODELING ACES Low acquired in situ magnetic field measurements that are consistent with the closure current; however, from these observations it is difficult to deduce the direction and the geometry of the closure current directly from the measurements. First, an ambiguity exists in which both meridional or zonal currents could cause gradients in the residual field-aligned component. Additionally, a crucial parameter is the direction of the currents relative to the DC electric field vector, that defines the direction of the Hall and Pedersen currents. Therefore, a prerequisite for any study of current closure must be knowledge of the electric field vector relative to the direction of the cross field current. Second, there is an ambiguity of the payload location within the closure current itself, which is unknown based on these observations. Even for a simple geometry, payload crossings at different locations in the closure current region could produce similar magnetic field signatures. With these considerations in mind, a simple model has been under development to interpret the magnetometer observations made by the ACES Low payload. This chapter will focus on the development of this model. 5.1 The Mallinckrodt Model As reviewed in Chapter 2, there have been few models that have described auroral electrodynamics within the lower region of the auroral ionosphere. The 2-D arc model by Boström [1964] was one of the first models to consider the competition between electric fields, ionospheric currents, and particle precipitation at altitude within the auroral ionosphere. The model by Mallinckrodt [1985] (hereafter referred to as the Mallinckrodt model ) presented numerical solutions that applied the work of Boström [1964] for various boundary conditions, including polarization and field aligned current type arcs. The Mallinckrodt model will be the primary model used to interpret data obtained by the

132 112 ACES payloads. There are a few key factors that make this model most appropriate for understanding auroral electrodynamics and the closure current. Most significantly, the Mallinckrodt model focuses on Hall and Pedersen current components within the auroral ionosphere. Other models of the auroral ionosphere [Doe et al., 1995; Karlsson and Marklund, 1998; Zettergren and Semeter, 2012] examine how downward field-aligned current can cause an evacuation of ionospheric electrons. One key advantage of the Mallinckrodt model is the inclusion of the Hall current as a potential closure current, which is neglected in the aforementioned models. The Mallinckrodt model includes other effects, such as, the contribution from neutral winds. The Mallinckrodt model uses a variety of assumptions that may impose limitations. The most significant assumption is that the model is a steady-state solution. For a stable, undisturbed arc this assumption is most valid. However, in the case of a dynamic arc or auroral substorm where there is rapid temporal evolution of the arc system, the validity of this assumption becomes questionable. The second crucial assumption was to exclude ionospheric feedback into the magnetosphere. One example of ionospheric feedback is the population of O + ions observed in the magnetosphere [Lotko, 2007]. The existence of these ions is highly suggestive of the ionosphere as the source. The assumption neglecting the ionospheric feedback into the magnetosphere is a simplifying assumption that elucidates the magnetospheric driving forces onto the ionosphere. The remaining assumptions used in the Mallinckrodt model were made for simplicity. First, the altitude range of km was considered in the model and nighttime conditions were considered. Given that the peak of the Hall and Pedersen conductivities and currents are below 150 km within the E-region of the ionosphere, this altitude range is appropriate. Second, the zonal (longitudinal) extent of the aurora was considered to be infinitely long; therefore, spatial gradients in the zonal direction are negligible. This

133 113 assumption effectively reduces the dimensionality from 3-D down to 2-D, that makes the problem more tractable. Mallinckrodt s model was a 2-D solution on a latitude and altitude grid. The magnetic field lines are considered to be equipotential contours, which allow fields to be mapped down to the topside of the ionosphere. At lower ionospheric altitudes, the electric field configuration will be dominated by Ohm s law, rather than fields being frozen-in to field lines. Mallinckrodt [1985] outlined five steps that were used to generate the current configuration in the auroral ionosphere. These five steps will be briefly outlined and the first four of these steps comprise the majority of the work that has been done up to this point. 1. Calculate the total electron flux distribution into the ionosphere that was used to determine the height-ionization profile and the input field-aligned current. The electron distribution included the low energy electron distribution of ionospheric origin, including secondary electrons and degraded primary electrons, which are electrons that have lost energy through collisions with ionospheric neutrals. 2. Calculate the height-ionization profile from the input flux distribution incident to the ionosphere. 3. Calculate the equilibrium electron number density by solving the continuity equation, [n e (z)u (x, z)] = S L (5.1) where the ionization source, S, is caused by precipitating electrons and recombination was the loss mechanism, L. The perpendicular convection of the ionization region, U, was also included and expressions by Kato [1963] were used to evaluate the motion of the ionization region. 4. The electron number density was then used to determine the height dependent Hall and Pedersen conductivities. These conductivities were integrated over an altitude

