ABSTRACT
 Title of dissertation: NEUTRAL GAS AND PLASMA
 INTERACTIONS IN THE POLAR CUSP
 David K. Olson, Doctor of Philosophy, 2012
 Dissertation directed by: Professor Douglas C. Hamilton
 University of Maryland
 When the solar wind interacts with the Earth?s magnetosphere, both energy
 and matter can be transferred across the magnetopause boundary. This transfer
 gives rise to numerous phenomena, including ion out ow and neutral upwelling in
 the polar cusps. These processes are caused by a transfer of energy to the ionospheric
 plasma and neutral gas through various mechanisms. The heated plasma or gas
 expands, increasing the density of the atmosphere at high altitudes by as much
 as a factor of two, and injecting ionospheric plasma into and even outside of the
 magnetosphere. These two phenomena are examined in two ways: A novel high
 energy (0.1-10 keV) spectrograph for ionospheric cusp ions was designed as part of
 the Rocket Experiment for Neutral Upwelling (RENU), a sounding rocket campaign
 carried out at the northern polar cusp to observe the electrodynamic properties of
 the cusp during a neutral upwelling event. This instrument is called the KeV Ion
 Magnetic Spectrograph (KIMS). Ion out ow in the ionosphere has shown evidence of
 correlation with both Poynting  ux and soft electron precipitation in the cusp. The
 heat input from these energy sources might also a ect neutral gas in the ionosphere,
contributing to upwelling phenomena seen at the dayside cusp. Using data from the
 Fast Auroral Snapshot Explorer (FAST) and the Challenging Minisatellite Payload
 (CHAMP) satellites, correlations of electromagnetic and particle energy inputs are
 examined with both ion out ow and neutral upwelling in the cusp. The added
 ability to process large quantities of data quickly and reference the data between
 separate satellites in this statistical survey gives clues to the consistency of the
 observed correlations with ion out ow over time and to the relative importance of
 these energy sources in the neutral upwelling phenomenon. It also provides the
 ability to understand these connections in a broad spectrum of conditions of the
 Sun and solar wind as well as in the Earth?s magnetosphere.
NEUTRAL GAS AND PLASMA INTERACTIONS
 IN THE POLAR CUSP
 by
 David K. Olson
 Dissertation submitted to the Faculty of the Graduate School of the
 University of Maryland, College Park in partial ful llment
 of the requirements for the degree of
 Doctor of Philosophy
 2012
 Advisory Committee:
 Professor Douglas C. Hamilton, Chair
 Dr. Thomas E. Moore, Advisor
 Professor Michael A. Coplan, Advisor
 Professor Russel R. Dickerson
 Professor William D. Dorland
 Professor James F. Drake
c Copyright by
 David K. Olson
 2012
Acknowledgments
 Though a dissertation is outwardly a very individual experience, no project
 of this magnitude could ever be undertaken without the assistance of many other
 people. The time spent in research is supported by many who are even unaware
 of their help and in ways that I found very surprising in my own experience. I
 could never express gratitude to all who have supported this project, but I will try
 to do so for a few particular individuals who have provided unique assistance and
 opportunity.
 My advisors, Dr. Moore and Dr. Coplan, have been very patient in guiding
 my work and my education in these past years. I appreciate the consistent encour-
 agement and support they o er, and have seen the same extended to other students
 and colleagues with whom they have worked.
 Dr. Marc Lessard, of the University of New Hampshire, provided the opportu-
 nity to participate in the RENU sounding rocket campaign. That was a marvelous
 opportunity, and I?m grateful for the experiences I had in Norway to work with
 him. Dr. Robert Strangeway, of the University of California in Los Angeles, pro-
 vided a lot of assistance in the statistical analysis. I enjoyed getting to know him
 and working with him this past year.
 The KIMS instrument design is based on a design created by Jack Moore. I had
 the privilege of working with Jack directly when he volunteered to come and assist
 with the magnetic circuit assembly. His input and support was very encouraging
 to me at that time, and I?m grateful he was able to come and help with that part
 of the project. Jack passed away shortly after our encounter; he is a great scientist
 and a good man. I?m honored that I was able to get to know him.
 My parents and family have always been there for me{ready to rejoice in
 successes and comfort over failures. I would not be where I am without my family.
 There is one individual to whom I owe all my inspiration and motivation. In
 reality, I owe Him all I am. This is, after all, His work.
 This work was funded in part by the NASA Graduate Student Research Program,
 under NASA Grant NNX08AT34H.
 ii
Table of Contents
 List of Tables viii
 List of Figures ix
 List of Abbreviations xii
 1 Introduction 1
 1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
 1.2 Magnetospheric Physics . . . . . . . . . . . . . . . . . . . . . . . . . 3
 1.2.1 The Atmosphere and Ionosphere . . . . . . . . . . . . . . . . . 5
 1.2.2 The Magnetosphere . . . . . . . . . . . . . . . . . . . . . . . . 8
 1.2.3 The Solar Wind . . . . . . . . . . . . . . . . . . . . . . . . . . 12
 1.2.4 Ionospheric Plasma . . . . . . . . . . . . . . . . . . . . . . . . 13
 1.3 Heating in the Ionosphere . . . . . . . . . . . . . . . . . . . . . . . . 14
 1.3.1 Joule Heating . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
 1.3.2 Ohmic Heating . . . . . . . . . . . . . . . . . . . . . . . . . . 16
 1.3.3 Electron and Ion Precipitation . . . . . . . . . . . . . . . . . . 17
 1.3.4 Alfv en and Other Plasma Waves . . . . . . . . . . . . . . . . 17
 1.4 Consequences of Ionospheric Heating . . . . . . . . . . . . . . . . . . 18
 1.4.1 Upwelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
 1.4.2 Jeans Escape . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
 1.4.3 Ion Out ow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
 1.5 Measurements of Ionospheric Heating . . . . . . . . . . . . . . . . . . 19
 1.5.1 Neutral Upwelling . . . . . . . . . . . . . . . . . . . . . . . . . 19
 1.6 This Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
 1.6.1 RENU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
 1.6.2 Statistical Analysis of Ionospheric Energy Sources . . . . . . . 23
 2 Ionospheric Ion Detection and the KIMS Instrument 24
 2.1 The KeV Ion Magnetic Spectrograph . . . . . . . . . . . . . . . . . . 26
 2.1.1 Energy Spectrum Dispersion . . . . . . . . . . . . . . . . . . . 26
 2.1.2 Field of View . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
 2.2 Microchannel Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
 2.2.1 KIMS Detector Response . . . . . . . . . . . . . . . . . . . . . 33
 2.3 Project Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
 2.3.1 Goals for KIMS . . . . . . . . . . . . . . . . . . . . . . . . . . 35
 2.3.2 Changes From Heritage . . . . . . . . . . . . . . . . . . . . . . 36
 2.3.3 Basic Parameters for KIMS . . . . . . . . . . . . . . . . . . . 37
 2.4 KIMS Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
 2.4.1 Magnetic Circuit Design . . . . . . . . . . . . . . . . . . . . . 40
 2.4.2 Mechanical Design . . . . . . . . . . . . . . . . . . . . . . . . 42
 2.4.3 Detector Design . . . . . . . . . . . . . . . . . . . . . . . . . . 44
 2.4.3.1 MCP Housing . . . . . . . . . . . . . . . . . . . . . . 44
 iii
2.4.3.2 MCP Stack . . . . . . . . . . . . . . . . . . . . . . . 45
 2.4.4 Electrical Design . . . . . . . . . . . . . . . . . . . . . . . . . 46
 2.4.4.1 Ampli ers and Telemetry . . . . . . . . . . . . . . . 49
 2.4.4.2 Electrical Stack Assembly . . . . . . . . . . . . . . . 50
 2.4.5 Ground Support Equipment . . . . . . . . . . . . . . . . . . . 54
 2.5 KIMS Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
 3 KIMS Analysis, Data, and Results 59
 3.1 Modeling and Operating Parameters . . . . . . . . . . . . . . . . . . 61
 3.1.1 Instrument Simulation . . . . . . . . . . . . . . . . . . . . . . 61
 3.1.2 Magnetic Field . . . . . . . . . . . . . . . . . . . . . . . . . . 64
 3.1.3 MCP Applied Voltage . . . . . . . . . . . . . . . . . . . . . . 66
 3.2 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
 3.3 Integration Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
 3.3.1 External Magnetic Field . . . . . . . . . . . . . . . . . . . . . 71
 3.3.2 Vibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
 3.3.3 Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
 3.4 RENU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
 4 Data Analysis Background 76
 4.1 Satellite Background . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
 4.1.1 FAST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
 4.1.2 CHAMP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
 4.2 The Strangeway Study . . . . . . . . . . . . . . . . . . . . . . . . . . 81
 4.3 Ion Out ow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
 4.4 Ionospheric Energy Sources . . . . . . . . . . . . . . . . . . . . . . . 85
 4.5 Statistics of Ionospheric Energy Sources . . . . . . . . . . . . . . . . 86
 4.6 Statistics in Neutral Upwelling . . . . . . . . . . . . . . . . . . . . . . 90
 4.7 Geophysical and Geomagnetic Coordinate Systems . . . . . . . . . . 92
 4.7.1 Geographic Coordinates (GEO) . . . . . . . . . . . . . . . . . 93
 4.7.2 Geocentric Equatorial Inertial Coordinates (GEI) . . . . . . . 93
 4.7.3 Geocentric Solar Magnetospheric Coordinates (GSM) . . . . . 94
 4.7.4 International Geomagnetic Reference Field . . . . . . . . . . . 94
 4.7.5 Solar Magnetic Coordinates (SM) . . . . . . . . . . . . . . . . 95
 4.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
 5 Data and Analysis Software 98
 5.1 Python . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
 5.1.1 Python Structures . . . . . . . . . . . . . . . . . . . . . . . . 100
 5.1.2 NumPy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
 5.1.3 SciPy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
 5.1.4 Matplotlib . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
 5.1.5 SpacePy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
 5.1.6 The Python Pickle . . . . . . . . . . . . . . . . . . . . . . . . 104
 5.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
 iv
5.2.1 FAST Data Processing . . . . . . . . . . . . . . . . . . . . . . 104
 5.2.2 FAST Field Data . . . . . . . . . . . . . . . . . . . . . . . . . 105
 5.2.2.1 Field Processing Tools . . . . . . . . . . . . . . . . . 105
 5.2.2.2 DC Electric Field . . . . . . . . . . . . . . . . . . . . 109
 5.2.2.3 ELF AC Electric Field . . . . . . . . . . . . . . . . . 110
 5.2.2.4 DC Magnetic Field . . . . . . . . . . . . . . . . . . . 112
 5.2.2.5 Poynting Flux . . . . . . . . . . . . . . . . . . . . . 114
 5.2.3 FAST Particle Data . . . . . . . . . . . . . . . . . . . . . . . . 114
 5.2.3.1 Particle Processing Tools . . . . . . . . . . . . . . . 116
 5.2.3.2 Electron Flux . . . . . . . . . . . . . . . . . . . . . . 121
 5.2.3.3 Ion Flux . . . . . . . . . . . . . . . . . . . . . . . . . 121
 5.2.3.4 Using FAST.py . . . . . . . . . . . . . . . . . . . . . 123
 5.2.4 FAST Statistical Analysis . . . . . . . . . . . . . . . . . . . . 126
 5.2.5 FAST Data Visualization . . . . . . . . . . . . . . . . . . . . . 131
 5.2.6 CHAMP Data Processing . . . . . . . . . . . . . . . . . . . . 133
 5.2.6.1 Orbit Data . . . . . . . . . . . . . . . . . . . . . . . 134
 5.2.6.2 Accelerometer Data . . . . . . . . . . . . . . . . . . 135
 5.2.6.3 Using champ.py . . . . . . . . . . . . . . . . . . . . . 139
 5.2.7 CHAMP Statistical Analysis . . . . . . . . . . . . . . . . . . . 141
 5.2.8 CHAMP Data Visualization . . . . . . . . . . . . . . . . . . . 143
 5.3 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
 5.3.1 Assumptions in Field Quantities . . . . . . . . . . . . . . . . . 143
 5.3.2 Assumptions in Particle Quantities . . . . . . . . . . . . . . . 144
 5.3.3 Assumptions in Neutral Density . . . . . . . . . . . . . . . . . 144
 5.3.4 Assumptions in Calculations . . . . . . . . . . . . . . . . . . . 145
 6 Statistical Analysis 146
 6.1 Time Average Consistency . . . . . . . . . . . . . . . . . . . . . . . . 149
 6.2 Poynting Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
 6.3 Electron Precipitation . . . . . . . . . . . . . . . . . . . . . . . . . . 157
 6.4 Cross Correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
 6.5 Neutral Upwelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
 6.5.1 Visual Observations from Selection of CHAMP Data . . . . . 161
 6.5.2 Poynting Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
 6.5.3 Electron Precipitation Density . . . . . . . . . . . . . . . . . . 165
 6.5.4 Ion Out ow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
 6.6 Summary of Findings . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
 7 Conclusion 173
 7.1 The KIMS Instrument . . . . . . . . . . . . . . . . . . . . . . . . . . 173
 7.2 Ion Out ow and Neutral Upwelling . . . . . . . . . . . . . . . . . . . 175
 7.3 Further Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
 v
A KIMS Hardware 180
 A.1 Magnetic Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
 A.2 Clamshell and Cover . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
 A.3 KIMS Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
 B KIMS Software 212
 B.1 Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . . 212
 B.1.1 mc sim.py . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
 B.2 FPGA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
 B.2.1 Telemetry/Ampli er Board . . . . . . . . . . . . . . . . . . . 217
 B.2.1.1 Telemetry Code . . . . . . . . . . . . . . . . . . . . . 217
 B.2.1.2 Ampli er/Counter Code . . . . . . . . . . . . . . . . 222
 B.2.2 GSE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
 B.3 MSP430 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
 B.4 Serial Communication . . . . . . . . . . . . . . . . . . . . . . . . . . 239
 C KIMS Project Images 241
 C.1 Magnetic Circuit Assembly . . . . . . . . . . . . . . . . . . . . . . . . 241
 C.2 KIMS Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
 C.3 Vibration Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254
 C.4 Magnetic Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
 C.5 Integration Photos . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
 D RENU Launch Information 264
 D.1 General Overview of Sounding Rocket Campaign RENU . . . . . . . 264
 D.1.1 Investigators and Team . . . . . . . . . . . . . . . . . . . . . . 265
 D.2 Vehicle Requirements and Performance . . . . . . . . . . . . . . . . . 266
 D.2.1 Trajectory Data/Attitude Solution . . . . . . . . . . . . . . . 266
 D.2.2 Outgassing, Magnetic Sensitivity, RFI Susceptibility . . . . . . 266
 D.2.3 Coning Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
 D.2.4 Despin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
 D.2.5 Horizon Sensors/Sun Sensors . . . . . . . . . . . . . . . . . . 267
 D.2.6 Range Support . . . . . . . . . . . . . . . . . . . . . . . . . . 267
 D.2.7 Launch Conditions . . . . . . . . . . . . . . . . . . . . . . . . 268
 D.3 Success Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270
 D.3.1 Comprehensive Mission Success . . . . . . . . . . . . . . . . . 270
 D.3.2 Minimum Success . . . . . . . . . . . . . . . . . . . . . . . . . 270
 D.4 RENU Launch Conditions . . . . . . . . . . . . . . . . . . . . . . . . 272
 E Statistical Analysis Software 278
 E.1 FAST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
 E.1.1 FAST.py . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
 E.1.2 FAPlot.py . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298
 E.1.3 FAST stats.py . . . . . . . . . . . . . . . . . . . . . . . . . . . 303
 E.2 CHAMP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
 vi
E.2.1 champ.py . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
 E.2.2 champformats.py . . . . . . . . . . . . . . . . . . . . . . . . . 319
 E.2.3 CHAMP stats.py . . . . . . . . . . . . . . . . . . . . . . . . . 320
 E.3 Coordinate System Transformation . . . . . . . . . . . . . . . . . . . 328
 E.3.1 cstrans2.py . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328
 E.4 Other Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334
 E.4.1 nantools.py . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334
 E.4.2 plot setup.py . . . . . . . . . . . . . . . . . . . . . . . . . . . 334
 Bibliography 336
 vii
List of Tables
 5.1 FAST Filenames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
 5.2 CHAMP Orbit Format . . . . . . . . . . . . . . . . . . . . . . . . . . 136
 5.3 CHAMP Spacecraft Coordinate System . . . . . . . . . . . . . . . . . 137
 5.4 STAR Accelerometer Coordinate System . . . . . . . . . . . . . . . . 138
 6.1 Poynting Flux Statistical Results . . . . . . . . . . . . . . . . . . . . 158
 6.2 Electron Precipitation Density Statistical Results . . . . . . . . . . . 161
 6.3 Summary of Poynting Flux|Neutral Upwelling Statistics . . . . . . . 165
 6.4 Summary of Electron Precipitation Density|Neutral Upwelling Statis-
 tics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
 6.5 Summary of Ion Out ow|Neutral Upwelling Statistics . . . . . . . . 168
 B.1 GSE Commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
 viii
List of Figures
 1.1 Earth?s atmosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
 1.2 Ionospheric and Atmospheric Composition . . . . . . . . . . . . . . . 7
 1.3 Earth?s ionosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
 1.4 Earth?s magnetosphere . . . . . . . . . . . . . . . . . . . . . . . . . . 10
 1.5 CHAMP Deceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
 1.6 STREAK Ionosphere Density Depletion . . . . . . . . . . . . . . . . . 21
 2.1 Cyclotron Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
 2.2 KIMS Field of View . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
 2.3 Perpendicular Acceptance . . . . . . . . . . . . . . . . . . . . . . . . 31
 2.4 Microchannel Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
 2.5 Detector Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
 2.6 Previous Results from KIMS Heritage . . . . . . . . . . . . . . . . . . 38
 2.7 Photos of the magnetic circuit . . . . . . . . . . . . . . . . . . . . . . 40
 2.8 Photo of the magnetic circuit grid . . . . . . . . . . . . . . . . . . . . 42
 2.9 Clamshell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
 2.10 KIMS Instrument . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
 2.11 MCP Stack Drawings . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
 2.12 MCP Stack Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
 2.13 Anode Board . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
 2.14 MCP Stack Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
 2.15 Ampli er/Telemetry Circuit . . . . . . . . . . . . . . . . . . . . . . . 51
 2.16 Ampli er/Telemetry Board . . . . . . . . . . . . . . . . . . . . . . . . 52
 2.17 High Voltage Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
 2.18 Electrical Stack Assembly . . . . . . . . . . . . . . . . . . . . . . . . 56
 3.1 Ion Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
 3.2 KIMS Simulation Histogram . . . . . . . . . . . . . . . . . . . . . . . 62
 3.3 KIMS Simulated Response . . . . . . . . . . . . . . . . . . . . . . . . 63
 3.4 KIMS  E=E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
 3.5 KIMS Interior Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
 3.6 KIMS Bare Anode . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
 3.7 KIMS Bare Anode Test . . . . . . . . . . . . . . . . . . . . . . . . . . 67
 3.8 KIMS MCP Bias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
 3.9 KIMS Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
 3.10 Stray Field Measuring Con guration . . . . . . . . . . . . . . . . . . 72
 3.11 Stray Field Measurements . . . . . . . . . . . . . . . . . . . . . . . . 73
 4.1 The FAST Satellite . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
 4.2 The CHAMP Satellite . . . . . . . . . . . . . . . . . . . . . . . . . . 81
 4.3 Ion pitch-angle spectrogram . . . . . . . . . . . . . . . . . . . . . . . 84
 4.4 Correlation Relationships in Ion Out ow . . . . . . . . . . . . . . . . 87
 4.5 Strangeway Correlations . . . . . . . . . . . . . . . . . . . . . . . . . 88
 ix
4.6 Electron Precipitation Density Correlation . . . . . . . . . . . . . . . 89
 5.1 Chauvenet?s Criterion . . . . . . . . . . . . . . . . . . . . . . . . . . 107
 5.2 Smoothing Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
 5.3 Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
 5.4 AC E- eld Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
 5.5 Interpolated ELF Data . . . . . . . . . . . . . . . . . . . . . . . . . . 112
 5.6 Interpolate B- eld Data . . . . . . . . . . . . . . . . . . . . . . . . . 113
 5.7 Interpolated Poynting Flux Data . . . . . . . . . . . . . . . . . . . . 115
 5.8 Ion Flux Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
 5.9 Electron Flux Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . 119
 5.10 Cuto Routine Example . . . . . . . . . . . . . . . . . . . . . . . . . 120
 5.11 Electron Fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
 5.12 Ion Fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
 5.13 Summary of FAST Orbit 08276 . . . . . . . . . . . . . . . . . . . . . 125
 5.14 Update Pickle Example . . . . . . . . . . . . . . . . . . . . . . . . . . 127
 5.15 Time Average Consistency . . . . . . . . . . . . . . . . . . . . . . . . 129
 5.16 Linear Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
 5.17 Orbital Coverage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
 6.1 July 2002 Event . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
 6.2 July 2002 Orbits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
 6.3 February 2002 Event . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
 6.4 February 2002 Orbits . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
 6.5 Time Average Consistency . . . . . . . . . . . . . . . . . . . . . . . . 153
 6.6 Time Average Trends . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
 6.7 Sep 1998 Poynting Flux Correlation . . . . . . . . . . . . . . . . . . . 156
 6.8 2002 Poynting Flux Correlation . . . . . . . . . . . . . . . . . . . . . 157
 6.9 Sep 1998 Electron Precipitation Correlation . . . . . . . . . . . . . . 159
 6.10 2002 Electron Precipitation Correlation . . . . . . . . . . . . . . . . . 160
 6.11 Poynting Flux{Electron Precipitation Cross Correlation . . . . . . . . 162
 6.12 Selection of CHAMP Data . . . . . . . . . . . . . . . . . . . . . . . . 164
 6.13 Neutral Density Correlations with Poynting Flux . . . . . . . . . . . 166
 6.14 Neutral Density Correlations with Electron Precipitation . . . . . . . 167
 6.15 Neutral Density Correlations with Ion Out ow . . . . . . . . . . . . . 169
 6.16 Ion Out ow Statistics Summary . . . . . . . . . . . . . . . . . . . . . 171
 6.17 Neutral Upwelling Statistics Summary . . . . . . . . . . . . . . . . . 172
 7.1 Ionospheric Correlations . . . . . . . . . . . . . . . . . . . . . . . . . 176
 C.1 Magnetic Circuit Parts . . . . . . . . . . . . . . . . . . . . . . . . . . 241
 C.2 Magnet Clamp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
 C.3 Upper Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
 C.4 Placing Lower Shell . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
 C.5 Partition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
 C.6 Magnetic Circuit Half . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
 x
C.7 Magnetic Circuit Assembled . . . . . . . . . . . . . . . . . . . . . . . 244
 C.8 Ground Screen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
 C.9 Mounting the Magnetic Circuit . . . . . . . . . . . . . . . . . . . . . 246
 C.10 Clamshell Fastened . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
 C.11 Telemetry/Ampli er Boards . . . . . . . . . . . . . . . . . . . . . . . 247
 C.12 Distribution Board . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
 C.13 Ground Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248
 C.14 Inserting the Detector . . . . . . . . . . . . . . . . . . . . . . . . . . 248
 C.15 High Voltage Board . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
 C.16 High Voltage Control Board . . . . . . . . . . . . . . . . . . . . . . . 249
 C.17 Clamshell Spacers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250
 C.18 Tray . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
 C.19 Cover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252
 C.20 KIMS Final Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . 253
 C.21 Axis de nitions for vibration testing. . . . . . . . . . . . . . . . . . . 255
 C.22 White noise vibration test result of the KIMS instrument X-axis. . . 256
 C.23 White noise vibration test result of the KIMS instrument Y-axis. . . 257
 C.24 White noise vibration test result of the KIMS instrument Z-axis. . . . 258
 C.25 Magnetic Testing Con guration . . . . . . . . . . . . . . . . . . . . . 259
 C.26 Magnetometer Spacing . . . . . . . . . . . . . . . . . . . . . . . . . . 260
 C.27 KIMS Finalized . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
 C.28 KIMS Mounted . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
 C.29 KIMS Flight Con guration . . . . . . . . . . . . . . . . . . . . . . . . 263
 D.1 All-sky Auroral Photo . . . . . . . . . . . . . . . . . . . . . . . . . . 272
 D.2 All-sky Red & Green Images . . . . . . . . . . . . . . . . . . . . . . . 273
 D.3 EISCAT Radar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
 D.4 Solar Wind Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 275
 D.5 Magnetometer Measurements . . . . . . . . . . . . . . . . . . . . . . 276
 D.6 SuperDARN Radar Measurements . . . . . . . . . . . . . . . . . . . . 277
 xi
List of Abbreviations
 acc CHAMP Accelerometer Data
 CDF Common Data Format
 CEM Channel Electron Multiplier
 CHAMP Challenging Minisatellite Payload
 CTS Conventional Terrestrial System (equivalen to GEO)
 dcefs FAST DC Electric Field Survey
 dcmag FAST DC Magnetic Field Survey
 DSP Digital Signal Processor
 dsp v58 FAST Low Frequency, V5-V8 AC Electric Field Data
 EDM Electrical Discharge Machining
 ees FAST Electron Energy Spectrometer
 ELF Extremely Low Frequency
 EUV Extreme Ultraviolet
 FAC Field aligned current
 FAST Fast Auroral Snapshot Explorer
 FPGA Field Programmable Gate Array
 GEI Geocentric Equatorial Inertial Coordinates
 GFZ GeoForschungsZentrum
 GHA Greenwich Hour Angle
 GSE Geocentric Solar Ecliptic Coordinates
 GSE Ground Support Equipment
 GSFC Goddard Space Flight Center
 GSM Geocentric Solar Magnetospheric Coordinates
 GST Greenwich Sidereal Time
 IC Integrated Circuit
 IDL Interactive Data Language
 ies FAST Ion Energy Spectrometer
 IGRF International Geomagnetic Reference Field
 ILT Invariant Latitude
 IPST Institute for Physical Science and Technology
 ISDC Information System and Data Center (Potsdam, Germany)
 KIMS KeV Ion Magnetic Spectrograph
 MCP Microchannel Plate
 MLT Magnetic Local Time
 MSP430 Texas Instruments Mixed Signal Processor (microcontroller)
 NASA National Aeronautics and Space Administration
 PCM Pulse Code Modulation
 RE Earth radii (unit)
 RENU Rocket Experiment for Neutral Upwelling
 rso CHAMP Rapid Science Orbit Data
 SM Solar Magnetic Coordinates
 STAR Spatial Triaxial Accelerometer for Research
 UART Universal Asynchronous Receiver/Transmitter
 UMD University of Maryland, College Park
 USB Universal Serial Bus
 xii
Chapter 1
 Introduction
 This dissertation describes a study involving two phenomena observed in the
 Earth?s atmosphere. The two phenomena, neutral upwelling and ion out ow, are
 similar in nature. Both are the result of heating processes in the atmosphere, and
 both end up in particles rising to higher altitudes within a very localized region. The
 goal of this study is to understand the neutral upwelling phenomenon, particularly
 in the context of processes similar to those that lead to ion out ow. Because both
 phenomena have similar characteristics and happen in the same location, the study
 is a search for connections that explain how these phenomena occur. Ultimately,
 the two processes stem from interactions at the boundary of Earth?s magnetic  eld.
 1.1 Background
 The boundary between the electromagnetic  elds of the Earth and the Solar
 System is a curious interface between the atmosphere and interplanetary space.
 From one aspect, the edge of the Earth?s magnetic  eld (the magnetopause) marks
 a physical boundary where the solar wind is de ected around the planet. From
 another aspect, the boundary links the electromagnetic  elds of the Sun and its
 solar wind with those of the Earth in such a way that motion of the solar wind leads
 to energy, and in some cases material, being transferred in and out of the Earth?s
 1
ionosphere. These interactions lead to complex phenomena that are challenging to
 study, but important to understand because of their direct in uence on the Earth.
 Among these phenomena, heating in the ionosphere can lead to easily observ-
 able results, such as the spectacular displays of light in auroral storms, or to less
 obvious consequences, such as local  uctuations in atmospheric density. In some
 cases, heating leads to an out ow of atmospheric material from the Earth itself.
 One of these less visible, but in uential, results is an upward movement of neutral
 gas within the polar cusp of the magnetosphere. Material from the mesosphere and
 lower thermosphere rise in this region to orbital altitudes in the middle and upper
 thermosphere (see Fig. 1.1).
 During these neutral upwelling events, the increased density in the thermo-
 sphere causes increased drag on satellites in polar orbits as they pass through up-
 welling regions, slowing the spacecraft and reducing their orbital lifetimes. A unique
 aspect about this phenomenon is that the heating is highly localized and con ned
 to the region around the Earth?s magnetic poles known as the cusps (see Fig. 1.4).
 While there have been a number of clear observations of the neutral upwelling phe-
 nomenon, the mechanisms behind neutral upwelling are not yet well understood.
 Considering the sharply de ned location of the neutral upwelling events within
 the cusps of the Earth?s magnetic  eld, we can reasonably suppose that the mech-
 anisms responsible for lifting the neutral gas are in some way connected to the
 electromagnetic  elds and plasmas that make up the Earth?s ionosphere and mag-
 netosphere. A number of electromagnetic and plasma e ects can transfer energy
 to the neutral atmosphere in the cusp region, either directly or indirectly, and thus
 2
contribute to the neutral upwelling phenomenon.
 1.2 Magnetospheric Physics
 There are many complicated interactions in the magnetosphere, but they can
 be understood in terms of basic physics. Dr. E. N. Parker once described the goal
 of magnetospheric physics as coming to \. . . understand the active magnetosphere
 in terms of the principles of Newton and Maxwell" [1]. In other words, our goal
 is to describe the Earth?s atmosphere and electromagnetic  elds using Newtonian
 mechanics (particularly in terms of gravitation and  uid mechanics) and Maxwell?s
 formulation of electromagnetism (in terms of  elds, wave propagation, and plasma
 properties). This formulation of the physics in the magnetosphere lets us separate
 the region into an atmospheric and ionospheric picture. Each picture can be further
 described in terms of distinct layers, each with unique properties, much as the
 interior of the Earth can be. The atmosphere and ionosphere are very di erent
 from the lithosphere in many ways, however, and the boundaries between layers are
 constantly moving. While there are speci c general properties in the various layers,
 the locations and sizes of the layers constantly vary. The dynamic properties of these
 di erent layers have consequences for radio communication, satellite trajectories,
 and the in uence of the sun on the Earth through the solar wind.
 3
Figure 1.1: Diagram of the Earth?s atmosphere. The Ionosphere varies in location
 and size, but typically starts in the upper Mesosphere and extends upward through
 the Exosphere. On the right, both pictures are depicted in terms of one of the
 parameters that distinguishes the layers in each. In this case, the atmospheric
 layers have di erent temperature pro les, and the ionospheric layers have di erent
 electron density pro les. (Figure credit NASA.)
 4
1.2.1 The Atmosphere and Ionosphere
 We  rst draw a distinction between the identi ed layers of the atmosphere
 and the ionosphere. The atmosphere refers to the di erent layers with distinct
 temperatures and compositions. We live in the troposphere, which only extends to
 about 0.2% of the entire height of the atmosphere, but it also contains approximately
 80% of the material in the atmosphere [2]. The other layers extend upward, to an
 altitude of approximately 10,000 km at the exopause (see Fig. 1.1). The atmosphere,
 the layers that compose it, and the di ering properties in each can be generally
 described by Newtonian physics.
 The ionosphere refers to the region of the atmosphere where a substantial
 portion of the material is in an ionized state. Atmospheric atoms and molecules
 are ionized primarily by ultraviolet (UV) radiation from the Sun [3]. Like the
 Newtonian atmosphere, the ionosphere also has layers with distinct characteristics,
 such as electron density and plasma composition. The ionosphere begins in the
 upper mesosphere (typically about 60 km above the Earth?s surface) and extends
 to the edge of the magnetosphere, but di erent conditions in the atmosphere, the
 sun, and interplanetary space have signi cant impact on locations, sizes, and even
 number of the ionospheric layers. Just as the atmospheric system can be described
 with Newtonian physics, the ionosphere can be described using a combination of
 Newtonian and Maxwellian (or electrodynamic) physics.
 The highest well de ned layer of the ionosphere is referred to as the F layer.
 The F layer is of particular interest because peak plasma density occurs there.
 5
This layer is generally between 200 and 500 km above the Earth?s surface, in the
 atmospheric layer called the thermosphere. It is in this region that neutral upwelling
 occurs. Beyond the F layer lies the topside layer, with gradually falling density and
 increasing ionization fraction. The topside layer extends through the exosphere and
 out to the magnetopause.
 A number of important parameters describe the atmosphere and ionosphere.
 One of the more important of these is the scale height. This parameter is a measure
 of how quickly a value decreases with height, and in terms of the atmosphere is
 derived as a description of the atmospheric pressure. The atmospheric scale height is
 a ratio of thermal energy to gravitational potential energy. For a given temperature,
 the scale height is given by
 H =
 kT
 Mg
 (1.1)
 using Boltzmann?s constant k, the temperature T , the molecular mass of air M , and
 gravitational acceleration g. For a given height above the surface z and base surface
 pressure P0, the pressure is then approximately
 P = P0e
  zH (1.2)
 As the temperature increases, so does the scale height, and thus the pressure at a
 given altitude. We then expect the density of the atmosphere at higher altitudes to
 increase because of an increase in temperature. Processes that heat the atmosphere
 will increase scale height. As such, scale height varies with time of day, day of year,
 latitude, and a number of other parameters that in uence the local temperature
 of the atmosphere. The Extended Mass Spectrometer{Incoherent Scatter (MSISE)
 6
Figure 1.2: Plot showing the densities of various components of both the ionosphere
 (solid lines) and the atmosphere (dashed lines). The neutral density in the F layer is
 typically 1{3 orders of magnitude greater than the plasma density. These data are
 based on multiple mass-spectrometer measurements compiled for the international
 quiet solar year in 1969 [6].
 atmospheric model [4], which is based on measurements of many di erent atmo-
 spheric and solar parameters, estimates a typical scale height for the Earth?s lower
 atmosphere of about 6.7 km [5].
 Density is a very important parameter for both the atmosphere and the iono-
 sphere. Even at the same altitude, however, both environments can have remarkably
 di erent densities and compositions (see Fig. 1.2). At orbital altitudes multiple
 scale heights above the Earth, the density of the neutral atmosphere can be orders
 of magnitude greater than the density of the ionospheric plasma.
 Related to density is the mean free path. The mean free path is a description
 of length scales between particle interactions, typically describing how far a particle
 7
may travel before colliding with another particle. This value can be described in
 terms of the density n and the cross-section area for collisions  by
  mfp =
 1
  n
 (1.3)
 The cross-section  depends on a number of parameters, including the temperature
 and composition of the ionosphere in the region of interest. A rough estimate can
 be found based on the temperature and density of the electrons, as given by Alfv en
 [7]:
   104
 T 2e
 Ne
 (1.4)
 For ionospheric plasma in the F region, we  nd temperatures between 1000 and
 2000 K, and densities peaking at 106cm 3. These values suggest a mean free path in
 the ionosphere of tens to a few hundreds of kilometers. This length is comparable
 to the mean free path of a con ned gas with a density approximately that of the
 neutral atmosphere at these altitudes, suggesting an overall pressure below 10 6 torr
 in this region.
 1.2.2 The Magnetosphere
 The Earth?s magnetic  eld creates a third system within the overall region
 of interest. The magnetic  eld interacts with the interplanetary magnetic  eld
 (generated by the Sun) and with the solar wind, creating a shell that surrounds the
 Earth to an extent of about 15{20 Earth radii (RE). The solar wind compresses
 the front of the shell to about 10{12 RE while the back is extended into a long
 \magnetotail", reaching beyond 200 RE (see Fig. 1.4). We call the boundary of this
 8
Figure 1.3: Diagram showing a con guration of Earth?s ionosphere in relation to the
 atmosphere. Conditions present during the daytime can also lead to another layer
 (the D layer) at lower altitudes, and at times a division is seen in the F layer (the
 two parts being called the F1 and F2 layers). (Figure credit M.C. Kelley [3].)
 9
Figure 1.4: Diagram of the Earth?s magnetosphere with key features identi ed. The
 bow shock is where the solar wind slows to below the local sound speed, creating a
 shock wave as the solar wind is de ected around the magnetosphere. The movement
 of the solar wind around the Earth draws the magnetic  eld lines out to create a
 long Magnetotail. The funnel shapes formed at the magnetic poles are called the
 polar cusps. Solar wind particles can pass into the cusps and precipitate into the
 atmosphere. Atmospheric particles can escape through the cusps. The plasma sheet,
 neutral sheet, and magnetosheath are all aspects of Earth?s magnetosphere that
 result from interactions of charged and neutral particles with the magnetosphere,
 but do not enter this study. (Figure credit NASA.)
 10
shell the magnetopause.
 Earth?s  eld is roughly dipolar, with an average strength of approximately
 50  T at the surface. It is currently believed that the  eld is created by electric cur-
 rents in the outer core according to the dynamo theory1. The north and south poles
 of Earth?s magnetic  eld shift in location independently, and both poles have drifted
 substantially (on the order of  100 km over the past 100 years [55]. Nevertheless,
 the magnetosphere can be modeled to fair accuracy as a magnetic dipole with a few
 small corrections in higher order terms of a multipole expansion. Standard models
 of the Earth?s magnetic  eld include the International Geomagnetic Reference Field
 (IGRF) [9]. The IGRF is often used to evaluate atmospheric and electromagnetic
 phenomena as they relate to local changes in the  eld.
 Of particular interest to the neutral upwelling phenomenon being discussed are
 the funnel-shaped regions of the magnetic  eld found at the magnetic poles. These
 regions, called the cusps, allow for energy (sourced from both  elds and particles)
 to be exchanged between the interplanetary medium and the ionosphere [10]. The
 nature of this exchange is an ongoing topic of interest in space physics. The cusps
 are surrounded by the annular shaped auroral regions, where solar wind interactions
 become visible through spectacular displays of light in the atmosphere commonly
 known as the northern lights.
 1Dynamo theory suggests that the rotation and convection of an electrically conductive  uid,
 such as the liquid outer core of the Earth, can sustain magnetic  elds for astronomical time scales,
 and thus may be the source of planetary and stellar magnetic  elds. The theory was  rst suggested
 by Larmor [8].
 11
1.2.3 The Solar Wind
 The Sun, due to the heat and pressure of the plasma in the corona, drives
 material away from itself into interplanetary space. This \solar wind" is made
 mostly of electrons and protons, and is accelerated away from the sun by both
 thermal and magnetic forces (according to current theories) [11]. Particles able
 to escape the Sun?s gravitational pull must have substantial kinetic energy, and in
 fact the solar wind is made of energetic particles with velocities of typically 400 to
 650 km/s. (For protons, this typical velocity is equivalent to energies on the order
 of a few keV per nucleon.)
 The solar wind expands through the solar system, interacting with the planets,
 moons, comets, and other various objects of the heliosphere (including man-made
 objects). The e ect the solar wind has in these encounters depends on the nature
 of the object; it is responsible for the tails in comets, for example. Other bodies
 with atmospheres directly impacted by the solar wind would have that atmosphere
 stripped away in like manner [12]. The solar wind would have a similar e ect on
 our own planet, were it not for the Earth?s magnetic  eld.