134 114 range to obtain the Hall and Pedersen conductances (or height-integrated conductivity). 5. The boundary condition electric fields and field-aligned currents were prescribed onto the simulated region and Ohm s law was solved to obtain the current structure within the auroral ionosphere on the 2-D grid. The work for this dissertation uses this framework and steps 1-4 will be discussed in further detail below. Step 5, that involves solving Ohm s law, is not part of this dissertation. The key results from the model of the current configuration are shown in Figures 4, 7, 9, and 11 of Mallinckrodt [1985]. Mallinckrodt [1985] relied heavily upon two other papers in performing his calculations. The model by Evans [1974] describing the evolution of an electron beam and the ionospheric response was used in the description of the electron beam. Evans et al. [1977] provided the background for the calculation of the electron density and calculation of the Hall and Pedersen conductivities similar to steps The Calculation of Electron Flux A model similar to Evans [1974] has been used to simulate the evolution of precipitating electrons from the magnetosphere into the ionosphere. There are two contributions to the total electron flux: primary electrons that have been accelerated by a parallel electric field to kev energies and electrons of ionospheric origin. The low energy ionospheric electrons will populate energies below the peak energy, that is, the magnitude of the parallel electrostatic potential drop Primary Electron Beam Kletzing et al. [2003] has shown that the plasmasheet in the magnetotail maps to the high latitude auroral zone and is the source region of auroral electrons. In the model, the

135 115 Phase Space Mapping Magnetosphere Ionosphere Figure 5.1: A schematic diagram of the velocity and distribution space mapping is presented. The velocities are gridded at the ionosphere and mapped up to the magnetosphere where the distribution function is well defined. By Liouville s theorem the distribution function can be mapped in phase space from the magnetosphere to the ionosphere. precipitating plasmasheet electrons are assumed to be described by a Maxwellian distribution, f ( v, v ) = n ( m 2πE o ) 3/2 exp ( m(v 2 + v 2 ) ) 2E o (5.2) where E o is the characteristic temperature in ev, n is the plasmasheet number density, and the distribution function has units of s 3 cm 6 [Baumjohann and Treumann, 1996]. The assumption that the plasmasheet distribution is a Maxwellian is an assumption out of simplicity, as it has been shown by Kletzing et al. [2003] that the plasmasheet is better fit by a κ distribution. Although, a Maxwellian distribution is the limiting case when the parameter κ, in the κ-distribution. Liouville s theorem enables mapping between different regions in phase space provided that collisional effects are negligible. Between the magnetosphere and the topside ionosphere boundary, the plasma tied to the field lines is collisionless. The motivation for velocity mapping from the magnetosphere down to the

136 116 ionosphere is because the distribution function is well-defined (Maxwellian) in the magnetosphere. The mapping technique used is schematically described in Figure (5.1). The velocity components at the magnetosphere can be connected to the ionospheric velocity components through the equations that conserve energy and the first adiabatic invariant, ( v M = v I 2 2V ( o ) ) v I 2 m e β (5.3) v M = v I β (5.4) where V o is the magnitude of the electrostatic potential corresponding to the parallel electric field and in units of ev. β = B I /B M is the ratio of the magnetic field strength at the topside ionosphere to the field strength at the location of the parallel electric field. As shown in Figure (5.1), Liouville s theorem can then be used to directly map the welldefined magnetospheric distribution function to the ionospheric distribution function, f ( v M, v M ) = f ( v I, v I ) (5.5) This mapping technique was applied to the evolution of the electron distribution function from the magnetosphere, through the parallel electric field down to the ionosphere. The left-hand side of Figure (5.2) is a schematic diagram detailing this process. As shown in Chapter 3, the differential number flux is related to the electron distribution function, J (E, α) = 2E f ( ) v m 2, v e where α is the pitch angle and has units of cm 2 s 1 ster 1 ev 1 (5.6) [Baumjohann and Treumann, 1996]. The right hand side of Figure (5.2) shows the evolution of the differential number flux as the electrons are accelerated by the electrostatic potential toward the ionosphere. Panel A of Figure (5.2) shows the differential number flux for a distribution that is consistent with a precipitating Maxwellian plasmasheet source population in the