 The Earth?s magnetosphere acts as a shield from the solar wind. When elec-
 trons and ions in the solar wind encounter the Earth?s  elds, the Lorentz force2
 causes the particles to slow and de ect around the outside of the  eld. The result-
 ing shock wave3 that results where the solar wind directly impacts the magnetic
 2The Lorentz force describes the forces felt by charged particles moving in a magnetic  eld,
 where F = q~v  ~B.
 3A shock wave occurs when the velocity of the particles rises above or drops below the local
 12
 eld and slows down is called the bow shock (see Fig. 1.4). Through this interac-
 tion, the solar wind particles are heated to energies ranging from 1{10 keV. Most
 of the solar wind is de ected completely around the Earth, which has the e ect of
 creating the long tail characteristic of the Earth?s magnetic  eld. The compression
 that occurs at the bow shock is dependent on the exact conditions of the solar wind.
 During periods of substantial solar activity, the Earth?s magnetic  eld can compress
 far enough to expose orbiting satellites directly to the solar wind. Though for the
 most part the solar wind material is de ected around the Earth, some of the mate-
 rial precipitates into the Earth?s atmosphere through the cusps, resulting in direct
 interaction between solar and ionospheric material.
 1.2.4 Ionospheric Plasma
 A description of the ionospheric plasma depends on the speci c region of the
 ionosphere. In the topside layer, where much of the direct interaction with the solar
 wind takes place, most of the ionospheric plasma is ionized oxygen atoms. The
 protons of the solar wind penetrate through the topside layer, and at lower altitudes
 account for a substantial portion of the plasma composition. At these altitudes, we
 also  nd ionized molecular oxygen (O+2 ), and at the lowest altitudes of the ionosphere
 we also  nd ionized nitric oxide (NO+). Each population of the ionospheric plasma
 has di erent properties, such as energy and density. Though there are potentially
 many constituents to the ionospheric plasma, within the region of the polar cusp at
 sound speed. The sound speed in a plasma is given by c2s =  p= , where  is the ratio of speci c
 heats, p is the plasma pressure, and  is the plasma density.
 13
orbital altitudes the dominant ions are oxygen ions (O+) at energies of up to 10 eV
 and 1{10 keV solar wind protons.
 The ionospheric plasma is quasi-neutral4, so a complete description should
 also include the electron population. In the F layer, the electron density (and by
 quasi-neutrality the ion density) will typically be 105{106 cm 3. Electrons released
 from photo-ionization in the ionosphere typically have thermal energies of up to a
 few eV [13], while the hotter solar wind electrons have thermal energies of a few 10?s
 of eV and can be accelerated to 100?s of eV [14].
 1.3 Heating in the Ionosphere
 The transfer of energy from outside the magnetosphere to the ionospheric
 plasma can result in an increase in temperature of either ions or electrons within
 the plasma, the neutral gas of the atmosphere interspersed with the plasma, or any
 combination of the particle states. In fact, heating of one component can result in
 heating of the others through common interactions. In this way, the neutral gas
 can be heated both directly and indirectly by heating processes that occur in the
 ionosphere.
 There are a number of heating processes that can occur in the ionosphere.
 While most of these are similar in the means of heating the neutral gas in the at-
 mosphere, the subtle distinctions between them give information about the initial
 4Quasi-neutrality is an assumption often made in plasma physics that the number of positive
 charges and the number of negative charges within an arbitrary volume of plasma are roughly
 equal.
 14
causes and sources of energy for the heating. In all cases, heating of the neutral gas
 causes it to expand, transporting neutral gas to higher altitudes. This rising, or up-
 welling, of the neutral gas increases the density at higher altitudes while decreasing
 the density at lower altitudes.
 The heating processes that are considered most important are electrodynamic
 in nature; while extreme ultraviolet (EUV) light from the sun does heat our atmo-
 sphere, magnetospheric inputs dominate the energy transfer to the neutral gas in the
 ionosphere [15]. These inputs are the result of an interaction between ionospheric
 plasma (created by solar EUV ionizations in the ionosphere) and the solar wind.
 1.3.1 Joule Heating
 When the solar wind passes over the Earth?s magnetosphere, it produces a
 current at the magnetopause. The presence of the current links the solar and ter-
 restrial magnetic  elds, allowing energy to be transferred from the solar wind to
 the ionosphere by induction. The electric  elds created between the solar wind
 and the ionosphere drive currents in the ionospheric plasma perpendicular to the
 magnetic  eld. Since the neutral gas density is much larger than ion density in the
 ionosphere, the ionospheric plasma dragged along by the solar wind currents pass
 through a collisional neutral gas. The friction created by collisions between the ions
 and the neutrals transfers energy from the solar wind to the neutral gas and causes
 it to heat. We refer to this speci c heating process as Joule heating.
 Joule heating is often seen when an increase in activity between the solar wind
 15
and the ionosphere causes a temporary perturbation in Earth?s magnetic  eld over
 a large area. These events are called geomagnetic storms. In typical storms, the
 peak Joule heating rate occurs near 150 km in altitude [16].
 1.3.2 Ohmic Heating
 As the solar wind passes over the Earth, the subsequent movement of the
 ionospheric plasma can distort the Earth?s magnetic  eld locally. Distortion of the
 magnetic  eld causes tension-like forces on the plasma. If the tension created by the
 distortion and the forces due to the pressure of the plasma itself are unbalanced,
 currents will  ow along magnetic  eld lines. These so-called  eld aligned currents
 (FACs) of ionospheric electrons and ions increase the collision rate between the
 charged particles, heating the ionospheric plasma in much the same way a resistor
 in an electric circuit is heated when current passes through it. When the electrons
 and ions upwell due to the increase in temperature, neutral gas is dragged along
 with the rising plasma, causing neutral upwelling.
 Though the overall e ect is the same as in Joule heating, where the heat
 transferred to the ionosphere causes the neutral gas to be heated and upwell, the
 distinction is made here that the collisions are primarily between electrons and ions
 rather than ions and neutrals. To distinguish this process from Joule heating, this
 process is called Ohmic heating to be consistent with literature discussing electron
 heating and cooling processes [17].
 16
1.3.3 Electron and Ion Precipitation
 Under certain conditions, where the solar and terrestrial magnetic  elds are
 aligned favorably for magnetic reconnection5 to occur, the particles in the solar wind
 are able to penetrate the magnetopause at the cusp. These particles are sometimes
 responsible for the aurora, and can also heat the ionosphere.
 Since the typical temperature of ionospheric plasma is on the order of 1{10 eV,
 mixing of solar wind plasma of temperature 1{10 keV with the ionosphere increases
 the overall temperature of the electron or ion plasma. An increased number of
 charged particles can also lead to increased Ohmic heating. The resulting electric
  elds from the movement of the heated plasma particles cause the ionospheric plasma
 to expand, again dragging the neutral gas along. This mechanism is distinct in that
 the source of energetic particles is the solar wind itself, and not the ionosphere.
 1.3.4 Alfv en and Other Plasma Waves
 At high altitudes, the ionospheric plasma is turbulent. In this turbulent region,
 a number of types of plasma waves can occur. In addition, small-scale  eld aligned
 currents can drive waves in localized regions of ionospheric plasma, particularly in
 the auroral zone. The energy in these waves can locally heat the ionosphere through
 5Magnetic reconnection describes an interaction of a plasma as it moves between magnetic  eld
 regions with di erent topologies, such as the interface between the interplanetary magnetic  eld
 and the Earth?s magnetosphere. Reconnection causes charged particles to accelerate outward from
 reconnection points. Southward pointing interplanetary magnetic  elds are most favorable for
 reconnection at the dayside magnetosphere. See, for example, [18] for further information.
 17
Joule and Ohmic heating. A key distinction in plasma wave heating is that it is
 very localized rather than heating broadly over the ionosphere.
 1.4 Consequences of Ionospheric Heating
 1.4.1 Upwelling
 Whenever a gas is heated at constant pressure, it will expand. The heating
 that occurs in the ionosphere has the same e ect. When the heating is localized
 within a particular altitude, the atmosphere expands upward. The expansion de-
 creases gas density at that altitude, and increases density at the altitudes to which
 it expands. The resulting density enhancement is what we call upwelling. The
 upwelling phenomenon can occur for both neutral gas and plasma.
 1.4.2 Jeans Escape
 The atoms, molecules, and ions in our atmosphere are con ned by Earth?s
 gravity. Just as a rocket with enough velocity can escape the gravitational  eld,
 so can any of these particles. If there is su cient heating, a particle can accelerate
 to a velocity above the escape velocity, and the particle can leave the atmosphere.
 This mechanism is often called Jeans escape, named after Sir James Jeans, who  rst
 described the process. The escape velocity, given by:
 ve =
 s
 2GM
 r
 (1.5)
 18
depends on the mass of the Earth M and the distance from the center of the Earth
 r. At orbital altitudes, this value is roughly 10 to 11 km/s. For hydrogen, that
 velocity is equivalent to an energy of only 0.5 eV, which is why we see so little
 hydrogen naturally occuring in our atmosphere.
 For the common constituents of our neutral atmosphere, heating processes
 could feasibly cause some of the gas to escape Earth?s gravity and  ow into space.
 The amount of heating we observe, however, is not su cient to cause signi cant loss
 of our neutral atmosphere.
 1.4.3 Ion Out ow
 While there is not a substantial loss of neutral gas through Jeans escape, there
 are periods of su cient heating, particularly in the cusp, of ions such that they are
 able to reach escape velocity. For oxygen atoms, the equivalent energy to escape
 velocity is 10 eV, low enough to be achieved through the heating processes we have
 described. A loss of ionospheric ions does occur under certain circumstances, and
 a  ow of ions from the polar cusps with energies  10 eV has been observed. This
 phenomenon is called ion out ow.
 1.5 Measurements of Ionospheric Heating
 1.5.1 Neutral Upwelling
 The phenomenon of neutral upwelling in the cusp has been observed since
 early in the space age. In 1963, the Injun-3 satellite experienced an unexpected
 19
increase in drag when traveling through the auroral zones [19]. The increased drag
 was attributed to an increased ionosphere density in that part of its orbit. Injun-3
 orbited at an altitude of only 250 km. Joule heating processes in the stratosphere
 and ionosphere seemed the likely source of the increase in neutral gas density.
 In 2000, the CHAMP satellite was put into a circular, polar orbit at approxi-
 mately 400 km altitude. CHAMP?s suite of instruments includes a very precise and
 sensitive 3-axis accelerometer that takes measurements on a much shorter time base
 (typically 10 s) than an orbital period. The high resolution data it provides are use-
 ful in resolving features in the atmosphere causing drag on the satellite. Using data
 from this instrument, L uhr et al. [20] observed that density enhancements could be
 as much as a factor of two greater than normal, and that the enhancements were
 highly localized to the cusp region. These enhancements were coincident with large
  eld-aligned currents in the ionosphere.
 More recently, a study using neutral density data from the STREAK mission
 found a density depletion, rather than an enhancement, at an altitude of 250 km in
 the south magnetic cusp [21]. The depletion was only 1{2% of nominal densities,
 however in the context of the results of L uhr et al., the results suggest that there is
 something causing the neutral density changes other than (or perhaps in addition
 to) Joule heating as previously assumed.
 One assumption that explains the observed upwelling is that more Joule heat-
 ing occurs than was expected. However, recent modeling suggests that much stronger
 Joule heating still is not su cient to cause the observed upwelling, and does not
 explain its distinctive localization [22],[23]. Other possible contributors to neutral
 20
Figure 1.5: Results from L uhr (2004) [20] showing the deceleration of the CHAMP
 satellite over multiple orbits on 25 Sep 2000. The results show signi cant density
 enhancements at high invariant latitude near magnetic noon, corresponding to the
 spacecraft passing through the cusp. Invariant latitude (ILT) of the spacecraft and
 magnetic local time (MLT) are labeled at each peak. ILT and MLT are essentially
 the equivalent of latitude and longitude in a coordinate system for Earth?s magnetic
  eld. (See Sec. 4.7.5.)
 Figure 1.6: Results from Clemmons (2008) [21] showing a depletion in neutral den-
 sity at altitudes where enhancement should be seen assuming Joule heating accounts
 for the upwelling. Coordinates are in ILT (radial) and MLT (angular), or latitude
 and longitude coordinates in the Solar Magnetic coordinate system (see Section
 4.7.5). The white oval suggests the approximate location of the day-side cusp, and
 matches the location of the depletion.
 21
upwelling include Alfv en waves in the aurora (a potential source of extra Joule
 heating), small and large scale  eld aligned currents, and electron precipitation.
 1.6 This Study
 1.6.1 RENU
 To better understand the neutral upwelling phenomenon and the processes
 that ultimately drive the heating of the neutral gas, a sounding rocket campaign was
 proposed and carried out. The Rocket Experiment for Neutral Upwelling (RENU)
 is a collaboration of six research groups that designed a sounding rocket payload
 consisting of 14 separate instruments. The payload was designed to launch on a
 Black Brant XII rocket and be carried to an altitude of 500 km over the north
 magnetic pole.
 Ultimately, the RENU campaign was unable to obtain the needed data due
 to a malfunction of the nose cone ejection system. The project is currently under
 consideration for refunding to launch again.
 Our group at the University of Maryland, College Park (UMD) and NASA?s
 Goddard Space Flight Center (NASA/GSFC) designed, built, and tested one of the
 instruments on board the RENU payload. The keV Ion Magnetic Spectrograph
 (KIMS) instrument measures high energy ion distributions between energies of 0.1
 and 10 keV. Chapters 2 and 3 of this dissertation describe the KIMS instrument and
 its testing. The design of the instrument developed new techniques for measuring
 ion energy distributions that are e ective for sounding rocket  ights, not the least of
 22
which is a new, inexpensive fast ampli er system for microchannel plate detectors.
 The mechanisms and design parameters of the KIMS instrument will be described
 in Chapter 2, and the testing results in Chapter 3.
 1.6.2 Statistical Analysis of Ionospheric Energy Sources
 With the loss of the RENU payload, another study was undertaken to bet-
 ter understand the role electrodynamic energy sources play in neutral upwelling.
 This analysis used data from the Fast Auroral Snapshot Explorer (FAST) in ad-
 dition to CHAMP data from the Spatial Triaxial Accelerometer for Research (or
 STAR accelerometer) to examine the statistical correlations between electromag-
 netic (Poynting) energy  ux and kinetic (particle) energy  ux. As a statistical
 study, no direct causal relations for the causes of neutral upwelling can be drawn
 from the correlations, but we can examine the relative importance of these energy
 sources. This analysis identi es the properties most useful to study when a second
 RENU-like payload is prepared. Further background for this study is provided in
 Chapter 4, a description of the analysis methods in Chapter 5, and the results of
 the analysis in Chapter 6.
 23
Chapter 2
 Ionospheric Ion Detection and the KIMS Instrument
 The environment in the ionosphere and in space is hostile and unforgiving
 to instruments of any sort. Any instrument designed to make measurements in
 these regions is a collection of compromises. The goal in developing an instrument
 to measure  elds or particle properties in space is to sense the properties needed
 without a ecting the environment itself. In reality, any detection scheme will exert
 some in uence on its surroundings at the detriment of accuracy in measuring the
 properties of interest. For particles, such as ions, instruments are designed to collect
 ions from the surroundings in such a way as to be able to determine their sources
 and their energies. In some cases, the instrument can also identify the di erent ion
 species present.
 Over the years, a number of di erent detection schemes have been developed.
 Each has its advantages for certain types of measurements and certain circum-
 stances. Many of these designs use electric  elds to select speci c energies per
 charge or, in some cases, direct particles to a speci c detector. These designs often
 require sweeping voltages in order to scan energy per charge and/or viewing angles.
 Such a detection scheme is termed a spectrometer, as it can only measure one value
 of the spectrum (be it energy or direction) at a time. There are also detectors
 that are able to measure a range of values simultaneously. Devices that are able to
 24
capture a range of values of a spectrum are termed spectrographs.
 Descriptions of many successful ion and electron instrument designs that have
  own on important and historical missions have been collected and compiled for
 reference [24]. The articles in this compilation help to understand how the various
 types of spectrometers and spectrographs were built and how they function. Though
 these instruments are very useful and well-designed, new instrument designs make
 it possible to examine new environments and phenomena in unique ways.
 An ion spectrograph that takes measurements of the local charged particle
 energy spectrum at millisecond time resolution is ideal for a study of the neutral
 upwelling phenomenon. On a sounding rocket  ight, mass is often not so much
 of a consideration as on orbiting spacecraft, and so a permanent magnetic  eld
 can be used to separate ions of di erent momenta in the instrument rather than
 using a sweeped voltage to scan ion energies. Aside from the mass of permanent
 magnets and its supporting structure (the yoke), this scheme has the disadvantage
 of a ecting the magnetic  elds in the region around the instrument. Materials with
 high magnetic permeability and high magnetic saturation points are used to shield
 other instruments and the local plasma external to the instrument from the strong
 internal  elds. In this chapter, we describe a spectrograph designed for the RENU
 sounding rocket campaign. This instrument is able to measure ions with energies
 between 0.1 and 10 keV (assuming singly charged hydrogen ions) at a rate of 250 Hz.
 The instrument design is called the KeV Ion Magnetic Spectrograph (KIMS).
 25
2.1 The KeV Ion Magnetic Spectrograph
 The KIMS design makes use of two permanent magnets in a high magnetic
 permeability yoke. The yoke is specially designed to provide two regions of constant
 magnetic  eld. The magnets and yoke assembly are referred to as the magnetic
 circuit. Inside the constant  eld regions, ions undergo cyclotron motion1. The radius
 of the circular ion trajectories is proportional to the momentum per charge of the
 ion. In this way, the magnetic  eld e ects a spatial separation of ions according to
 their momentum per charge. In the Earth?s cusp, the bulk of the ion composition
 is singly-ionized hydrogen atoms (protons) from the precipitating solar wind, and
 so, to a reasonable approximation in this region, the momentum distribution is
 equivalent to an energy distribution of the ionospheric protons.
 2.1.1 Energy Spectrum Dispersion
 The predicted energy distribution for the design can be modeled simply. Since
 cyclotron motion is circular, we can  nd the radius of rotation simply:
 rc =
 v
 !c
 =
 mv
 qB
 =
 p
 2mE
 qB
 (2.1)
 By placing a detector in the same plane as the instrument entrance aperture, parti-
 cles will be detected after half of a cyclotron rotation. The position on the detector
 where an ion will land is one diameter from the entrance point, or, accounting for a
 1 Cyclotron motion refers to the gyration of charged particles in a magnetic  eld. The Lorentz
 force q~v ~B causes charged particles moving perpendicular to the magnetic  eld to follow a circular
 path (helical if the velocity has a component parallel to ~B).
 26
Figure 2.1: Diagram showing the motion of ions in the KIMS magnetic  eld. Ions
 with more momentum (or energy for like-species) per charge have a larger radius,
 intersecting the detector farther from the entrance aperture.
  nite width aperture,
 d = 2rc + s =
 2
 p
 2mE
 qB
 + s (2.2)
 where s is the entrance point measured from the center of an aperture of width w
 with s positive when located closer to the detector than the aperture center. With
 these conventions, the value d is the distance from the aperture center to the impact
 point, providing a useful reference from which to measure the detector position.
 2.1.2 Field of View
 In reality, ions do not always enter the instrument at normal incidence. The
 incidence directions to this instrument will be described as azimuthal (angles away
 from normal parallel to the planes of the magnet surfaces, but still perpendicular
 27
to the magnetic  eld) and perpendicular (as in perpendicular to the magnet surface
 plane, but parallel to the magnetic  eld, see Fig. 2.2). A more general expression
 for the trajectory that accounts for the azimuthal angle of incidence is
 d = 2 cos  
p
 2mE
 qB
 + s (2.3)
 where  runs between the angular limits on the instrument?s view with  = 0 im-
 plying normal incidence. The KIMS instrument is designed with an azimuthal  eld
 of view that ranges between +19 and -6 . KIMS is mounted on the RENU payload
 with the azimuthal directions pointing in an arc along the direction of movement
 of the rocket. This results in a  eld of view looking radially outward and slighty
 elevated to the payload trajectory. Since the trajectory of RENU is designed to be
 aligned with the local magnetic  eld, ions travelling in directions nearly perpendic-
 ular to the local magnetic  eld are measured by the KIMS instrument.
 The instrument also has a  nite acceptance angle perpendicular to the plane
 of the magnets. Cyclotron motion only results from the perpendicular component
 of the ion?s velocity, so the ions are distributed according to their perpendicular
 momentum. The e ect of nonzero angles in this perpendicular direction is to reduce
 the observed energy of the particle. Since nonzero perpendicular motion implies
 motion parallel to the magnetic  eld, the velocity component in this direction is
 not subject to magnetic forces, and the cyclotron motion will be determined by the
 remaining component perpendicular to ~B.
 The height h of the spaces between the magnets and the partition of the
 28
Figure 2.2: Field of view for the KIMS instrument. Azimuthal direction looks
 upward, between +19 and -6 . Perpendicular direction looks radial, limited by the
 mechanical design to between  5 .
 29
instrument de nes the perpendicular acceptance angle  , as given by
 jsin j <
 h
  
qB
 mv
 (2.4)
 At large enough angles, ions will no longer be detected as they will collide with the
 magnetic circuit before reaching the detection plane. For increasing energy, the angle
 at which this occurs decreases with 1p
 E
 . At small vertical angles, the ion velocity
 component parallel to ~B is negligible. Small,  nite acceptance perpendicular to the
 plane of the magnets, then, only limits the view of the instrument and does not have
 an appreciable e ect on the energy response. In KIMS, the height of each partition
 is approximately 12.7 mm. With the given magnetic  elds of 0.1 and 0.27 T and
 measured energies of 0.1 to 10 keV, the perpendicular angular acceptance must be
 less than 16 with a corresponding reduction in measured energy of less than 8% (see
 Fig. 2.3). At this angle, only the lowest energy ions ( 100 eV) are detected, and so
 the mechanical structure of the instrument aperture further limits this acceptance
 to 5 on either side. This limit lowers the e ective measured energy reduction to at
 most a negligible 0.8%.
 2.2 Microchannel Plates
 The detector used in the KIMS instrument consists of a pair of microchannel
 plates (MCPs) [25]. The MCP is a matrix of narrow glass tubes, or channels, sliced
 into thin wafers. Each face of the wafer is coated with a conductive material. An
 incident particle of su cient energy will cause electron emission from the semicon-
 ductive wall of the channel struck by the particle. When a strong electric  eld is
 30
Figure 2.3: Particles can only reach the detector in KIMS if they enter the instru-
 ment within a  nite  eld of view in the perpendicular direction. A particle entering
 at 5 will reach the detector with a negligible di erence in its e ective energy. A 100
 eV particle entering at 17 would have a more noticible energy reduction, but would
 collide with the magnetic circuit?s partition before reaching the detector. Higher
 energy ions collide at lower angles. In KIMS, the mechanical structure holding the
 magnetic circuit limits the view to  5 in the perpendicular direction.
 31
Figure 2.4: Diagram of MCP function, taken from Wiza [1979].
 created by applying an electric potential across the plate, the secondary electrons
 are accelerated until they collide with the channel wall themselves, producing ad-
 ditional secondary electron emissions. The end e ect is an avalanche of secondary
 emissions as each newly emitted electron is driven further down the channel by the
 electric  eld. The result of a single particle incident on the MCP is an emission of a
 large number of electrons, usually on the order of 103. A second plate added to the
 system increases the total gain to 106, providing easily detectable current pulses for
 single particle events.
 Output current pulses from the MCP are collected with a segmented anode. A
 circuit board is etched to leave a number of exposed pads located behind the MCP
 output. The charge pulses are collected by the plates and ampli ed by a charge
 sensitive ampli er that triggers a logic pulse from a discriminator. The logic pulses
 are counted to record the number of events that occur at a given pad over a given
 time. Since electron emission in the MCP is a statistical process, a varying number
 of electrons can be emitted for each event. The resulting distribution of charge
 32
pulse amplitudes are commonly known as the pulse height distribution (PHD). The
 pulse height distribution of an MCP can be described as a negative exponential
 when the plates are not saturated [26], and have been found to be a property of
 the plates themselves, being nearly independent of the type of incident particles
 [27]. These properties simplify the detector, as its calibration requires only an
 appropriate threshold for counted pulses rather than a full pulse height analysis
 [28]. This threshold is selected to separate the PHD from the background noise in
 the detector electronics.
 2.2.1 KIMS Detector Response
 For a given momentum and angle of incidence, a uniform distribution of ions
 across the aperture width will map to a region of the same width at the detector
 plane. This creates a nearly triangular probability distribution for the energies of
 particles detected by any given pad on the segmented anode for a given angle of
 incidence (see Fig. 3.3). Including all angles of incidence creates a more Gaussian
 distribution. A Monte Carlo simulation including a range of energies, aperture
 positions, and angles of incidence provided a model of the energy response function
 for the instrument design. (See Section 3.1.1 for more details.)
 2.3 Project Scope
 The concepts behind the design of KIMS are general and can be adjusted to
 suit the needs of a variety of enivronments. The design of the KIMS instrument was
 33
Figure 2.5: Response of one of the anode segments at normal incidence only, and
 with the full range (-6 to +19 ) of azimuthal incidence. The triangular shape at a
 given incidence results from the mapping of the aperture width to the same width
 at the detector plane.
 34
based on previous designs done at the University of Maryland and used spare com-
 ponents from those instruments. These earlier designs were also intended for cusp
 ion measurements. The basic parameters for the earlier instruments matched well
 with the needs of the RENU project. Changes to the heritage design were necessary
 to accommodate a new MCP detector system and a new telemetry interface.
 2.3.1 Goals for KIMS
 When KIMS was added to the instrument suite on RENU, a low-energy ion
 detector (observing ions of thermal energy to 800 eV) had already been included on
 the payload. The primary goal for KIMS, then, was to observe high-energy ions in
 the 1{10 keV range. The overlap of the lower energy range of KIMS with the other
 ion instrument on the payload provided the added bene t of redundancy and cross
 calibration between ion detectors.
 KIMS is designed to take measurements at a rate of 250 Hz, determined pri-
 marily by the capabilities of the telemetry unit included on RENU. This sample rate
 is fast enough to potentially observe the cyclotron motion of ionospheric atomic oxy-
 gen. (O+ in the Earth?s magnetic  eld has a cyclotron frequency of about 100 Hz.)
 The ability to observe this motion would have the added bene t to KIMS of allowing
 a coarse mass discrimination not possible using only the momentum separation via
 cyclotron motion in the instrument?s magnetic  elds. Such a mass discrimination
 would be of interest, but not essential for the goals of the KIMS instrument.
 35
2.3.2 Changes From Heritage
 The original instrument design called for use of a set of 20 discrete channel
 electron multipliers (CEMs), separated into groups of 10 channels for each energy
 range (100{1000 eV and 1{10 keV). While robust and reliable, the CEM detectors
 proved to be prohibitively expensive with a long lead-time for manufacture. The
 KIMS design instead uses an MCP stack with a segmented anode as the detector.
 The anode design uses 10 pads for each of the energy ranges, keeping a similar
 con guration to the original CEM design. MCPs have been used in a number of
 sounding rocket  ights, and various shapes and sizes are available commercially, o 
the shelf. However, the design for KIMS was constrained by the volume in which
 the original CEM detectors were to  t. As a result, a custom size MCP plate and
 holder were designed, manufactured, and quali ed for robustness on a sounding
 rocket  ight.
 To accompany the MCP design, the instrument electronics were also redesigned.
 The new electronics make use of an inexpensive IC ampli er (as opposed to the more
 costly AmpTek A111 discrete ampli ers). The circuit was designed to operate at
 a high frequency, and the overall cost for the complete ampli er circuitry for all
 20 channels was less than the price of one of the original ampli ers. The new de-
 sign was tested and proved satisfactory for the anticipated  ux rates of 104{105 per
 (cm2  s  sr  eV) as observed by one of the earlier instruments on which the KIMS
 design is based (see Fig. 2.6). While ideal on a sounding rocket  ight, the ampli er
 design is not radiation hardened, and would require further modi cation for orbital
 36
or exploratory satellites.
 The MCP detector allowed the use of a lighter, lower power high-voltage power
 supply because of its low power consumption in operation. The high voltage circuit is
 designed with two supplies for redundancy, and still weighs less than the one supply
 design used in the earlier instruments. The design of the circuit allows changes to
 the applied voltage on the MCPs, requiring the change of only one or two resistors.
 2.3.3 Basic Parameters for KIMS
 The KIMS design uses two  elds of magnitude 0.1 T and 0.27 T. These  elds
 give energy ranges (for protons) of approximately 100{1000 eV and 1{10 keV over
 the length of the detection area. The detection area (or the size of the MCPs)
 is roughly the size of a standard microscope slide (2.5 cm x 7.6 cm). An aperture
 3 mm wide and 17 mm high opens each region to a  eld of view that spans  6 to
 +19 in azimuth and  5 in elevation (see Fig. 2.2).
 An anode pad pattern of quadratically increasing pad widths was chosen to
 provide a similar  E=E response over the full energy range to that of the original
 CEM design (see Fig. 3.4). The chosen pad widths were constrained by the size
 of the detector itself, and so a constant  E=E, requiring a much larger detector
 size for reasonable pad widths, was not feasible in this design. Each anode pad is
 connected to an individual ampli er and discriminator circuit with an output to an
 FPGA that counts the number of detected pulses in every 4 ms interval. The FPGA
 reports the count values of each anode pad to the rocket telemetry system at a rate
 37
Figure 2.6: Figure showing results from measurements taken with instrument de-
 signs on which the KIMS instrument was based. The overlayed curves describe the
 rocket orientation applicable to this previous study. The contour plot indicates the
  ux values one can expect in the polar cusps. For KIMS, with a subtended solid
 angle of approximately 8:55 10 3 sr, a  E of about 200 eV ( E/E of about 0.25),
 and an anode size of roughly 1 cm2 indicates an expected maximum count rate of
 roughly 104 counts per second per anode at low energies. The KIMS electronics are
 designed to be able to handle up to 106 counts per second.
 38
of 250 Hz.
 Power is provided to the instrument from the +28 V battery on the rocket.
 This voltage is regulated to 12 V for the high voltage power supply control and 3.3 V
 for the ampli er, discriminator, and FPGA telemetry circuitry. Two high voltage
 power supplies connected in parallel provide feedback-controlled -1.6 kV to the MCP
 stack. Total power consumption for the instrument during operation is estimated
 at a maximum of 8.4 W. Data from integration testing indicated the instrument
 performed at half this power on the ground when the MCPs were not fully powered.
 Full power consumption was estimated generously to provide a comfortable margin
 of error for  ight conditions.
 The instrument and electronics are enclosed in a  -metal case with dimensions
 9 cm x 17 cm x 20 cm. The combined yoke of the magnetic circuit and this enclosure
 are e ective in shielding the strong magnetic  elds inside the instrument, and reduce
 the stray  eld to 10 nT at a distance of 1 m, as tested at the Magnetic Calibration
 Facility at NASA?s Goddard Space Flight Center (see Sec. 3.3.1). An aluminum
 bracket was designed to mount the instrument vertically on the rocket payload, with
 the azimuthal view along the rocket?s  eld-aligned trajectory. The instrument view
 is centered at about +6 above a directly radial view to the magnetic  eld. The
 entire assembly weighs less than 4.5 kg.
 39
Figure 2.7: Photos of the magnetic circuit. The apertures are the smaller openings
 on the right side. The partition can be seen between the two halves through the
 space where the detector is mounted on the left side. The permanent magnets
 are attached to the interior of the top and bottom plates, secured with aluminum
 clamps. These mangets create  elds of 0.1 T on the top and 0.27 T on the bottom.
 2.4 KIMS Design
 2.4.1 Magnetic Circuit Design
 The magnetic circuit refers to the portion of the instrument that creates the
 constant magnetic  elds needed to accurately disperse the incoming ions by their
 momentum per charge. The magnetic circuit is an assembly of specially designed
 pieces (the yoke) around two permanent magnets. The yoke provides a return path
 for the magnetic  eld and shields the exterior of the instrument from the strong
 magnetic  elds inside. The two permanent magnets, of di erent strengths, are
 mounted inside the yoke to create the magnetic  eld.
 The hallmark of the magnetic circuit design is the Vanadium Permendur2
 yoke that encases the magnets. Vanadium Permendur is a steel alloy with a high
 cobalt concentration and a small portion of vanadium. The alloy is heat treated
 2Vanadium Permendur is also called Hiperco 50TM
 40
carefully before machining, giving it a high magnetic permeability that does not
 saturate in strong magnetic  elds. The thickness of each Vanadium Permendur
 part is determined through careful simulation of the magnetic  elds to optimize the
 homogeneity of the  eld strength inside the instrument throughout the detection
 region. Vanadium Permendur is brittle and its magnetic properties sensitive to
 both heat and shock. All of the parts made from this alloy were machined via wire
 EDM.
 The magnetic circuit assembly consists of two halves, with one magnet for
 each side of the instrument. Each magnet is a semi-circular plate with a 6 cm ra-
 dius. Each is fabricated with an assembly of custom designed segments to create a
 uniform  eld across the face of the plate. The magnets in our design have di ering
 strengths of approximately 0.1 T and 0.27 T. Each magnet is placed carefully on
 one of two Vanadium Permendur plates that become the top and bottom of the
 magnetic circuit. The magnets alone are strong enough to keep themselves in place,
 however aluminum clamps around the magnet pole faces prevent them from shifting
 during vibration. Each magnet is then surrounded with a Vanadium Permendur
 shell. Openings in the shells provide for the instrument apertures and the detector
 assembly. The two sides of the magnetic circuit are brought together with a Vana-
 dium Permendur partition that separates the two regions of magnetic  eld. The
 entire assembly is aligned using three non-magnetic, stainless steel roll pins. Brass
 screws are used to secure the clamps in place.
 The  nal part in the magnetic circuit is a wire mesh grid placed at the face of
 the detection plane opening. This grid is grounded along with the entire magnetic
 41
Figure 2.8: Photo showing the mesh grid in place on the magnetic circuit. An
 aluminum clamp holds the grid in place. The entrance apertures for the two sides
 of the instrument are visible on the right.
 circuit to prevent the electric  elds of the detector assembly from distorting the
 cyclotron motion of ions inside the instrument. The grid is 70 lpi, 90% transmission,
 nickel mesh sandwiched and spot welded between two phosphor bronze frames.
 2.4.2 Mechanical Design
 The magnetic circuit is held in a close  tting, aluminum bracket referred to
 as the clamshell. The clamshell halves bolt together, securely holding the magnetic
 circuit while eliminating the need for fasteners in the brittle Vanadium Permendur
 parts. The clamshell also serves as a mounting platform for all of the electronics
 and the detector assembly. The entrance aperture on the clamshell is cut to provide
 the  6 to +19 azimuthal  eld of view into the instrument.
 42
Figure 2.9: The clamshell halves and assembled around the magnetic circuit. The
 detector and electronics are all fastened to the clamshell using tapped bosses on the
 outside surfaces.
 The circuit boards are mounted on the instrument sides with threaded stand-
 o s. The stando s also support the high-permeability,  -metal shield that covers
 the entire instrument. The shield has openings for the two apertures, the three
 cable connectors for power and telemetry, and a safety plug that prevents the high
 voltage from being activated accidentally while at atmospheric pressure. All of the
 fasteners and connectors in the instrument are made of non-magnetic materials.
 A mounting bracket designed speci cally for the RENU sounding rocket was
  tted for the KIMS instrument. The bracket fastened into the bottom and the
 back of the instrument while leaving access to the cable connections. The bracket
 is bolted to the rear bulkhead of the payload, giving the KIMS instrument a view
 radial to the axis of the payload.
 43
Figure 2.10: The KIMS instrument enclosed in its  -metal case and attached to its
 mounting bracket, and mounted on the RENU main payload. The red plate in the
  rst image covers the aperture to the instrument for shipping.
 2.4.3 Detector Design
 The MCP detector stack was designed to  t in the space originally allotted
 for the CEM detector array. An MCP stack is typically held by compression in a
 housing made of an insulating material. The compressive housing, by its nature,
 masks a small portion of the detection area of an MCP. The KIMS detector thus
 has a 24% reduction in detector area in comparison to the CEM array due to the
 housing, however the di erence is negligible for the anticipated ion  uxes in the
 cusp.
 2.4.3.1 MCP Housing
 The MCP housing is built from four pieces: an outer housing, an inner housing,
 and two \rabbit ears" that extend to the position of the high voltage supply board.
 The rabbit ears are  xed to the inner housing, but the inner and outer housings are
 44
Figure 2.11: Engineering drawing and cross-section of the KIMS MCP detector.
 The individual components seen in the cross-section are, from bottom to top: outer
 housing, HV grid, insulator, contact ring, MCP 1, contact ring, MCP 2, contact
 ring, insulator, anode board, spring plate, and inner housing.
 maintained in place when connected directly to the instrument. This arrangement
 eliminates excess connections, minimizing the size and weight of the detector.
 2.4.3.2 MCP Stack
 The MCP stack assembly consists of (in order) a grid frame held at a high
 negative voltage, an insulator, an electrical contact, the  rst MCP, an electrical
 contact, the second MCP, an electrical contact, an insulator, the anode board, and
  nally the spring plate. The spring plate and inner housing have matching blind
 holes that accommodate a set of ten small springs. This mechanism provides ade-
 quate compression for maintaining electrical contact to the plates while protecting
 the plates from vibration during launch.
 The electrical contacts, including the front grid, are rectangular frames with
 extended tabs bent at 90 . These tabs are fastened to a set of conductive tabs on the
 rabbit ears. The rabbit ear contacts are bent over the top of the rabbit ears, where
 45
they are fastened to the high voltage board. This con guration provides electrical
 connection between the electrical contacts in the stack to the high voltage board.
 To prevent shorts between the extended tabs and the frames within the stack, a pair
 of thin UltemTM inserts on either side of the stack slide between the tabs and the
 stack pieces.
 The anode board is a gold plated, etched PCB with a set of 22 pins extending
 from the rear. Each region of the magnetic  eld is exposed to one half of the board.
 The ten pads on each half are sized to produce reasonable  E=E values over the
 full range of energies while maintaining safe pad spacings to minimize cross-talk
 between the pads. The pins, a set of 22 0.1" pitch square header pins, connect to
 the  rst board in the electrical stack assembly to send the charge pulses of each
 pad to their respective ampli ers. Two of the pins provide a ground connection for
 ground planes above and around the anode pads.
 The detector assembly is fastened to a plate that mounts on the face of the
 instrument. When in place, the front of the detector is su ciently o set from the
 grounded grid inside the magnetic circuit to prevent arcing when the negative high
 voltage is applied to the MCP stack. This mounting method also allows easy access
 and removal for assembly and testing of the instrument.
 2.4.4 Electrical Design
 The electrical system consists of two primary components: the two ampli-
  er/telemetry boards, which have the electronics for counting, processing, and for-
 46
Figure 2.12: Exploded view of the MCP stack as a rough sketch for all the parts.
 From bottom to top are the outer housing, the grid frame, an insulating ring, elec-
 trical contact, the  rst MCP, electrical contact, second MCP, electrical contact,
 insulator, the anode board, the spring plate, and the inner housing. Not shown in
 this sketch are the tabs on the electrical contacts or the ears on the inner housing.
 47
Figure 2.13: View of the anode board inside the detector. Glass slides are used here
 in place of the MCPs for mechanical testing to prevent contamination of the MCPs.
 Figure 2.14: Mechanical  t check of the MCP stack design. The front end of the
 detector is o set from the grid inside the magnetic circuit to prevent arcing.