137 117 Earth B-field 0 9 1x Directional Flux (J[ # cm s ster ev ]) Plasmasheet Electrons V (cm/s) 9 2x10 9 3x10 9 4x10 9 5x10-6x10 A9 9-4x10 9-2x10 0 V (cm/s) 9 2x10-3 n o = 1.5 cm T e = 800 ev V = 0 V β = 1 9 4x10 9 6x10 V o Accelerated Electrons B A V (cm/s) 0 9 1x10 9 2x10 Ionospheric Electrons 9 3x10 V 9 4x10 B o 9 5x x10-4x Directional Flux (J[ # cm s ster ev ]) 9-2x10 0 V (cm/s) 9 2x10-3 n o = 1.5 cm T e = 800 ev V = 2000 V β = 1 9 4x Directional Flux (J[ # cm s ster ev ]) 9 6x10 Accelerated & Mirror force Electrons BI Ionosphere β= B I /B A V (cm/s) 9 1x10 9 2x10 9 3x10 V o 9 4x10 9 5x10 C9 9-6x10-4x10 9-2x10 0 V (cm/s) 9 2x10-3 n o = 1.5 cm T e = 800 ev V = 2000 V β = 2 9 4x10 9 6x10 Figure 5.2: A schematic diagram of the evolution of a precipitating electron beam from Evans [1974]. The left-hand side is a schematic diagram showing the precipitating magnetospheric electrons that are accelerated by the parallel electric field. The mirror force then interacts with the velocity distribution, transferring parallel velocity to perpendicular velocity as the particles move toward the ionosphere. The right-hand side of the figure shows the evolution of the electron beam in velocity space. A discussion is given in the text of each panel on the right-hand side. downward direction. Panel B shows the effect of accelerating electrons by the parallel electric field; the electron flux has gained energy in the parallel velocity component equal to the magnitude of the parallel electric field, that is, the peak energy. There is a region devoid of electron flux at energies less than the peak energy. Conservation of the first adiabatic invariant causes an increase in the perpendicular velocity components and a decrease in the parallel velocity component, to conserve energy, as the strength of the magnetic field increases toward the ionosphere. This effect is shown in Panel C and causes the distribution function to form a banana shape in velocity space.

138 118 To calculate the height-ionization profiles, the distribution function must be integrated at the ionosphere to obtain the number flux. There are two number fluxes of interest: the parallel number flux (Φ ) and the omni-directional number flux (Φ). The parallel number flux corresponds to the number flux that passes through a sheet [Reif, 1965], and the omni-directional number flux corresponds to the number flux passing through a unit sphere. The total parallel flux, composed of the precipitating plasmasheet electrons and the low-energy ionospheric electrons, will be used to calculate the height-ionization. The omni-directional number flux was used to determine the low-energy electron flux of ionospheric origin. The total number flux can be represented as, Φ = dω v 3 f ( v, v ) dv = dω j (E, α) de (5.7) where Φ is the total omni-directional number flux in units of cm 2 s 1, Ω is the solid angle, and α is the pitch angle. The differential number flux is represented as j (E, α) in equation (5.7) with units of cm 2 s 1 ster 1 ev 1. The differential omni-directional number flux is, Φ(E) = j (E, α) dω (5.8) with units of cm 2 s 1 ev 1. The parallel differential number flux through the unit sheet includes a directional cosine, that accounts for the velocity component normal to the sheet, Φ (E) = cos(θ)j (E, α) dω = j (E) πsin 2 (α max ) (5.9) where α max corresponds to the maximum pitch angle of the beam and the flux has units of cm 2 s 1 ster 1 ev 1. The integration routines were verified analytically above the parallel electric field in velocity space (cylindrical coordinate space) and energy/pitch angle space (spherical coordinate space). Evans [1974] provided parallel number fluxes and energy fluxes that were also used to validate the numerical integration routines, which are the same values used in Figure (5.2). To summarize, the primary electron beam using the model by Evans [1974] can be