 48
matting for transmission during  ight; and the electrical stack, which provides power
 to the MCP stack. The two ampli er boards attach to the sides of the clam shell,
 while the electrical stack assembly attaches to the front of the clam shell, directly
 above the detector. The stack assembly itself consists of three parts: a distribution
 board, which connects the anode board pads to the two ampli er boards; a ground
 plane, which shields the pulse signals from noise; and the high voltage supply and
 control boards, which turn the high-voltage power supplies on at the appropriate
 time during  ight.
 2.4.4.1 Ampli ers and Telemetry
 The ampli er portion of the detector system consists of a charge sensitive pre-
 ampli er followed by a shaping ampli er. These functions are both provided by
 an individual OPA 2354 dual op-amp chip for each pad on the anode board in the
 detector. Each ampli er output is sent to an individual discriminator, provided by
 an LMV331 comparator, to detect pulses. The input of the pre-ampli er is also
 connected to a 1 pF test input for calibration purposes (see Appendix A.4). Each
 of the two ampli er boards has a collection of 10 ampli er-discriminator pairs, one
 for each pad on the corresponding side of the instrument.
 Calibrating the amplitude of the shaped pulse from a known charge input
 allowed us to determine the voltage threshold for detected pulses. Pulses with a
 minimum of 500,000 electrons are counted. The pulse discrimination threshold is
 typically set by examining the dark count pulse height distribution of the MCPs
 49
[29], but this property was not examined for the KIMS instrument MCPs due to
 time and equipment constraints. Instead, a threshold typical to the types of MCPs
 used in the instrument was chosen. The gains of the MCPs used are high enough
 that there are typically more than 106 electrons in an event pulse from a pair of
 plates, so 5  105 electrons is a reasonable threshold while keeping above typical
 noise levels.
 Each discriminator provides a logic pulse output that is connected to one of 10
 inputs of an FPGA. The FPGA is programmed to count pulses over a 4 ms period.
 The counts for each channel are bu ered, formatted, and sent to the main payload?s
 pulse code modulation (PCM) stack to be transmitted down to the tracking station.
 All formatting for the KIMS instrument data is done on-board, so a simple serial
 data stream of the values in each ampli er?s counter in the FPGA is sent to PCM
 stack of the rocket.
 2.4.4.2 Electrical Stack Assembly
 The electrical stack assembly consists of four circuit boards stacked together
 and attached to the detector stack. These boards distribute the anode signals to the
 two ampli er/telemetry boards and control the high voltage applied to the detector.
 The distribution board has traces that connect the anodes in the anode board
 to the individual ampli ers. The traces on the anode board lead to a pin con g-
 uration such that we have a pattern of pads A0, B0, A1, B1, ... , A9, B9. This
 designation uses A and B to distinguish between the two magnetic  eld regions,
 50
Figure 2.15: Diagram showing the detector signal processing. There are 10 ampli er
 units for each side of the instrument. The 10 units are counted individually in an
 FPGA that formats the data for the telemetry stream.
 51
Figure 2.16: Ampli er/Telemetry board mounted on the KIMS instrument. An
 identical board is mounted on the opposite side. Each ampli er (a{j) consists of
 a pre-ampli er and shaping ampli er in a dual op-amp package. The ampli ers
 are followed by a discriminator. The outputs of each of the 10 discriminators are
 connected to individual channels in the FPGA and counted. The FPGA reports the
 counts from each 4 ms interval to the payload telemetry unit. Note that because
 the boards are identical, ampli er a is connected to anode pad 0 on the KIMS-A low
 energy side, but to anode pad 9 on the KIMS-B high energy side. The telemetry is
 formatted in the ampli er order A-a, B-a, A-b, B-b, etc., or equivalently to anodes
 A0, B9, A1, B8, etc.
 52
with A corresponding to the 0.1 T side and B to the 0.27 T side. The numbers 0-9
 identify the individual pads in order of increasing energy. The pad widths increase
 from pad 0 to pad 9. The ampli ers on each board are labeled a through j. Since
 the ampli er boards are identical, the ampli er sequence reverses between the two
 sides due to the ampli er board orientation on the instrument; A0-9 connect to
 ampli ers a{j respectively on their ampli er board, while B0-9 connect to ampli ers
 j{a respectively on their board (see Fig. 2.16).
 The ground plane is a two-sided PCB with no traces. The soldermask is
 removed in the areas where the assembly is fastened together to ground the two sides
 of the board to the instrument case. This piece is simply to isolate and minimize
 noise in the MCP anodes.
 The high voltage supply board consists of two independently controlled Emco
 Q30-12 high voltage DC{DC converters. These power supplies have a proportional
 output controlled by a 0{12 V input. They are connected in parallel to provide
 redundancy during  ight. The rabbit ears from the detector stack extend beyond the
 distribution board and ground plane to contact the pads on this board that provide
 the voltages at the various points. These are fastened with 0-80 screws to secure
 the electrical connection. The high voltage supply is connected across a voltage
 divider, using the resistance of the MCPs in series with high-voltage resistors on
 the supply board. The supplies are set to provide -1.6 kV across the entire detector
 stack, with an approximately 70 V drop from the front grid (at -1.6 kV) to the  rst
 MCP, as well as the second MCP to the anode board (at ground). This voltage
 was determined to be within the optimal operating range for the MCPs used in the
 53
detector.
 Finally, the high voltage control board that drives the HV supplies connects
 to the supply board. A feedback loop on this board is used to maintain a constant
 -1.6 kV output from each supply. In addition to controlling the high voltage supplies,
 this board also connects to the PCM stack to report three analog values in each 4 ms
 time interval. The feedback voltage on each high voltage supply is reported, as is
 the temperature of the control board.
 2.4.5 Ground Support Equipment
 Ground support electronics (GSE) were developed to accompany the instru-
 ment during testing and integration. The GSE system provides a simulated con-
 nection to the rocket?s telemetry unit to check the condition of the instrument
 and obtain calibration data. The GSE uses an FPGA to simulate the telemetry
 communication and a TI MSP430 microcontroller to interface the instrument to a
 computer via USB. The GSE was used for both testing and calibration of the KIMS
 instrument.
 The ampli er boards are programmed to provide a test signal into each am-
 pli er. Pulses at a speci ed frequency are sent from the FPGA to the test input of
 each ampli er on the board, using progressively lower frequencies on each successive
 ampli er (dividing by a factor of 2 at each ampli er). This test signal provides a
 known count-rate pattern that is reported back to verify that the circuit is work-
 ing properly. Each ampli er/telemetry board is programmed with a unique base
 54
Figure 2.17: Diagram showing the high voltage system. A feedback loop from the
 high voltage supply output is used to keep the output steady through  ight, even
 if the bus voltage were to change. Three analog signals monitoring the health of
 the power supplies are measured and included in the telemetry. These measure the
 temperature and voltage values of the high voltage control board.
 55
Figure 2.18: Electrical Stack Assembly mounted on the KIMS instrument. The
 top board seen here is the high voltage control board. The high voltage power
 supplies are on the board immediately behind it, followed by the ground plane and
 distribution board that connects to the ampli er boards on either side.
 56
frequency to distinguish the signals between the two sides of the instrument, using
 100 kHz on the KIMS-A board (each subsequent frequency is reduced by a factor
 of two for the 10 ampli ers on the board) and 200 kHz on the KIMS-B board. The
 GSE is programmed to issue the same commands to the boards for testing purposes.
 For testing and calibration, the GSE uses an MSP430 microcontroller to in-
 terface an FPGA simulating the rocket PCM stack with a USB serial connection to
 a computer. The MSP430 programming is a simple system that triggers from the
 simulated telemetry signals given by the GSE FPGA. When the FPGA simulates
 a frame-ready state of the PCM, the MSP430 reads out the proper data from the
 telemetry frames corresponding to KIMS data, formats the values into 16-bit hex-
 adecimal, and reports the values via serial USB to the computer. A serial terminal
 program capable of logging the data stream to a  le is used to record the data.
 The instrument itself continually takes and reports data, but data are only recorded
 when requested. For testing purposes, the MSP430 was programmed to wait for
 a single character command input from the terminal program and then record the
 next 100 samples reported by the instrument telemetry boards.
 2.5 KIMS Summary
 In summary, the KIMS instrument uses an e cient permanent-magnet sys-
 tem to disperse ions by their momentum. For a given ion mass, this dispersion is
 equivalent to a separation by energy. Each side of the instrument measures ten
 ranges of energy simultaneously, with side A measuring 100 to 1000 eV, and side
 57
B measuring 1 to 10 keV. An MCP detector is used to count individual ions inci-
 dent to the detector plane, with 10 anodes on each side collecting the charge pulses
 from the MCP stack. The charge pulses are counted with an inexpensive integrated
 circuit ampli er/discriminator pair and formatted for telemetry by an FPGA. The
 MCP stack is powered with a high-voltage DC{DC converter using feedback con-
 trol to maintain a constant bias voltage to the MCPs through the course of  ight.
 The entire instrument is enclosed and shielded to minimize stray magnetic  elds,
 and provides an excellent data collection rate at a size and mass compatible with
 sounding rocket requirements.
 58
Chapter 3
 KIMS Analysis, Data, and Results
 The KIMS instrument was thoroughly tested and calibrated prior to  ight.
 Instrument properties were also modeled numerically, and the tests performed show
 excellent agreement with the model calculations. The instrument electronics were
 also tested and adjusted to optimize operating parameters for the particular sound-
 ing rocket  ight. In addition, the instrument underwent vibration and magnetic
 testing to qualify for the rocket  ight pro le and parameters. The magnetic testing
 also provides understanding of what impact stray magnetic  elds from KIMS might
 have on other instruments on the payload.
 Operational testing done at the University of Maryland used an established
 vacuum chamber system. MCPs require pressures below 2 10 6 torr for safe op-
 eration. Calibration testing was done at a pressure of approximately 1 10 6 torr.
 An electron bombardment ion source provided the ions for the tests in this chamber
 (see Fig. 3.1). This type of ion source uses a hot tungsten  lament as a source of
 electrons. These electrons are accelerated into a chamber with the gas to be ionized.
 The ions are then accelerated from the chamber, passsing through an electrostatic
 lens to form a focused beam of ions. A positive voltage applied to the ionization
 chamber is used to accelerate the ions. Because the ions are created with a very low
 directed velocity, this voltage also determines the energy of the ions in the beam
 59
Figure 3.1: The ion source used for KIMS testing and calibration. The test gas is
 leaked in through the  ange seen at the bottom of the stack. Tungsten  laments
 fastened to the ceramic plate emit electrons that are accelerated into a collision
 chamber just above the ceramic plate. The energetic electrons ionize the gas in
 the collision chamber. The ions are extracted into the electrostatic lens above the
 collision chamber. The resulting ion beam can be de ected by applying a voltage
 to the two plates at the top of the source.
 leaving the source. The design of the particular source being used could be operated
 safely to a maximum ion energy of 3 keV.
 60
3.1 Modeling and Operating Parameters
 3.1.1 Instrument Simulation
 A Monte Carlo simulation of the KIMS instrument operation, written in the
 Python language, provided a benchmark for instrument performance. The magnetic
  elds in the instrument and the ion masses are  xed in the simulation. Simulated
 ions are given uniform distributions of energy over a speci ed range, entrance o set
 from the aperture center, and azimuth within the instrument  eld of view by random
 sampling over each parameter. Su cient random samples are accumulated to scan
 the entire response of the instrument with adequate statistics. By calculating the
 position an ion strikes the MCP at the end of its trajectory, we can determine the
 energies, o sets, and angles that reach particular sections of the detector plane.
 These correspond to the expected response of a chosen anode design. The code for
 this simulation can be found in Appendix B.1.
 As anticipated from the linear relationship of the detection position to the
  nite aperture width, the response functions for each anode take a nearly Gaussian
 shape as seen by the obtained histograms as seen in Figure 3.2. The histograms
 provide an expected energy distribution over each anode, and are characterized by
 the mean expected energy. The histograms also provide a width measurement  E
 given by taking the width of a rectangle having the same height and area as the
 histogram. By using normalized histograms, this width is simply given for each curve
 by  E = 1hmax . A plot of the calculated mean energies and their corresponding  E
 values is given in Figure 3.3.
 61
Figure 3.2: Histograms from a simulation for the high energy side of KIMS using a
 uniform energy distribution , o set distribution from aperture center, and entrance
 angle distribution. The histograms are normalized over the total counts in the
 simulation such that each curve has an area of 1. This set of curves provides a mean
 energy and energy spread ( E=E) for each anode segment, with the curves from
 left to right corresponding to pads B0 through B9.
 62
Figure 3.3: Simulation calculations showing the mean energy and expected  E for
 each anode. The mean energy is given by the location of each point and the value
 of  E by the vertical bar at each point on the plot.
 63
Figure 3.4: Plot of  E=E from the KIMS simulation. The dashed line corresponds
 to a best  t of a quadratic curve to the values. The anode pad dimensions were
 chosen to give a response similar to the original CEM design, but with a smoother
 change in  E=E over the array of anode segments.
 3.1.2 Magnetic Field
 The magnetic  eld of the instrument was measured in two di erent ways. The
  rst used a gaussmeter with a Hall probe. A jig made from Delrin placed inside the
 opening for the detector allowed the Hall probe to be precisely located at half of the
 gap height on either side of the magnetic circuit. Field strengths were measured in
 the center of each side of the instrument at various depths into the magnetic circuit
 to produce the maps shown in Figure 3.5. A major issue with the gaussmeter is
 the lack of a precise calibration, though a comparison to a typical value for Earth?s
 magnetic  eld suggested it was accurate to within 20%. An estimate of the Hall
 probe calibration provided a measurement of the low  eld at 0.098 T and the high
  eld side at 0.278 T. This measurement may have signi cant absolute error, but it
 does show clearly the uniformity of the  eld in the interior of the KIMS instrument.
 64
Figure 3.5: Measured  elds on the interior of the KIMS instrument. A refers to the
 low energy side (with anodes A0-9), and B to the high energy side (with anodes
 B0-9).
 The homogeneous  eld is expected for the magnetic circuit design. Preliminary
 measurement of the magnetic  eld as a function of height in each side of the magnetic
 circuit also showed uniformity within 10%.
 The instrument was then placed in a vacuum chamber with a bare anode de-
 tector in place of the MCPs. An electrometer was used to detect the small currents
 collected on each anode. The ion source, using hydrogen gas, scanned the responses
 of each anode over ion energies from 50 to 1200 eV. The dominant signal corre-
 sponding to the H+2 base is clear, but background gas also provided weaker signals
 65
Figure 3.6: Photo of the bare anode detector used for measuring the absolute  eld
 strength. The conductive pads are exposed directly to the  ux of ions at the de-
 tection plane in the instrument. The pads collect incident ions and the generated
 currents (on the order of 10?s of pA) are measured by an electrometer. The detector
 is attached to a plate that fastens to the instrument?s clam shell.
 in water and nitrogen. A weak proton signal can be seen as well. The results of this
 test are shown in the contour plot of Fig. 3.7. Superimposed on this plot are the
 predicted positions of each ion species from the Monte Carlo model. Because the
 model predictions match these results well, we can conlude that the absolute values
 of the magnetic  elds are, in fact, very close to the intended design values of 0.1 T
 and 0.27 T used in the model.
 3.1.3 MCP Applied Voltage
 MCPs require a bias voltage across their thickness to operate, and can be
 operated over a range of voltages. The optimal voltage for operation depends on
 the plate properties and resistances, and is unique to each set of plates. As a general
 rule of thumb, a nominal voltage of about 1 kV per plate is needed. To determine the
 optimum voltage for the plates used in KIMS, we examined the response of the MCP
 66
Figure 3.7: Bare anode results with simulated response lines overlayed for the two
 sides of the KIMS instrument. Simulation curves correspond to, from top to bot-
 tom, H+, H+2 , H2O
 +, and N+2 . The contour plot shows the general response of the
 instrument in energy for anode pads 0{9 across the horizontal axis. The current at
 a given pad is a function of energy as previously discussed. The measured response
 using the bare anode matches the simulation quite well, with the di erence being
 attributed to the uncalibrated values of the magnetic  eld measurement. This plot
 uses the estimated 0.098 and 0.278 T of each  eld. The low energy side suggests the
 estimate is low, and actually closer to the expected 0.1 T.
 67
Figure 3.8: Plot showing the MCP response vs. applied voltage (control voltage
 to the supplies) for various channels of the instrument. The general shape of each
 curve is independent of the energy, and MCPs in detection systems are typically
 operated at the \knee" of this curve. The actual applied voltage used on KIMS is
 marked on the plot.
 detector at di erent applied voltages. For particle detection, we typically choose
 an operating voltage that approaches the point of maximum sensitivity without
 saturating the plates. This saturation can be seen in Fig. 3.8. The plates saturate
 when very little signal gain is obtained for an increase in voltage. An MCP can be
 easily damaged if too high of a voltage is applied. (Operating at these voltage levels
 is safe at the recommended operating pressure of 10 6 torr.) From this plot, we are
 able to determine the optimal operating potential by selecting a voltage just above
 the \knee". In the case of the MCPs used in the KIMS instrument, the value turns
 out to be -1.6 kV, or 800 V per plate.
 68
3.2 Calibration
 Full calibration of a particle instrument requires measuring the instrument
 response across a full range of energies using ion beams of known current and en-
 ergy. KIMS was calibrated using an un-calibrated ion source, limiting knowledge of
 the absolute densities being measured. The ion source could, however, accurately
 determine the range of energies measured at each anode pad, leaving the absolute
 densities somewhat undetermined (though the actual densities will be at least as
 great as that measured by KIMS). Though not ideal, this time and cost-saving mea-
 sure is helped by the presence of a second ion instrument on the payload. Cross
 calibration between the two instruments over their overlapping energy range can
 provide knowledge of the absolute scale of ion  uxes being measured. In any case,
 the primary interest in this mission was the relative pro le of the energetic ions with
 height, and the absolute  uxes are not essential.
 The nominal energy ranges quoted for KIMS, 100{1000 eV and 1{10 keV,
 correspond to the energies of protons (H+) with a momentum per charge that leads
 to the ion reaching the detector. Because the ion source could only be used with an
 accelerating voltage of no more than 3 kV, helium (He+) gas was used for calibrating
 the instrument. Because the position on the detector scales as
 p
 mE, this test is
 equivalent to measuring the response with H+ of energies up to 12 keV, which is
 adequate to cover the full range of the KIMS instrument.
 The response of both the KIMS-A low energy and KIMS-B high energy sides
 of the instrument can be considered identical, assuming uniform magnetic  elds and
 69
Figure 3.9: Calibration data from the high-energy side of the KIMS instrument.
 Overlayed are the simulation results for various background gas elements.
 identical anode pad con gurations. Using He+ has the disadvantage of lowering the
 equivalent energy range for KIMS-A to 25{250 eV, a regime where the ion source
 is less reliable. Fortunately, initial testing with hydrogen gas (H+2 ) between 50 and
 500 eV indicated the expected response found in the model, and so this assumption
 is not unreasonable. For brevity, then, only the results for the KIMS-B calibration
 are presented here.
 The calibration data, shown as a contour plot in Figure 3.9, show excellent
 agreement with the simulation results. Again, model calculations for various gasses
 are overlaid on the contour plot. The strongest signal is, by far, the He+ used as the
 base gas, though other background gasses do appear in the instrument signals. It
 70
should also be noted that the widths of energies measured at each pad are in good
 agreement with the model.
 These data were taken with the ion source beam directed at the aperture with
 no azimuthal component (ie. at 0 ). Data were also taken with the ion source at -5 ,
 +5 , and +10 . These data sets show nearly identical curves with reduced count
 rates at the extreme angles. As found in the simulation, the azimuthal acceptance
 range designed into the instrument is small enough to not signi cantly a ect the
 instrument response, but large enough to provide a su cient number of counts
 during  ight for good statistics. The solid angle subtended by the view of the KIMS
 instrument is approximately 0.075 sr.
 3.3 Integration Testing
 3.3.1 External Magnetic Field
 In addition to the internal magnetic  elds, the external  elds were measured.
 These measurements were performed at the magnetic calibration facility at NASA
 Goddard Space Flight Center. Sensitive magnetometers were placed at distances
 of 20, 40, 60, and 80 cm from the center of the KIMS instrument (see Fig. 3.10).
 The 3-axis data from the magnetometers were combined to obtain magnetic  eld
 magnitudes at these distances. There are noticeable fringe  elds at the surface of
 the instrument case, but for reasonable distances (other payload instruments were
 not within 30{40 cm of the KIMS instrument) the  elds fall as 1r3 , characteristic of
 a dipole  eld. The weak  eld at these distances indicates the e ectiveness of the
 71
Figure 3.10: Photo showing placement of the magnetometers during the stray  eld
 measurement.
 shielding from the magnetic circuit and  -metal case.
 The external  elds can be  t to a function of the form
 B =
 a
 x3
 +
 b
 x2
 +
 c
 x
 + d (3.1)
 The measured external  elds are well  t with the coe cients a =  4:02 106 nT cm3,
 b = 1:79  106 nT  cm2, c =  2:06 104 nT  cm, and d = 96:7 nT. This  t gives
 an accurate representation of the near  eld of the KIMS instrument to a distance
 of about 100 cm.
 A second  t to a roughly dipolar form is given by:
 B =
 a
 x3
 +
 b
 x2
 (3.2)
 where a = 24:8 106 nT  cm3 and b = 0:4 106 nT  cm2. As seen in Fig. 3.11, this
 second  t gives a good description of the external  elds for distances greater than
 40 cm, with an accuracy of better than 10 nT.
 While these  ts do not show the direction of the magnetic  eld, they give an
 idea for overall o set the instrument will cause to the instruments on the payload.
 72
Figure 3.11: Fits to stray  eld measurement results. These values are absolute
 magnitudes and do not indicate  eld direction.
 Near the instrument, this o set is roughly comparable to the typical 30  T of the
 Earth?s magnetic  eld in the ionosphere. However, since the instrument is designed
 with permanent magnets, the o set is constant and easily measured at the magne-
 tometer locations so that the o set may be subtracted from their measurements.
 3.3.2 Vibration
 The KIMS instrument was subjected to vibration tests individually and on the
 RENU payload. A typical  ight pro le for a Blackbrant XII rocket was used for the
 test, with accelerations up to 12 times that of Earth?s gravity per Hz. To prevent
 contamination of or damage to the MCPs, the vibration tests were done with glass
 slides in place of the MCPs. Since MCPs have shown to be robust in vibration
 tests of previous instrument designs, this substitution was satisfactory for meeting
 73
the overall payload requirements. The slides were cut to match the dimensions of
 the MCPs, and no issues with vibration were found. Since the orientation of the
 MCPs is such that the trajectory lies along their long axis, the strongest anticipated
 vibrations would be along the most rigid dimension of the plates. Because the slides
 showed no damage or shifting, the KIMS detector stack design proved to be su cient
 to keep the microchannel plates intact through the launch of the sounding rocket.
 3.3.3 Electronics
 During integration testing, the interface between the KIMS instrument and
 the telemetry module of the sounding rocket was also examined. This test sim-
 ply ensured that the communication between the KIMS telemetry boards and the
 payload PCM stack was done properly. With the telemetry board test patterns ini-
 tiated, the expected signals were reported through the PCM stack, indicating good
 handshaking and data transfer for the instrument.
 3.4 RENU
 The KIMS instrument was mounted on the lower bulkhead of the RENU pay-
 load with a view oriented radially outward (directed slightly up due to the designed
  eld of view). RENU launched from the And ya Rocket Range in Andenes, Norway
 on 12 Dec 2010 with a nominal trajectory over Longyearbyen, Svalbard. The nomi-
 nal apogee was expected to be 473.2 km altitude. Further details about the launch
 criteria and conditions can be found in Appendix D.
 74
Unfortunately, a failure in the nose cone ejection prevented RENU from ob-
 taining the data. While the loss of the payload is unfortunate, there are other means
 of examining the neutral upwelling phenomenon that led to the development of an-
 other study using satellite data to examine the importance of various electrodynamic
 energy sources in neutral upwelling and ion out ow.
 75
Chapter 4
 Data Analysis Background
 The primary problem in understanding the neutral upwelling phenomenon is
 a lack of data observing the various electromagnetic energy inputs to the ionosphere
 in conjunction with neutral up owing events. While it would be preferable to make
 such measurements in situ, which is what the RENU project hopes to accomplish,
 there is another means of observing this phenomenon indirectly using statistical
 correlations of parameters measured by satellites. While no satellite exists that
 can observe all of the parameters of interest to this particular phenomenon at the
 necessary orbital con guration, a careful study using multiple spacecraft can provide
 insight into the most likely places to search for the cause of the neutral upwelling
 phenomenon.
 As the RENU project was unsuccessful at providing meaningful data for the
 study, we will turn to examining this phenomenon using data acquired by two satel-
 lites: the Fast Auroral Snapshot Explorer (FAST) and the Challenging Minisatellite
 Payload (CHAMP). Both of these missions are highly successful and have already
 provided signi cant results to the space science community. (See for example [30],
 [31], and [32] for examples of FAST results, and [33], [34], and [35] for examples of
 CHAMP results.)
 It is worth noting that this study cannot, by its very nature, substitute for
 76
direct (prefereably in situ) measurements. A correlation study of neutral upwelling
 with various energy inputs cannot determine the sources of the phenomenon, as
 correlation alone does not imply causality. The bene t of such a study, rather, lies
 in pointing to features in the ionosphere that appear in conjunction with upwelling
 events. By determining how other parameters of the ionosphere change when the
 neutral density in the cusp increases, we have information about the particular
 measurements that may be most bene cial in determining the overall cause.
 4.1 Satellite Background
 4.1.1 FAST
 The FAST satellite was the second mission chosen for NASA?s Small Explorer
 Satellite Program (SMEX). FAST was launched on 21 August 1996 into a highly
 elliptical orbit with an inclination of 83 . FAST was deployed in a reverse cartwheel
 con guration1 with a 5 s period. The instruments included on the spacecraft were a
 leap forward in the technologies used to study auroral phenomena. The instruments
 provide a full, 360 view of plasma particles in the spin plane of the spacecraft at a
 much faster data rate than had been done previously [36].
 The FAST electric  eld instrument consists of six booms. Four booms extend
 28 m radially from the spacecraft, each with two spheres located at the end and at
 5 m in from the end. The other two booms extend along the spacecraft?s spin axis
 1A reverse cartwheel con guration has the spacecraft spinning opposite the direction of travel.
 As such, the spin angular momentum vector points opposite the orbital angular momentum vector.
 77
Figure 4.1: Diagram of the FAST satellite and its instruments. (Figure taken from
 [36].)
 78
3.8 m from the spacecraft center. Each of these two booms have only one sphere.
 On deployment, one of the four radial booms did not extend fully [37].
 The FAST magnetic  eld instrument uses a three-axis  uxgate magnetome-
 ter for measuring DC magnetic  elds and a three-axis search coil magnetometer
 for measuring AC magnetic  elds. Both magnetometers are placed on 2 m booms
 extending radially from the spacecraft [38].
 FAST also includes a set of 16 electrostatic analyzers for measuring charged
 particle energy distributions. Sets of four top-hat style analyzers are distributed at
 90 intervals around the spacecraft. Each analyzer has a 180  eld of view, providing
 a full 360 view at all times for the FAST spacecraft with  90 overlap between
 adjacent instruments. The 180  eld of view is separated into 16 individual segments
 in each spectrometer. Each set of four includes an ion spectrometer, an electron
 spectrometer, and a pair of electron spectrometers operating in conjunction with
 the other sets as an electron spectrograph [39]. Further details about the particle
 instruments are provided in Section 5.2.3.
 4.1.2 CHAMP
 The CHAMP satellite was a project developed at the GeoForschungsZen-
 trum (GFZ) in Potsdam, Germany, with sponsoring groups including NASA. It
 was launched 15 July 2000 into a nearly circular polar orbit with a nominal altitude
 of 454 km. CHAMP was 3-axis stabilized, providing a consistent reference system
 for the instruments on board. The goal of CHAMP was to provide measurements
 79
of the gravitational and magnetic  elds of the Earth as well as atmospheric density
 and composition. The extremely sensitive accelerometer on CHAMP provides pre-
 cise data on the forces exerted on the satellite that are used to measure both gravity
  uctuations and atmospheric density through measurements of satellite drag [40].
 The primary instrument of interest for this study on CHAMP is the STAR
 accelerometer. The instrument design consists of a proof-mass electrostatically sus-
 pended in a cage. The instrument applies voltages to keep the mass translationally
 and rotationally stable. The applied forces are directly counter to the outside forces
 acting on the satellite. The STAR instrument was placed at the center of mass
 of the CHAMP satellite to remove the in uence of gravity on it. It measures the
 very small changes in gravitational acceleration and forces caused by air drag, the
 Earth?s albedo, and solar radiation.
 The STAR accelerometer is aligned with one axis along the spacecraft direction
 of travel. The measured acceleration along this axis provides the data necessary for
 determining the density of the atmosphere by the drag felt in this direction. There
 are detailed methods of deriving atmospheric density from this data [41], however a
 simpler model as used by L uhr et al. [20] is su cient for this study. In the simple
 model, drag in the direction of travel is proportional to density by
 d =
 1
 2
  cf
 A
 m
 v2 (4.1)
 The values cf (drag coe cient), A (cross sectional area of the satellite), and m (mass
 of the satellite) are all constant, and so for a constant velocity, d is proportional to
  , and the decceleration measured in this direction is a su cient measure of the
 80
Figure 4.2: Diagram of the CHAMP satellite and its instruments. (Figure credit
 GFZ Potsdam.)
 atmospheric density.
 4.2 The Strangeway Study
 On 24{25 September 1998, a particularly interesting ion out ow event was ob-
 served by the Polar satellite [42]. This event was also observed by the FAST satellite,
 along with strong  eld-aligned currents in the ionosphere [43]. Using the electric
 and magnetic  eld data provided by the instruments on FAST, it was observed that
 the out ow exhibited a strong correlation with Poynting  ux in the direction of the
 local magnetic  eld. An e ort was then made by Strangeway [44] to examine the
 correlations of this particular event with other parameters, particularly in terms of
 81
precipitating electron  ux.
 These two studies used a collection of 33 orbits of the FAST satellite, centered
 about the September 1998 out ow event. To  lter out high frequency  eld  uctu-
 ations, Strangeway averaged the  eld data over 4 s intervals, then interpolated the
 averaged data to 1 s intervals. Only data at times where ion out ow was measured
 in each orbit were included. The selected times were found to correspond to the
 satellite passing over the dayside cusp. The parameters used in the statistics were
 also averaged over the entire selected window of each orbit, giving a single data
 point for each of the 33 orbits in the linear regression.
 Because the study was done on such a distinct and limited time period, there
 are many unanswered questions about these correlations. Do the correlations per-
 sist over time, or are they singular to this particular event? With the aggressive
 averaging used in the study, would the results change with changes in the averaging
 periods, or inclusion of more data in each average? And, most particularly, what is
 the change in neutral density during such periods?
 The statistical study presented in this dissertation addresses these questions
 and expands on Strangeway?s work to examine these correlations in greater detail.
 While it is unfortunate that the CHAMP satellite was not in orbit in 1998, prevent-
 ing the examination of the neutral density during the September 1998 event, there
 are a number of time periods where the orbits of FAST and CHAMP overlap su -
 ciently to get meaningful information from of a cross-study between these two data
 sets. The month of July 2002 proves to be a particularly good period for study, as
 the orbital planes of the two satellites are within 5 of each other, a number of neu-
 82
tral upwelling and ion out ow events were observed, and data are readily available
 from both satellites during the month.
 Unfortunately, one of the FAST satellite?s electric  eld probes developed a
 fault in September, 2001. Electric  eld data are available during the time intervals
 studied, however the faulty probe compromises their integrity. While the faulty
 data make a correlation result for Poynting  ux values inconclusive during this
 time period, Strangeway found that Poynting  ux and electron precipitation density
 themselves show a correlation. This suggests that particle data should be su cient
 in this analysis.
 4.3 Ion Out ow
 This study correlates energy inputs with neutral upwelling and ion out ow.
 Ion out ow is a phenomeon that occurs at the polar cusps when ions are heated to
 energies such that they are able to escape Earth?s gravitational  eld. This mecha-
 nism can be compared to atomspheric, or Jeans, escape [45].
 In ion out ow, a stream of charged particles (primarily oxygen)  ow along
 magnetic  eld lines out of the cusp, but at a slight angle of a few tens of degrees.
 A satellite passing over the cusp would observe a maximum ion  ux at pitch angles
 on either side of the direction anti-parallel to the local magnetic  eld, and a low
  ux directly anti-parallel to the  eld line. This resulting pattern is characteristic of
 what is referred to as an ion conic [46], [47]. (See Fig. 4.3 as an example of these
 signatures.)
 83
Figure 4.3: An example of a pitch-angle spectrogram of ions in the cusp, from
 FAST 9/25/1998. The  rst three panels show energy spectra at directions 0 {30 ,
 40 {140 , and 150 {180 from the local magnetic  eld direction respectively. The
 following panels show the pitch angle spectra for low energy (< 1 keV) and high
 energy (> 1 keV) particles. The 180 direction is anti-parallel to the local magnetic
  eld, or pointing roughly upward from the Earth?s northern pole. In the pitch angle
 spectra, a reduced count of particles is observed at all energies in this direction.
 However, in directions a few tens of degrees to either side, a large  ux of low energy
 particles is observed. This pattern is characteristic of an ion conic.
 84
Ion out ows reach high enough altitudes in the ionosphere to be injected into
 the plasma sheet and ring current of the magnetosphere [48]. Some with su cient
 energy even leave the Earth?s magnetosphere completely, joining the solar wind as
 \pick-up ions" [49]. For oxygen atoms at these altitudes, the required energy for
 escape (assuming the Jean?s escape mechanism) is around 10 eV, which corresponds
 to the typical energies measured in ion out ow streams.
 4.4 Ionospheric Energy Sources
 The sources of energy that cause ion out ow have been associated with elec-
 trodynamic systems, particularly from waves in the aurora [50] and Poynting  ux
 from the electric and magnetic  elds in the ionosphere [43]. Out ow has also been
 associated with electron precipitation in the cusp [51].
 The unexpected result of Strangeway et al. showed that these three parameters
 all show strong correlations with the ion out ow  ux over the 33 orbit period. The
 parameters also exhibited strong correlations with each other. These correlations
 indicate the possibility of a power law scaling between the energy inputs and the
 ion out ow. As it is statistical in nature, this result does not necessarily mean that
 the particular inputs cause ion out ow, but rather that there exists some connection
 between them that can be described mathematically.
 85
4.5 Statistics of Ionospheric Energy Sources
 Three electrodynamic systems have shown to be strongly correlated with ion
 out ow: Poynting  ux; electron precipitation; and extremely low frequency (ELF)
 waves. ELF waves are a known mechanism for heating ionospheric oxygen su -
 ciently for out ow to occur [52], and heating processes such as Joule heating or
 electron ionization are known to lead to ELF waves, indirectly linking Poynting  ux
 and electron precipitation with ion out ow [43]. It comes as no surprise, then, that
 the Poynting  ux and electron precipitation would show good correlation with ELF
 waves.
 Surprisingly, both Poynting  ux and electron precipitation show good correla-
 tion with ion out ow directly, and with each other. Strangeway et al. used the  eld
 and particle  ux data from the FAST satellite to examine the correlation between
 Poynting  ux, electron number  ux, and electron energy  ux with ion number  ux,
 as seen in  gure 4.5. Of these, only electron energy  ux exhibited weak correlation.
 However, by using dimensional analysis, a parameter using the electron energy and
 number  uxes was established to describe the electron precipitation density within
 the cusp [44]. This parameter is given by
 nep / f
 3=2
 en =f
 1=2
 ee (4.2)
 where fen is the electron number  ux in cm 2 s 1, and fee is the electron energy  ux
 in mW/m2. Correlation of this parameter with the ion number  ux proves to have a
 higher correlation than all of the other parameters examined in the Strangeway study
 (see  g. 4.6). Strangeway found the proportionality constant to be 2:134 10 14. A
 86
Figure 4.4: Diagram depicting the statistical relationships between energy input
 parameters in the ionosphere with ion out ow. Solid arrows are used in relationship
 that are known to be causal, medium-tone outline arrows where a causal relation-
 ship might exist, and light-tone outline arrows where a statistical correlation exists
 between two otherwise independent parameters. The correlation coe cients are re-
 ported for correlations with ion out ow measurements, and show good correlations
 in each. Figure from [44].
 87
Figure 4.5: Correlation relations of the energy inputs measured by the FAST satellite
 for 33 orbits centered on the 25 Sep 1998 event (orbits 8260-8292).
 similar result was obtained using data from the Polar spacecraft (at a higher altitude
 then FAST) for the year 2000 [53].
 In this portion of the dissertation, the consistency of these correlations are
 examined over a larger number of orbits and at di erent periods of time. Because of
 the known relationship between Poynting  ux and electron precipitation with ELF
 waves, and because the electron precipitation density parameter encompasses both
 the number and energy  uxes, we limit our study to correlations with the Poynting
 88
Figure 4.6: Correlation of the electron precipitation density parameter nep. This
 plot uses a symetrical logarithm plot, with a linear scale for the intervals closest
 to zero and a logarithmic scale for the other intervals. Negative values of the ion
  ux indicate in- ow as opposed to out ow, and negative values of the electron
 precipitation density indicate upwelling as opposed to precipitation. Individual data
 points and the orbital averages are both plotted, showing not only the excellent
 correlation obtained for nep, but also the consistency of the averages in comparison
 to the individual data points.
 89
 ux and electron precipitation density.
 4.6 Statistics in Neutral Upwelling
 From the measured values of ion out ow and energy  uxes with the FAST
 satellite, it is apparent that there is a large discrepancy in the energy balance from
 the di erent sources. The amount of energy available in the ionosphere for heating
 processes is orders of magnitude greater than the energy required to obtain the
 observed out ows. As the plasma density at these altitudes is signi cantly less than
 the neutral density, we expect that some of the remaining energy goes into heating
 processes of the neutral gas. If this is the case, a correlation between the energy
 inputs with the neutral density should exist.
 Because the FAST satellite does not have an instrument that measures neutral
 gas density, we use the acceleration data from the CHAMP satellite to obtain this
 information. It is non-trivial to correlate data sets from two separate satellites. To
 calculate correlations, it would be ideal to have  eld, charged particle, and neutral
 density measurements all measured at the same point in space and instant in time,
 which is impossibile using two spacecraft. Since the study uses orbital averages, we
 can instead use averages from similar time periods for each satellite. As long as the
 orbital inclinations of the two satellites are close together and the phenomena being
 observed have lifetimes longer than an orbital period, the exact conjunction of time
 is less essential and this averaging scheme provides an adequate measurement of the
 process.
 90
In the case of the correlations between FAST and CHAMP, time periods were
 selected where the orbits of the two satellites lie within 15 of each other. The
 two time periods chosen are July and February 2002. The July period has the
 two satellites orbiting within 5 , while the February period is between 5 and 10 .
 CHAMP, at a 400 km altitude, has a shorter orbital period than FAST. During a
 single orbit of FAST, CHAMP will pass over the polar cusp at least once but no more
 than twice. Data from CHAMP is selected by identifying the positions in latitude
 where FAST data are included for the study. CHAMP data showing a deviation
 from the orbital trend in the density variation near the same time period as each
 pass of the FAST satellite over the dayside cusp are selected for inclusion in the
 analysis. Averages and local maxima of these deviations, or spikes, are compared
 to the selected orbital averages of the FAST data.
 Before being able to use the CHAMP data, the orbital positions of the data
 need to be compared from within the same coordinate system. FAST coordinates
 are reported in Solar Magnetic (SM) coordinates, while CHAMP orbits are reported
 in Geocentric Equatorial Intertial (GEI) coordinates. To work with the two datasets
 together, the CHAMP orbital data is transformed into SM coordinates. The follow-
 ing section describes the computations needed in order to transform the coordinates,
 and the code used to do so is found in Appendix E.3.1.
 91
4.7 Geophysical and Geomagnetic Coordinate Systems
 In space physics, there are a number of coordinate systems in common use,
 each used to describe positions, velocities, and directions in terms of some convenient
 inertial reference frame. For examining the motion of celestial bodies in relation to
 the Earth, we often use a coordinate system centered on the Earth with an axis
  xed to point to the First Point of Aries (or the point in the constellation Aries that
 is perpendicular to the line between the sun and the Earth on the Vernal Equinox),
 which we call the Geocentric Equatorial Inertial (GEI) system. In describing events
 dealing with interactions between the sun and the Earth, however, it is often more
 convenient to work in a geocentric system with an axis  xed along the line between
 the sun and the Earth, called Geocentric Solar Ecliptic (GSE). More commonly,
 most people are familiar with the lines of latitude and longitude used in describing
 location on the surface of the earth, called the Geographic (GEO) coordinate system.
 The magnetospheric system is best described in a di erent set of coordinates, similar
 to GEI but rotated to the location of the magnetic poles. Two types of coordinates
 often used in magnetospheric studies are Geocentric Solar Magnetospheric (GSM)
 coordinates and Solar Magnetic (SM) coordinates.
 Each of these systems as well as others are commonly used, and transfor-
 mations between systems are well understood. Russell has provided an excellent
 summary describing the systems and the transformations between them [54]. Here
 we will describe the coordinate systems and transformations pertinent to this par-
 ticular study.
 92
4.7.1 Geographic Coordinates (GEO)
 Geographic Coordinates describe a system centered on the earth with the
 z-axis through the North geopgraphic pole and the x-axis through the equator and
 prime meridian. Usually expressed in terms of latitude, longitude, and altitude,
 these coordinates are commonly used by anyone familiar with geographic maps.
 This system is often used in transformations between other systems as well.
 4.7.2 Geocentric Equatorial Inertial Coordinates (GEI)
 For systems that need to reference the earth without its rotation, we switch
 to a coordinate system where the x-axis does not rotate with the earth. Convention
 sets the x-axis to point perpendicular to the Earth-sun line on the Vernal Equinox.
 This direction happens to point toward the constellation Aries, and is known as the
 First Point of Aries.
 Transformation from GEO to GEI is simply a rotation about the z-axis, but
 the angle of rotation must be calculated based upon the date and time. This angle,
 known as the Greenwich Hour Angle (GHA) or Greenwich Sidereal Time (GST),
 can be found with a number of di erent formulas of varying accuracy. A commonly
 used formula, given by Russell, is as follows:
  GST = 279:690983 + 0:9856473354 DJ + 360 fD + 180 (4.3)
 In this formula, DJ is given by the Julian Date, while fD is the time of day expressed
 as a fraction of a day. The result is the Greenwich Hour Angle in degrees. The
 resulting value can be restricted to be within the range of 0|360 by calculating
 93
the result modulo 360.
 4.7.3 Geocentric Solar Magnetospheric Coordinates (GSM)
 For systems related to the Earth?s magnetic  eld, it is useful to have a coor-
 dinate system relative to the magnetic poles rather than the geographic poles. In
 addition, the position of the sun is a convenient  xed point for these systems. GSM
 aligns the z-axis to be in the same plane as the Earth?s magnetic dipole moment.
 The x-axis points toward the sun.
 Transformation from GEI to GSM is linear, however it also requires a calcu-
 lation of not just the GHA, but also the position of the sun. Again, formulae are
 available to make this transformation easy, particularly those given by Russell which
 provide an accuracy to within 0.006 [54].
 4.7.4 International Geomagnetic Reference Field
 In addition to solar position, GSM requires knowledge of Earth?s magnetic
  eld. Unfortunately, the magnetic  eld is not constant, particularly over long time
 periods. The magnetic poles are not aligned and drift independently. Models have
 been developed, however, that allow us to predict the Earth?s magnetic  eld to
 good accuracy. While it is not a perfect dipole, the dipole term of these models is
 generally su cient to locate the position of the north magnetic pole and make the
 transformation from GEI to GSM.
 One of the more commonly used models of the magnetic  eld (and that used
 94
in this study) is the International Geomagnetic Reference Field (IGRF) [55]. As
 more data are acquired, updates to the model are released periodically. The most
 recent model is IGRF-11, released in 2010. Strangeway uses IGRF-7 (1995) in his
 calculations, and high resolution data for the FAST satellite are processed using the
 same model regardless of the time period selected. To remain in a consistent coor-
 dinate system with the orbital parameters provided for the FAST satellite, IGRF-7
 is used in transforming CHAMP orbital data for this study.2
 4.7.5 Solar Magnetic Coordinates (SM)
 GSM is particularly useful for studying the magnetosphere and solar wind. For
 systems closer to earth and more strongly associated with the local magnetic  eld,
 a slight adjustment can improve the accuracy. The Solar Magnetic (SM) coordinate
 system rotates the GSM system about its y-axis to bring the z-axis parallel to the
 dipole moment. We can then express this system in terms of latitude and longitude,
 just as we do in Geographic coordinates. In this system, latitude, measured in
 degrees, is called Invariant Latitude (ILT). Longitude, measured in hours with 12:00
 being the line of longitude aligned with the x-axis, is called Magnetic Local Time
 (MLT). (Note that magnetic noon in this system, the x-axis, is aligned with the
 sub-solar point, or the point where solar radiation directly impinges the Earth. The
 x-axis does not, however, point directly at the sun in this system.)
 SM coordinates are used in this study, and have the same assumptions and
 2Further information on and the matrix coe cients used in the IGRF model can be found at
 http://www.ngdc.noaa.gov/IAGA/vmod/igrf.html (retrieved 27 Sep 2011).
 95
requirements described above for GSM coordinates. A simple way to view the
 transformation is to take GEI coordinates, and rotate about the z and y axes by the
 angles given by the longitude and latitude of the north magnetic pole respectively,
 in that order. Then a rotation about the new z-axis brings the x-axis to point at
 the sun. Russell gives this transformation as a single rotation matrix as follows:
 2
 6
 6
 6
 6
 6
 6
 6
 6
 4
 X1 X2 X3
 Y1 Y2 Y3
 D1 D2 D3
 3
 7
 7
 7
 7
 7
 7
 7
 7
 5
 2
 6
 6
 6
 6
 6
 6
 6
 6
 4
 Vx
 Vy
 Vz
 3
 7
 7
 7
 7
 7
 7
 7
 7
 5
 GEI
 =
 2
 6
 6
 6
 6
 6
 6
 6
 6
 4
 Vx
 Vy
 Vz
 3
 7
 7
 7
 7
 7
 7
 7
 7
 5
 SM
 (4.4)
 The vectors X and Y are obtained from the vectors S and D, which describe
 the Earth-Sun direction and the dipole direction in GEI, respectively. After calcu-
 lating the vectors S and D,
 ~Y =
 ~D  ~S
 j ~D  ~Sj
 (4.5)
 ~X = ~Y  ~D (4.6)
 4.8 Summary
 The goal of this portion of the dissertation is to perform a statistical analysis
 relating ionospheric energy inputs to ion out ow and neutral upwelling by using
 data from the FAST and CHAMP satellites. The techniques are based on Strange-
 way?s work and used to expand the results reported by him. To correlate neutral
 density data taken from the CHAMP satellite?s accelerometer, time periods within
 the orbital period of FAST are selected for computing the average densities corre-
 sponding to the averages from each FAST orbit. The study is limited to two energy
 96
inputs: electromagnetic energy (Poynting  ux) and electron precipitation density.
 The results of this study will demonstrate that the power law relationship observed
 for these inputs with ion out ow is indeed a consistent result and that a correlation
 exists between ion out ow and neutral upwelling, suggesting a relationship with
 these energy inputs.
 97
Chapter 5
 Data and Analysis Software
 In this chapter, we give a description of the analysis techniques and software
 employed in analyzing the FAST and CHAMP data sets. FAST data are available
 for download from a website established at the University of California, Berkeley
 [57]. Data are downloaded by orbit number in the Common Data Format (CDF)
 [58]. CHAMP data are available at the Information System and Data Center at the
 Helmholtz Center, Potsdam, Germany [59].
 One of the underlying goals of this study was to create a software framework
 that simpli es the analysis of data from both FAST and CHAMP in examining
 these correlations. Our hope was to make the process as autonomous as possible
 and to be able to provide processed data in an easily accessible format. The Python
 language was chosen to do the analysis of the data, partly because it provides
 a binary data storage method that makes data products compact, portable, and
 easily documented. An overview of basic Python tools needed in this study is given
 in Section 5.1.
 The data processing consists of preparing the various spacecraft measurements
 and interplating each to a common time base. DC electric and magnetic  eld data
 are smoothed and interpolated to provide the calculation of Poynting  ux, as de-
 scribed in Section 5.2.2. AC electric  eld data are integrated to examine extremely
 98
low frequency waves (see the same Section). Particle data are integrated to pro-
 vide ion and electron  ux measurements using methods described in Section 5.2.3.
 Particle data used in the analysis are selected based on ion out ow signatures and
 adjusted when necessary to account for the spacecraft motion. Neutral gas density is
 derived from acceleration measurements, using methods described in Section 5.2.6.
 Because these data come from the CHAMP satellite rather than the FAST satellite,
 special handling is done to identify data for analysis by examining CHAMP orbits
 over the northern cusp at times corresponding to FAST orbits over the cusp within
 an orbit period. The processed data are then averaged and analyzed with statistical
 methods described in Sections 5.2.4 and 5.2.7.
 5.1 Python
 To meet the goals of the software development, the Python programming lan-
 guage is an ideal environment for establishing a consistent framework. Because of
 its scripting capabilities, Python is very good at handling the ASCII text format
 of the CHAMP satellite, something that typical computation enviornments such as
 Matlab or IDL do not handle well. The recent public release of the SpacePy library
 made it possible to also work with CDF archives within Python, which was the pri-
 mary motivation to use Matlab or IDL. The C language also does well with parsing
 text  les and handling CDF, but visualizing and plotting the data would require a
 great deal of e ort. By combining the power of Python with the NumPy [60], SciPy
 [61], Matplotlib [62], and SpacePy [63] libraries, all of the needed tools to easily
 99
handle the data sets are available within a single environment.
 Finally, Python provides a binary data storage format that makes it simple to
 store computational results for further processing later. This format, the \pickle",
 allows transferring data and metadata easily from one user to another. The code
 used in this dissertation (found in Appendix E) was built to be a general framework
 for using FAST and CHAMP data sets. There are some di erences between how
 the two satellites are handled in the code, partly due to the di erent data formats
 and availablity, and partly to explore di erent ideas of interaction in the inital
 processing.
 Currently, two somewhat incompatible versions of Python are available. This
 code was developed using the Python 2.7 branch. Ideally, the data products of the
 code would be useable in either the 2.x or 3.x branches, and indeed the pickle format
 was designed to be able to do that. However, the NumPy array structure encodes
 in pickles slightly di erently between the 2.x and 3.x systems (as of this writing, at
 least), and so provision must be made to use the same branch of Python as that in
 which the data products are made.
 5.1.1 Python Structures
 The code used in this study make extensive use of two structures provided
 by the Python framework: the list and the dictionary. A list is simply an ordered
 collection of data, and is denoted using the bracket:
 list = [1, 2, 3]
 100
The data included in a list can be of any type, and there is no stipulation that each
 entry in the list must be of the same type. Elements are referenced by index, with
 the leftmost starting at 0 (ie. list[0] = 1 and list[2] = 3 in the above example).
 Elements can also be referenced using a negative index, with the rightmost starting
 at -1 (ie. list[-1] = 3 and list[-3] = 0 in this example). Portions of lists can
 be referenced using the slice, with the subset including the starting index and not
 including the ending index (ie. list[0:2] = [1, 2]. The notation list[:2] is
 equivalent to a slice starting at the  rst (0th) element and including up to index 2.
 list[1:] would start at index 1 and include all the following elements, and list[:]
 includes all elements.
 The dictionary is a structure that is similar to the list, but with a user de ned
 index. Dictionaries are denoted with braces. For example,
 dict = {0:1, 1:2, 2:3}
 creates a structure similar to the above list, with dict[0] = 1 and so forth. Users
 are not limited to integer indicies, however, and the following is equally valid:
 dict = {?a?:1, ?b?:2, ?c?:3}
 This example would allow us to reference each element as dict[?a?] = 1 and so
 forth. The dictionary structure is particularly useful in creating data structures for
 storage, as saved arrays can be referenced by their function rather than having to
 specify the arrangement of data in the  le.
 101
5.1.2 NumPy
 Numerical Python, or NumPy, is an extension to the Python language that
 provides array-like structures and extensive computational libraries. NumPy arrays
 can be made of any dimension or size within the bounds of the computer?s memory.
 The array is essential in scienti c computing not only for vector calculations, but
 also for performing operations on any time or spatial series. For example, to scale
 a standard Python list such as 3 [1; 2; 3], a loop is required to create a new list:
 list = [1, 2, 3]
 newlist = []
 for i in list:
 newlist.append(3*i)
 NumPy simpli es this process by allowing operations to extend across the array:
 import numpy
 list = numpy.array([1, 2, 3])
 newlist = 3*list
 NumPy also provides essential libraries, such as  t, histogram generation, and
 various mathematical operations for array computations. The NumPy package can
 be included in a Python program by importing the entire library or individual parts.
 import numpy will bring in the entire library, accessible by referencing various func-
 tions as numpy.function . The notation from numpy import function provides
 access to a speci c function by name directly into the local namespace, rather than
 having to reference the numpy namespace. The code listings in Appendix E make
 use of the latter method. Imports are done at the beginning of each listing for quick
 reference to what libraries and functions are needed in the code.
 102
5.1.3 SciPy
 Scienti c Python, or SciPy, builds on the NumPy package to provide further
 functions useful in scienti c computing. SciPy includes functions for integration,
 optimization, linear algebra, interpolation, and statistics, to name only a few. Fur-
 ther information on the NumPy and SciPy packages is available, along with binary
 installation  les and source code, at the SciPy website [61].
 5.1.4 Matplotlib
 Matplotlib is a package that provides 2D plotting capability. Some 3D plot
 ability is available as well, and will continue to improve as the package is further
 developed. The syntax and functionality of Matplotlib is similar to that available
 in Matlab. All graphs and plots provided in this dissertation are created using
 Matplotlib.
 5.1.5 SpacePy
 SpacePy is a new package, released publicly under an open source license dur-
 ing the course of this study. The purpose of SpacePy is to provide a Python interface
 to computational libraries developed for space physics modeling and analysis. For
 this study, the particular functionality needed is an interface to NASA?s Common
 Data Format. CDF is a binary  le format that is used for storing data and meta-
 data in the space physics community. The FAST data is provided as a CDF  le, and
 this package made it possible to work directly with those  les rather than having to
 103
extract the data and convert it to a di erent format.
 5.1.6 The Python Pickle
 The pickle module in Python is a method of converting data objects in memory
 into a byte stream that can be saved to a disk for later retrieval. Data products in
 this study are saved as a pickle format which are then used for doing the statistical
 analysis.
 The Python langauge also provides a data structure called a shelf. The shelf is
 a way of storing multiple pickles in a single  le, each referenced in a similar manner
 to a dictionary. This function is similar to pickling a dictionary structure as is done
 in this work. Future work would bene t from using the built in pickle shelf for
 simplicity.
 5.2 Methods
 5.2.1 FAST Data Processing
 A variety of data types from the FAST satellite are made available at the FAST
 website. The data types used in this study include the despun DC electric  eld, the
 despun DC magnetic  eld, the electron spectrometer survey, the ion spectrometer
 survey, the low frequency V5-V8 AC electric  eld, and the orbital parameters. The
 magnetic  eld data is built o a model including the IGRF-7, and requires a full
 orbit?s worth of data to ensure its accuracy. Hence, each data type is downloaded by
 orbit number rather than by a speci ed time period. Each  le is stored in directories
 104
dcefs ooooo.cdf DC Electric Field
 dcmag ooooo.cdf DC Magnetic Field
 ees ooooo.cdf Electron Survey
 ies ooooo.cdf Ion Survey
 dsp v58 ooooo.cdf AC Electric Field
 orbit ooooo.cdf Orbit Parameters
 Table 5.1: Filename conventions used for FAST CDF data  les. ooooo is given by
 the orbit number with padded zeros to give 5 characters.
 named by orbit number using the  lenames given in Table 5.1.
 The data types are all measured independently and come with their own time
 bases. Each must be extracted individually and interpolated to a common time
 base. The routines in FAST.py (Appendix E.1.1) were written to take a collection
 of orbit numbers as inputs and automatically extract and interpolate all of the data
 types for that orbit. The following sections will describe the various components of
 this code.
 5.2.2 FAST Field Data
 5.2.2.1 Field Processing Tools
 Three functions are provided for preparing electric and magnetic  eld data in
 this study. These functions are:
 105
FAST.chauvenet(data, window, weight)
 DC electric  eld data from FAST often has periodic spikes corresponding to
 the rotation of the spacecraft. These spikes can be large enough to throw o averages
 and interpolations, and so the Chauvenet criterion is used to  lter these spikes out
 of the data used in averaging and interpolating. This criterion removes any data
 points that are farther from the sample mean than a given threshold, usually given
 in multiples of the standard deviation.
 In this function, a window and weight are passed along with the data to be
  ltered. The window speci es how many points to include in calculating the sample
 mean, and the weight sets the threshold in standard deviations. The  rst window/2
 points are compared to a set of the  rst window points, the last window/2 points
 to a set of the last window points, and all others to a set of size window centered
 about the point under consideration. Provision must be made to accommodate data
 with a value of nan1, lest the average and standard deviation are returned as nan
 values. The nantools.py routines (Appendix E.4.1) provide this ability. Any data
 point farther than the number of standard deviations from the sample mean given
 by weight is itself set to the value nan. This study used a window of 100 points
 and a weight of 2 standard deviations when applying this  lter. All DC electric  eld
 data was  ltered.
 1The nan value indicates a non-numerical result, or \not a number".
 106
Figure 5.1: DC electric  eld data from a portion of FAST orbit 8276 showing the
 e ect of applying Chauvenet?s criterion with a window of 100 points and a weight
 of 2 standard deviations.
 FAST.smooth(data, r data, interval)
 All  eld data are smoothed, or averaged, to 4 s intervals. The smooth function
 takes the data, the corresponding time series, and the new, smoothed time series
 to create an averaged array of the data. The new time series is created by making
 an array with the same endpoints as the raw data, but at intervals of 4 s. A  xed-
 width window is used in this scheme, averaging only data points between  2 s. For
 end data points where data do not exist in the entire window, only data within the
 window are used.
 Smoothing is applied to all the  eld data types before interpolating to 1 s
 intervals. The e ect of the aggressive smoothing algorithm is to limit data to slowly
 varying changes in the DC  eld data.
 107
Figure 5.2: DC electric  eld data from a portion of FAST orbit 8276 showing the
 e ect of applying the the despiking and smoothing algorithms to the raw data. The
 data are smoothed to 4 s intervals.
 FAST.interpolate(x, y, x new, width, int kind)
 An interpolation routine is provided that makes use of the interp1d function
 within scipy.interpolate. The FAST.interpolate function accepts the raw time
 and data values (x and y) and the time base to which the data should be interpolated
 (x new). In addition, a width is given to limit the amount of data used in the
 interpolation as well as an optional parameter to specify the interpolation type.
 (Cubic spline interpolation is used by default.) The width limit was necessary to
 avoid calculating cubic splines over the entire data set for a single point. A width
 of 30 s was used in the study, or in other words, 7 data points from the smoothed
 data were used for each interpolation point.
 The time base used for interpolation is obtained from the orbital parameters
 data of the orbit. These data are given in a 1 s interval time base, and for con-
 108
Figure 5.3: DC electric  eld data from a portion of FAST orbit 8276 showing the
 e ect of applying the interpolation algorithm over 1 s intervals.
 venience the same base was used for all other data types. Note that this function
 will only work if the end points of the raw data are at least width/2 further than
 the end points of the time base to which the interpolation is done. (Extrapolation
 is not provided in this code.) To accommodate the time values in the orbit where
 data are not provided, the function sets the interpolated values to nan.
 5.2.2.2 DC Electric Field
 FAST.get E(orbit, t base, margin, subset)
 The FAST.get E function imports the data from the CDF  le corresponding to
 the speci ed orbit. Electric  eld data are sampled at 3.125 ms intervals on FAST.
 t base is passed to the function from outside, and as mentioned previously the
 time series from the orbit data was used. A default margin of 30 s was given for
 109
the interpolation window. By default the function parses the entire data set, but
 provision is made to process only a subset of the data if desired. This functionality
 was not used beyond testing purposes in this study.
 From the dcefs data, two time limits are found. The t min/t max pair limit
 the time values in the electric  eld data to the end points of the interpolation
 (extended by margin/2 on either side to accommodate the interpolation). The
 ti/tf pair limit the time values in the interpolation time base where data will be
 provided. In the context of processing the entire orbit, only the latter pair is needed.
 Once the time endpoints are found, the raw data are converted to numpy
 arrays. The electric  eld data are  ltered with FAST.chauvenet, smoothed with
 FAST.smooth, and  nally interpolated with FAST.interpolate. The interpolated
 E  eld at the time values given in t base is then returned. An example of the result
 is given in Figure 5.3.
 A fault in the V5 electric  eld probe in Sep. 2001 has a ected the quality of the
 electric  eld data obtained by FAST. The fault causes the data to show oscillations
 on scales larger than the ambient electric  elds. Because of this fault, electric  eld
 data from after Sep. 2001 should be considered as compromised.
 5.2.2.3 ELF AC Electric Field
 FAST.get ELF(orbit, t base, margin, subset)
 AC electric  eld data is processed by the FAST.get ELF function. The function
 parameters being passed indicate an intentional similarity in how this function is
 110
Figure 5.4: Spectrum of the AC electric  eld from FAST orbit 8276.
 written to the FAST.get E function, and so those details will not be rediscussed
 here.
 The dsp v58 data provides a power spectrum at frequencies between 0 and
 16 kHz (see Fig. 5.4). The power spectrum is integrated over frequency using the
 trapezoid method. A separate smoothing algorithm is used to smooth the ELF data
 by replacing each data point with the average of the  ve points centered about it.
 (The separate routine was done to avoid a complication in the di erences of how
 the data type is provided.) Finally, the data are also interpolated to the orbit time
 base. An example of the result of this function is given in Figure 5.5.
 111
Figure 5.5: Interpolated data from the DSP V5-V8 power spectrum from a portion
 of FAST orbit 8276.
 5.2.2.4 DC Magnetic Field
 FAST.get B(orbit, t base, margin, subset)
 The FAST magnetometers provide three-axis magnetic  eld data as devia-
 tions from Earth?s magnetic  eld as provided by the IGRF model. DC magnetic
  eld data are processed by the FAST.get B function. This function is analogous
 to the FAST.get E function, and uses a nearly identical routine. For the magnetic
  eld, however, Chauvenet?s criterion is not needed, and three components of ~B are
 provided. ~B  eld data are sampled at 7.8125 ms intervals. The data are smoothed
 to 4 s intervals to remove high frequency changes and interpolated to 1 s intervals
 just as the ~E  eld data are.
 The FAST magnetic  eld data provided are the measured deviations from the
 model provided by IGRF-7. The coordinate system used is a spacecraft-centric,  eld-
 112
Figure 5.6: Interpolated data of the magnetic  eld deviation from a portion of FAST
 orbit 8276. The three components given are along the local magnetic  eld (b^),
 perpendicular to the magnetic  eld and the spacecraft-Earth line pointing eastward
 (e^), and the right-handed complement pointing outward, or away from the Earth
 (o^).
 aligned, right-handed coordinate system using the notation o^; b^; e^. The b^ component
 points in the direction of the local magnetic  eld (downward, in the case of the
 northern cusp). The e^ component points perpendicular to the plane de ned by the
 magnetic  eld and the radius vector to the spacecraft, or perpendicular to the local
 magnetic meridian with the positive direction pointing eastward. The o^ component
 completes the triad, and points \outward", meaning in a northerly direction in the
 northern hemisphere and a southerly direction in the southern hemisphere. Note
 that for a given magnetic  eld line, a transition over the cusp results in a rotation
 of this coordinate system by 180 about the b^-axis.
 An example of the result from FAST.get B is given in Figure 5.6.
 113
5.2.2.5 Poynting Flux
 FAST.get EBS(orbit, t base, margin)
 The Poynting  ux is found by
 ~S =
 1
  0
 ~E  ~B (5.1)
 The FAST spacecraft only measures the electric  eld along the  eld direction and
 along the spacecraft trajectory. At the cusp, the spacecraft velocity is nearly per-
 pendicular to the magnetic  eld, and so the Poynting  ux along the magnetic  eld
 lines can be found by
 Sz =
 1
  0
 EVsc   Be (5.2)
 The FAST.get EBS function gets the interpolated  elds from FAST.get E and
 FAST.get B, and calculates Sz according to formula 5.2. The electric  eld along the
 trajectory, the three components of the magnetic  eld deviation, and the Poynting
  ux are all returned as interpolations along a common time base.
 5.2.3 FAST Particle Data
 FAST particle data are provided as  ux per energy  solid-angle at various
 energies over the 64 detector segments covering the full 360 view with a 6 resolution
 around the spacecraft spin axis. The data for each species are aggregated from the
 four ion and electron spectrometers around the spacecraft. Energies are measured
 in 48 steps ranging from 3 eV to 25 keV for electrons, and 4 eV to 30 keV for ions.
 The spacing between samples was chosen for an approximately constant  E/E for
 114
Figure 5.7: Interpolated data of the Poynting  ux calculated from E- eld and B- eld
 measurements from a portion of FAST orbit 8276.
 the detectors.
 Data are provided as frames for a given moment in time, or timestamp. Each
  ux density frame is a 2-D array of energy versus detector number. Because of
 the spacecraft?s rotation, each energy measurement is taken at a slightly di erent
 angle, and so a pitch angle spectrum is provided with each frame to give the average
 pitch angle view for each detector during the time it was accumulating data at each
 energy.
 The  ux density I(E;  ) is averaged over either energy or pitch angle to pro-
 vide pitch angle or energy spectra, respectively. Integrating over both dimensions
 provides energy or number  ux in the spacecraft spin plane, with the (z^) direction
 aligned with the magnetic  eld, according to
 Jz =
 Z Z
 I(E;  ) d dE (5.3)
 Nz =
 Z Z I(E;  )
 E
 d dE (5.4)
 115
where Jz refers to the energy  ux, Nz refers to the number  ux, and d is the usual
 spherical expression sin  d d .  refers to the spin plane, or pitch, angle. Because
 the FAST detectors do not view the more than 10 in the direction along the spin
 axis, we assume isotropy in  , or around the magnetic  eld lines. Allowing  to run
 over the full 360 in the spin plane, we must introduce an extra factor of 1/2 to the
 integral, giving the expression
 d =  j sin  j cos  d (5.5)
 The  uxes are then calculated with
 Jz =
 Z 16kHz
 0
 Z 2 
0
 I(E;  )   j sin  j cos  d dE (5.6)
 Nz =
 Z 16kHz
 0
 Z 2 
0
 I(E;  )
 E
   j sin  j cos  d dE (5.7)
 5.2.3.1 Particle Processing Tools
 FAST.get flux(I, E, dE, theta)
 The FAST.get flux function performs the integration to obtain  ux versus
 time for a given orbit. Energy  ux is obtained by passing an array of ones with the
 same dimension as E so that the division in equation 5.7 is equivalent to equation
 5.6. Integration is done using the trapezoidal rule, and so the array dE contains the
 di erences between each energy bin value.
 An alternative function FAST.get flux2 is also provided. This method per-
 forms the same integration, but removes the spacecraft velocity from the measured
 116
energies. The di erence in  ux values obtained between the two methods is neg-
 ligible, but is more noticeable for high populations of low energy ions. Even in
 these cases, the di erence is no more than 10%. To reduce computation time,
 FAST.get flux is used for obtaining the electron  uxes and FAST.get flux2 is
 used for the ion  uxes.
 The FAST.get spectra(orbit, species) function creates energy and pitch
 angle spectra from the FAST data for both ions and electrons. The function returns
 the two spectra as well as the average pitch angle for each detector. The function
 was built for diagnostic purposes, and is not used in the preparation of data for
 statistical analysis.
 Only lower energy ions contribute to ion out ow, but the speci c range of
 energies of out owing ions can vary. As such, we cannot set a hard limit on what
 energies to include when measuring ion out ow. This limit was previously deter-
 mined by viewing the ion energy spectrum and selecting an obvious limit by eye.
 For example, the ion spectrum in Figure 5.8 has an obvious division near 300 eV.
 The lower energy ions have negative  ux values while the higher energy ions have
 positive  ux values, indicating both out owing and precipitaing ions2. An algorithm
 was developed to predict this division and was shown to give reasonable judgements
 on the separation of out owing from precipitating ions compared to the spectra.
 This algorithm is found in the function FAST.cutoff(orbit, maxE).
 2Since at the northern cusp the magnetic  eld points downward, using the 0 mark aligned with
 ~B gives negative values for out ow and positive values for precipitation. The ion  uxes reported
 in the next chapter are multiplied by -1 to indicate out ow.
 117
Figure 5.8: Energy and pitch angle spectra for ion  uxes measured in FAST orbit
 8276. In the coordinate system used by FAST, 0 corresponds to the local magnetic
  eld direction. Since at the northern cusp the  eld points downward, out owing
 ions will be near the 180 direction, where we see a large  ux in this example.
 118
Figure 5.9: Energy and pitch angle spectra for electron  uxes measured in FAST
 orbit 8276. See Figure 5.8 for a description of the pitch angle variable.
 119
Figure 5.10: Example of the FAST.cutoff function results with the automated
 choice (solid red) nearly matching a visually selected choice (dashed cyan). The
 algorithm consistently matches cuto s selected by hand.
 The FAST.cutoff function calculates the ion number  uxes for each individual
 energy over a given orbit. Negative ion number  uxes indicate out owing ions, so
 the cuto is found by analyzing a number of characteristics of the data set. The
 energy steps where the mean number  ux is negative and greater than 0.01% of the
 maximum out owing number  ux in magnitude are identi ed. These are further
  ltered to those showing at least 30% of the measurements over the orbit indicating
 out ow. The lesser of the highest energy matching these criteria and the speci ed
 maximum energy is selected as the cuto for the analysis.
 120
5.2.3.2 Electron Flux
 FAST.get EES(orbit, t base, margin, subset)
 The electron number and energy  uxes are obtained with the FAST.get EES
 function. This function is similar to the treatment described in section 5.2.2.2. Time
 endpoints are found, and the  ux, energy, and pitch angle products are extracted
 from the CDF  le. Fluxes are calculated for all energies above 50 eV. These data
 are not smoothed to 4 s intervals as the  eld data are, but are interpolated to the
 same time base. The time intervals between frames for the particle data are typically
 0.3 s, and no smoothing is done in accordance with the treatment by Strangeway
 et al. [44]. This function returns both the energy  ux and number  ux over the
 interpolated time series.
 5.2.3.3 Ion Flux
 FAST.get IES(orbit, t base, margin, subset)
 Ion number and energy  ux are obtained in the same way as the electron
  uxes, using FAST.get IES. The only di erence in this routine, aside from using
 ies data, is that energies are limited to above 4 eV and below the value obtained
 from FAST.cutoff. An arbitrary maximum limit of 500 eV is used for the cuto 
value. The energy limits are returned along with the energy and number  uxes for
 reference.
 A function FAST.get IES2 was written to obtain ion  uxes with corrections for
 121
Figure 5.11: Electron energy and number  uxes from a portion of FAST orbit 8276.
 122
Figure 5.12: Ion energy and number  uxes from a portion of FAST orbit 8276.
 Fluxes obtained using satellite velocity corrections are overlayed for comparison.
 The velocity correction is only noticeable in situations where the energies of the
 ions are low. Note that in the last 100 s of this plot the energy  ux falls by a factor
 of 4, and the number  ux di ers by  10% in the same time period.
 the spacecraft motion using FAST.get flux2. It is a little slower than FAST.get IES,
 but does provide better accuracy for low energy ions (see Fig. 5.12).
 5.2.3.4 Using FAST.py
 The functions in FAST.py can be used individually after importing into a
 Python shell, or can be used in an automated fashion by making use of the function
 processFAST(orbits, getelf). This function uses all of the other functions to
 create a data set including each data type interpolated to a common time base. The
 123
results are saved to the disk as a pickle.
 processFAST expects a list of orbits to process. The CDF  les for each data
 type should be saved to individual directories named by orbit, and the basedir
 variable should point to the directory where these directories are located. If a
 single orbit is to be processed it must still be passed as a list of length 1 (eg.
 orbits=[?08276?]). The getelf parameter is an optional boolean parameter to
 specify whether ELF data is available for the orbit. It is set as True by default.
 Once run, processFAST will extract the orbit parameter data and create a  ag
 array CUSPF that simply marks times where the orbit is over the cusp, as judged by
 being between invariant latitudes of 70 and 80 . Field and particle data are then
 processed, and a dictionary is created for the pickle. This dictionary has two other
 dictionaries as its elements. The ?data? dictionary holds the actual data being
 saved, while the ?meta? dictionary contains metadata pertinent to each element in
 the ?data? dictionary, such as units and the software versions used in creating the
 data. The pickles are named by orbit and include information on the software version
 and Python version compatible with the pickle. Each pickle is saved within the same
 directory as its corresponding CDF  les. The pickles can be loaded individually into
 Python as necessary for future processing.
 The processFAST function runs for about 30 min. for each orbit in the list on
 a typical desk-top computer.
 124
Figure 5.13: Summary of data from FAST orbit 8276 made using the routines in
 FAST.py to process the data. The panels show, from top to bottom, the electric
  eld along the spacecraft trajectory, the three components of the magnetic  eld
 deviation, the Poynting  ux, the electron number  ux, the electron energy  ux, the
 ELF wave amplitude, and the ion number  ux. This  gure is analogous to Fig. 3
 in Strangeway 2005 [44]. 125
5.2.4 FAST Statistical Analysis
 This and the following section rely on the two Python programs FAPlot.py
 and FAST stats.py (see Appendix E.1.2 and E.1.3 respectively). Before any statis-
 tical analysis can be done for the FAST data, the pickles returned by the function
 FAST.processFAST need to be updated to add an array identifying periods of ion
 out ow to be included in the study. While an automated method of doing this was
 sought, the number of changes from one orbit to another in the way ion out ow is
 identi ed proved too di cult, and this task remains to be done by hand. Much of
 the preparation to identify these periods can be automated, and so a function was
 created to be combined with user input as a means of identifying appropriate data
 for inclusion.
 FAPlot.update pickle(orbits)
 The FAPlot.update pickle function makes identifying periods of ion out ow
 simple. For each orbit in the list passed to the function, an ion pitch-angle spectrum
 is created using FAST.get spectra. The spectrum is displayed with lines showing
 the invariant latitude (divided by two for convenience) and magnetic local time
 for reference. The code then pauses and asks for input to identify the starting
 and stopping indicies of data to be included. The plot is displayed against index
 number, making it simple to identify the desired points. Lines are displayed at the
 input indicies to verify the selection. Multiple segments of the data can be included.
 When all desired segments have been identi ed, an array is marked with ones for all
 126
Figure 5.14: Example showing the spectrum for selecting ion out ow times from
 FAST orbit 8276. The two vertical lines correspond to the period selected. All
 data between these lines will be  agged as points to include in the statistics. In
 this study, data were not limited to only those regions where strong ion out ow is
 observed, as seen in this example.
 points to be included. The array is then put into the dictionaries from the pickle,
 and the pickle is resaved with a modi ed name.
 Periods to be included are primarily identi ed by including data showing
 strong ion conics, such as that seen in Figure 5.14. A di erence in this study from
 the Strangeway study is that data from a larger time window were included in each
 orbit. Some orbits did not have strong ion conic signatures, but portions within
 the dayside cusp were included for a more comprehensive coverage of ionospheric
 conditions in the study.
 FAPlot.py also includes a basedir variable to be used in the same manner
 as that in FAST.py. The filesuff variable should be set to match the su x of the
 127
 lenames for the pickles being processed.
 FAST stats.get averages(orbits, has elf, alt scale, length)
 Once the pickles have been updated, averages can be calculated. Averages
 are found using the FAST stats.get averages function, that provides a way to
 automatically collect averages from the FAST data with optional altitude scaling
 and period selection for the averages. By default, the function includes ELF data,
 does not do altitude scaling, and averages over the entire orbit. If desired, an integer
 number can be passed for the length parameter, allowing speci c time intervals for
 the averages. (Eg. length=60 would do averages over 60 points, or 60 s in the case
 of this study. See Figure 5.15.)
 This function calls the FAST stats.get nep(orbit, alt scale) function to
 generate the electron precipitation density, given by equation 4.2. When altitude
 scaling is enabled, all values are scaled to a standard 1000 km altitude assuming the
  ux scales as
 p
 B, or equivalently as r 
3
 2 .
 When a collection of averages is obtained, linear regression is used to  nd
 linear  t parameters between pairs of data types. The 1-D linear regression routine
 in scipy.stats is used, which returns slope and intercept, the r-value correlation
 coe cient, the p-value test, and the standard error. Fits are made to the base-10
 logarithm of each data type. As such, the slope indicates a power-law scaling value
 between energy inputs and the values to which they are regressed (in the case of the
 FAST data, the ion out ow).
 128
Figure 5.15: Plot showing orbital averages and 60 s averages for Poynting  ux and
 ion number  ux. Averaging over an entire orbit does give a good representation of
 shorter time averages, as the orbit averages maintain the general trend seen in the
 shorter averages. While there is more scatter in the shorter average data, a linear
 regression to the orbital average data is a good representation of the shorter average
 data.
 129
Figure 5.16: Linear Regression of FAST data from orbits 8260 to 8292. Each point
 is an average over an entire orbit. The regression parameters are similar to the
 values obtained by Strangeway for the same orbits.
 130
5.2.5 FAST Data Visualization
 FAPlot.gen pole plot(orbits, ofp)
 Two sets of code were developed to assist in examining the results of the data
 processing and statistics. In FAPlot.py, a polar plot of the orbit paths with the
 regions chosen for inclusion is useful to identify that the region of interest is, in
 fact, the dayside cusp (see Fig. 5.17). This plot is similar to one presented by
 Strangeway, and a comparison between them highlights the di erence in the way
 the included data for the statistical averages were chosen. Our data inclusion is more
 comprehensive, and thus covers larger portions of each orbit than in Strangeway et
 al. [44].
 The plot can be easily generated using the function FAPlot.gen pole plot.
 This function is passed a list of orbits with an optional parameter to plot only the
 portions where out ow is observed as chosen in the FAPlot.update pickle routine.
 The plot in Fig. 5.17 was generated by running this function once with ofp=False
 and again with ofp=True.