139 119 generated by four parameters: 1. n, the magnetospheric plasmasheet electron number density 2. E o, the characteristic energy or temperature of the magnetospheric electron distribution 3. V o, the infinitesimal electrostatic potential corresponding to the magnitude of the parallel electric field 4. β, the ratio of the magnetic field strength at the location of the electrostatic potential to the ionosphere In addition, the routines that integrate the primary beam to determine the parallel and omni-directional number flux were defined Ionospheric Response The electrons accelerated by the parallel electric field (the beam) accounted for the majority of the electrons with energies above the peak energy. However, electrons with energies less than the peak energy contribute to the flux measured at the ionosphere. Evans [1974] suggested that the low energy electrons of ionospheric origin were from two sources: degraded primary electrons (hereafter referred to as backscattered ) and secondary electrons generated through ionization by the primary beam electrons. At that time, Banks et al. [1974] had a model which generated an upward directed flux composed of backscattered and secondary electrons. This population will be reflect back toward the ionosphere if the electrons do not have sufficient energy to overcome the parallel electric field. To model the low energy upward directed flux, Evans [1974] used the Figure 7 from Banks et al. [1974] that described the upward directed flux created by an incident 10 kev electron beam. There was an energy division that distinguished the secondary electron population from the degraded primaries and the energy of this division was approximately

140 ev. Banks et al. [1974] suggest that secondary electrons with energies less than 500 ev will experience discrete energy losses, and higher energy electrons (E > 500 ev) will have continuous energy loss. Evans [1974] modified the upward directed flux calculated by Banks et al. [1974] so that the contribution from backscatter and secondary electron produced by an incident electron beam at any peak energy could be determined. The secondary electron flux response for the 10 kev upward flux consisted of energies ranging from ev; however, the response of electrons above 100 ev was two orders of magnitude less than electrons at 10 ev. The division between backscatter and secondary response was 600 ev. The secondary electron response was independent of the peak energy of the primary electron beam. The backscattered response was composed of the upward flux curve from 600 ev - 10 kev. To generate the backscatter response at any peak energy less than 10 kev, the ordinates of the curve were scaled with respect to the peak energy of the beam. However, the area under the backscatter response remained constant. This rescaling, in effect, created self-similar curves that were generated based on the peak energy. The area of the total ionospheric response is interpreted as the probability that a precipitating electron will be degraded or have an interaction that produces secondary electrons [Evans, 1974]. The following routine was used to calculate the ionospheric response using the differential omni-directional number flux from the primary electron beam. The omnidirectional flux was used because it accounts for electrons that may have small parallel energy, but significant perpendicular energy that could collide to produce degraded primary electrons or generate secondaries. The upward directed flux produced from the beam (Φ 1up (E)) was determined by integrating over the secondary and backscatter response to obtain, Φ 1up (E) = [B (E, E ) + S (E, E )] Φ beam (E )de (5.10) where E is the energy grid that corresponded to the differential number flux of the primary

141 121 beam, B (E, E ) and S (E, E ) are the backscatter and secondary response, respectively. The upward directed flux produced is in units of cm 2 s 1 ev 1 and it is assumed to be isotropic [Evans, 1974]. The upward directed flux will be reflected by the parallel electric field and will precipitate back onto the ionosphere, as shown in the left-hand side of Figure (5.2). The generation of additional ionospheric secondary and backscatter electrons is caused by this first reflected electron flux (Φ 1up (E)) back onto the ionosphere. This first generation of ionospheric electrons will move upward, be reflected, and precipitate to generate a second generation of ionospheric electron flux. This process will continue until a steady-state has been attained. Therefore, reaching an equilibrium is a key consideration when evaluating the upward directed flux. A basketball bouncing on the ground is a similar analogy to ionospheric electrons that continue to precipitate into the ionosphere. With each successive bounce, fewer electrons are generated that contribute to the precipitating ionospheric population, similar to the height of a basketball after successive bounces. Therefore, convergence of the area under the total response, composed of the backscatter and secondary response, is crucial for determining the equilibrium. If the total response is greater than 1, the contribution of electron flux from the ionosphere will increase without bound and not achieve a steady-state. In order to calculate the total ionospheric flux from the backscatter and secondaries electrons, both of these components were treated separately. The physical basis for determining the ionospheric contribution was that backscattered electron flux could produce additional backscatter (on subsequent bounces ) and secondary electron flux. However, being that secondary electrons produce significant fluxes at low energy, these electrons would generate negligible additional backscattered flux. Therefore, the secondary electrons can generate additional secondary electrons on subsequent bounces, but not additional backscatter.