 FAST stats.get plot(x, y)
 The FAST stats.get plot function is used to generate a log-log plot of the
 two data types passed as x and y, with a linear  t and the key statistical parameters
 displayed as seen in Figure 5.16. The function  rst removes any data points with nan
 values, then generates the scatter plot with linear  t. Note that since ion out ow
 has a negative  ux along the magnetic  eld line, the ion out ow data are given a
 131
Figure 5.17: Plots showing portions of the orbits used in the statistics presented in
 Fig. 5.16 (above) and in the Strangeway study [44] (below).
 132
sign change to generate this plot, as well as in all other plots showing the ion number
  ux.
 FAPlot.gen summary plot(orbit)
 Finally, a simple routine in FAPlot.gen summary plot is provided to produce
 a plot similar to the one seen in Figure 5.13 for any speci ed orbit. This function asks
 for user input to select the starting time in the format YYYY,M,D,h,m,s. Leading
 0?s should be left out in this input.
 5.2.6 CHAMP Data Processing
 CHAMP data types are available at the ISDC website in di erent formats. The
 types pertinent to this study include the STAR accelerometer data (acc) and the
 rapid science orbit data (rso). Both of these data types are found in an ASCII text
 format detailed in the CHAMP Data Format [64] and the CHAMP Orbit Format
 [65].
 Because the CHAMP data come in an ASCII format rather than CDF, a
 di erent coding scheme was necessary to parse the data for use. CHAMP data are
 also organized by day rather than by orbit, and each  le includes data from multiple
 orbits. The scheme developed for processing the CHAMP data uses an interactive
 menu to identify what data types are available in a given  le and select which data
 types will be extracted.
 Care must be given to applying the following code to any data from CHAMP,
 133
as some  les are formatted with slight changes. While the changes are unimportant
 when looking at the text  le directly, they make any automated data extraction
 scheme impossible. The code presented here was tested and worked successfully for
 the time periods used in this study (both in 2002). Some changes may be necessary
 to generalize it to other time periods.
 5.2.6.1 Orbit Data
 champ.pso extract()
 CHAMP orbit parameters come in three types: rapid science orbits (RSO),
 predicted science orbits (PDO), and post-processed science orbits (PSO). Because
 the availability of the post-processed orbit data is not complete, the rapid science
 orbit data are used. The RSO data come in 14-hour  les. The  lename is descriptive
 of the data set, with the format CH-OG-3-RSO+CTS-CHA <YYYY> <DOY> <HH>.dat. In
 this  lename, CTS refers to the coordinate system used, the Conventional Terrestrial
 System, or GEO. CHA speci es the data is for the CHAMP satellite. <YYYY>, <DOY>,
 and <HH> give the year, day of year, and hour for the start of the  le. In the time
 periods studied, data were available in two  les per day, starting at 10:00 AM and
 10:00 PM UT.
 The CHAMP orbit data format provides time, position, velocity, and attitude
 data in addition to  ags indicating the conditions for the satellite at that particular
 time (eg. over land/water, in the Earth?s shadow, etc.). Time is provided as the
 number of days from the J2000.0 epoch (noon on 1 January 2000) and the fraction
 134
of a day in microseconds. Data are provided for 30 s intervals. Position is given
 as X, Y, and Z in mm for the GEO coordinate system. Velocity is given for X, Y,
 and Z in 10 7 m/s. A column is provided in the orbit data format for the neutral
 gas density, however it will only be non-zero in PSO data, and for the time periods
 studied was not used even there.
 Orbit data are provided with one line of data per time stamp. The locations
 of each data type are speci ed and consistent, allowing easy parsing of the data.
 The champ.pso extract function automates this process with input from the user
 to select which data types should be extracted. Because the data format is the same
 for both PSO and RSO data, the routine can be used for either type.
 5.2.6.2 Accelerometer Data
 champ.acc extract()
 CHAMP accelerometer data also come in ASCII format, but are handled dif-
 ferently than the orbit data. The  lename follows a similar convention, where
 CH-OG-2-ACC+<YYYY> <DOY> <HH>.n.dat indicates the data type (accelerometer),
 the year, day of year, and starting hour as before. The numerical value n indicates
 the revision number of the software that produced the data  le. In general, the most
 recent revision should be used when multiple  les are available.
 The ACC  les include important information in the header. Most of the
 information is unnecessary for the data itself, but calibration constants are included
 that are necessary to obtain the correct values from the accelerometer data. These
 135
Char # Description
 1{6 Time tag (10**-1 d since J2000.0)
 7{17 Time tag (10**-6 s since 0 hours)
 18{29 X coordinate of position (10**-3 m)
 30{41 Y coordinate of position (10**-3 m)
 42{53 Z coordinate of position (10**-3 m)
 54{65 X coordinate of velocity (10**-7 m/s)
 66{77 Y coordinate of velocity (10**-7 m/s)
 78{89 Z coordinate of velocity (10**-7 m/s)
 90{96 Roll angle (10**-3 deg)
 97{103 Pitch angle (10**-3 deg)
 104{110 Yaw angle (10**-3 deg)
 111{115 Neutral gas density (10**-16 g/cm**3)
 116 Maneuver  ag (M = yes, else blank)
 117 Land/water  ag (L = Land, W = Water)
 118 Ascending/descending arc  ag (A = ascending, D = descending)
 119 Eclipse  ag (E = satellite in Earth?s shadow, else blank)
 Table 5.2: Summary of the CHAMP orbit data format.
 136
CHAMP Spacecraft Coordinate System
 Origin Spacecraft center of gravity
 X^sc Aligned with the long side of the spacecraft towards the boom, in
 nominal attitude pointing in  ight direction (roll axis)
 Y^sc Forming a right-handed system with X^sc and Z^sc (pitch axis)
 Z^sc Nadir pointing in nominal attitude (yaw axis)
 Table 5.3: Description of the coordinate system used to reference the position of
 instruments relative to the CHAMP satellite. The  rst column lists the coordinate
 system component, and the second a description of how that component is de ned.
 Instruments de ne their viewing direction relative to this coordinate system.
 constants provide a scale and o set to the individual components of acceleration
 and should be applied to the data before use.
 Accelerometer data are provided for 10 s intervals and come in an instrument
  xed, inertial coordinate system as described in the CHAMP Reference Systems,
 Transformations and Standards [66]. The spacecraft coordinate system is body-
  xed, with X^sc aligned with the long dimension of the spacecraft, nominally in the
  ight direction, Z^sc pointing in the nadir direction (or always toward the Earth), and
 Y^sc completing a right-handed triad. The instrument coordinate system is aligned
 such that X^acc is anti-parallel to Z^sc, Y^acc is parallel to X^sc, and Z^acc is anti-parallel
 to Y^sc. In this coordinate system, Y^acc points along the trajectory and gives the
 acceleration felt by the spacecraft from atmospheric drag. This component provides
 the desired density information, and is the only component used in this study.
 137
STAR Accelerometer Reference Coordinate System
 Origin Accelerometer proof-mass centre = (nominal)
 Spacecraft Center of Gravity
 X^acc Anti-parallel to Z^sc (less sensitive axis)
 Y^acc Parallel to X^sc
 Z^acc Anti-parallel to Y^sc
  Rotation about X^acc
  Rotation about Y^acc
  Rotation about Z^acc
 Table 5.4: Description of the coordinate system used by the STAR accelerometer.
 Note that the vector components are de ned relative to the spacecraft coordinate
 system given in Table 5.3.
 138
ACC data is given in chunks, with one line giving the time stamp and subse-
 quent lines prior to the next time stamp providing other data types. Not every data
 type appears in every time stamp, and so parsing the  le to extract the data requires
 watching for key words to identify when the di erent data types are used. When a
 data type is missing for a given time stamp, a nan value is inserted to ensure the
 array lengths are equal. The champ.acc extract function extracts the calibration
 data and the data values for each time stamp with user input to identify which data
 types should be kept.
 5.2.6.3 Using champ.py
 champ.extract data()
 The champ.py code is written as an interactive menu for selecting the data to
 be extracted. The champ.filename variable should be set to the name of the  le
 to be extracted. champ.extract data asks the user to specify the  le type given
 in champ.filename. A menu comes up listing the data types found in the  le. By
 default, all data are included in the extraction, but the menu allows the user to select
 only the data types desired. When the list of included data is deemed satisfactory,
 the function calls the appropriate extraction function for the speci c data  le type.
 champ.process CHAMP orb(directory, days)
 In addition to the individual  le handling routines, there are two routines
 provided in champ.py to automate the extraction of data for a given list of days.
 139
champ.process CHAMP orb handles the orbit data processing for multiple  les. The
 directory where  les are located is speci ed, and a list of days (given in the format
 ?yyyy ddd?) is passed to the function for processing. The individual  les are located
 that contain data for each day to be processed, and data is extracted from each us-
 ing the generalized champ.extract data routine. The time stamps are converted to
 UNIX time with champ.time convert(d, s), and the position and velocity compo-
 nents are converted to SM coordinates using the routines provided in cstrans2.py.
 The data for each day are put into a dictionary and saved as a pickle. Note that
 while an entire day of data is spanned by three  les as provided by GFZ Potsdam,
 starting with the later  le of the previous day, the pickles merge the data from the
 di erent  les to create one single  le per day, starting at 00:00 UT. For this study,
 only the time, position, and velocity data are used. Other data included in the
 CHAMP  les may be selected out in the champ.extract data menu.
 champ.process CHAMP acc(directory, days)
 The champ.process CHAMP acc function handles the accelerometer data pro-
 cessing for multiple  les. As before, the proper data  les are identi ed, though for
 ACC data only one  le exists per day. The CHAMP data revision number is speci-
  ed in the code, and this must be modi ed if that particular revision is not available
 for that day. The menu is used to select the desired data types. The extracted time
 stamps are converted to UNIX time and the calibration data are applied to the Y^acc
 component acceleration data. The time and calibrated decceleration are added to
 140
the dictionary, which is then saved to a pickle. For this study, only the time and
 calibrated decceleration are necessary.
 5.2.7 CHAMP Statistical Analysis
 The choice of data is the primary di culty in comparing CHAMP data to
 FAST data. The two satellites have di erent orbits and do not make measurements
 in the same region at the same time. Even when the orbital planes are aligned, the
 two satellites have very di erent altitudes, with FAST at 350{4175 km, and CHAMP
 near 400 km. By selecting orbits that have nearly aligned orbital planes, however, it
 is possible to choose portions of data for analysis if we assume the altitude di erence
 is unimportant.
 CHAMP stats.create pickle(days)
 To be used together, the extracted CHAMP data are interpolated onto a com-
 mon time base, using the standard 10 s intervals provided by the accelerometer data.
 The acceleration data must also be interpolated to allow for missing time stamps.
 The CHAMP stats.create pickle function creates an interpolation time base and
 provides interpolated data for invariant position (ie. invariant latitude, magnetic
 local time, and altitude), velocity, and decceleration.
 141
CHAMP stats.find upwelling(fa orbit, fa basedir)
 Identifying the proper data for inclusion in the study is done using the function
 CHAMP stats.find upwelling. For a speci ed orbit of the FAST satellite (including
 the directory where the orbit data is stored), the invariant latitude of both the
 FAST and CHAMP satellites are plotted with the CHAMP decceleration data. The
 FAST data are examined to identify the range of invariant latitudes on the dayside
 of the magnetosphere that have been pre-selected for inclusion in the statistics.
 (Ideally, this corresponds to the region where ion out ow is observed by FAST.)
 The corresponding regions (dayside invariant latitudes in the same range as those
 identi ed in the FAST out ow data) are marked in the CHAMP accelerometer
 data, as is the time during which FAST was passing through the region. From this
 information, the CHAMP data to include in the statistical analysis is selected. An
 example of this process is shown in Figure 6.12, and discussed further in section
 6.5.1.
 The CHAMP data that are selected correspond with the region of interest that
 exhibits neutral upwelling, evidenced by an increase in decceleration, an indication
 of an increase in atmospheric density. The increased decceleration region is then
 marked for interpolation, using data of an equal time window to that selected on
 either side of the spike. The di erence between the decceleration increase and the
 interpolation from the baseline density from that observed on either side is used to
 provide a measure of the amount of neutral upwelling occurring for the given orbit.
 The baseline decceleration was found using a linear interpolation routine. The mean
 142
and peak value of the di erence is returned by the function.
 5.2.8 CHAMP Data Visualization
 When averages are obtained for a list of corresponding FAST orbits, the func-
 tions in FAST stats.py and FAPlot.py can be used to examine the data. No further
 routines speci c to CHAMP were used in this study.
 5.3 Assumptions
 Any analysis is subject to uncertainty due to the underlying assumptions made
 in the analysis. Space missions require many simplifying assumptions in order to
 work with data, and care was taken to ensure the underlying assumptions of this
 study were reasonable and justi ed. This section will describe the key assumptions
 in this study.
 5.3.1 Assumptions in Field Quantities
 Electric  eld data are assumed to be an accurate representation of electric  eld
 strengths along the spacecraft trajectory. This assumption is valid for FAST data
 prior to Sep 2001, however due to a faulty probe on the spacecraft the assumption
 is less certain for the 2002 data analyzed. Examination of the 2002 electric  eld
 data showed that the data had been compromised by the faulty probe as evidenced
 by large oscillations in the data. However, the averages may still show the general
 trends as evidenced by the results presented in the next chapter.
 143
Magnetic  eld variations are calculated by  nding the di erence between mea-
 surements made with the FAST magnetometers and the IGRF-7 1995 modeled mag-
 netic  eld. We assume that the con guration (strength and position) of Earth?s
 magnetic  eld has not changed signi cantly since 1995. Since IGRF-7 was only
 designed to be valid until the year 2000, this assumption is a little weaker for the
 2002 data. However, since all FAST data (including recent data) are processed with
 this model, IGRF-7 was used to remain consistent with the data set.
 5.3.2 Assumptions in Particle Quantities
 The particle detectors on FAST have a limited view perpendicular to the
 spin plane of the spacecraft. Flux values are found under the assumption that the
 ionospheric plasma is isotropic in this direction. This assumption is typically made
 in plasma analyzers, and seems to be a reasonable simpli cation in measuring plasma
  uxes in the ionosphere, where much of the plasma is attached to the magnetic  eld.
 5.3.3 Assumptions in Neutral Density
 While the CHAMP spacecraft decceleration is proportional to the neutral den-
 sity, it is also proportional to the square of the spacecraft velocity. The CHAMP
 orbit is nearly circular, and so the velocity changes only slightly over the course
 of an orbit. The resulting change in the corrected decceleration accounting for a
 di erence in orbit velocity is negligible, and the decceleration data are assumed to
 scale only with density.
 144
The primary goal of the STAR accelerometer was to measure gravitational
  uctuations. We also assume that any gravitational  uctuation in this direction is
 negligible compared to the atmospheric drag. Since we only use the decceleration
 component in the direction of motion of the spacecraft, which is nearly perpendicular
 to the vector toward the center of the Earth, this assumption is reasonable.
 5.3.4 Assumptions in Calculations
 In calculating Poynting  ux, only the e^ component of magnetic  eld is used.
 The desired quantity of Sz should also have a contribution from the o^ component,
 but deviations from the model in this direction are small compared to those in the
 e^ direction. This component is assumed to always be negligible in comparsion, and
 is left out in the calculation of Sz. In addition, the calculation of the cross-product
 assumes that  Be is perpendicular to EVsc . The spacecraft trajectory over the cusp
 is nearly perpendicular to the local magnetic  eld, and so this assumption is also
 reasonable.
 Precipitating electron density is calculated using the formula derived by Strange-
 way et al. [44]. This formula, as given in Equation 4.2, was derived through dimen-
 sional analysis, and is assumed to be an accurate representation of the density of
 electrons precipitating into the cusp.
 145
Chapter 6
 Statistical Analysis
 Statistical analysis of the data was done on three di erent time periods. The
  rst of these periods centered on the 25 Sep 1998 event studied by Strangeway,
 but includes orbits 8227 through 8325, spanning nearly 219 hours of time between
 20 Sep and 29 Sep 1998. Five of these orbits were not included due to the software
 not detecting any signi cant ion out ow (viz. orbits 8236, 8295, 8302, 8305, and
 8308). In this time period, the results show the consistency of the relationships
 found in the Strangeway study, even with more data over a broader range of out ow
 conditions included.
 The second time period studied is centered on an event identi ed on 6 July 2002.
 This event (as seen in Fig. 6.1) is similar in nature to that observed in the 1998
 event, and there is excellent conjunction between the FAST and CHAMP satellites,
 both crossing the northern cusp aligned with the 09:00{21:00 magnetic meridian
 (see Fig. 6.2). Data from FAST orbits 23387 through 23418 are included, spanning
 a little less than 70 hours between 4 Jul and 7 Jul 2002. Data from all orbits in
 this time period were used. The results from this time period are compared to the
 Strangeway results. This event is also used to examine neutral upwelling.
 The third time period studied is a collection of 60 orbits during the  rst week
 of February 2002. These data were used because a di erent type of out ow signature
 146
Figure 6.1: Pitch-angle spectrogram summary of the observed event in July 2002.
 This event has characteristics similar to the Sep 1998 event, showing strong ion
 conics in the low-energy pitch-angle spectrum, and large  uxes of out owing ions in
 the energy spectra. (See Fig. 4.3 for comparison.)
 147
Figure 6.2: Orbital coverage of the time period studied in July 2002. The FAST
 and CHAMP satellites are aligned to within 5 and oriented along the 09:00{21:00
 magnetic meridian.
 148
was seen fairly constantly throughout the month of February in this year, and also
 because of good alignment between the FAST and CHAMP satellites along the
 noon{midnight magnetic meridian (see Fig.s 6.3 and 6.4). Because of the weaker
 signals in this month, not every orbit contributed to this data set. FAST orbits
 21688 through 21747 were analyzed, with 21694, 21696, 21701, 21703, 21707, 21718,
 21733, 21742, and 21744 not contributing. The overall time period spans just over
 130 hours from 1 Feb through 6 Feb 2002. This event examines the correlations at
 a di erent time and under di erent ionospheric conditions. This time period is also
 used to examine neutral upwelling.
 All data sets are evaluated at a scaled altitude of 1000 km to account for
 variations in altitude. The scaling process used is described in Section 5.2.4. In
 each of the following plots, the data presented are scaled to this altitude.
 6.1 Time Average Consistency
 One of the assumptions to be examined is the validity of correlating average
 values when taken over the entire selected time period of each orbit as opposed to
 multiple points averaged over shorter time periods. In each orbit, the measured
 values can vary over a wide range. For example, in orbit 8276, the Poynting Flux
 measurements can range between 0.1 and 100 mW/m2. The upper portion of Fig-
 ure 6.5 shows the change in orbital average by averaging over data that has been
 smoothed further to 10 through 90 s intervals (by 10 s increments) compared to the
 average over the entire orbit from the 1 s data used in the study. The average value
 149
Figure 6.3: Pitch-angle spectrogram summary of the observed event in February
 2002. While the ion conics in the low-energy pitch-angle spectrum are weak, strong
 ion out ow are seen at energies less than 10 eV. The energy spectra of down- owing
 ions at high energies are seen in many passes of the FAST satellite during this
 month.
 150
Figure 6.4: Orbital covereage of the time period studied in February 2002. The
 FAST and CHAMP satellites are aligned to within 10 , with an orientation along
 the 12:00{00:00 magnetic meridian.
 151
for the orbit does not change signi cantly with the added smoothing, and so the
 orbital average is a good representation of the orbit as a whole.
 In addition, an examination of the orbital average as it compares to 10 s
 and 60 s averages for each orbit is presented in the lower portion of Figure 6.5.
 This  gure shows that the use of an average value over the entire orbit as opposed
 to a number of shorter averages for each orbit is an adequate representation of
 the ionospheric conditions measured. While beyond the scope of this work, it is
 interesting to note the di erence in orbit 8275 (before the onset of the storm) varies
 greatly in ion out ow with reduced ion number  uxes, while orbits 8276, 8277, and
 8278 (all during the storm) show greater variation in Poynting  ux and an order of
 magnitude or greater increase in ion number  ux. A logarithmic average may also
 be appropriate to use here, but to a simple linear average was used in this study.
 It is also worth examining whether the trends established by the orbital aver-
 ages are consistent with individual data. Figure 6.6 shows that the orbital average
 points are indeed consistent with trends seen using averages of 10 s and 60 s. Shorter
 time intervals broaden the distribution in the scatter plot, but the general trend is
 still clearly visible.
 6.2 Poynting Flux
 The results of the statistical correlation between Poynting  ux and ion out ow
 for the Sep 1998 data are shown in Fig. 6.7. We see good agreement between the
 Strangeway result and this result, especially when considering only the same orbit
 152
Figure 6.5: Plots showing the e ect of using shorter time intervals for averaging.
 The overall change is not signi cant from using the average over the entire orbit
 rather than averaging over shorter intervals. Below are scatter plots using all data
 for incremental average intervals. The orbital average represents the overall data
 well.
 153
Figure 6.6: Data from FAST orbits 8260{8292 by averaging interval. The orbital
 averages are an accurate representation of the overall trend seen in the shorter
 interval data.
 154
set (FAST orbits 8260{8292). The parameters of the linear regression of these
 averages also agrees with the Strangeway result, supporting the general validity of
 the correlation between Poynting  ux and ion out ow. Because the methods used
 to select data for inclusion in this study selected a broader range of data from
 each orbit, this agreement indicates that arguments against his  ndings based on
 selectivity of data are unlikely to be correct. The included data for this study cover
 a much longer period of time, extend beyond the impact of the studied event on
 both ends, and include a more larger portion of each orbit?s data in the calculated
 averages. Even with all of these changes, the results are consistent, suggesting it is
 valid to describe a power law relation between the Poynting  ux and the ion out ow
 at the northern dayside cusp. The observed power law exponent is approximately
 1.2.
 Electric  eld data from FAST are compromised in 2002, however the statistical
 analysis of this time period shows a correlation similar to that found in 1998, with a
 slope within 10% of the previous  t. The observed power law exponent in this data
 set is approximately 1.3. The shift observed in the data seen in Fig. 6.8 could be
 attributed to a strong attenuation of the measurement of the real  elds observed in
 the damaged V5 probe. The fact that a correlation consistent with the 1998 period
 results may indicate that on average some of the signal may retain a portion of the
 actual electric  elds observed by the FAST satellite in this time period and not just
 the faulty oscillations. This conclusion is supported by the correlation found for
 electron precipitation density to be presented shortly. Nevertheless, because of the
 degredation in data quality this result should not be taken as a con rmation of the
 155
Figure 6.7: Poynting  ux correlation for the orbits in September 1998. This and
 the subsequent plots all show the measured data scaled to a 1000 km altitude. See
 Sec. 5.2.4 for details on the altitude scaling.
 156
Figure 6.8: Poynting  ux correlation for the orbits in February and July 2002.
 Strangeway result.
 6.3 Electron Precipitation
 The results of the statistical correlation between electron precipitation density
 and ion out ow for the Sep 1998 data are shown in Fig. 6.9. As in the case of the
 Poynting  ux statistics, we again see agreement with the Strangeway result. When
 157
Data Set Slope r-value t-test
 Strangeway-2005 1.27  0.45 0.72 5.80
 Sep 1998 1.18  0.24 0.65 9.64
 All 2002 1.27  0.63 0.55 4.05
 Table 6.1: Summary of the statistical results for the Poynting  ux correlation.
 Uncertainties are for a 95% con dence interval. The r-value gives the correlation
 coe cient, which is a measure of the linearity of the data. (Larger r-values are
 better.) The t-test is a statistical test describing how likely the result is to be
 signi cant. (Again, larger numbers are better.)
 removing a few outlying data points for the purpose of obtaining a more descriptive
  t, we  nd again that a power law description is appropriate, with an exponent of
 2.1. While other factors play a role in ion out ow, electron precipitation density is
 consistently found to correlate with ion out ow.
 The result of the electron precipitation density correlation in 2002 reveals a
 similar trend to that found in 1998 (again, with outlying data points removed in
 the linear regression). Particularly, the Jul 2002 data are found to agree with the
 Sep 1998 data, as can be seen in Fig. 6.10. The Feb 2002 data also agrees in the
 trend, showing a nearly identical slope to the regressions of the other data sets.
 An increase in the observed ion out ows in this month may indicate a di erence
 between the types of events studied, but it is clear that the statistical relation
 between electron precipitation density and ion out ow is consistent over the times
 studied.
 158
Figure 6.9: Electron precipitation density correlation for the orbits in September
 1998.
 159
Figure 6.10: Electron precipitation density correlation for the orbits in February
 and July 2002.
 160
Data Set Slope r-value t-test
 Strangeway-2005 2.20  0.49 0.86 9.18
 Sep 1998 2.11  0.38 0.77 10.98
 Feb 2002 1.41  0.37 0.76 7.72
 Jul 2002 1.83  0.56 0.82 6.72
 Jul 02 & Sep 98 2.07  0.63 0.68 6.60
 Table 6.2: Summary of the statistical results for the electron precipitation density
 correlations. Uncertainties are for a 95% con dence interval.
 6.4 Cross Correlations
 The cross-correlation found by Strangeway between the ionospheric energy in-
 puts studied is also present in the data used in this study. The selected data from
 2002 show a weaker cross-correlation between Poynting  ux and electron precipita-
 tion density than found by Strangeway, due to a larger spread in the February data
 (see Fig. 6.11). The July data alone show a strong cross-correlation, with a slope
 of 1.18 and corresponding r-value of 0.73.
 6.5 Neutral Upwelling
 6.5.1 Visual Observations from Selection of CHAMP Data
 Not every orbit of the CHAMP satellite sees evidence of neutral upwelling.
 Many factors go into whether a density enhancement is observed, but two observa-
 161
Figure 6.11: Cross correlation between Poynting  ux and electron precipitation
 density for FAST data in 2002. Note that the July data alone is found to show a
 stronger correlation.
 162
tions made while selecting data to include from the CHAMP accelerometer provide
 good insight to some of those factors. First, when an enhancement is seen in the
 data, it always occurs at or around the same range of invariant latitudes of the day-
 side magnetosphere where the FAST satellite observes ion out ow. This observation
 leads us to expect some sort of correlation at least in location. Second, on some
 orbits (see for example the data from FAST orbit 21688 in Fig. 6.12) CHAMP will
 pass over the cusp twice in the orbital period of FAST. There are cases where both
 passes observe neutral upwelling, and others where only one pass will show a density
 enhancement in the cusp. In the latter case, the second pass is always the one to
 show the enhancement, indicating there may be some time delay between the onset
 of an ion out ow event and the upwelling of the neutral gas.
 Correlations were obtained for the various ionospheric energy inputs with the
 neutral density represented by the decceleration of the CHAMP satellite. The dec-
 celeration value used is the deviation from the baseline decceleration as interpolated
 from the orbital trends observed by CHAMP. Both the mean deviation and the peak
 deviation from the baseline were examined.
 6.5.2 Poynting Flux
 Examining the correlations for neutral density showed no correlation between
 Poynting  ux and CHAMP decceleration (see Fig. 6.13). This result may be due
 to the compromised electric  eld data from FAST. Another possibility may be that
 Poynting  ux is negligible during neutral upwelling events. Schlegel et al. found
 163
Figure 6.12: Sample plot showing how CHAMP data are selected for study using
 FAST orbit 21688. On the lower plot, invariant latitude for both satellites is plotted
 against time, indicating the synchronicity of their passing over the CUSP. On the
 upper plot, the CHAMP accelerometer data are plotted with indicators to assist se-
 lection. The green regions indicate portions of CHAMP data from the same latitude
 range of the dayside magnetosphere where ion out ow was observed by FAST. The
 red region indicates the time interval when FAST is passing over those latitudes.
 The black, vertical dashed lines indicate the portion of data selected for study, and
 the red dashed line below the selected data shows the baseline density interpolation
 for the selected region.
 164
Data Set Slope r-value t-test
 Feb 2002 -0.15  0.19 0.27 1.58
 Jul 2002 0.17  0.40 0.22 0.85
 All 2002 -0.07  0.18 0.11 0.75
 Table 6.3: Summary of the statistical results for correlations between Poynting
  ux and average neutral density deviation. Uncertainties are for a 95% con dence
 interval.
 that electric  eld strengths were quite small during upwelling events [22]. In any
 case, even removing orbits with negative average Poynting  ux yields no correlation
 for these data. (See Table 6.3.)
 6.5.3 Electron Precipitation Density
 Correlations between the neutral density and electron precipitation density
 showed little correlation. Correlations for each period individually were better, but
 the derived power law scalings varied widely. (See Fig. 6.14 and Table 6.4.)
 6.5.4 Ion Out ow
 Neither of the studied ionospheric energy inputs provide good correlation with
 neutral upwelling as observed by the decceleration of the CHAMP satellite. How-
 ever, a good correlation does exist between the measured ion out ow by FAST with
 the CHAMP decceleration deviations. (See Fig. 6.15 and Table 6.5.) While more
 scatter is observed in this correlation than in those for the ion out ow data in the
 165
Figure 6.13: Plots of the average Poynting  ux versus decceleration deviation (pro-
 portional to neutral density). Poynting  ux shows no coorelation for both average
 deviation and peak deviation.
 166
Figure 6.14: Plots of the average electron precipitation density versus deccelera-
 tion deviation. Electron precipitation density shows a lack of correlation for both
 deviation measurements.
 167
Data Set Slope r-value t-test
 Feb 2002 0.19  0.24 0.22 1.55
 Jul 2002 0.15  0.17 0.36 1.87
 All 2002 0.12  0.14 0.19 1.68
 Table 6.4: Summary of the statistical results for correlations between electron pre-
 cipitation density and average neutral density deviation. Uncertainties are for a
 95% con dence interval.
 Data Set Slope r-value t-test
 Feb 2002 0.30  0.12 0.58 4.96
 Jul 2002 0.16  0.09 0.59 3.61
 All 2002 0.20  0.06 0.60 6.49
 Table 6.5: Summary of the statistical calculations for correlations between ion out-
  ow and average neutral density deviation. Errors are for the 95% con dence inter-
 val.
 previous sections, the data here are spread over nearly  ve orders of magnitude in
 ion out ow. A correlation of the ion out ow and neutral upwelling phenomena in-
 dicate some connection between the two, even though correlations with the energy
 sources that correlate with ion out ow do not exist for neutral upwelling.
 168
Figure 6.15: Plots of the average ion out ow versus decceleration deviation. Ion
 out ow has good correlation with both measurements.
 169
6.6 Summary of Findings
 This study  nds agreement with the Strangeway results after using a larger
 data set centered on the September 1998 event. Both Poynting  ux and electron
 precipitation density are found to correlate well with ion out ow  ux in the dayside
 cusp. In addition, similar correlations are found for both ionospheric energy inputs
 with ion out ow  uxes in the two periods studied in 2002, though the Poynting
  ux data su er from a faulty electric  eld probe on the FAST satellite. The no-
 ticeable di erence between the February and July data is likely indicative of the
 di erent types of ionospheric conditions, as the July data is similar to the Septem-
 ber 1998 data in ion out ow signatures. Finally, no strong correlations are observed
 between the energy inputs with neutral density in the dayside cusp, however a good
 correlation is found between ion out ow itself with the CHAMP decceleration.
 170
Figure 6.16: Summary of the statistical results for ion out ow, showing the power
 law scaling parameter with statistical uncertainty for a con dence interval of 95%.
 The overlapping con dence intervals indicate the consistent results, showing a power
 law scaling exponent of 1.2 for Poynting  ux to ion out ow and 2.1 for electron
 precipitation to ion out ow (1.7 in 2002).
 171
Figure 6.17: Summary of the statistical results for neutral upwelling, showing the
 power law scaling parameter with statistical uncertainty for a con dence interval of
 95%. Poynting  ux and electron precipitation scaling law exponents are near zero,
 and are considered uncorrelated. A scaling law exponent of 0.2 is found for the
 correlation between ion out ow and neutral density.
 172
Chapter 7
 Conclusion
 Ultimately, the best way to determine the true causes and relationships be-
 tween various ionospheric energy inputs and the ion out ow and neutral upwelling
 phenomena is to make in situ measurements of each property from the vantage point
 of a common spacecraft. Both sounding rocket and satellite platforms would be use-
 ful, since sounding rockets can target very speci c locations and conditions for study,
 while satellites can aggregate a large quantity of data over a long period of time.
 Both would be very useful in understanding the neutral upwelling phenomenon, and
 it is hoped that in the future there will be a new RENU campaign.
 7.1 The KIMS Instrument
 The techonology to make these measurements is readily available to us today;
 we have presented one such instrument that would be very useful in the study of
 high energy ions in this context. This instrument (KIMS, as designated in this
 instance) is suited to a sounding rocket platform. KIMS provides unique bene ts
 in its design, primarily as a means of assessing the energy distribution of the local
 ion plasma over short time scales because it is able to measure a range of energies
 simultaneously rather than requiring steps to sample the energy spectrum of the
 local plasma.
 173
KIMS does have a few limitations, with its large mass and non-negligible
 external magnetic  eld. However, the external  eld is constant and small compared
 to the Earth?s  eld, and careful measurements can provide necessary o sets for
 magnetometers. Particle instruments placed near the KIMS instrument may still be
 adversly a ected, depending on the design, and so use of a KIMS type instrument
 necessitates careful planning and layout of a payload to minimize any adverse e ects
 from the external magnetic  elds.
 Our experience in the assembly and testing of KIMS found that the magnetic
 circuit concept was very e ective in practice. The assembly of the parts is straight-
 forward, and the resulting magnetic  elds are uniform and well-suited for e ecting
 a separation of ions by their energy per charge. The calibration data showed very
 clearly that the overall instrument design worked as expected, and that the resulting
 response of the MCP detector matched the numerical model. If desired, a similar
 instrument design could be created for other energy ranges of ions, or even for
 electrons.
 The MCP detector design and its accompanying electronics provide a lighter,
 less-expensive system than other particle detectors. The ampli er circuit design
 provides a fast, inexpensive pulse-counting system for such detectors and easily
 scales to any number of detector segments. The circuit design can easily be adjusted
 for other instruments used on sounding rocket payloads. The circuit design may also
 be of use for satellites with, at the added cost of further testing and use of radiation
 hardened components.
 The electronics for the instrument were further simpli ed by using an FPGA
 174
for interfacing with the payload?s telemetry unit. The GSE developed for testing and
 calibration made e ective use of both FPGA and microcontroller design to interface
 the instrument with a computer.
 7.2 Ion Out ow and Neutral Upwelling
 Though the technology is available, the question still remains as to the value
 and feasibility of further missions to examine the neutral upwelling and ion out ow
 phenomena in the polar cusps. It is clear from the results of this study that the
 statistical relations derived by Strangeway et al. are consistent, and we expect
 there to be a power-law scaling for ion out ow from both Poynting  ux and electron
 precipitation as energy sources (see Fig. 7.1). However, the amount of energy
 available in both of these sources is orders of magnitude more than is seen in the
 typical  uxes in ion out ow. The most likely place for the excess energy to go is the
 neutral gas in the ionosphere. It is reasonable to assume, then, that there is some
 electrodynamic contribution to the neutral upwelling phenomenon, and it may help
 to explain why this upwelling occurs.
 A clear correlation is, in fact, found between the ion out ow and neutral
 upwelling phenomena. As the heating processes that lead to ion out ow are elec-
 trodynamic in nature, we expect there to be an electrodynamic connection to the
 heating of the neutral atmosphere, leading to the neutral upwelling phenomenon.
 Unfortunately, there is at best a poor correlation between the ionospheric energy
 sources considered in this work with the neutral density as measured by the CHAMP
 175
Figure 7.1: Figure similar to that in Strangeway et al., 2005 [44], showing the
 correlations found in this study for the same ion out ow parameters (in blue) and
 for the neutral upwelling parameters (in red). In the case of neutral upwelling,
 only the ion out ow correlation was signi cant. The r-values from the ion out ow
 correlations compare well with those found in Strangeway (in black), as do the
 derived power law scaling values. Quoted values are for 2002 data unless otherwise
 speci ed.
 176
satellite?s accelerometer.
 The most likely explanation of these results is that as energy is transferred
 to the ionospheric plasma from the  elds and particles in the cusp, energy is also
 transferred to the neutral atmosphere as ion streams out ow from the ionosphere.
 In the case of the Poynting  ux measurements, the low correlations observed may be
 due to compromised data or possibly a lack of Poynting  ux during neutral upwelling
 events. The large spatial and temporal separation between the FAST and CHAMP
 satellites may be in uential in the case of precipitating electrons. If  eld aligned
 currents at scales smaller than the spacecraft separation between the two satellites
 are driving the heating in the neutral atmosphere, this picture may be reasonable.
 If, however, there is no correlation to be found between these energy sources
 and the neutral density, the correlation with ion out ow could indicate something
 entirely di erent, such as the out owing ions themselves being the mechanism of
 transferring heat to the neutral gas. In this case, either the ions would be heated to
 well above escape velocity and lose the excess energy to the atmosphere, or the lost
 energy would be replenished through the same processes that drive the ion out ow
 in the  rst place.
 What we can certainly conclude from these results is that there is good evi-
 dence for an electrodynamic connection between the two phenomena that justi es
 further study, preferably using in situ data from a common platform. A sounding
 rocket campaign such as RENU would be the most bene cial start in a further study
 searching for these connections.
 177
7.3 Further Work
 Were the KIMS instrument to be used in such a study, there are a few as-
 pects where improvement could be made. Though the results of the calibration of
 this instrument show that we can be con dent in the magnetic  eld strengths and
 uniformity we expected, it would be reassuring to have a calibrated measurement
 of the  elds themselves. Ultimately the energy response of each anode segment is
 all that is necessary, so this measurement would be for further con dence in the
 overall instrument design. Use of a calibrated ion source would make it possible to
 obtain an absolute  ux calibration for the instrument. A more comprehensive range
 of energies used in calibration would also be helpful, particularly at low energies. In
 addition, a more accurate scan in azimuth would lead to a more complete picture
 of the instrument response and would help in deciphering the actual data.
 With little change to the instrument design itself, a very e ective ion spec-
 trograph could easily be made for another sounding rocket campaign. (An electron
 spectrograph could also be designed by using much lower magnetic  elds in the
 magnetic circuit.) The instrument would  y in conjunction with other instruments,
 including other particle, neutral gas, and  eld detectors. Though there are many
 options for a high energy ion instrument, this design has excellent qualities that
 are bene cial to this type of study. A satellite platform may bene t from a lighter
 weight design, however.
 Satellite measurements would also be very helpful in analyzing the two phe-
 nomena examined in this dissertation. Ideally the satellite would be able to provide
 178
all of the necessary data itself, but it is not unreasonable to use other satellites in
 conjunction to study these processes. The unfortunate loss of electric  eld data in
 the FAST satellite would suggest the need to use other satellites instead to further
 this study. Potentially useful satellites for this type of study may include the Defense
 Meteorological Satellite Program (DMSP) satellites. A new satellite, carrying a full
 suite of instrumentation in a polar orbit at an altitude between 300 and 500 km
 would be an ideal means of a long term study of the neutral upwelling phenomenon,
 but inclusion of these other satellites can extend our understanding.
 As we develop new methods of understanding how to correlate data sets from
 multiple spacecraft in environments as complex as the Earth?s atmosphere, iono-
 sphere, and magnetosphere, new insights and understandings will be discovered in
 relation to these phenomena as well as a number of others. The only way to com-
 pletely untangle the complex interactions and changes that occur in these boundary
 regions is to examine both the broad and small scale properties simultaneously.
 While we continue to develop the tools and instruments necessary to undertake that
 task, there is much we can do with what we have. The statistical techniques used
 in this dissertation make it evident that there is a connection between the neutral
 upwelling and ion out ow phenomena. As we try to understand that connection,
 we will further our progress in being able to unravel these mysteries.
 179
Appendix A
 KIMS Hardware
 A.1 Magnetic Circuit
 The following pages include the diagrams for the major components of the
 magnetic circuit, and the assembly checklist procedure for assembling the parts
 together. As the magnets are very strong, the checklist is recommended to ensure
 proper assembly the  rst time.
 180
PART NO:  CUSP-1015
 TITLE:  UPPER SHELL
 NO. REQ'D:  ONE
 MAT'L:  VANADIUM PERMENDUR
 TOL: X.XXX = ?.001
 DATE:  18 JAN 1997
 U. MD.  -  J. H. MOORE   -   (301)-405-1
 NOTE 1:  THREE HOLES FOR 1/8D TYPE 302 STAINLESS
 STEEL ROLL PINS.  THESE HOLES MUST ALIGN WITH
 HOLES IN PARTS CUSP-1016, CUSP-1017, CUSP-1018,
 AND CUSP-1019.
 NOTE 2:  PARTS CUSP-1015, CUSP-1016, CUSP-1017,
 CUSP-1018, AND CUSP-1019 ALIGN ON THIS CENTER.
 .6691.000 .331
 2.593
 2.728
 1.255
 1.969
 2.469 1.131
 1.651
 2.286
 2.473
 .370
 .094R
 .094R
 .250R
 .062R
 .063R
 NOTE 1
 .490 .508
 NOTE 1
 3.047R
 3.126R
 4-40, 4 PLCS
 .567 .646
 .250R
 SEE ASSY DWG, CUSP-1020, FOR SURFACE FINISH
 SURFACES FLAT AND PARALLEL WITHIN .001
 .125R
 .512 .630
 NOTE 2
 3.001
 1.039
 .125R
 .833
 1.288
 2.985
 3.143
 .125R BOTH SIDES
 NOTE 1
 181
PART NO:  CUSP-1016
 TITLE:  LOWER SHELL
 NO. REQ'D:  ONE
 MAT'L:  VANADIUM PERMENDUR
 TOL: X.XXX = ?.001
 DATE:  20 JAN 1997
 U. MD.  -  J. H. MOORE   -   (301)-405-1
 NOTE 1:  THREE HOLES FOR 1/8D TYPE 302 STAINLESS
 STEEL ROLL PINS.  THESE HOLES MUST ALIGN WITH
 HOLES IN PARTS CUSP-1015, CUSP-1017, CUSP-1018,
 AND CUSP-1019.
 NOTE 2:  PARTS CUSP-1015, CUSP-1016, CUSP-1017,
 CUSP-1018, AND CUSP-1019 ALIGN ON THIS CENTER.
 3.126R 2.953R
 2.593 (NOTE 1) 1.255 (NOTE 1)
 2.728 1.390
 .370 .490 (NOTE 1) .472 .050R
 .150R
 .250R
 .646
 NOTE 1
 .060R .050R
 2.469 1.131
 1.651
 2.286
 .791
 .125R .512
 SEE ASSY DWG, CUSP-1020, FOR SURFACE FINISH
 SURFACES FLAT AND PARALLEL WITHIN .001
 NOTE 2
 NOTE 1
 .833
 1.039
 1.288
 3.143
 3.001
 2.985
 NOTE 1
 .125R
 .125R BOTH SIDES
 182
PART NO:  CUSP-1017 (rev 1)
 TITLE:  UPPER COVER
 NO. REQ'D:  ONE
 MAT'L:  VANADIUM PERMENDUR
 TOL: X.XXX = ?.001 ;  X.X? = ?  .02?
 DATE:  20 JAN 1997
 U. MD.  -  J. H. MOORE   -   (301)-405-1
 NOTE 1:  THREE HOLES FOR 1/8D TYPE 302 STAINLESS
 STEEL ROLL PINS.  THESE HOLES MUST ALIGN WITH
 HOLES IN PARTS CUSP-1015, CUSP-1016, CUSP-1018, AND
 CUSP-1019.
 NOTE 2:  PARTS CUSP-1015, CUSP-1016, CUSP-1017,
 CUSP-1018, AND CUSP-1019 ALIGN ON THIS CENTER.
 42.5? 3.126R
 2.593 (NOTE 1)
 1.255 (NOTE 1)
 .490 (NOTE 1) .646
 SEE ASSY DWG, CUSP-1020, FOR SURFACE FINISH
 SURFACES FLAT AND PARALLEL WITHIN .001
 NOTE 2
 .669
 1.669
 .331
 1.969
 NOTE 1
 .185
 .508
 .118
 .250R
 42.5?
 2.677R
 CLEAR 4-40, 11 PLCS.
 NOTE 1
 .833
 1.039
 1.288
 2.985
 3.001
 3.143
 .125R
 .125R BOTH SIDES
 NOTE 1
 1.355
 1.355
 183
NOTE 1:  THREE HOLES FOR 1/8D TYPE 302 STAINLESS
 STEEL ROLL PINS.  THESE HOLES MUST ALIGN WITH
 HOLES IN PARTS CUSP-1015, CUSP-1016, CUSP-1017,
 AND CUSP-1019.
 NOTE 2:  PARTS CUSP-1015, CUSP-1016, CUSP-1017,
 CUSP-1018, AND CUSP-1019 ALIGN ON THIS CENTER.
 PART NO:  CUSP-1018 (rev 1)
 TITLE:  LOWER COVER
 NO. REQ'D:  ONE
 MAT'L:  VANADIUM PERMENDUR
 TOL: X.XXX = ?.001 ; X.X? = ?.02?
 DATE:  20 JAN 1997
 U. MD.  -  J. H. MOORE   -   (301)-405-1
 3.126R
 2.593 (NOTE 1)
 1.255 (NOTE 1)
 .490 (NOTE 1) .646
 SEE ASSY DWG, CUSP-1020, FOR SURFACE FINISH
 SURFACES FLAT AND PARALLEL WITHIN .001
 NOTE 2
 NOTE 1
 .185
 .250R
 .276
 NOTE 1
 CLEAR 4-40, 7 PLCS
 42.5?
 42.5?
 2.677R
 .833
 1.039
 1.288
 2.985
 3.001
 3.143
 .125R
 .125R BOTH SIDES
 NOTE 1
 1.355
 1.355
 184
NOTE 1:  THREE HOLES FOR 1/8D TYPE 302 STAINLESS
 STEEL ROLL PINS.  THESE HOLES MUST ALIGN WITH
 HOLES IN PARTS CUSP-1015, CUSP-1016, CUSP-1017,
 AND CUSP-1018.
 NOTE 2:  PARTS CUSP-1015, CUSP-1016, CUSP-1017,
 CUSP-1018, AND CUSP-1019 ALIGN ON THIS CENTER.
 PART NO:  CUSP-1019
 TITLE:  PARTITION
 NO. REQ'D:  ONE
 MAT'L:  VANADIUM PERMENDUR
 TOL: X.XXX = ?.001 ; X.X? = ?.02?
 DATE:  20 JAN 1997
 U. MD.  -  J. H. MOORE   -   (301)-405-1
 3.126R
 2.593 (NOTE 1) 1.255 (NOTE 1)
 .490 (NOTE 1) .646
 SEE ASSY DWG, CUSP-1020, FOR SURFACE FINISH
 SURFACES FLAT AND PARALLEL WITHIN .001
 NOTE 2
 NOTE 1
 .250R
 NOTE 1
 .833
 1.039
 1.288
 2.985
 3.001
 3.143
 .125R
 .125R BOTH SIDES
 NOTE 1
 2.469 1.131
 .118
 .125R
 185
186
187
188
189
190
191
192
KIMS/Proton?Magnetic?Spectrograph?
 Magnetic?Circuit?Assembly?
 Rev.?D??????26?Jan?2010?
 ?
 1.?Locate?and?clean:?
 ?
 ? 1015???Upper?Shell?
 ? 1016???Lower?Shell?
 ? 1017???Upper?Cover?
 ? 1018???Lower?Cover?
 ? 1019???Partition?
 ? 1036/2036???Lower?Magnet?Clamp?
 ? Lower?Aperture?
 ? 1034/3034???Modified?Upper?Magnet?Clamp?
 ? Upper?Aperture?
 ? Lower?Magnet?(Thick)?
 ? Upper?Magnet?(Thin)?
 ? 4?40?x?1??Slotted?Screws?(6)?
 ? 4?40?x????Phillips?Screws?(8)?
 ? 4?40?x?3/8??Phillips?Screws?(8)?
 ? 4?40?x????Phillips?Screws?(8)?
 ? 2?56?x?3/16??Phillips?Screws?(6)?
 ? 2?56?x????Slotted?Screws?(8)?
 ? 1/8??x?2??Roll?Pins?(5)?
 ? 1/8??rods?6??long?
 ? Jig?Base?
 ? Jig?Nuts?&?Washers?(4?ea.)?
 ? Pads?A,?B,?C,?and?D?
 ? Spacers?L?and?U?
 ? Non?Magnetic?Stainless?Washers,?0.045??thickness?(8)?
 ? Non?Magnetic?Slotted?Screwdriver?
 ? Non?Magnetic?Phillips?Screwdriver?
 ? Non?Magnetic?Needle?Nose?Pliers?and/or?Tweezers?
 ? Non?Magnetic?Mallet?
 ? Chunk?of?plastic?for?setting?pins?
 ? 9V?Battery?
 ? Length?of?Insulated?Wire?
 193
2.?Lower?Shell?Assembly?
 ?
 ? Put?Lower?Cover?in?jig,?tab?right.?
 ? Place?Pad?A?in?jig?(letter?down).?
 ? Thread?and?tighten?4?jig?nuts?on?the?jig?bolts.?
 ? Attach?Lower?Aperture?to?Lower?Clamp,?bevel?in,?with?2?
 56?x?3/16??screws?and?Loctite.?
 ? Place?Lower?Magnet?on?the?pad,?pole?face?up.?
 ? Place?Lower?Clamp?over?the?Lower?Magnet.?
 ? Check?that?current?running?up?the?magnet?(into?the?
 aperture)?deflects?left.?
 ? Slide?magnet?onto?the?Lower?Cover,?carefully?line?up?with?
 holes?1?5.?
 ? Thread?holes?1?and?5?with????screws.?(Screws?will?be?
 upside?down,?and?don?t?actually?attach?the?clamp?to?the?
 cover.??This?is?only?to?keep?the?clamp?from?shifting?on?
 removal.)?
 ? Remove?Pad?A.?
 ? Remove?Assembly.?
 ? Thread?holes?2?and?4?with?1??screws.?
 ? Remove?screws?in?1?and?5.?
 ? Replace?Lower?Assembly?in?jig,?tab?right.?
 ? Attach?Spacer?L?and?thread?holes?1,?3,?and?5?with?1??
 screws.?
 ? Slide?Lower?Shell?onto?assembly,?aperture?to?the?right.?
 ? Remove?screws?in?1,?3,?and?5.?
 ? Remove?Spacer?L.?
 ? Remove?Assembly.?
 ? Thread?holes?1,?3,?5,?and?6?with????screws.?
 ? Remove?screws?in?2?and?4,?replace?with????screws.?
 ? Carefully?set?Lower?Assembly?to?the?side,?away?from?any?
 magnetic?materials.?
 194
3.?Upper?Shell?Assembly?
 ?
 ? Place?Upper?Cover?in?jig,?tab?left.?
 ? Place?Pad?D?in?jig?(letter?down).?
 ? Thread?and?tighten?4?jig?nuts?on?the?jig?bolts.?
 ? Attach?Upper?Aperture?to?Upper?Clamp,?bevel?in,?with?2?
 56?x????screws?and?Loctite.?
 ? Place?Upper?Magnet?on?the?pad,?pole?face?up.?
 ? Place?Upper?Clamp?over?the?Upper?Magnet.?
 ? Check?that?the?current?running?up?the?magnet?(into?the?
 aperture)?deflects?right.?
 ? Slide?magnet?onto?the?Upper?Cover,?carefully?line?up?with?
 holes?1?5.?
 ? Thread?holes?1?and?5?(screws?upside?down).?
 ? Remove?Pad?D.?
 ? Remove?Assembly.?
 ? Thread?screws?2?and?4?with?1??long?screws.?
 ? Remove?screws?in?1?and?5.?
 ? Thread?hole?6?with?1??long?screws?(upside?down),?flush?to?
 top?of?cover.?
 ? Attach?Spacer?U?and?thread?holes?1,?3,?and?5?with?1??
 screws.?
 ? Slide?Upper?Shell?onto?assembly,?aperture?to?the?left.?
 ? Remove?screws?in?1,?3,?and?5.?
 ? Remove?Spacer?U?
 ? Remove?screw?in?6.?
 ? Remove?assembly.?
 ? Thread?holes?1,?3,?and?5?with?3/8??screws.?
 ? Remove?screws?in?2?and?4.?
 ? Thread?holes?2?and?4?with?3/8??screws.?
 195
4.?Circuit?Assembly?
 ?
 ? Place?Partition?in?jig,?tab?right.?
 ? Place?Pad?D?in?jig?(letter?down).?
 ? Thread?and?tighten?4?jig?nuts?on?the?jig?bolts.?
 ? Slide?Upper?Assembly?onto?Partition.?
 ? Remove?Pad?D?
 ? Remove?Upper?Assembly?with?Partition.?
 ? Place?2?Washers?ea.?on?jig?bolts.?
 ? Replace?Upper?Assembly?with?tab?left;?the?partition?will?
 be?on?top.?
 ? Place?Pads?A,?B,?C,?and?D?in?jig.?
 ? Thread?and?tighten?4?jig?nuts?on?the?jig?bolts.?
 ? Slide?Lower?Assembly?onto?the?partition.?
 ? Insert?pins?1,?2,?and?3.?
 ? Remove?Pads?A,?B,?C,?and?D.?
 ? Remove?Finished?Circuit?and?Inspect.?
 ? Thread?Upper?holes?5,?a,?b,?c,?and?d?with????screws.?
 ? Wrap?carefully?for?storage?to?prevent?contamination?of?
 the?magnetic?poles.?
 196
A.2 Clamshell and Cover
 The following pages include the diagrams for the clamshell and cover for the
 KIMS instrument.
 197
198
199
200
201
202
A.3 KIMS Electronics
 The following pages include the circuit schematics for the KIMS electronics.
 203
204
205
206
207
208
209
210
211
Appendix B
 KIMS Software
 B.1 Monte Carlo Simulation
 B.1.1 mc sim.py
 from numpy import array,arange,append,shape,zeros,histogram
 from pylab import loadtxt,plot,figure
 from math import cos,sqrt,pi
 from random import random
 q = 2*1.60218e-19
 mp = 1.67262e-27
 B0 = 0.096
 cel = -2.286*0.0254 # collimator edges
 cer = -1.651*0.0254
 dhel = -1.130*0.0254 # detector housing edges
 dher = 2.469*0.0254
 pcb_w = 3.265*0.0254
 pcb_h = 0.945*0.0254
 mask = 0.115*0.0254
 partition = 0.118*0.0254
 pad_height = (pcb_h-partition)/2. - mask
 off = (dhel + dher - pcb_w)/2.0 # offset to edge of pcb: pcb edge is 0
 alpha = (cer + cel)/2.0 - off # location of aperture center
 w = 0.118*0.0254 # aperture half width
 N_pads=10
 x=loadtxt(raw_input(?Filename: ?))
 tm = -6.0*pi/180.
 tp = 19.0*pi/180.
 212
def locate(E,theta,s,m,B):
 return alpha + s + 2*sqrt(2*m*E/q)/B * cos(theta)
 def pad_sim(N,E_min,E_max,theta_min,theta_max,s_min,s_max,a,b,m=mp,B=B0):
 hits = []
 done = 0.10
 for n in range(N):
 e = E_min + (E_max-E_min)*random()
 t = theta_min + (theta_max-theta_min)*random()
 s = s_min + (s_max-s_min)*random()
 pos = locate(e,t,s,m,B)
 if pos >= a and pos <= b:
 hits.append((e,t,s))
 if n > N*done:
 print done*100,?% done?
 done += 0.10
 print 100.0, ?% done?
 out = zeros(shape(hits))
 I,J = shape(hits)
 for i in range(I):
 for j in range(J):
 out[i,j]=hits[i][j]
 return out
 def KIMS_hist(E,a,b,m=mp,B=B0):
 hits=pad_sim(int(2e7),E[0],E[1],tm,tp,-w,w,a,b,m,B)
 dE=5.0
 edges=arange(E[0],E[1]+dE,dE)
 centers=zeros(len(edges)-1)
 for i in range(len(centers)):
 centers[i]=(edges[i]+edges[i+1])/2.0
 hist,junk=histogram(hits[:,0],bins=edges,normed=True)
 plot(centers,hist)
 return hits,edges,hist
 def full_sim():
 E=array([0,0])
 E[0]=float(raw_input("Lowest energy in eV: "))
 E[1]=float(raw_input("Highest energy in eV: "))
 BA=float(raw_input("Low Energy B: "))
 BB=float(raw_input("High Energy B: "))
 m=float(raw_input("Particle Mass: "))
 B = BA
 213
figure()
 EA = zeros(10)
 dEA = zeros(10)
 print(":: A0 ::")
 hits_a0,edges,hist_a0 = KIMS_hist(E,x[0],x[1],m,B)
 centers=zeros(len(edges)-1)
 for i in range(len(centers)):
 centers[i]=(edges[i]+edges[i+1])/2.0
 EA[0] = sum(centers*hist_a0*5.0)
 dEA[0] = 1./max(hist_a0)
 print(":: A1 ::")
 hits_a1,edges,hist_a1 = KIMS_hist(E,x[2],x[3],m,B)
 EA[1] = sum(centers*hist_a1*5.0)
 dEA[1] = 1./max(hist_a1)
 print(":: A2 ::")
 hits_a2,edges,hist_a2 = KIMS_hist(E,x[4],x[5],m,B)
 EA[2] = sum(centers*hist_a2*5.0)
 dEA[2] = 1./max(hist_a2)
 print(":: A3 ::")
 hits_a3,edges,hist_a3 = KIMS_hist(E,x[6],x[7],m,B)
 EA[3] = sum(centers*hist_a3*5.0)
 dEA[3] = 1./max(hist_a3)
 print(":: A4 ::")
 hits_a4,edges,hist_a4 = KIMS_hist(E,x[8],x[9],m,B)
 EA[4] = sum(centers*hist_a4*5.0)
 dEA[4] = 1./max(hist_a4)
 print(":: A5 ::")
 hits_a5,edges,hist_a5 = KIMS_hist(E,x[10],x[11],m,B)
 EA[5] = sum(centers*hist_a5*5.0)
 dEA[5] = 1./max(hist_a5)
 print(":: A6 ::")
 hits_a6,edges,hist_a6 = KIMS_hist(E,x[12],x[13],m,B)
 EA[6] = sum(centers*hist_a6*5.0)
 dEA[6] = 1./max(hist_a6)
 print(":: A7 ::")
 hits_a7,edges,hist_a7 = KIMS_hist(E,x[14],x[15],m,B)
 EA[7] = sum(centers*hist_a7*5.0)
 214
dEA[7] = 1./max(hist_a7)
 print(":: A8 ::")
 hits_a8,edges,hist_a8 = KIMS_hist(E,x[16],x[17],m,B)
 EA[8] = sum(centers*hist_a8*5.0)
 dEA[8] = 1./max(hist_a8)
 print(":: A9 ::")
 hits_a9,edges,hist_a9 = KIMS_hist(E,x[18],x[19],m,B)
 EA[9] = sum(centers*hist_a9*5.0)
 dEA[9] = 1./max(hist_a9)
 B = BB
 figure()
 EB = zeros(10)
 dEB = zeros(10)
 print(":: B0 :")
 hits_b0,edges,hist_b0 = KIMS_hist(E,x[0],x[1],m,B)
 EB[0] = sum(centers*hist_b0*5.0)
 dEB[0] = 1./max(hist_b0)
 print(":: B1 ::")
 hits_b1,edges,hist_b1 = KIMS_hist(E,x[2],x[3],m,B)
 EB[1] = sum(centers*hist_b1*5.0)
 dEB[1] = 1./max(hist_b1)
 print(":: B2 ::")
 hits_b2,edges,hist_b2 = KIMS_hist(E,x[4],x[5],m,B)
 EB[2] = sum(centers*hist_b2*5.0)
 dEB[2] = 1./max(hist_b2)
 print(":: B3 ::")
 hits_b3,edges,hist_b3 = KIMS_hist(E,x[6],x[7],m,B)
 EB[3] = sum(centers*hist_b3*5.0)
 dEB[3] = 1./max(hist_b3)
 print(":: B4 ::")
 hits_b4,edges,hist_b4 = KIMS_hist(E,x[8],x[9],m,B)
 EB[4] = sum(centers*hist_b4*5.0)
 dEB[4] = 1./max(hist_b4)
 print(":: B5 ::")
 hits_b5,edges,hist_b5 = KIMS_hist(E,x[10],x[11],m,B)
 215
EB[5] = sum(centers*hist_b5*5.0)
 dEB[5] = 1./max(hist_b5)
 print(":: B6 ::")
 hits_b6,edges,hist_b6 = KIMS_hist(E,x[12],x[13],m,B)
 EB[6] = sum(centers*hist_b6*5.0)
 dEB[6] = 1./max(hist_b6)
 print(":: B7 ::")
 hits_b7,edges,hist_b7 = KIMS_hist(E,x[14],x[15],m,B)
 EB[7] = sum(centers*hist_b7*5.0)
 dEB[7] = 1./max(hist_b7)
 print(":: B8 ::")
 hits_b8,edges,hist_b8 = KIMS_hist(E,x[16],x[17],m,B)
 EB[8] = sum(centers*hist_b8*5.0)
 dEB[8] = 1./max(hist_b8)
 print(":: B9 ::")
 hits_b9,edges,hist_b9 = KIMS_hist(E,x[18],x[19],m,B)
 EB[9] = sum(centers*hist_b9*5.0)
 dEB[9] = 1./max(hist_b9)
 return EA,dEA,EB,dEB
 216
B.2 FPGA
 B.2.1 Telemetry/Ampli er Board
 B.2.1.1 Telemetry Code
 ---------------------------------------------------------------------------
 -- Company: University of Maryland
 -- Engineer: Larry Lutz
 --
 -- Create Date: 01/17/2010
 -- Module Name: IonSpectr_TM - Behavioral
 --
 -- Revision:
 --
 ---------------------------------------------------------------------------
 library IEEE;
 use IEEE.STD_LOGIC_1164.ALL;
 use IEEE.STD_LOGIC_ARITH.ALL;
 use IEEE.STD_LOGIC_UNSIGNED.ALL;
 entity IonSpectr_TM is
 Port ( Clock : in STD_LOGIC; -- Telemetry Clock Input (10 MHz)
 MFSync : in STD_LOGIC; -- Major Frame Sync
 GtdClk : in STD_LOGIC; -- Gated Clock
 Counter_Input : in STD_LOGIC_VECTOR (9 downto 0);
 -- Counter Inputs from CSAs
 DataOut : out STD_LOGIC; -- Data Output to Telemetry
 Test_On : in STD_LOGIC; -- Test On Command
 Calibrate_Out : out STD_LOGIC_VECTOR (9 downto 0);
 -- Calibration Outputs
 TP : out STD_LOGIC_VECTOR (8 downto 0)
 -- Test Points
 217
);
 end IonSpectr_TM;
 architecture Behavioral of IonSpectr_TM is
 component Counter
 port (
 Clock : in STD_LOGIC;
 Reset : in STD_LOGIC;
 Counter_In : in STD_LOGIC;
 Dataout : out STD_LOGIC_VECTOR (19 downto 0)
 );
 end component;
 signal Shiftreg : std_logic_vector (199 downto 0);
 -- Shift Register
 signal Shiftin : std_logic_vector (199 downto 0);
 -- Shift Register Input
 signal CalCount : std_logic_vector (14 downto 0);
 -- Calibration Counter/Divider
 signal MFCount : std_logic_vector (2 downto 0);
 -- MFSync Timing Counter
 signal Reset : std_logic; -- Counter Reset
 signal Srload : std_logic; -- Shift Register Load
 begin
 process (Clock, MFSync, MFCount) -- MFSync Timing Counter
 218
begin
 if MFSync = ?0? then MFCount <= "000";
 elsif rising_edge (Clock) then
 if MFCount /= "111" then
 MFCount <= MFCount + ?1?;
 end if;
 end if;
 end process;
 Srload <= ?1? when MFCount = "001" else ?0?;
 Reset <= ?1? when MFCount = "011" else ?0?;
 process (Srload, GtdClk, Shiftreg, Shiftin)
 -- Shift Register
 begin
 if Srload = ?1? then Shiftreg <= Shiftin;
 elsif rising_edge (GtdClk) then
 Shiftreg <= Shiftreg (198 downto 0) & ?0?;
 end if;
 end process;
 DataOut <= Shiftreg (199);
 219
process (Clock, Test_On, CalCount) -- Calibration Counter/Divider
 begin
 if Test_On = ?0? then CalCount <= "000000000000000";
 elsif rising_edge (Clock) then
 CalCount <= CalCount + ?1?;
 end if;
 end process;
 Calibrate_Out <= CalCount (14 downto 5);
 TP(0) <= GtdClk;
 TP(1) <= Shiftreg (199);
 TP(2) <= Clock;
 TP(3) <= Counter_Input (0);
 TP (8 downto 4) <= "00000";
 Counters: -- Generate Counters
 for I in 0 to 9 generate
 begin
 CounterGen : Counter
 port map (
 Clock => Clock,
 Reset => Reset,
 220
--Counter_In => CalCount (I+5),
 Counter_In => Counter_Input (I),
 Dataout => Shiftin (((I*20)+19) downto (I*20))
 );
 end generate;
 end Behavioral;
 221
B.2.1.2 Ampli er/Counter Code
 ---------------------------------------------------------------------------
 -- Company: University of Maryland
 -- Engineer: Larry Lutz
 --
 -- Create Date: 01/17/2010
 -- Module Name: Counter - Behavioral
 --
 -- Revision:
 --
 ---------------------------------------------------------------------------
 library IEEE;
 use IEEE.STD_LOGIC_1164.ALL;
 use IEEE.STD_LOGIC_ARITH.ALL;
 use IEEE.STD_LOGIC_UNSIGNED.ALL;
 entity Counter is
 Port ( Clock : in STD_LOGIC; -- Clock Input
 Reset : in STD_LOGIC; -- Reset Input
 Counter_In : in STD_LOGIC; -- Counter Input
 DataOut : out STD_LOGIC_VECTOR (19 downto 0)
 -- Data Output
 );
 end Counter;
 architecture Behavioral of Counter is
 signal Count : std_logic_vector (15 downto 0);
 -- Count Value
 signal InputReg : std_logic; -- Input Registered
 signal InputEdge : std_logic; -- Input Edge
 222
begin
 process (Clock, InputReg, Counter_In) -- Input Edge Detector
 begin
 if rising_edge (Clock) then
 InputReg <= Counter_In;
 end if;
 end process;
 InputEdge <= ?1? when InputReg = ?1? and Counter_In = ?0? else ?0?;
 process (Reset, Clock, InputEdge, Count) -- Counter
 begin
 if Reset = ?1? then Count <= "0000000000000000";
 elsif rising_edge (Clock) then
 if InputEdge = ?1? then
 Count <= Count + ?1?;
 end if;
 end if;
 end process;
 DataOut (19 downto 16) <= "0000";
 DataOut (15 downto 0) <= Count;
 223
--DataOut <= "10100000000000000000";
 end Behavioral;
 224
B.2.2 GSE
 ---------------------------------------------------------------------------
 -- Company: University of Maryland
 -- Engineer: Larry Lutz
 --
 -- Create Date: 05/31/2010
 -- Module Name: IonSpectr_GSE - Behavioral
 --
 -- Revision:
 --
 ---------------------------------------------------------------------------
 library IEEE;
 use IEEE.STD_LOGIC_1164.ALL;
 use IEEE.STD_LOGIC_ARITH.ALL;
 use IEEE.STD_LOGIC_UNSIGNED.ALL;
 entity IonSpectr_GSE is
 Port ( Osc : in STD_LOGIC; -- Oscillator (40 MHz)
 -- TM Interface
 ClockOut : out STD_LOGIC; -- Clock Out (10 MHz)
 MFSync : out STD_LOGIC; -- Major Frame Sync
 GatedClock : out STD_LOGIC; -- Gated Clock
 Enable : out STD_LOGIC; -- Enable
 DataIn1 : in STD_LOGIC; -- Data Input Side 1
 DataIn2 : STD_LOGIC; -- Data Input Side 2
 -- MicroController Interface
 DataOut : out STD_LOGIC_VECTOR (15 downto 0);
 -- Data from Shift Registers
 Sync : out STD_LOGIC; -- Frame Sync
 SyncAck : in STD_LOGIC; -- Sync Acknowledge
 225
DataRdy : out STD_LOGIC; -- Data Ready
 DataAck : in STD_LOGIC; -- Data Acknowledge
 Chan2 : in STD_LOGIC; -- Channel 2 Data Select
 -- Test Points
 TP : out STD_LOGIC_VECTOR (8 downto 0)
 -- Test Points
 );
 end IonSpectr_GSE;
 architecture Behavioral of IonSpectr_GSE is
 signal Clockdiv : std_logic_vector (1 downto 0);
 -- Clock Divider
 signal Divide20 : std_logic_vector (4 downto 0);
 -- 20 Bit Word Divider
 signal WordCnt : std_logic_vector (12 downto 0);
 -- Word Counter
 signal GateCnt : std_logic_vector (4 downto 0);
 -- Gate Counter
 signal DataReg1 : std_logic_vector (15 downto 0);
 -- Data 1 Shift Register
 signal DataReg2 : std_logic_vector (15 downto 0);
 -- Data 2 Shift Register
 signal DataInt : std_logic; -- Data Interval
 signal Word20 : std_logic; -- Word Synch Bit
 signal Clock10 : std_logic; -- 10 MHz Synch Bit
 signal Frame : std_logic; -- Frame Sync
 signal GateCtEn : std_logic; -- Gate Counter Enable
 226
signal Gate : std_logic; -- Gate for Gated Clock
 signal GtdClock : std_logic; -- Gated Clock
 signal GatCkEdg : std_logic; -- Gated Clock Edge
 signal DataMicr : std_logic; -- Data Ready for MicroController
 constant Count20 : std_logic_vector := "10011";
 -- 20 Bit Word End Count (19)
 begin
 process (Osc, Clockdiv) -- Clock Divider for 10 MHz
 begin
 if rising_edge (Osc) then
 Clockdiv <= Clockdiv + ?1?;
 end if;
 end process;
 Clock10 <= ?1? when Clockdiv = "00" else ?0?;
 ClockOut <= Clockdiv(1);
 process (Osc, Clock10, Word20, Divide20) -- Clock Divider for 20 Bit Words
 227
begin
 if rising_edge (Osc) then
 if Clock10 = ?1? then
 if Word20 = ?1? then Divide20 <= "00000";
 else Divide20 <= Divide20 + ?1?;
 end if;
 end if;
 end if;
 end process;
 Word20 <= ?1? when Divide20 = Count20 else ?0?;
 process (Osc, Clock10, Word20, WordCnt) -- Word Counter
 begin
 if rising_edge (Osc) then
 if Clock10 = ?1? and Word20 = ?1? then
 WordCnt <= WordCnt + ?1?;
 end if;
 end if;
 end process;
 Frame <= ?1? when WordCnt (12 downto 6) = "00000000" else ?0?;
 MFSync <= Frame;
 228
Sync <= Frame;
 DataInt <= ?1? when WordCnt (8 downto 6) = "00000" else ?0?;
 DataMicr <= DataInt and not Gate and not Frame;
 DataRdy <= DataMicr;
 process (Osc, DataInt, Clock10, GateCtEn, GateCnt)
 -- Gate Clock Divider (20 Bits)
 begin
 if DataInt = ?0? then GateCnt <= "00000";
 elsif rising_edge (Osc) then
 if Clock10 = ?1? and GateCtEn = ?1? then
 GateCnt <= GateCnt + ?1?;
 end if;
 end if;
 end process;
 GateCtEn <= ?0? when GateCnt = "10100" else ?1?;
 Gate <= DataInt and GateCtEn and not Frame;
 Enable <= Gate;
 GtdClock <= Gate and Clockdiv(1);
 GatedClock <= GtdClock;
 GatCkEdg <= ?1? when GtdClock = ?1? and Clockdiv = "10" else ?0?;
 229
process (Osc, GatCkEdg, DataReg1, DataIn1)
 -- Data 1 Shift Register
 begin
 if rising_edge (Osc) then
 if GatCkEdg = ?1? then
 DataReg1 <= DataReg1(14 downto 0) & DataIn1;
 end if;
 end if;
 end process;
 process (Osc, GatCkEdg, DataReg2, DataIn2)
 -- Data 2 Shift Register
 begin
 if rising_edge (Osc) then
 if GatCkEdg = ?1? then
 DataReg2 <= DataReg2(14 downto 0) & DataIn2;
 end if;
 end if;
 end process;
 DataOut <= DataReg1 when Chan2 = ?0? else DataReg2;
 TP(0) <= Frame;
 TP(1) <= DataMicr;
 TP(2) <= GtdClock;
 TP(3) <= GatCkEdg;
 TP(4) <= SyncAck;
 230
TP(5) <= DataAck;
 TP(6) <= DataIn1;
 TP(7) <= DataIn2;
 TP(8) <= ?0?;
 end Behavioral;
 231
B.3 MSP430
 The following code programmed the MSP430F5438 on the GSE board to in-
 terface with the KIMS telemetry boards. The MSP430 served to send the data
 received from the telemetry boards by an FPGA to a computer where they could
 be recorded to a  le.
 /* KIMSF5438 v. 0.5: 24 August 2010
 * GSE programming for the MSP430F5438.
 * Increase operating/transmission rates to see if it affects data read.
 */
 #include <msp430f5438.h>
 #include <stdio.h>
 #include <string.h>
 #define CHAN2 BIT2
 #define DATAACK BIT3
 #define SYNCACK BIT4
 #define DATARDY BIT5
 #define SYNC BIT6
 #define V24_MON BIT0
 #define HV_MON2 BIT1
 #define HV_MON1 BIT2
 #define TEMP BIT3
 void port_init(void);
 void xtal_init(void);
 void uart_init(void);
 void adc12_init(void);
 void call_0(void);
 void call_1(void);
 void call_2(void);
 void call_3(void);
 void call_r(void);
 void send_message(void);
 int analog[4];
 int ad_ready;
 232
char command = ?p?;
 void main(void) {
 int i, j, data_value, count; // Two iterators and storage for data
 char hex_word[5]; // String for converting data to ASCII hex
 char message[36];
 WDTCTL = WDTPW + WDTHOLD; // WDT off
 port_init();
 xtal_init();
 uart_init();
 adc12_init();
 _enable_interrupts(); // Allow interrupts without entering LPM
 i=0; j=0; ad_ready=0; count=0; // initialize software flags/iterators
 for (;;) {
 switch (command) {
 case ?p?:
 break; // hold until command issued
 case ?s?:
 sprintf(message, "P4IN: %d\tSYNC: %d\tP4SY:%d\r\n", P4IN,
 SYNC, (P4IN & SYNC));
 j=0;
 while (message[j] !=?\0?) {
 while (!(UCA3IFG&UCTXIFG));
 UCA3TXBUF = message[j++];
 }
 command=?p?;
 break;
 case ?r?:
 while (count++ < 100) {
 while ((P4IN & SYNC) == SYNC); // Pass any missed frames
 while ((P4IN & SYNC) != SYNC); // Wait for MFRAME SYNC
 P4OUT |= BIT4; // Acknowledge SYNC
 for (i=0; i<10; i++) { // 10 sets of data
 while ((P4IN & DATARDY) != DATARDY); // Wait for DATARDY
 P4OUT |= DATAACK; // Acknowledge DATARDY
 data_value = PAIN; // Read KIMS_A word
 sprintf(hex_word, "%04x\t", data_value);
 for (j=0; j<5; j++) { // Send KIMS_A word
 233
while (!(UCA3IFG & UCTXIFG)); // Wait for TX finish
 UCA3TXBUF = hex_word[j];
 }
 /* data_value = P2IN;
 sprintf(hex_word, "%02x\t", data_value);
 for (j=0; j<3; j++) {
 while (!(UCA3IFG & UCTXIFG));
 UCA3TXBUF = hex_word[j];
 }
 data_value = P1IN;
 sprintf(hex_word, "%02x\t", data_value);
 for (j=0; j<3; j++) {
 while (!(UCA3IFG & UCTXIFG));
 UCA3TXBUF = hex_word[j];
 }
 */ P4OUT |= CHAN2; // Switch to KIMS_B (CHAN2 on)
 __delay_cycles(1000); // Wait for data to settle
 data_value = PAIN; // Read KIMS_B word
 sprintf(hex_word, "%04x\t", data_value);
 for (j=0; j<5; j++) { // Send KIMS_B word
 while (!(UCA3IFG & UCTXIFG)); // Wait for TX finish
 UCA3TXBUF = hex_word[j];
 }
 P4OUT &= ~CHAN2; // Switch to KIMS_A (CHAN2 off)
 P4OUT &= ~DATAACK; // Data received, wait for next
 // DATARDY
 }
 P4OUT &= ~SYNCACK; // Sample received, wait for next
 // MFRAME SYNC
 ADC12CTL0 |= ADC12SC; // Start ADC conversions
 while (!(ad_ready)); // wait for ADC data
 for (i=0; i<4; i++) { // Send Analog words
 sprintf(hex_word, "%04x\t", analog[i]);
 for (j=0; j<5; j++) { // Send V24_MON word
 while (!(UCA3IFG & UCTXIFG)); // Wait for TX finish
 UCA3TXBUF = hex_word[j];
 }
 }
 ad_ready = 0; // reset software flag
 234
while (!(UCA3IFG & UCTXIFG)); // Done with data, send newline
 UCA3TXBUF = ?\r?;
 while (!(UCA3IFG & UCTXIFG));
 UCA3TXBUF = ?\n?;
 }
 count = 0;
 command = ?p?;
 break;
 default:
 sprintf(message, "Unknown command %c-- holding.\r\n", command);
 j=0;
 while (message[j] != ?\0?) {
 while (!(UCA3IFG & UCTXIFG));
 UCA3TXBUF = message[j++];
 }
 command = ?p?;
 break;
 } // switch
 } // for(;;)
 } // main
 void port_init(void) {
 P1DIR = 0x00; // Ports 1 and 2 are data in (Port A word)
 P2DIR = 0x00;
 P3OUT = 0x06; // Set P3.1 and P3.2 on, all others off
 P3DIR = 0xFF;
 P4OUT = 0x00; // P4.0,1,7 unused, P4.2,3,4 initially off
 P4DIR = 0x9F; // P4.5,6 inputs, all others out.
 P5OUT = 0x00;
 P5DIR = 0xFF; // P5.2,3 already set to XT2
 P6OUT = 0x00;
 P6DIR = 0xF0; // P6.0-3 are ADC12, all others off
 P7OUT = 0x00;
 P7DIR = 0xFF; // All other ports off
 P8OUT = 0x00;
 P8DIR = 0xFF;
 P9OUT = 0x00;
 P9DIR = 0xFF;
 P10OUT = 0x00;
 P10DIR = 0xFF;
 } // port_init
 void xtal_init(void) {
 /* LFXT1 is the default source for ACLK and FLL. These sources must be
 * changed in order to prevent XT1 fault flags from interrupting the code.