142 122 The secondary electron response was used as an analytical check of the numerical integration routines and convergence. The secondary response as defined in Evans [1974] is independent of the peak energy of the beam, so S (E, E ) = S(E). This implies that the secondary response resulting from the primary beam will be Φ 0 (E) = S(E)Φ, where Φ is the number flux from the primary electron beam (Φ beam = Φ). After the first bounce of ionospheric electrons precipitate onto the ionosphere the response will be Φ 1 (E) = S(E)Φ 0 (E) = S(E) 2 Φ, after the second bounce Φ 2 (E) = S(E)Φ 1 (E) = S(E) 3 Φ, and so on. The secondary electron contribution converges to, Φ Secondary = S(E)Φ + S(E) 2 Φ + S(E) 3 Φ + = Φ 1 R (5.11) where R is defined to be R = S(E)dE, and R had a value of 0.1 based on the responses found in Evans [1974]. The backscatter electron flux were iterated to convergence. The backscattered flux from a previous iteration (N th ) was used as the input flux on the next iteration ((N + 1) th ). It was similarly found that the area under the backscatter curve had a value of 0.40, which was in good agreement with similar values in Evans [1974]. The secondary flux contribution was determined using the number flux of the backscattered electron, for each iteration ( bounce ). It is noted that summing up the total secondary response generated from the backscattered flux was equivalent to using equation (5.11). Up to six iterations of ionospheric electrons were run, but the backscatter flux was found to converge after four iterations, and that number of iterations was used for the remainder of the model. The converged backscatter and secondary fluxes were numerically summed together to produce the total upward directed number flux (Φ UP (E)) used for the remainder of the model. The differential parallel flux from this ionospheric population was J I (E) = Φ UP (E)/π and the omni-directional differential number flux was J I (E) = Φ UP (E)/2π, both in units of cm 2 s 1 ster 1 ev 1.

143 123 Evans [1974] Figure # cm s ster ev Model o PA: 0 Evans Model Model o PA: 45 Evans Model Energy(eV) Figure 5.3: An overplot comparison between our model results in red versus the results from Evans [1974] Figure 5 in black. As can be seen, with respect to the primary beam there is excellent agreement. The ionospheric contribution from the model has slightly overestimated the flux near the peak energy of the primary beam,. However, there is good agreement of the model results with the results from Evans [1974] Validation with Evans [1974] The model developed was validated with Figure 5 of Evans [1974] that shows slices of the differential number flux of the primary beam and the ionospheric contribution at two pitch angles: 0 and 45. Figure (5.3) shows pitch angle slices from our model in red using the beam parameters that were specified in Evans [1974]. As is shown in Figure (5.3) there is very good agreement between the primary beam of our model with the results of Evans [1974]. The ionospheric electrons are overestimated in our model near the peak energy, but the general trend of the ionospheric contribution matches well. Note that in the 45 pitch angle slice, there is a contribution from the ionospheric electrons at energies greater than the peak energy that appear as a knee. This trend is consistent with using the omni-directional differential number flux for the ionospheric contribution to the flux. One of the reasons as to why the ionospheric contribution may have been overestimated was because the backscatter and secondary curves were characterized through

144 124 a chi-by-eye analysis. No tabulated characterization of these curves was available in Evans [1974]. As a result, a digitization of the curve was required, which will inevitably generate error. Nevertheless, there are two important considerations. First, the model generated and the results from Evans [1974] are generally within better than a factor of two of each other, except, near the peak energy. More importantly, the key consideration is how well the model matches with data from the payloads, which was generally very well, as shown in Section (5.6). Second, it is important to note that the number flux contribution from the primary beam is most significant and will dictate where the peak of the height-ionization profile resides. 5.3 Height-Ionization Profiles The total parallel electron flux from the primary beam and the ionospheric response are used to generate the height ionization profile, q(z). Rees [1963] created a model that showed how precipitating electrons generate ionization as a function of altitude (heightionization). This technique was later extended to ions by Rees [1989]. Recently, Semeter and Kamalabadi [2005] have revisited this technique for application to incoherent scatter radar studies. Equation 8 from Semeter and Kamalabadi [2005] describes how the heightionization is generated, q(z) = ρ(z) Emax λ 35.5 E min ( ) Φ (E) R(E) EdE (5.12) S R(E) and has units of cm 3 s 1. The typical energy lost per ion-electron pair produced is 35.5 ev. R(E) defines the range-energy relation in units of g cm 2 and is defined as, R(E) = E 1.67 peak (5.13) where E peak is the peak energy of the beam electron flux. This relation is valid for electrons with energies > 300eV [Grün, 1957; Barrett and Hays, 1976]. The range energy function

145 125 defines the amount of material that particles will traverse, rather than the precise path of the particle in the medium [Kivelson and Russell, 1995]. Semeter and Kamalabadi [2005] note that the range energy relation can be determined either empirically through laboratory experiments [Grün, 1957; Barrett and Hays, 1976] that implicitly includes the relevant physics or theoretically using the electron transport equations [Strickland et al., 1983]. The Mass Spectrometer and Incoherent Scatter (MSIS) model [Hedin, 1991] was used to obtain the neutral mass density ρ(z) of the ionosphere as a function of altitude. This model is publicly available and is one of the standard neutral atmosphere models. The parameter S is defined in a similar way to the range-energy relation as the amount of material an electron will penetrate along the magnetic field line before it is scattered, S = sec(θ) z ρ(z)dz (5.14) where θ is the magnetic inclination angle. The magnetic inclination angle, measured relative to the vertical at Fort Yukon, Alaska is approximately The effect of this angle is negligible, so it is sufficient to assume the magnetic field lines are of vertical incidence. The final variable in the height ionization equation is λ(s/r), the universal energy dissipation function which specifies the fraction of energy lost per unit mass traversed [Semeter and Kamalabadi, 2005]. This universal energy dissipation curve is normalized so energy is conserved such that, 1 1 [ ] S λ d[s/r(e)] = 1 (5.15) R(E) Rees [1963] defined three different universal energy dissipation curves: isotropic (over a pitch angle range), cosine dependent, and monoenergetic. Semeter and Kamalabadi [2005] updated this convention by explicitly defining λ(s/r) for the isotropic curve, which was used in the calculation of the height-ionization profiles.

146 126 Altitude (km) Model Ionization Comparison Beam Energy Ionization (m s ) Figure 5.4: An overplot comparison of results between Semeter and Kamalabadi [2005], in black, to the model being developed, in color. The beams at each of the energy distributions was assumed to be a monoenergetic beam of precipitating electrons. As it can been seen, there is excellent agreement with the higher energy monoenergetic beams, especially above 10 kev. At lower energies, the energies between what was published versus our models are inconsistent. The code that generated q(z) was validated against Figure 2 of Semeter and Kamalabadi [2005] using a monoenergetic beam as shown in equation: Φ = 10 8 δ(e E o ) (5.16) in units of cm 2 s 1 and E o corresponded to the peak energy of the beam. For the calculation, the MSIS model was run for the date 01 January Figure (5.4) shows an overplot of our model (in color) versus the model by Semeter and Kamalabadi [2005] in black. Above 10 kev, there is very good agreement between both models. However, at lower energies while the agreement is still good, there is some uncertainty between whether the curves in the paper were mislabeled, as indicated by the results of our model. There

147 127 can also be uncertainty with respect to which day the MSIS model was run to produce the neutral mass density used. Regardless, the agreement is good for the monoenergetic distributions at various peak energies. A test case involving electron beams that were characterized by a Gaussian distribution was devised to test the numerical integration routine to arrive at the total heightionization profile. The integral height-ionization response is the sum of individual heightionization profiles at various peak energies, q(z) = q (E i, z) de i q (E i, z) E (5.17) where E i corresponds to the peak energy of the incident electron flux with a given parallel differential number flux, Φ i. A normalized Gaussian was used to emulate an input flux distribution, G(E) = exp (E E peak) T (5.18) πt where E peak is the peak energy of the Gaussian and T is a characteristic width of the distribution (temperature). Over the full energy range, the integral of the Gaussian response is equal to 1. Using G(E) at three energies, 500 ev, 2 kev, and 10 kev, the individual height ionization profiles and the total height ionization profiles were calculated. Figure (5.5) shows the three beams that peak at progressively lower altitudes. As can be seen, the total height ionization profile, shown in black, is equal to the sum of the beams at individual energies. Moreover, there are distinct peaks in the total ionization corresponding to 500 ev, 2 kev, and 10 kev beams, respectively. Figure (5.5) is a visual validation our numerical integration routine.

148 128 Altitude (km) q(z) total 500 ev 2 kev 10 kev Ionization (cm s ) Figure 5.5: An example of the total integrated response for the height ionization profiles. Three individual Gaussian beams at energies of 500 ev, 2 kev, and 10 kev (in color) are summed together to get the total ionospheric response (in black). This figure was shown as a check of our numerical integration routine. 5.4 Electron Density The continuity equation describes the time evolution of the electron number density. In steady-state, the continuity equation reduces to: [n e (z)u (x, z)] = q(z) αn 2 e(z) (5.19) where U(x, z) is the perpendicular convection of the ionization region. For simplicity, it was assumed that there were no convective flows of the ionization region, so the left-hand side of the equation (5.19) goes to zero. The equilibrium electron density can be solved, n e (z) = q(z) α (5.20) in units of cm 3, where q(z) is the total height-ionization profile, and α is the recombination rate of ionospheric neutrals.