 235
* FLL is changed to source from XT2 and ACLK from REFO. When the
 * oscillators are considered stable, ACLK is changed to source from XT2.
 */
 P5SEL |= 0x0c; // Port 5 select XT2
 UCSCTL6 &= ~XT2OFF; // Enable XT2
 UCSCTL3 |= SELREF_2; // Source FLL with XT2 since XT1 is not
 // present in the circuit.
 UCSCTL4 |= SELA_2; // ACLK = REFO, SMCLK = DCO, MCLK = DCO
 __bis_SR_register(SCG0); // Disable the FLL control loop
 UCSCTL0 = 0x0000; // Set lowest possible DCOx, MODx
 UCSCTL1 = DCORSEL_5; // Select DCO range 16MHz operation
 UCSCTL2 = FLLD_1 + 374; // Set DCO Multiplier for 8MHz
 // (N + 1) * FLLRef = Fdco
 // (249 + 1) * 32768 = 8MHz
 // Set FLL Div = fDCOCLK/2
 __bic_SR_register(SCG0); // Enable the FLL control loop
 // Worst-case settling time for the DCO when the DCO range bits have been
 // changed is n x 32 x 32 x f_MCLK / f_FLL_reference. See UCS chapter in
 // 5xx User?s Guide for optimization.
 // 32 x 32 x 8 MHz / 32,768 Hz = 250000 = MCLK cycles for DCO to settle
 __delay_cycles(375000);
 // Loop until Oscillators stabilize
 do {
 // Clear XT1, XT2, DCO fault flags
 UCSCTL7 &= ~(XT1LFOFFG + XT1HFOFFG + XT2OFFG + DCOFFG);
 SFRIFG1 &= ~OFIFG; // Clear osc. fault interrupt flag
 } while (SFRIFG1 & OFIFG); // Check osc. fault interrupt flag
 UCSCTL6 &= ~XT2DRIVE0; // Drive for 7.3728 MHz
 UCSCTL4 |= SELA_5; // ACLK = XT2
 } // xtal_init
 void uart_init(void) {
 P10SEL = 0x30; // Port 10 select USCI_A3 TxD/RxD
 UCA3CTL1 |= UCSWRST; // Reset USCI state machine
 UCA3CTL1 |= UCSSEL_1; // USCI CLK = ACLK (sourced by XT2)
 UCA3BR0 = 0x10; // 7.3728 MHz / 230400 = 32 -> 0x20
 UCA3BR1 = 0x00; // 0x0020 gives 230400 baud
 // 0x0080 gives 57600 baud
 // 0x0300 gives 9600 baud
 UCA3MCTL = UCBRS_0 + UCBRF_0; // No modulation needed at this frequency
 236
UCA3CTL1 &= ~UCSWRST; // Initialize USCI state machine
 UCA3IE |= UCRXIE; // Enable USCI_A3 Rx interrupt.
 } // uart_init
 void adc12_init(void) {
 P6SEL |= 0x0F; // P6.0-3 ADC select
 ADC12CTL0 = ADC12MSC + ADC12SHT0_2 + ADC12ON; // Sampling time, ADC12 on
 ADC12CTL1 = ADC12SHP + ADC12CONSEQ_1; // Use sampling timer
 ADC12MCTL0 = ADC12INCH_0; // channel A0 = V24_MON
 ADC12MCTL1 = ADC12INCH_1; // channel A1 = HV_MON2
 ADC12MCTL2 = ADC12INCH_2; // channel A2 = HV_MON1
 ADC12MCTL3 = ADC12INCH_3+ADC12EOS; // channel A3 = TEMP, End of sequence
 ADC12IE = 0x08; // ADC12 interrupt flags data ready:
 // ADC12IFG.3
 ADC12CTL0 |= ADC12ENC; // Enable ADC conversion
 } // adc12_init
 // Interrupt Service for UCA3 Rx interrupt
 #pragma vector=USCI_A3_VECTOR
 __interrupt void USCI_A3_ISR(void) {
 switch(__even_in_range(UCA3IV,4)) {
 case 0: break; // Vector 0 - no interrupt
 case 2: // Vector 2 - RXIFG
 command = UCA3RXBUF;
 break;
 case 4: // Vector 4 - TXIFG
 break;
 default: break;
 }
 } // USCI_A3_ISR
 #pragma vector=ADC12_VECTOR
 __interrupt void ADC12ISR (void)
 {
 switch(__even_in_range(ADC12IV,34))
 {
 case 0: break; // Vector 0: No interrupt
 case 2: break; // Vector 2: ADC overflow
 case 4: break; // Vector 4: ADC timing overflow
 case 6: break; // Vector 6: ADC12IFG0
 case 8: break; // Vector 8: ADC12IFG1
 case 10: break; // Vector 10: ADC12IFG2
 case 12: // Vector 12: ADC12IFG3
 analog[0] = ADC12MEM0; // Move results, IFG is cleared
 analog[1] = ADC12MEM1; // Move results, IFG is cleared
 237
analog[2] = ADC12MEM2; // Move results, IFG is cleared
 analog[3] = ADC12MEM3; // Move results, IFG is cleared
 ad_ready = 1;
 break;
 case 14: break; // Vector 14: ADC12IFG4
 case 16: break; // Vector 16: ADC12IFG5
 case 18: break; // Vector 18: ADC12IFG6
 case 20: break; // Vector 20: ADC12IFG7
 case 22: break; // Vector 22: ADC12IFG8
 case 24: break; // Vector 24: ADC12IFG9
 case 26: break; // Vector 26: ADC12IFG10
 case 28: break; // Vector 28: ADC12IFG11
 case 30: break; // Vector 30: ADC12IFG12
 case 32: break; // Vector 32: ADC12IFG13
 case 34: break; // Vector 34: ADC12IFG14
 default: break;
 }
 }
 238
B.4 Serial Communication
 Communication with the GSE is done through a CP2102 Serial USB interface.
 This chip allows you to use the USB port of a computer as a serial port, from which
 you can communicate with the MSP430 via any serial terminal emulator. The open
 source software RealTerm [56] was used in this study.
 Communication requires proper setup of the terminal. The MSP430 UART
 uses 8N1 (8 data bits, no parity, 1 stop bit), the common standard in UART trans-
 mission. The baud rate is set in the MSP430 code with the assignments to the
 registers UCA3BR0 and UCA3BR1. These registers give the number of clock cy-
 cles to divide to produce the correct timing for serial communication. With the
 crystal oscillator used, a division of 768 is required to get a baud rate of 9600. (ie.
 7372800=768 = 9600) In order to accommodate the faster rates of the telemetry
 board, faster baud rates are required. The code presented in the previous section
 sets the division factor to 0x0010, which provides a rate of 460800 baud. This rate
 should be set in the terminal accordingly.
 Within the terminal, commands can be sent and data received. The valid
 commands in this version of the MSP430 code are as follows:
 239
p Hold and wait for another command. (Default mode)
 s Print a status message (used for debugging). Currently set to
 show the values in key registers to demonstrate timings are correct.
 r Read the next 100 data values received.
 Anything else returns an error to the terminal window and sets
 the mode to hold.
 Table B.1: Description of commands available in the KIMS GSE.
 240
Appendix C
 KIMS Project Images
 Assembly Photos
 C.1 Magnetic Circuit Assembly
 The following pages include photographs taken during the magnetic circuit
 assembly. See the checklist in Appendix A.1 for reference.
 Figure C.1: Gathered parts for the magnetic circuit assembly.
 241
Figure C.2: Clamp placed on low  eld magnet. The magnet is slid onto the upper
 cover.
 Figure C.3: The upper half of the magnetic circuit fully assembled. The nylon
 spacer was used to help keep alignment.
 242
Figure C.4: Placing the lower shell around the magnet. A nylon spacer is used to
 help keep alignment.
 Figure C.5: The upper assembly is slid onto the partition.
 243
Figure C.6: Half of the magnetic circuit fully assembled. The  nal step is to slide
 the lower assembly onto the partition.
 Figure C.7: The completed magnetic circuit. Stainless steel roll pins are used to
 align the parts. Brass screws secure the clamps to keep the magnets from shifting
 on launch.
 244
C.2 KIMS Assembly
 The following pages include photographs of the assembly of the KIMS instru-
 ment in preparation for vibration testing.
 Figure C.8: The ground screen is placed inside the magnetic circuit and held in
 place with a compressive clamp.
 245
Figure C.9: The magnetic circuit is placed inside one of the clamshell halves.
 Figure C.10: The other half of the clamshell is attached and bolted to secure the
 magnetic circuit inside. The magnetic circuit itself is not fastened, but held securely
 by the close  tting clamshell.
 246
Figure C.11: The two telemetry/ampli er boards are fastened to each side of the
 clamshell with stando s.
 Figure C.12: The distribution board is fastened to the MCP stack. Spacers are
 threaded on to secure the board.
 247
Figure C.13: The ground plane board is attached with another set of threaded
 spacers.
 Figure C.14: The MCP stack is inserted into the magnetic circuit, and the distri-
 bution board connects to each telemetry/ampli er board.
 248
Figure C.15: The high voltage board is connected to the electrical stack assembly.
 Note that the high voltage supplies are not connected yet in this photo.
 Figure C.16: The high voltage control board is the  nal component of the electrical
 stack assembly.
 249
Figure C.17: Spacers are placed on the top of the clamshell.
 250
Figure C.18: The tray of the KIMS cover is fastened to the back plate.
 251
Figure C.19: The cover is slid onto the instrument. The material has just enough
 give to slide over the DB-15 connections on the telemetry/ampli er boards.
 252
Figure C.20: The KIMS instrument completely assembled. The cover is fastened to
 the stando s on the clamshell to prevent vibration at launch. The entire instrument
 is attached to an aluminum bracket for mounting on the lower bulkhead of the
 RENU payload.
 253
Testing Photos
 C.3 Vibration Testing
 The following pages show the vibration test results for the KIMS instrument.
 The X, Y, and Z axes are as denoted in Fig. C.21. Natural modes are seen in all
 three directions at frequencies of 100?s of Hz, but at the vibration levels of launch
 are not of concern. Note that the Z-axis is the thrust axis of the payload.
 254
Figure C.21: Axis de nitions for vibration testing.
 255
Figure C.22: White noise vibration test result of the KIMS instrument X-axis.
 256
Figure C.23: White noise vibration test result of the KIMS instrument Y-axis.
 257
Figure C.24: White noise vibration test result of the KIMS instrument Z-axis.
 258
C.4 Magnetic Testing
 The following pages show the con guration of the magnetometers for measur-
 ing the external  elds of the KIMS instrument.
 Figure C.25: Con guration for magnetic calibration
 259
Figure C.26: Close up view of the magnetometer spacing at calibration
 260
C.5 Integration Photos
 The following pages include photographs from the  nal integration of the KIMS
 instrument on the RENU payload in And ya, Norway.
 Figure C.27: Final state of the KIMS instrument prior to integration with the RENU
 payload.
 261
Figure C.28: KIMS mounted at the base of the RENU payload
 262
Figure C.29: KIMS with aperture exposed and high-voltage safety removed, ready
 for launch
 263
Appendix D
 RENU Launch Information
 D.1 General Overview of Sounding Rocket Campaign RENU
 RENU is a sounding rocket project for investigating neutral upwelling in the
 cusp. The rocket launched in the winter of 2011 from And ya Rocket Range. RENU
 is designed to transit the cusp region during a neutral upwelling event, equipped with
 a suite of instruments that will build on previous observations of this phenomenon,
 as well as acquire new types of data to provide a fresh perspective on this problem.
 Successful acquisition of these data provide fundamental information, essential for
 the advancement of our understanding of this problem. The speci c objectives of
 the mission are:
 1. To measure netural gas, ion and electron temperature enhancements, which
 will provide an initial assessment of the upwelling process.
 2. To measure large{ and small{scale Joule heating in the cusp during the RENU
  ight. Large{scale data will be acquired by EISCAT; small{scale data (per-
 haps associated with Alfv en waves) will be acquired using onboard electric
  eld measurements.
 3. To measure the precipitating electron energy input.
 264
4. To use measured quantities as inputs to thermodynamic and electrodynamic
 models for comparison to the observed upwelling.
 D.1.1 Investigators and Team
 Principle Investigator Dr. Marc Lessard, University of New Hampshire
 Co-investigators Dr. Jim Clemmons, Aerospace
 Dr. James Hecht, Aerospace
 Dr. Payl M. Kintner, Cornell University
 Dr. Kristina Lynch, Dartmouth College
 Dr. Matthew G. McHarg, USAF Academy
 Engineering Designers Dr. Parris Neal, USAF Academy
 Dr. Kevin G. Rhoads, Dartmouth College
 David K. Olson, University of Maryland
 Steven Powell, Cornell University
 Paul Riley, University of New Hampshire
 Mission Manager Jay Scott, NSROC
 Project Manager Libby West, NASA Goddard Space Flight Center
 Flight Performance Mike Disbrow, NSROC
 Mechanical Systems Shane Thompson, NSROC
 Mechanical Technician Clay Merscham, NSROC
 Telemetry Systems Jim Diehl, NSROC
 Power Systems Tom Malaby, NSROC
 265
Attitude Control System (ACS) Valerie Gsell, NSROC
 Vehicle Systems Nick Wroblewski, NSROC
 SQA James Alexander, NSROC
 Ground Safety Chico Ayers, CSC
 Flight Safety Jim Veney, NASA Goddard Space Flight Center
 D.2 Vehicle Requirements and Performance
 D.2.1 Trajectory Data/Attitude Solution
 Absolute trajectory knowledge is required at the 500 meter level. These re-
 quirements are satis ed by the accuracy of the data supplied by the NSROC and
 Cornell GPS receivers. The science team requires an attitude solution with an ac-
 curacy within one degree.
 D.2.2 Outgassing, Magnetic Sensitivity, RFI Susceptibility
 The Dartmouth/UNH particle detector experiments on the main payload are
 sensitive to payload outassing and steps need to be taken to keep outgassing to
 a minimum. These steps include proper material selection (see NASA Reference
 Publication 1124) and payload cleanliness.
 266
D.2.3 Coning Angle
 Prior to subpayload ejection, the main payload coning should be driven as
 close as possible to zero and the payload aligned to the background magnetic  eld.
 In order to keep the payload within the deadband, ACS updates may be required,
 although we emphasize that particle data acquired during ACS maneuvers are not
 usable and, so, ACS maneuvers should be kept to a minimum by ensuring that the
 payload is very well balanced.
 The  nal spin rate of the payload should be 0.5 Hz. While the accuracy of
 the actual  nal spin rate is not critical, the imagers will need to ?despin? and will
 need an accurate measure of the roll rate provided continuously.
 D.2.4 Despin
 After all deployments, a  nal main payload spin rate of approximately 0.5 Hz
 is desired to ensure payload stability and achieve the scienti c objectives.
 D.2.5 Horizon Sensors/Sun Sensors
 A horizon sensor and/or a sun sensor will be needed for each payload to assist
 in the attitude solution.
 D.2.6 Range Support
  Dry nitrogen purge of payload (particle detectors, imager) required during
 build{up and on launcher. This minimizes the moisture absorption of the
 267
particle detectors. Once the nose cone is installed, the dry nitrogen purge is
 to be connected to the payload skin through a \ y{a{way" disconnect.
  Liquid Nitrogen cooling support for Aerospace PMT
  Standard Wallops \lunchbox" parallel interface for real time UNH imager sys-
 tem
  Distribution of real time trajectory data and/or look angles for use by the
 ground based imaging instruments at the Longyearbyen science station
  On-site generation of  ight telemetry data on CD within 4 hours of launch
 using Programmable Telemetry Processor (PTP) with data in PTP Stamp
 time format.
  TDP bit sync for Aerospace Instrumentation, both in the TM building and at
 the science center
 D.2.7 Launch Conditions
  And ya Rocket Range | Nov 28 to Dec 12
  5 hour period within 0300{1100 UT, nominally 0600{1100 UT (0700{1200
 Local Time)
  Moon in last or  rst quarter or below the horizon at Longyearbyen
  Solar depression angle greater than 10 degrees at Longyearbyen
 268
 The payload must be in sunlight to permit nominal functioning of the on-
 board solar aspect sensor during the prime data taking period (above 500 km
 altitude)
  Azimuth and launch angle chosen for apogee over Svalbard at 1000 km down-
 range | this is northward. We desire the apogee point to be chosen such that
 the projection of the B{ eld vector at apogee down to 100 km altitude results
 in a point directly overhead Longyearbyen. If this is not possible, then the
 magnetic footprint of the trajectory should pass overhead Longyearbyen.
  It will be necessary to hold the count at T minus 2 minutes for up to 30
 minutes at a time
 Launch requires:
  An active cleft ionosphere with 5577 and 6300 light emissions overhead at
 either Longyearbyen of Ny{ Alesund.
  At least 20 nT of magnetometer activity at either Longyearbyen or Ny{
  Alesund.
  Clear skies at either Longyearbyen or Ny- Alesund such that either auroral TV
 or meridian scanning photometers provide data.
  EISCAT Svalbard Radar recording ion out ows and elevated electron temper-
 aturs.
  No  shing vessels in impact area.
 269
D.3 Success Criteria
 D.3.1 Comprehensive Mission Success
 Comprehensive success means that we meet the minimum success criteria and
 that we also acquire supportive data, including in{situ observations of:
 1. Apogee of 500 km
 2. Onboard auroral images
 3. Upward looking PMTs
 4. Medium energy ions (to observe out ow)
 5. Ion composition (BEEPS)
 6. Energetic ions (KIMS)
 D.3.2 Minimum Success
 Minimum success means that the data needed to provide a basic assessment
 of thermospheric upwelling associated with ionospheric processes is acquired. This
 requires the following in-situ measurements, acquired in the vicinity of the EISCAT
 radar:
 1. Apogee of at least 410 km
 2. Electron temperature (ERPA)
 3. Electron precipitation
 270
4. Ion temperature
 5. Neutral gas temperature
 6. Electric  elds
 7. Magnetic  elds
 271
Figure D.1: All-sky photograph of the aurora at launch.
 D.4 RENU Launch Conditions
 The RENU sounding rocket launched at 06:33 UT on 12 December 2010. The
 following images describe the conditions present when it was decided to launch.
 272
Figure D.2: All-sky view of red and green wavelengths from the observatory at
 Svalbard.
 273
Figure D.3: EISCAT radar measurements of precipitating electrons.
 274
Figure D.4: Solar wind conditions measured by the ACE satellite.
 275
Figure D.5: Collected magnetometer measurements in the Svalbard and northern
 Norway regions.
 276
Figure D.6: SuperDARN radar measurements showing ionospheric convection.
 277
Appendix E
 Statistical Analysis Software
 Some lines in this code are longer than will  t on a printed page. Places where
 an arti cial line break has been inserted are marked with the characters \:::" at the
 beginning of the line.
 E.1 FAST
 E.1.1 FAST.py
 # Routines for analysis of FAST data
 # v1.7 changelog:
 # :: changed to automatically deal with differing energy scales
 # for particle data
 # :: 1.6 error had ees energy > 4 and ies energy > 50. Corrected
 # to ees > 50 and ies > 4.
 from sys import stdout,version
 from nantools import nanmean,nanstd
 from numpy import nan,isnan,array,zeros,arange,shape,sum,mean,log10,arccos
 from pylab import find,contourf
 from math import sin,cos,sqrt,pi
 from scipy.interpolate import interp1d
 from spacepy import pycdf
 from time import time,gmtime
 import pickle
 softversion="FAST.py 1.71"
 basedir="/home/david/research/FAST/data/"
 f=open(?FAST-values.pkl?,?rb?)
 standard_E=pickle.load(f)
 f.close()
 278
def chauvenet(data,window,weight):
 f_data=zeros(len(data))
 for i in range(len(data)):
 if i<window/2:
 m=nanmean(data[i:i+window/2])
 s=nanstd(data[i:i+window/2])
 elif (len(data)-i)<window/2:
 m=nanmean(data[i-window/2:])
 s=nanstd(data[i-window/2:])
 else:
 m=nanmean(data[i-window/2:i+window/2])
 s=nanstd(data[i-window/2:i+window/2])
 if abs(data[i]-m)>weight*s:
 f_data[i]=nan
 else:
 f_data[i]=data[i]
 return f_data
 def smooth(data,r_data,interval):
 s_data=zeros(len(interval))
 for i in range(len(interval)):
 if i==0:
 r_min=interval[i]
 else:
 r_min=(interval[i]+interval[i-1])/2.
 if i==len(interval)-1:
 r_max=interval[i]
 else:
 r_max=(interval[i]+interval[i+1])/2.
 a=find(r_data<r_max)
 collect=find(r_data[a[0]:a[-1]]>r_min)
 s_data[i]=nanmean(data[collect])
 return s_data
 def interpolate(x,y,x_new,width,int_kind=?cubic?):
 y_new=zeros(len(x_new))
 for i in range(len(x_new)):
 j=0
 while(x[j]<x_new[i]):
 j+=1
 collect=arange(j,j+1)
 279
while x[collect[0]]>x_new[i]-width/2. and collect[0]!=0:
 collect=arange(collect[0]-1,collect[-1]+1)
 while x[collect[-1]]<x_new[i]+width/2. and collect[-1]!=len(x)-1:
 collect=arange(collect[0],max(collect)+2)
 if len(collect)<4:
 y_new[i]=nan
 else:
 f=interp1d(x[collect],y[collect],kind=int_kind)
 y_new[i]=f(x_new[i])
 return y_new
 def get_E(orbit,t_base,margin=30.,subset=False):
 dcefs=pycdf.CDF(basedir+orbit+?/dcefs_?+orbit+?.cdf?)
 print("Getting Time array...")
 t_E=dcefs[?TIME?]
 if subset:
 ti=0
 tf=len(t_base)-1
 i=0
 while(t_E[i]<t_base[0]-margin):
 t_min=i
 i+=1
 print(" found t_min...")
 while(t_E[i]<t_base[-1]+margin):
 t_max=i
 i+=1
 print(" found t_max...")
 else:
 t_min=0
 t_max=len(t_E)
 i=0
 while(t_base[i]<t_E[0]):
 ti=i+1
 i+=1
 print(" found ti...")
 while(i<len(t_base) and (t_base[i]<t_E[-1])):
 tf=i
 i+=1
 print(" found tf...")
 tnew=zeros(t_max-t_min)
 for j in range(len(tnew)):
 tnew[j]=t_E[t_min+j]
 t_E=tnew
 280
print(" done!")
 print("Getting E_along V array...")
 E_V=zeros(len(t_E))
 for j in range(len(t_E)):
 E_V[j]=dcefs[?E_ALONG_V?][t_min+j]
 print(" Filtering E_V...")
 E_V=chauvenet(E_V,100,2)
 t_avg=arange(t_E[0],t_E[-1]+4.,4.)
 print(" Smoothing E_V...")
 E_avg=smooth(E_V,t_E,t_avg)
 print(" Interpolating E_V...")
 E_base=zeros(len(t_base))
 if ti>0:
 E_base[:ti]=nan
 if tf<len(t_base)-1:
 E_base[tf:]=nan
 E_base[ti:tf]=interpolate(t_avg,E_avg,t_base[ti:tf],margin)
 print(" done!")
 return E_base
 def get_ELF(orbit,t_base,margin=30.,subset=False):
 dsp=pycdf.CDF(basedir+orbit+?/dsp_v58_?+orbit+?.cdf?)
 print("Getting Time array...")
 t_elf=dsp[?TIME?]
 if subset:
 ti=0
 tf=len(t_base)-1
 i=0
 while(t_elf[i]<t_base[0]-margin):
 t_min=i
 i+=1
 print(" found t_min...")
 while(t_elf[i]<t_base[-1]+margin):
 t_max=i
 i+=1
 print(" found t_max...")
 else:
 t_min=0
 t_max=len(t_elf)
 i=0
 while(t_base[i]<t_elf[0]):
 ti=i+1
 281
i+=1
 print(" found ti...")
 while(i<len(t_base) and (t_base[i]<t_elf[-1])):
 tf=i
 i+=1
 print(" found tf...")
 tnew=zeros(t_max-t_min)
 for j in range(len(tnew)):
 tnew[j]=t_elf[t_min+j]
 t_elf=tnew
 print(" done!")
 print("Getting frequencies...")
 f=zeros(512)
 for i in range(512):
 f[i]=dsp[?FREQ?][i]
 print(" done!")
 print("Getting DSP data...")
 spec=zeros((len(t_elf),512))
 for j in range(len(t_elf)):
 spec[j]=dsp[?DSP?][j]
 print(" Integrating DSP data...")
 P=zeros(len(t_elf))
 for i in range(len(t_elf)):
 d=array(spec[i])
 for j in range(511):
 P[i]+=10**mean(d[j:j+2])*(f[j+1]-f[j])*1000.
 print(" Smoothing DSP Power...")
 Ps=zeros(len(P))
 for i in range(len(t_elf)):
 if i<2:
 Ps[i]=mean(P[:i+3])
 elif i>len(Ps)-3:
 Ps[i]=mean(P[i-2:])
 else:
 Ps[i]=mean(P[i-2:i+3])
 print(" Interpolating DSP Power...")
 P_base=zeros(len(t_base))
 if ti>0:
 P_base[:ti]=nan
 if tf<len(t_base)-1:
 P_base[tf:]=nan
 P_base[ti:tf]=interpolate(t_elf,Ps,t_base[ti:tf],margin)
 print(" done!")
 282
return P_base
 def get_B(orbit,t_base,margin=30.,subset=False):
 dcmag=pycdf.CDF(basedir+orbit+?/dcmag_?+orbit+?.cdf?)
 print("Getting Time array...")
 t_B=dcmag[?TIME?]
 if subset:
 ti=0
 tf=len(t_base)-1
 i=0
 while(t_B[i]<t_base[0]-margin):
 t_min=i
 i+=1
 print(" found t_min...")
 while(t_B[i]<t_base[-1]+margin):
 t_max=i
 i+=1
 print(" found t_max...")
 else:
 t_min=0
 t_max=len(t_B)
 i=0
 while(t_base[i]<t_B[0]):
 ti=i+1
 i+=1
 print(" found ti...")
 while(i<len(t_base) and (t_base[i]<t_B[-1])):
 tf=i
 i+=1
 print(" found tf...")
 tnew=zeros(t_max-t_min)
 for j in range(len(tnew)):
 tnew[j]=t_B[t_min+j]
 t_B=tnew
 print(" done!")
 print("Getting dB_o array...")
 dBo=zeros(len(t_B))
 for j in range(len(dBo)):
 dBo[j]=dcmag[?DB_FAC_O?][t_min+j]
 t_avg=arange(t_B[0],t_B[-1]+4.,4.)
 print(" Smoothing dB_o...")
 283
dBo_avg=smooth(dBo,t_B,t_avg)
 print(" Interpolating dB_o...")
 dBo_base=zeros(len(t_base))
 if ti>0:
 dBo_base[:ti]=nan
 if tf<len(t_base)-1:
 dBo_base[tf:]=nan
 dBo_base[ti:tf]=interpolate(t_avg,dBo_avg,t_base[ti:tf],margin)
 print(" done!")
 print("Getting dB_e array...")
 dBe=zeros(len(t_B))
 for j in range(len(dBe)):
 dBe[j]=dcmag[?DB_FAC_E?][t_min+j]
 print(" Smoothing dB_e...")
 dBe_avg=smooth(dBe,t_B,t_avg)
 print(" Interpolating dB_e...")
 dBe_base=zeros(len(t_base))
 if ti>0:
 dBe_base[:ti]=nan
 if tf<len(t_base)-1:
 dBe_base[tf:]=nan
 dBe_base[ti:tf]=interpolate(t_avg,dBe_avg,t_base[ti:tf],margin)
 print(" done!")
 print("Getting dB_b array...")
 dBb=zeros(len(t_B))
 for j in range(len(dBb)):
 dBb[j]=dcmag[?DB_FAC_B?][t_min+j]
 print(" Smoothing dB_b...")
 dBb_avg=smooth(dBb,t_B,t_avg)
 print(" Interpolating dB_b...")
 dBb_base=zeros(len(t_base))
 if ti>0:
 dBb_base[:ti]=nan
 if tf<len(t_base)-1:
 dBb_base[tf:]=nan
 dBb_base[ti:tf]=interpolate(t_avg,dBb_avg,t_base[ti:tf],margin)
 print(" done!")
 return dBo_base,dBe_base,dBb_base
 def get_EBS(orbit,t_base,margin=30.):
 tic=time()
 print("Processing E-fields...")
 284
Ev=get_E(orbit,t_base,margin)
 toc=time()
 tet=toc-tic
 print(" ET: {0}".format(toc-tic))
 tic=time()
 print("Processing B-fields...")
 dBo,dBe,dBb=get_B(orbit,t_base,margin)
 toc=time()
 tet+=toc-tic
 print(" ET: {0}".format(toc-tic))
 tic=time()
 print("Calculating S...")
 S=Ev*(dBe*1e-9)/(4e-7*pi)
 print(" done!")
 toc=time()
 print(" ET: {0}".format(toc-tic))
 tet+=toc-tic
 print("\nTotal ET: {0}".format(tet))
 return Ev,dBo,dBe,dBb,S
 def get_flux(I,E,dE,theta):
 Na,Nb=shape(I)
 dOmega=zeros((Na,Nb))
 for a in range(Na-1):
 for b in range(Nb):
 th1=theta[a,b]*pi/180.
 th2=theta[a+1,b]*pi/180.
 if abs(th1-th2)>pi:
 dth=abs(th1-th2)-2*pi
 else:
 dth=abs(th1-th2)
 dOmega[a,b]=pi*abs(sin(th1))*cos(th1)*dth
 int_wz=sum(I*dOmega,0)
 Jz=sum(dE/E*int_wz)
 return Jz
 def get_flux2(I,E,dE,theta,KE,alpha):
 Na,Nb=shape(I)
 285
Jz=0
 for a in range(Na-1):
 for b in range(Nb):
 th1=theta[a,b]*pi/180.
 th2=theta[a+1,b]*pi/180.
 if abs(th1-th2)>pi:
 dth=abs(th1-th2)-2*pi
 else:
 dth=abs(th1-th2)
 dOmega=pi*abs(sin(th1))*cos(th1)*dth
 if type(E)==int:
 Jz+=I[a,b]*dOmega*dE[b]
 else:
 E_eff=E[b]-KE*cos(theta[a,b]-alpha)
 Jz+=I[a,b]*dOmega*dE[b]/E_eff
 return Jz
 def get_spectra(orbit,species):
 ies=pycdf.CDF(basedir+orbit+?/ies_?+orbit+?.cdf?)
 t=array(ies[?TIME?])
 th=arange(0,360,360./64)
 Es=zeros((len(t),48))-1
 PAs=zeros((len(t),64))-1
 for i in range(len(t)):
 print(" {0}%...\r".format(int(float(i+1)/len(t)*100))),
 stdout.flush()
 Efa=array(ies[?Eflux?][i])
 Ea=array(ies[?energy?][i])
 PAa=array(ies[?angle?][i])
 if (Ea==standard_E[species+? energy?]).all() and not isnan(Efa).any():
 Es[i,:]=sum(Efa,0)/64.
 for j in range(64):
 for k in range(48):
 if PAa[j,k]<0:
 PAa[j,k]+=360.
 l=max(find(th<=PAa[j,k]))
 PAs[i,l]+=Efa[j,k]
 return Es,PAs,th
 286
def cutoff(orbit,maxE):
 ies=pycdf.CDF(basedir+orbit+?/ies_?+orbit+?.cdf?)
 print("Calculating ion cutoff energy with maximum {0} eV...".format(maxE))
 print(" Getting Time array...")
 t=array(ies[?TIME?])
 print(" done!")
 print(" Getting dayside cusp array...")
 ilt=array(ies[?ILAT?])
 mlt=array(ies[?MLT?])
 cusp=zeros(len(ilt))
 for i in range(len(ilt)):
 if ilt[i]>70. and ilt[i]<80. and abs(12-mlt[i])<6.:
 cusp[i]=1
 if sum(cusp)==0:
 for i in range(len(ilt)):
 if ilt[i]>65. and ilt[i]<85. and abs(12-mlt[i])<7.:
 cusp[i]=1
 print(" done!")
 print(" Getting Flux list...")
 Ef=ies[?Eflux?]
 print(" Getting Energy list...")
 E=ies[?energy?]
 print(" Getting Pitch Angle list...")
 PA=ies[?angle?]
 print(" done!")
 N=nan*zeros((len(t),47)) # Flux arrays by energy
 m=zeros(47) # Mean flux over orbit by energy
 c=zeros(47) # percent of outflow measurements by energy
 k=0
 K=len(find(cusp==1))
 print(" Getting {0} flux arrays by energy...".format(K))
 for i in find(cusp==1):
 k+=1
 print("\r {0}%...".format(int(float(k)/K*100))),
 stdout.flush()
 Efa=array(Ef[i])
 Ea=array(E[i])
 s=1
 if (Ea==standard_E[?ion energy?]).all():
 PAa=array(PA[i])
 dE=abs(Ea[:-1]-Ea[1:])
 287
for j in range(len(dE)-1):
 N[i,j]=get_flux(Efa[:,j+1:j+2],Ea[j+1:j+2],dE[j:j+1],
 ::: PAa[:,j+1:j+2])
 print(" done!")
 print(" Averaging fluxes...")
 for j in range(47):
 m[j]=nanmean(N[:,j])
 if sum(isnan(N[:,j]))==len(N[:,j]):
 c[j]=nan
 else:
 c[j]=float(sum(N[:,j]<0))/float(len(N[:,j])-sum(isnan(N[:,j])))
 print(" done!")
 k=46
 kmin=max(min(find(m/min(m)>1e-4)),min(find(Ea[1:]<maxE)))
 kmin=max(kmin,min(find(c>0.3)))
 found=False
 while not found:
 if (m[k]>0 and m[k-1]>0) or (k<=kmin):
 found=True
 else:
 k-=1
 cut=k+1
 return cut #,t,N,m,c
 def get_EES(orbit,t_base,margin=30.,subset=False):
 ees=pycdf.CDF(basedir+orbit+?/ees_?+orbit+?.cdf?)
 print("Getting Time array...")
 t_ees=ees[?TIME?]
 if subset:
 ti=0
 tf=len(t_base)-1
 i=0
 while(t_ees[i]<t_base[0]-margin):
 t_min=i
 i+=1
 print(" found t_min...")
 while(t_ees[i]<t_base[-1]+margin):
 t_max=i
 i+=1
 print(" found t_max...")
 288
else:
 t_min=0
 t_max=len(t_ees)
 i=0
 while(t_base[i]<t_ees[0]):
 ti=i+1
 i+=1
 print(" found ti...")
 while(i<len(t_base) and (t_base[i]<t_ees[-1])):
 tf=i
 i+=1
 print(" found tf...")
 tnew=zeros(t_max-t_min)
 for j in range(len(tnew)):
 tnew[j]=t_ees[t_min+j]
 t_ees=tnew
 print(" done!")
 print("Getting Flux list...")
 Ef=ees[?Eflux?][t_min:t_max]
 print(" done!")
 print("Getting Energy array...")
 E=ees[?energy?][t_min:t_max]
 print(" done!")
 print("Getting Pitch Angle list...")
 PA=ees[?angle?][t_min:t_max]
 print(" done!")
 print("Getting flux arrays...")
 Jz=zeros(len(t_ees))
 NJz=zeros(len(t_ees))
 for i in range(len(t_ees)):
 print("\r {0}%...".format(int(float(i+1)/len(t_ees)*100))),
 stdout.flush()
 Ea=array(E[t_min+i])
 if not isnan(Ea).any():
 Efa=array(Ef[t_min+i])
 PAa=array(PA[t_min+i])
 dE=abs(Ea[:-1]-Ea[1:])
 Eh=0
 El=min(find(Ea<50.))
 if len(Ea[Eh:El])==0:
 NJz[i]=nan
 Jz[i]=nan
 289
else:
 NJz[i]=get_flux(Efa[:,Eh:El],Ea[Eh:El],dE[Eh:El],PAa[:,Eh:El])
 Jz[i]=get_flux(Efa[:,Eh:El],1,dE[Eh:El],PAa[:,Eh:El])
 else:
 NJz[i]=nan
 Jz[i]=nan
 # print("\n Smoothing flux arrays...")
 # t_avg=arange(t_ees[0],t_ees[-1]+4.,4.)
 # Jz_avg=smooth(Jz,t_ees,t_avg)
 # NJz_avg=smooth(NJz,t_ees,t_avg)
 print(" Interpolating flux arrays...")
 Jz_base=zeros(len(t_base))
 NJz_base=zeros(len(t_base))
 if ti>0:
 Jz_base[:ti]=nan
 NJz_base[:ti]=nan
 if tf<len(t_base)-1:
 Jz_base[tf:]=nan
 NJz_base[tf:]=nan
 Jz_base[ti:tf]=interpolate(t_ees,Jz,t_base[ti:tf],margin)
 NJz_base[ti:tf]=interpolate(t_ees,NJz,t_base[ti:tf],margin)
 print(" done!")
 return Jz_base,NJz_base
 def get_IES(orbit,t_base,margin=30.,subset=False):
 ies=pycdf.CDF(basedir+orbit+?/ies_?+orbit+?.cdf?)
 print("Getting Time array...")
 t_ies=ies[?TIME?]
 if subset:
 i=0
 while(t_ies[i]<t_base[0]-margin):
 t_min=i
 i+=1
 print(" found t_min...")
 while(t_ies[i]<t_base[-1]+margin):
 t_max=i
 i+=1
 print(" found t_max...")
 else:
 t_min=0
 t_max=len(t_ies)
 290
i=0
 while(t_base[i]<t_ies[0]):
 ti=i+1
 i+=1
 print(" found ti...")
 while(i<len(t_base) and (t_base[i]<t_ies[-1])):
 tf=i
 i+=1
 print(" found tf...")
 tnew=zeros(t_max-t_min)
 for j in range(len(tnew)):
 tnew[j]=t_ies[t_min+j]
 t_ies=tnew
 print(" done!")
 print("Getting Flux list...")
 Ef=ies[?Eflux?][t_min:t_max]
 print(" done!")
 print("Getting Energy list...")
 E=ies[?energy?][t_min:t_max]
 print(" done!")
 print("Getting Pitch Angle list...")
 PA=ies[?angle?][t_min:t_max]
 print(" done!")
 Eh=cutoff(orbit,500.)
 print("Getting flux arrays...")
 Jz=zeros(len(t_ies))
 NJz=zeros(len(t_ies))
 for i in range(len(t_ies)):
 print("\r {0}%...".format(int(float(i+1)/len(t_ies)*100))),
 stdout.flush()
 Ea=array(E[t_min+i])
 if not isnan(Ea).any():
 Efa=array(Ef[t_min+i])
 PAa=array(PA[t_min+i])
 dE=abs(Ea[:-1]-Ea[1:])
 El=max(find(Ea>4.))+1
 if len(Ea[Eh:El])==0:
 NJz[i]=nan
 Jz[i]=nan
 else:
 NJz[i]=get_flux(Efa[:,Eh:El],Ea[Eh:El],dE[Eh-1:El-1],
 291
::: PAa[:,Eh:El])
 Jz[i]=get_flux(Efa[:,Eh:El],1,dE[Eh-1:El-1],PAa[:,Eh:El])
 else:
 NJz[i]=nan
 Jz[i]=nan
 # print("\n Smoothing flux arrays...")
 # t_avg=arange(t_ies[0],t_ies[-1]+4.,4.)
 # Jz_avg=smooth(Jz,t_ies,t_avg)
 # NJz_avg=smooth(NJz,t_ies,t_avg)
 print("\n Interpolating flux arrays...")