149 129 The recombination rate, α, depends on the concentration of the domination ions within the auroral ionosphere. The dominant ions below 250 km altitudes are NO +, O + 2, and O +. Evans et al. [1977] published values of the recombination rates between km. Unfortunately, these recombination rates were provided through private communication leaving it unclear how they were derived. Schunk and Nagy [2004] have published more current recombination rates for NO +, α NO + = T e 0.5 (5.21) and for O + 2, α O = T e (5.22) both in units of cm 3 s 1 and T e is the electron temperature of the background ionosphere. The recombination process for O + is a two-step process [Schunk and Nagy, 2004] with the first step, O + + N 2 NO + + N (5.23) and the second reaction is the usual recombination for NO +, with the reaction rate corresponding to equation (5.21). This slower recombination rate explains why O + is the dominant ion above 200 km [Kelley, 2009], and the recombination rate is 5 orders of magnitude slower than NO + and O + 2. To obtain the total recombination rate, only the contribution from NO + and O + 2 were considered and a weighted average was used, α = [αc] NO + + [αc] O + 2 (5.24) where C ion was the ion concentration derived from the International Reference Ionosphere (IRI) model, in units of percentage. The IRI model is another standard model that has

150 130 been used to determine the dominant ion species concentration and the ionospheric electron temperature, both as functions altitudes. One of the limitations of the IRI model is that it is a global average of ionospheric conditions and may not precisely capture nightside ionospheric conditions [R. Varney, private communication, 2013]. The values of α calculated using the weighted average were compared against Evans et al. [1977] and generally good agreement was found at all altitudes. 5.5 Hall and Pedersen Conductivities The procedure described in Evans et al. [1977] was the same procedure that was used in this model to calculate the Hall and Pedersen conductivities. The Pedersen conductivity is defined as follows [Evans et al., 1977], σ P (z) = en e(z) C i ν in/ω i ( ) B(z) 2 + ν en/ω e ( ) 2 (5.25) ν i 1 + in ν Ω i 1 + en Ω e and the Hall conductivity, σ H (z) = en e(z) B(z) i C i 1 ( ) 2 ν 1 + in Ω i ( ) 2 ν en Ω e (5.26) where both the Hall and Pedersen conductivities are defined as a function of altitude (z). The electron density, n e (z) was calculated from the height-ionization profiles. C i corresponds to the ion species concentration for the dominant ions within the auroral ionosphere defined by the IRI model. The standard equations for the cyclotron frequency found in the NRL plasma formulary were used for the ions and the electrons, Ω i and Ω e, respectively. The magnetic field B(z) varies as a function of altitude and to good approximation is equal to: B(z) = B o ( RE (z + R E ) ) 3 (5.27)

151 131 where B o is equal to 0.55 G and R E is the radius of the Earth in km. At the altitude of 300 km, the magnetic field is approximately 13% the magnitude at the surface of the Earth, so for rocket altitudes this is approximation is reasonable. The remaining terms to be defined in equations (5.25) and (5.26) are the ion-neutral and electron-neutral collision frequencies. The ion-neutral collision frequency consists of the collisional frequency over all atmospheric neutrals per ion species ν in = n ν ij (z) (5.28) j where i corresponds to a single ion species and j includes all the neutral species, N 2, O 2, O, He, and H (although helium and hydrogen do not contribute significant at altitudes below 200 km). Out of simplicity equation 3 from Evans et al. [1977] was used to define the ion-neutral collision frequency and simplified to the following form, ( ) ( ν ij = Zj Ti (z) N j (z) + T ) j(z) Z i + Z j Z i Z j (5.29) where N j is the neutral density for the jth species, Z corresponds to the atomic number, and T corresponds to the temperature in Kelvin, for the jth species of neutrals and the ith species of ions. The temperatures, as a function of altitude, of the ions and neutrals were assumed to be the same and the value from the IRI model was used. Equation 3 from Evans et al. [1977] has a form similar to a hard-sphere model of ion-neutral collisions, in which ν = N n σ ni U in N n 2Ti /m i, where is an order of magnitude cross section for ion-neutral collisions. The electron collisionality can be decomposed into two components: electronneutral collisions and electron-ion Coulomb collisions. The electron neutral collision frequency used was equation 4 from Evans et al. [1977], ν en = N n Te (5.30) where N is the total neutral number density and T e is the electron temperature derived

152 132 from the IRI model. The Coulomb collisional terms between the ions and the electrons, ν ei = n e ( ln(te /n Te 3/2 e ) 3) (5.31) From Figure 2 of Boström [1964], the electron-neutral contribution will be 1-2 orders of magnitude more significant than the Coulomb contribution to the total electron collisionality. An approximate form of the Hall conductivity was used rather than solving equation (5.26). Particularly at the higher altitudes, the difference between the ion contribution and electron contribution in equation (5.26) generated both negative and positive values. This was a numerical issue in which the difference between the ion and electron contributions attempted to find large differences between values near one to a few decimal points of precision. To circumvent this issue, an approximate form for the Hall conductivity was determined, and is shown in Appendix (B), to produce, σ H (z) = en e(z) 1 C i ( B(z) i 1 + which is equivalent to equation 10 in Boström [1964]. ) 2 Ω i ν in (5.32) 5.6 Comparison with ACES Low Data The model electron flux was fit to the electron flux data observed by ACES Low and used to calculate the height-ionization profiles, electron density, and the Hall and Pedersen conductivities. Figure (5.6) shows the event chosen on ACES Low at 09:54: UT and the comparison between data from the EEPAA instrument to the model. The top panel shows the slice of the differential energy flux from when ACES Low was near the inverted V peak energy of 4 kev. The bottom panel shows the differential number flux observed on the ACES Low payload for the 0 pitch angle bin in red, and the model results of the differential number flux in black. The primary beam parameters of the magnetospheric

153 133 number density, peak energy of the electrostatic potential drop, and the temperature of the primary beam are shown in Figure (5.6). These beam parameters were fit to the high energy portion of the differential number flux observed by ACES Low, as shown on the right side of the dashed line in Figure (5.6). The magnetic ratio between the ionosphere and the location of the potential drop, β, was used to determine how narrow the beam was in pitch angle. The pitch angle slices of the differential number flux from the model was compared to similar pitch angle slices of the differential number flux observed on ACES Low. It was found that β = 6 fit the ACES observations of the precipitating beam electrons at higher pitch angles. This value of β corresponds to a potential drop located at an altitude of approximately 0.8 R e. This altitude has been shown to be consistent with observations of the acceleration region [Bennett et al., 1983]. The ionospheric response model was then run using these model primary beam parameters. It can be seen in Figure (5.6) that the ionospheric response is slightly underestimated relative to the low energy number flux observed on ACES Low; yet the model does maintain the general trend of the low energy portion of the data. There are two important points regarding the ionospheric response. First, while the ionospheric response may not match exactly in magnitude, it does track the general trend of the data observed on ACES Low. Second, the ionospheric response from Evans [1974] was used for its simplicity, rather than its rigorous treatment of the complete ionospheric response. Nevertheless, there is good agreement between the differential number flux from the model and the data observed on ACES Low. Figure (5.7) shows the key results from the auroral ionosphere model that has been developed for this test case. Panel A of Figure (5.7) shows the parallel number flux that was incident onto the ionosphere based on the model fit to the data from ACES Low. Note that the parameters characterizing the primary electron beam are consistent with plasmasheet parameters. Panel B shows the height-ionization profile using the parallel

154 134 Energy (ev) Differential Number Flux( # cm s ster ev ) :54:00 UT 131 km :54:57 UT ACES Low (21.139) Electron Flux 09:54:30 UT 132 km o ACES Low EEPAA Data (0 PA) Model Data Secondary/Backscatter Flux 09:55:00 UT 124 km o 15 PA V: 3400 ev -3 n: 1.25 cm T: 1150 ev β: 6 Primary Beam Flux Energy(eV) Figure 5.6: The top panel presents the location that was chosen in the differential energy flux spectrogram observed by ACES Low. The bottom panel is a comparison between the differential number flux observed by ACES in red versus the model beam and ionospheric response, in black. The ionospheric response was slightly underestimated relative to the observed differential number flux. Overall, there is good agreement between the modeled flux and the flux observed by ACES Diff E Flux ( ev # cm s ster ev ) number flux shown in panel A. The altitude of the peak corresponds well to what would be expected for a monoenergetic beam at approximately 3.4 kev, which is the peak energy of the potential drop.