 Jz_base=zeros(len(t_base))
 NJz_base=zeros(len(t_base))
 if ti>0:
 Jz_base[:ti]=nan
 NJz_base[:ti]=nan
 if tf<len(t_base)-1:
 Jz_base[tf:]=nan
 NJz_base[tf:]=nan
 Jz_base[ti:tf]=interpolate(t_ies,Jz,t_base[ti:tf],margin)
 NJz_base[ti:tf]=interpolate(t_ies,NJz,t_base[ti:tf],margin)
 print(" done!")
 return Jz_base,NJz_base,[Ea[Eh],Ea[El-1]]
 def get_IES2(orbit,t_base,margin=30.,subset=False):
 ies=pycdf.CDF(basedir+orbit+?/ies_?+orbit+?.cdf?)
 orb=pycdf.CDF(basedir+orbit+?/orbit_?+orbit+?.cdf?)
 print("Getting Time array...")
 t_ies=ies[?TIME?]
 if subset:
 i=0
 while(t_ies[i]<t_base[0]-margin):
 t_min=i
 i+=1
 print(" found t_min...")
 while(t_ies[i]<t_base[-1]+margin):
 t_max=i
 i+=1
 print(" found t_max...")
 else:
 t_min=0
 t_max=len(t_ies)
 292
i=0
 while(t_base[i]<t_ies[0]):
 ti=i+1
 i+=1
 print(" found ti...")
 while(i<len(t_base) and (t_base[i]<t_ies[-1])):
 tf=i
 i+=1
 print(" found tf...")
 tnew=zeros(t_max-t_min)
 for j in range(len(tnew)):
 tnew[j]=t_ies[t_min+j]
 t_ies=tnew
 print(" done!")
 print("Getting Flux list...")
 Ef=ies[?Eflux?][t_min:t_max]
 print(" done!")
 print("Getting Energy list...")
 E=ies[?energy?][t_min:t_max]
 print(" done!")
 print("Getting Pitch Angle list...")
 PA=ies[?angle?][t_min:t_max]
 print(" done!")
 print("Getting FAST velocity...")
 Vo=array(orb[?FA_VEL?])
 print(" vx...")
 vx=interpolate(t_base,Vo[:,0],t_ies,margin)
 print(" vy...")
 vy=interpolate(t_base,Vo[:,1],t_ies,margin)
 print(" vz...")
 vz=interpolate(t_base,Vo[:,2],t_ies,margin)
 print(" done!")
 print("Getting B-field direction...")
 Bo=array(orb[?B_MODEL?])
 print(" Bx...")
 Bx=interpolate(t_base,Bo[:,0],t_ies,margin)
 print(" By...")
 By=interpolate(t_base,Bo[:,1],t_ies,margin)
 print(" Bz...")
 Bz=interpolate(t_base,Bo[:,2],t_ies,margin)
 print(" done!")
 293
print("Getting energy and correction angle...")
 KE=zeros(len(t_ies))
 alpha=zeros(len(t_ies))
 for i in range(len(t_ies)):
 vdB=vx[i]*Bx[i]+vy[i]*By[i]+vz[i]*Bz[i]
 v=sqrt(vx[i]**2+vy[i]**2+vz[i]**2)
 B=sqrt(Bx[i]**2+By[i]**2+Bz[i]**2)
 KE[i]=0.083575035*v**2 # 1/2 mv^2 for oxygen
 alpha[i]=arccos(vdB/v/B)
 print(" done!")
 print("Getting cutoff energy...")
 Eh=cutoff(orbit,500.)
 print(" done!")
 print("Getting flux arrays...")
 Jz=zeros(len(t_ies))
 NJz=zeros(len(t_ies))
 for i in range(len(t_ies)):
 print("\r {0}%...".format(int(float(i+1)/len(t_ies)*100))),
 stdout.flush()
 Ea=array(E[t_min+i])
 if not isnan(Ea).any():
 Efa=array(Ef[t_min+i])
 PAa=array(PA[t_min+i])
 dE=abs(Ea[:-1]-Ea[1:])
 El=max(find(Ea>4.))+1
 if len(Ea[Eh:El])==0:
 NJz[i]=nan
 Jz[i]=nan
 else:
 NJz[i]=get_flux2(Efa[:,Eh:El],Ea[Eh:El],dE[Eh-1:El-1],
 ::: PAa[:,Eh:El],KE[i],alpha[i])
 Jz[i]=get_flux2(Efa[:,Eh:El],1,dE[Eh-1:El-1],PAa[:,Eh:El],
 ::: KE[i],alpha[i])
 else:
 NJz[i]=nan
 Jz[i]=nan
 print("\n Interpolating flux arrays...")
 Jz_base=zeros(len(t_base))
 NJz_base=zeros(len(t_base))
 if ti>0:
 Jz_base[:ti]=nan
 294
NJz_base[:ti]=nan
 if tf<len(t_base)-1:
 Jz_base[tf:]=nan
 NJz_base[tf:]=nan
 Jz_base[ti:tf]=interpolate(t_ies,Jz,t_base[ti:tf],margin)
 NJz_base[ti:tf]=interpolate(t_ies,NJz,t_base[ti:tf],margin)
 print(" done!")
 return Jz_base,NJz_base,[Ea[Eh],Ea[El-1]]
 def processFAST(orbits,getelf=True):
 tic=time()
 for o in orbits:
 print("Processing orbit {0} information...".format(o))
 orb=pycdf.CDF(basedir+o+?/orbit_?+o+?.cdf?)
 print(" Extracting base time...")
 T_base=zeros(len(orb[?TIME?]))
 for j in range(len(T_base)):
 T_base[j]=orb[?TIME?][j]
 print(" Extracting satellite position...")
 X=zeros((len(T_base),3))
 for j in range(len(T_base)):
 X[j]=orb[?FA_POS?][j]
 print(" Extracting invariant latitude...")
 ILT=zeros(len(T_base))
 for j in range(len(T_base)):
 ILT[j]=orb[?ILAT?][j]
 print(" Extracting magnetic local time...")
 MLT=zeros(len(T_base))
 for j in range(len(T_base)):
 MLT[j]=orb[?MLT?][j]
 print(" Extracting altitude...")
 ALT=zeros(len(T_base))
 for j in range(len(T_base)):
 ALT[j]=orb[?ALT?][j]
 print(" Creating in-cusp flag...")
 CUSPF=range(len(ILT))
 for j in range(len(CUSPF)):
 if (ILT[j]>70. and ILT[j]<80.):
 CUSPF[j]=1
 else:
 CUSPF[j]=0
 print(" done!")
 toc=time()
 print("Orbit {0} elapsed time: {1}".format(o,toc-tic))
 295
print("Processing orbit {0} DC fields...".format(o))
 Ev,dBo,dBe,dBb,S=get_EBS(o,T_base)
 toc=time()
 print("Orbit {0} elapsed time: {1}".format(o,toc-tic))
 if getelf:
 print("Processing orbit {0} AC fields...".format(o))
 elf=get_ELF(o,T_base)
 toc=time()
 print("Orbit {0} elapsed time: {1}".format(o,toc-tic))
 else:
 elf=[]
 print("Processing orbit {0} electrons...".format(o))
 eJz,eNJz = get_EES(o,T_base)
 toc=time()
 print("Orbit {0} elapsed time: {1}".format(o,toc-tic))
 print("Processing orbit {0} ions...".format(o))
 iJz,iNJz,E_ends = get_IES(o,T_base)
 toc=time()
 print("Orbit {0} elapsed time: {1}".format(o,toc-tic))
 # print("Getting orbit {0} outflow times...".format(o))
 # print(" Creating spectra...")
 # Es,PAs,t,th=get_spectra(o,?ion?)
 # contourf(log10(PAs.T))
 # ti=t[int(raw_input("Enter the start time for outflow: "))]
 # tf=t[int(raw_input("Enter the stop time for outflow: "))]
 # OUTFLOW=0*range(len(ILT))
 # for j in range(len(OUTFLOW)):
 # if T_base[j]>ti and T_base[j]<tf:
 # OUTFLOW[j]=1
 # print(" done!")
 print("Pickling orbit {0} data...".format(o))
 print(" Creating data structure...")
 data={}
 data[?Time?]=T_base
 data[?Position?]=X
 data[?Invariant Position?]=[ILT,MLT,ALT]
 data[?In Cusp?]=CUSPF
 # data[?Outflow?]=OUTFLOW
 data[?E along Vsc?]=Ev
 296
data[?dB fac?]=[dBo,dBe,dBb]
 data[?Poynting Flux?]=S
 data[?ELF Amplitude?]=elf
 data[?eln_Eflux?]=eJz
 data[?eln_Nflux?]=eNJz
 data[?ion_Eflux?]=iJz
 data[?ion_Nflux?]=iNJz
 print(" Creating meta data structure...")
 units={}
 units[?Time?]=?UNX sec?
 units[?Position?]=?GEI km?
 units[?Invariant Position?]=[?ILAT deg?,?MLT hrs?,?ALT km?]
 units[?In Cusp?]=?flag?
 # units[?Outflow?]=?flag?
 units[?E along Vsc?]=?mV/m?
 units[?dB fac?]=[?o nT?,?e nT?,?b nT?]
 units[?Poynting Flux?]=?mW/m**2?
 units[?ELF Power?]=?(V/m)**2?
 units[?eln_Eflux?]=?mW/m**2?
 units[?eln_Nflux?]=?#/cm**2/s?
 units[?ion_Eflux?]=?mW/m**2?
 units[?ion_Nflux?]=?#/cm**2/s?
 meta={}
 meta[?orbit?]=o
 meta[?time covered?]=[T_base[0],T_base[-1]]
 meta[?date processed?]=gmtime(time())
 meta[?software version?]=softversion
 meta[?python version?]=version[:3]
 meta[?units?]=units
 meta[?ion energies?]=E_ends
 print(" Pickling data to file...")
 filename=basedir+o+"/FAST_"+o+"-"+softversion[8:]+"-py"+version[0]
 ::: +".pkl"
 f=open(filename,?wb?)
 pickle.dump({?meta?:meta,?data?:data},f)
 f.close()
 print(" Orbit {0} processing complete.".format(o))
 toc=time()
 print(" Total elapsed time: {0}".format(toc-tic))
 297
E.1.2 FAPlot.py
 from matplotlib.pyplot import *
 from pylab import r_,find
 from numpy import sqrt,sin,cos,pi,array,zeros,nanmin,log10
 import plot_setup
 import pickle
 import FAST
 import calendar
 basedir="/home/david/research/FAST/data/"
 filesuff="-1.7-py2.pkl"
 def update_pickle(orbits):
 for o in orbits:
 print("Orbit "+o)
 print(" Extracting data...")
 ies=FAST.pycdf.CDF(basedir+o+"/ies_"+o+".cdf")
 t=array(ies[?TIME?])
 mlt=array(ies[?MLT?])
 ilt=array(ies[?ILAT?])
 f=open(basedir+o+"/FAST_"+o+filesuff,?rb?)
 d=pickle.load(f)
 f.close()
 it=d[?data?][?Time?]
 print(" done!")
 OUTFLOW=zeros(len(it))
 Es,PAs,th=FAST.get_spectra(o,?ion?)
 figure()
 contourf(log10(PAs.T),N=75,antialiased=False)
 plot(mlt,?r-?,linewidth=2)
 plot(ilt/2.,?m-?,linewidth=2)
 ti=0
 while ti != -1:
 ti=input("Start time (-1 is done): ")
 tf=input("Stop time: ")
 if ti!= -1 and tf != -1:
 plot([ti,ti],[0,64])
 plot([tf,tf],[0,64])
 ok=raw_input("Good times?: ")
 if ok==?y?:
 298
for j in range(len(it)):
 if it[j]>=t[ti] and it[j]<=t[tf]:
 OUTFLOW[j]=1
 d[?data?][?Outflow?]=OUTFLOW
 d[?meta?][?units?][?Outflow?]=?flag?
 f=open(basedir+o+"/FAST_"+o+"-a"+filesuff,?wb?)
 pickle.dump(d,f)
 f.close()
 def gen_pole_plot(orbits=[],ofp=False):
 if not ofp:
 plot_setup.set_params(8,?square?,14,linewidth=1.)
 p=plot([0,0],[-50,50],?k-?)
 plot([-50,50],[0,0],?k-?)
 plot([-40,40],[40,-40],?k-?)
 plot([-40,40],[-40,40],?k-?)
 x=r_[-10:10:1000j]
 plot(x,sqrt(100-x**2),?k-?)
 plot(x,-sqrt(100-x**2),?k-?)
 x=r_[-20:20:1000j]
 plot(x,sqrt(400-x**2),?k-?)
 plot(x,-sqrt(400-x**2),?k-?)
 x=r_[-30:30:1000j]
 plot(x,sqrt(900-x**2),?k-?)
 plot(x,-sqrt(900-x**2),?k-?)
 x=r_[-40:40:1000j]
 plot(x,sqrt(1600-x**2),?k-?)
 plot(x,-sqrt(1600-x**2),?k-?)
 axis([-68,68,-68,68])
 setp(gca(), ?xticklabels?, [])
 setp(gca(), ?yticklabels?, [])
 a=3*pi/8
 text(10*cos(a),10*sin(a),r?$80^\circ$?)
 text(20*cos(a),20*sin(a),r?$70^\circ$?)
 text(30*cos(a),30*sin(a),r?$60^\circ$?)
 text(40*cos(a),40*sin(a),r?$50^\circ$?)
 text(-7,51,?12 MLT?)
 text(-67,-1.8,?18 MLT?)
 text(51,-1.8,?06 MLT?)
 text(-7,-54.3,?00 MLT?)
 for orb in orbits:
 print("Orbit " + orb)
 299
f=open(basedir+orb+ "/FAST_" +orb+"-a"+filesuff, ?rb?)
 d=pickle.load(f)
 f.close()
 ilt=d[?data?][?Invariant Position?][0]
 mlt=d[?data?][?Invariant Position?][1]
 of=d[?data?][?Outflow?]
 i=[]
 m=[]
 o=[]
 for j in range(len(ilt)):
 if ilt[j]>=45.:
 i.append(90.-ilt[j])
 m.append((mlt[j]-6)*pi/12.)
 o.append(of[j])
 i=array(i)
 m=array(m)
 if not ofp:
 plot(i*cos(m),i*sin(m),?r-?)
 io=[]
 mo=[]
 for j in range(len(i)):
 if o[j]==1:
 io.append(i[j])
 mo.append(m[j])
 io=array(io)
 mo=array(mo)
 if ofp:
 plot(io*cos(mo),io*sin(mo),?k-?,linewidth=5.)
 def gen_summary_plot(orbit):
 f=open(basedir+orbit+"/FAST_"+orbit+"-a"+filesuff,?rb?)
 d=pickle.load(f)
 f.close()
 plot_setup.set_params(8.5,?long?,12,1)
 start=raw_input("Enter start time as yyyy,m,d,h,m,s: ").split(?,?)
 for i in range(len(start)):
 start[i]=int(start[i])
 t0=calendar.timegm(start)
 t=(d[?data?][?Time?]-t0)/60.
 figure()
 300
subplot(711)
 title("FAST Orbit "+orbit)
 plot(t,d[?data?][?E along Vsc?],?k-?)
 oa=axis()
 axis([0,17,oa[2],oa[3]])
 plot([0,17],[0,0],?k--?)
 ylabel("E along V$_{sc}$\n[DC] (mV/m)\n",horizontalalignment=?center?)
 subplot(712)
 plot(t,d[?data?][?dB fac?][0],?r-?)
 plot(t,d[?data?][?dB fac?][1],?g-?)
 plot(t,d[?data?][?dB fac?][2],?b-?)
 legend([?o?,?e?,?b?])
 oa=axis()
 axis([0,17,oa[2],oa[3]])
 plot([0,17],[0,0],?k--?)
 ylabel("$\delta$B fac\n[DC] (nT)\n",horizontalalignment=?center?)
 subplot(713)
 plot(t,d[?data?][?Poynting Flux?],?m-?)
 oa=axis()
 axis([0,17,oa[2],oa[3]])
 plot([0,17],[0,0],?k--?)
 ylabel("Poynting Flux\n[DC] (mW/m$^2$)\n",horizontalalignment=?center?)
 subplot(714)
 plot(t,d[?data?][?eln_Nflux?],?k-?)
 oa=axis()
 axis([0,17,oa[2],oa[3]])
 plot([0,17],[0,0],?k--?)
 ylabel("Electron Flux\n(#/cm$^2$/s)\n",horizontalalignment=?center?)
 subplot(715)
 plot(t,d[?data?][?eln_Eflux?]*1.6022e-12,?r-?)
 oa=axis()
 axis([0,17,oa[2],oa[3]])
 plot([0,17],[0,0],?k--?)
 ylabel("Electron\nEnergy Flux\n(mW/m$^2$)\n",horizontalalignment=?center?)
 subplot(716)
 plot(t,sqrt(d[?data?][?ELF Amplitude?]),?g-?)
 oa=axis()
 axis([0,17,oa[2],oa[3]])
 plot([0,17],[0,0],?k--?)
 ylabel("ELF Amplitude\n(V/m)\n",horizontalalignment=?center?)
 301
subplot(717)
 plot(t,-d[?data?][?ion_Nflux?],?b-?)
 oa=axis()
 axis([0,17,oa[2],oa[3]])
 plot([0,17],[0,0],?k--?)
 ylabel("Ion FLux\n(#/cm$^2$/s)\n",horizontalalignment=?center?)
 xlabel("Time from {0:04d}/{1:02d}/{2:02d} {3:02d}:{4:02d}:{5:02d} (min)"
 ::: .format(start[0],start[1],start[2],start[3],start[4],start[5]))
 302
E.1.3 FAST stats.py
 from matplotlib.pyplot import *
 from pylab import find
 from numpy import array,zeros,arange,isnan,nansum,nanmin,log10,r_,delete
 from scipy.stats import stats
 import pickle
 import plot_setup
 basedir="/home/david/research/FAST/data/"
 filesuff="-a-1.71-py2.pkl"
 def get_averages(orbits,has_elf=True,alt_scale=False,length=?Full?):
 if length==?Full?:
 iNf=zeros(len(orbits))
 S=zeros(len(orbits))
 eNf=zeros(len(orbits))
 eEf=zeros(len(orbits))
 elf=zeros(len(orbits))
 nep=zeros(len(orbits))
 orbit=orbits
 else:
 iNf=[]
 S=[]
 eNf=[]
 eEf=[]
 elf=[]
 nep=[]
 orbit=[]
 for i in range(len(orbits)):
 o=orbits[i]
 f=open(basedir+o+"/FAST_"+o+filesuff,?rb?)
 d=pickle.load(f)
 f.close()
 infr=d[?data?][?ion_Nflux?]
 ofr=d[?data?][?Outflow?]
 sr=d[?data?][?Poynting Flux?]
 enfr=d[?data?][?eln_Nflux?]
 eefr=d[?data?][?eln_Eflux?]
 if has_elf:
 elfr=d[?data?][?ELF Amplitude?]
 if alt_scale:
 alt=d[?data?][?Invariant Position?][2]
 303
infr*=(1000./alt)**(-3./2)
 sr*=(1000./alt)**(-3./2)
 enfr*=(1000./alt)**(-3./2)
 eefr*=(1000./alt)**(-3./2)
 if length==?Full?:
 iNf[i]=nansum(infr*ofr)/nansum(ofr)
 S[i]=nansum(sr*ofr)/nansum(ofr)
 eNf[i]=nansum(enfr*ofr)/nansum(ofr)
 eEf[i]=nansum(eefr*ofr)/nansum(ofr)
 if has_elf:
 elf[i]=nansum(elfr*ofr)/nansum(ofr)
 nep[i]=nansum(get_nep(o,alt_scale)*ofr)/nansum(ofr)
 else:
 idx=find(d[?data?][?Outflow?]==1)
 j=idx[0]
 while j<=idx[-1]:
 iNf.append(nansum(d[?data?][?ion_Nflux?][j:j+length]
 ::: *d[?data?][?Outflow?][j:j+length])
 ::: /nansum(d[?data?][?Outflow?][j:j+length]))
 S.append(nansum(d[?data?][?Poynting Flux?][j:j+length]
 ::: *d[?data?][?Outflow?][j:j+length])
 ::: /nansum(d[?data?][?Outflow?][j:j+length]))
 eNf.append(nansum(d[?data?][?eln_Nflux?][j:j+length]
 ::: *d[?data?][?Outflow?][j:j+length])
 ::: /nansum(d[?data?][?Outflow?][j:j+length]))
 eEf.append(nansum(d[?data?][?eln_Eflux?][j:j+length]
 ::: *d[?data?][?Outflow?][j:j+length])
 ::: /nansum(d[?data?][?Outflow?][j:j+length]))
 if has_elf:
 elf.append(nansum(d[?data?][?ELF Amplitude?][j:j+length]
 ::: *d[?data?][?Outflow?][j:j+length])
 ::: /nansum(d[?data?][?Outflow?][j:j+length]))
 nep.append(nansum(get_nep(o)[j:j+length]
 ::: *d[?data?][?Outflow?][j:j+length])
 ::: /nansum(d[?data?][?Outflow?][j:j+length]))
 orbit.append(o)
 j+=length
 if not length==?Full?:
 iNf=array(iNf)
 S=array(S)
 eNf=array(eNf)
 eEf=array(eEf)
 if has_elf:
 304
elf=array(elf)
 nep=array(nep)
 return iNf,S,eNf,eEf,elf,nep,orbit
 def get_plot(x,y):
 remove=find(x<=0)
 x=delete(x,remove)
 y=delete(y,remove)
 remove=find(y<=0)
 x=delete(x,remove)
 y=delete(y,remove)
 remove=find(isnan(x))
 x=delete(x,remove)
 y=delete(y,remove)
 remove=find(isnan(y))
 x=delete(x,remove)
 y=delete(y,remove)
 plot_setup.set_params(8,?square?,16,linewidth=3)
 slp,itc,r,p,stderr=stats.linregress(log10(x),log10(y))
 loglog(x,y,?ko?)
 a=r_[axis()[0]:axis()[1]:100j]
 plot(a,a**slp*10**itc,?r-?)
 text(min(x),max(y),"slope = {0:.3f}\nr = {1:.3f}\np = {2:.3e}"
 ::: .format(slp,r,p))
 def get_nep(orbit,alt_scale=False):
 f=open(basedir+orbit+"/FAST_"+orbit+filesuff,?rb?)
 d=pickle.load(f)
 f.close()
 enf=d[?data?][?eln_Nflux?]
 eef=d[?data?][?eln_Eflux?]
 if alt_scale:
 alt=d[?data?][?Invariant Position?][2]
 enf*=(1000./alt)**(-3./2)
 eef*=(1000./alt)**(-3./2)
 return 2.134e-14*(enf**1.5/eef**0.5)
 def get_4qplot(x,y):
 limx=nanmin(abs(x))/2.
 limy=nanmin(abs(y))/2.
 print("Using {0:.3e},{1:.3e}".format(limx,limy))
 plot(x,y,?k.?)
 xscale(?symlog?,linthreshx=1e-3,linthreshy=1e5)
 305
yscale(?symlog?,linthreshx=1e-3,linthreshy=1e5)
 def gen_4qp(orbits,xtype,ytype,full=False):
 for o in orbits:
 print o
 f=open(basedir+o+"/FAST_"+o+filesuff,?rb?)
 d=pickle.load(f)
 f.close()
 if ytype==?ion_Nflux?:
 c=-1
 else:
 c=1
 if xtype==?nep?:
 X=get_nep(o)
 Y=d[?data?][ytype]
 else:
 X=d[?data?][xtype]
 Y=d[?data?][ytype]
 valid=find(d[?data?][?Outflow?]==1)
 if not isnan(X[valid]).all():
 if not full:
 scatter(X[valid],c*Y[valid],1)
 else:
 scatter(X,c*Y,1)
 def count_orbits(orbits,T):
 n=zeros(len(T))
 for o in orbits:
 print o
 f=open(basedir+o+"/FAST_"+o+filesuff,?rb?)
 d=pickle.load(f)
 f.close()
 of=d[?data?][?Outflow?]
 t=d[?data?][?Time?]
 if sum(of)>0:
 st=t[min(find(of==1))]
 sp=t[max(find(of==1))]
 i=0
 while i<len(T) and st>T[i]:
 i+=1
 j=i
 while j<len(T) and sp>T[i]:
 j+=1
 if i==j:
 n[i-1]+=1
 306
else:
 n[i-1]+=1
 n[j-1]+=1
 return n
 def time_to_latitude(orbit,lat):
 f=open(basedir+orbit+"/FAST_"+orbit+filesuff,?rb?)
 d=pickle.load(f)
 f.close()
 ilt=d[?data?][?Invariant Position?][0]
 alt=d[?data?][?Invariant Position?][2]
 of=d[?data?][?Outflow?]
 inf=d[?data?][?ion_Nflux?]*(1000./alt)**(-1.5)
 s=d[?data?][?Poynting Flux?]*(1000./alt)**(-1.5)
 enf=d[?data?][?eln_Nflux?]*(1000./alt)**(-1.5)
 eef=d[?data?][?eln_Eflux?]*(1000./alt)**(-1.5)
 nep=get_nep(orbit,True)
 linf=zeros(len(lat))
 ls=zeros(len(lat))
 lenf=zeros(len(lat))
 leef=zeros(len(lat))
 lnep=zeros(len(lat))
 n=zeros(len(lat))
 for i in range(len(ilt)):
 if ilt[i]>lat[0] and of[i]==1:
 nogo=isnan(inf[i]) or isnan(s[i]) or isnan(enf[i]) or isnan(eef[i])
 ::: or isnan(nep[i])
 if not nogo:
 j=0
 while j<len(lat) and lat[j]<ilt[i]:
 j+=1
 j-=1
 linf[j]+=inf[i]
 ls[j]+=s[i]
 lenf[j]+=enf[i]
 leef[j]+=eef[i]
 lnep[j]+=nep[i]
 n[j]+=1
 return linf,ls,lenf,leef,lnep,n
 def get_latavg(orbits,t,lat=arange(70.,80.,0.5)):
 307
size=(len(t),len(lat))
 inf=zeros(size)
 s=zeros(size)
 enf=zeros(size)
 eef=zeros(size)
 nep=zeros(size)
 cts=zeros(size)
 n=count_orbits(orbits,t)
 used=[]
 for i in range(len(t)):
 print("Time Range {0}".format(i))
 print(" Finding used orbits...")
 used.append([])
 for j in arange(n[i])+sum(n[:i]):
 used[i].append(orbits[int(j)])
 print(used[i])
 print("\n Getting values...")
 for o in used[i]:
 linf,ls,lenf,leef,lnep,lcts=time_to_latitude(o,lat)
 inf[i]+=linf
 s[i]+=ls
 enf[i]+=lenf
 eef[i]+=leef
 nep[i]+=lnep
 cts[i]+=lcts
 return inf,s,enf,eef,nep,cts,used
 308
E.2 CHAMP
 E.2.1 champ.py
 # champ.py: tools for extracting and manipulating the datasets from the
 # CHAMP satellite.
 #
 # Rev. beta-3 16 Nov 2011
 #
 # Beta status. Began adding routines to process champ data for study.
 from sys import stdout
 from numpy import nan,isnan,array,zeros,shape
 from math import atan2,sqrt
 from scipy.interpolate import interp1d
 import cstrans2
 import champformats
 import pickle
 import time
 import calendar
 # ::: not Py3 compatible; needs to be changed to input() for Py3.
 # On import, prompts for dataset to work. Calling the load() function
 # allows for dataset changing without reimporting champ.py
 version = ?b3?
 filename=raw_input("Working dataset filename: ")
 def load():
 global filename
 filename=raw_input("Working dataset filename: ")
 def process_CHAMP_orb(directory,days):
 global filename
 for d in days:
 print(d)
 filename=directory+"CH-OG-3-RSO+CTS-CHA_"+d[:-1]+str(int(d[-1])-1)
 ::: +"_22.dat"
 dat=extract_data()
 t=zeros(len(dat[?dJ2?]))
 T=[]
 Xgeo=[]
 309
Vgeo=[]
 for i in range(len(t)):
 t[i]=time_convert(dat[?dJ2?][i],dat[?sJ2?][i])
 if time.gmtime(t[i])[7]==int(d[5:]):
 T.append(t[i])
 Xgeo.append(dat[?pos?][i])
 Vgeo.append(dat[?vel?][i])
 filename=directory+"CH-OG-3-RSO+CTS-CHA_"+d+"_10.dat"
 dat=extract_data()
 t=zeros(len(dat[?dJ2?]))
 for i in range(len(t)):
 t[i]=time_convert(dat[?dJ2?][i],dat[?sJ2?][i])
 T.append(t[i])
 Xgeo.append(dat[?pos?][i])
 Vgeo.append(dat[?vel?][i])
 filename=directory+"CH-OG-3-RSO+CTS-CHA_"+d+"_22.dat"
 dat=extract_data()
 t=zeros(len(dat[?dJ2?]))
 for i in range(len(t)):
 t[i]=time_convert(dat[?dJ2?][i],dat[?sJ2?][i])
 if time.gmtime(t[i])[7]==int(d[5:]):
 T.append(t[i])
 Xgeo.append(dat[?pos?][i])
 Vgeo.append(dat[?vel?][i])
 T=array(T)
 Xgeo=array(Xgeo)*1e-6
 Vgeo=array(Vgeo)*1e-10
 print(shape(Xgeo))
 ipos=zeros((len(T),3))
 for i in range(len(T)):
 Xgei=cstrans2.geo2gei(Xgeo[i],T[i])
 Xmag=cstrans2.gei2mag(Xgei,T[i])
 ipos[i,0:2]=Xmag[1:3]
 ipos[i,2]=sqrt(sum(Xgeo[i]**2))
 new_dat={}
 new_dat[?t?]=T
 new_dat[?pos?]=Xgeo
 new_dat[?vel?]=Vgeo
 new_dat[?ipos?]=ipos
 fs=open(directory+?RSO_?+d+?-?+version+?.pkl?,?wb?)
 pickle.dump(new_dat,fs)
 310
fs.close()
 def process_CHAMP_acc(directory,days):
 global filename
 for d in days:
 f="CH-OG-2-ACC+"+d+"_00.9.dat"
 filename=directory+f
 print(filename)
 dat=extract_data()
 t=zeros(len(dat[?tim?]))
 dcy=zeros(len(t))
 for i in range(len(t)):
 t[i]=calendar.timegm(dat[?tim?][i])
 dcy[i]=(dat[?acl?][i][1]-dat[?lk?][0][1])*dat[?lk?][1][1]
 dat[?t?]=t
 dat[?dcy?]=dcy
 fs=open(directory+?ACC_?+f[12:20]+?-?+version+?.pkl?,?wb?)
 pickle.dump(dat,fs)
 fs.close()
 # Routine checks to ensure working dataset matches the requested
 # set type
 def check_dataset(set_type):
 known_sets={?acc?:?%chacc?, ?pso?:?DSIDP ?, ?rso?:?DSIDP ?}
 if set_type not in known_sets:
 error("CD01", set_type)
 return 0
 dataset=open(filename,?r?)
 format_id=dataset.read(6)
 if format_id != known_sets[set_type]:
 error("CD02", set_type)
 dataset.close()
 return 0
 else:
 print("Found correct file type " + format_id)
 dataset.close()
 return 1
 # Data extractor, general routine. Sets dataset type, checks the file
 # for set consistency, and prompts to select data elements for extraction
 def extract_data():
 extractor={?acc?:acc_extract, ?pso?:pso_extract, ?rso?:pso_extract}
 311
# ::: not Py3 compatible; needs to be changed to input() for Py3.
 set_type=raw_input("Set type for dataset: ")
 print(??)
 if set_type not in extractor:
 error("ED01")
 return []
 if not check_dataset(set_type):
 error("ED02")
 return []
 data = extractor[set_type]()
 return data
 ### data extraction routines ###
 def pso_extract():
 line_format={?dJ2?:float, ?sJ2?:float, ?pos?:float, ?vel?:float,
 ::: ?orn?:float, ?ngd?:float, ?flg?:str}
 data={}
 dataset=open(filename,?r?)
 last=?file unread?
 while(dataset.read(5) != ?ORBIT? and last != ??):
 last=dataset.readline()
 if(last == ??):
 error("EX01",?pso?)
 return []
 last=dataset.readline()
 setkey={0:?dJ2?, 1:?sJ2?, 2:?pos?, 3:?vel?, 4:?orn?, 5:?ngd?, 6:?flg?}
 used=key_select(setkey)
 datasize={0:(1,6), 1:(1,11), 2:(3,12), 3:(3,12), 4:(3,7), 5:(1,5), 6:(4,1)}
 for key in used:
 data.update({key:[]})
 while(last != ??):
 for key in datasize.keys():
 if datasize[key][0]>1:
 new_data = []
 for i in range(datasize[key][0]):
 new_data.append(line_format[setkey[key]](
 312
::: dataset.read(datasize[key][1])))
 else:
 new_data = dataset.read(datasize[key][1])
 if new_data==??:
 break
 else:
 new_data=line_format[setkey[key]](new_data)
 if (setkey[key] in used and new_data != ??):
 data[setkey[key]].append(new_data)
 last=dataset.readline()
 dataset.close()
 return data
 # accelerometer data extraction
 def acc_extract():
 # define the format of the lines in the data file. These formats
 # do not include the 3 byte label in the first three characters
 # of the line in the champ data files, which is accounted for in
 # the scanning for position before parsing the data.
 line_format={?tim?:champformats.tim, ?acl?:champformats.acl,
 ?aca?:champformats.aca, ?att?:champformats.att,
 ?thr?:[], ?acc?:[]}
 data={} # initialize the extracted data set
 marked={} # flag used to identify when a data type is missing
 # from a given timestamp
 dataset=open(filename,?r?)
 last=?file unread? # last is a place to dump the remainder of
 # a read line that is preserved to identify
 # the %eof
 while(dataset.read(10) != ?+data_____? and last != ??):
 last=dataset.readline() # Scan to find the data description
 if(last == ??):
 error("EX01",?acc?)
 return []
 setkey={} # If not at %eof, start extracting the data types
 i=0 # included in the file, 3 byte labels with spaces
 while(dataset.read(1) != ?\n?): # between them.
 setkey.update({i:dataset.read(3)})
 i += 1
 313
used=key_select(setkey) # run key selection routine with the keys
 # found in the dataset.
 if ?acl? in used: # extract acl calibration constants
 while(dataset.read(10) != ?+acl_k0___? and last != ??):
 last=dataset.readline()
 if(last == ??):
 error("EX02",?acl?)
 return[]
 lk0=[0,0,0]
 for i in range(3):
 lk0[i]=float(dataset.read(16))
 lk0_app=int(dataset.read(2))
 last=dataset.readline()
 while(dataset.read(10) != ?+acl_k1___? and last != ??):
 last=dataset.readline()
 if(last == ??):
 error("EX02",?acl?)
 return []
 lk1=[0,0,0]
 for i in range(3):
 lk1[i]=float(dataset.read(16))
 lk1_app=int(dataset.read(2))
 last=dataset.readline()
 print("Linear ACC Calibration values: "),
 print(lk0,lk1)
 data.update({?lk?:[lk0,lk1]})
 if ?aca? in used: # extract aca calibration constants
 while(dataset.read(10) != ?+aca_k0___? and last != ??):
 last=dataset.readline()
 if(last == ??):
 error("EX02", ?aca?)
 return []
 ak0=[0,0,0]
 for i in range(3):
 ak0[i]=float(dataset.read(16))
 ak0_app=int(dataset.read(2))
 last=dataset.readline()
 while(dataset.read(10) != ?+aca_k1___? and last != ??):
 last=dataset.readline()
 314
if(last == ??):
 error("EX02", ?aca?)
 ak1=[0,0,0]
 for i in range(3):
 ak1[i]=float(dataset.read(16))
 ak1_app=int(dataset.read(2))
 last=dataset.readline()
 print("Angular ACC calibration values: "),
 print(ak0,ak1)
 data.update({?ak?:[ak0,ak1]})
 for key in used: # load data and marked dictionaries with used keys
 data.update({key:[]})
 marked.update({key:1}) # flags set to 1 to prevent initial
 # timestamp from triggering a line of nan?s
 # for the other extracted variables
 key=dataset.read(3) # scan to data lines
 while(key != ?tim? and last != ??):
 last=dataset.readline()
 key=dataset.read(3)
 while(key != ??): # parse until %eof
 if (key == ?tim?): # first fill in data holes of used types
 for i in used: # with nan?s for previous timestamp
 if marked[i] == 0:
 new_data=[]
 for j in range(len(line_format[i])):
 if line_format[i][j][0] != ?blank?:
 new_data.append(nan)
 data[i].append(new_data)
 else:
 marked[i]=0 # reset flag
 ### Parsing routine
 # currently set to avoid use of thr and acc until coded
 # check if key is used, otherwise pass to the next line
 if (key in used and key not in (?thr?,?acc?)):
 new_data=[]
 for i in range(len(line_format[key])):
 315
# line definitions with blanks should be parsed across
 if line_format[key][i][0]==?blank?:
 dataset.read(line_format[key][i][1]+1)
 # all others are formatted according to their datatype
 # as defined in champformats.py
 else:
 new_data.append({?int?:int,?float?:float,?bin?:str
 ::: }[line_format[key][i][0]](
 ::: dataset.read(line_format[key][i][1]+1)))
 # add the line of data and flag marked as done
 data[key].append(new_data)
 marked[key]=1
 ### temporary warning until thr and acc code is done ###
 if (key in used and key in (?thr?,?acc?)):
 print("Not programmed for {0} yet.".format(key))
 # final step to parse line is to finish the readline (ideally only
 # picks up the \n at the line end) and read the key on the next
 # line. Returns to while loop.
 last=dataset.readline()
 key=dataset.read(3)
 # Finished parsing, close the file and return the extracted data
 ### currently does not return calibration values, only displayed on
 ### screen.
 dataset.close()
 return data
 # key_select() and key_menu() are used to modify the extracted data set
 # selection visually.
 def key_select(setkey):
 choice = ?z?
 used=setkey.keys() # defaults to using all extracted keys
 key_menu(setkey)
 while (choice != ?c?):
 print("> Current set uses {0} (order not preserved)".format(used))
 print("> Enter ?d? to redisplay, ?a? to add, ?r? to remove, "),
 print("or ?c? to continue.")
 choice=raw_input("> ")
 316
if (choice == ?d?):
 key_menu(setkey)
 if (choice in [?a?,?r?]):
 print("> Enter a value to {0}: ".format({?a?:?add?, ?r?:?remove?
 ::: }[choice]))
 entry = int(raw_input("> "))
 if entry in {?a?:setkey.keys(),?r?:used}[choice]:
 {?a?:used.append,?r?:used.remove}[choice](entry)
 else:
 print("No value with key {0}".format(entry))
 used_names=[]
 for i in used:
 used_names.append(setkey[i])
 return used_names
 def key_menu(menu):
 print(??)
 for i in menu.keys():
 print(" : {0} : {1}:".format(i,menu[i]))
 print(??)
 ### Error Code Definitions for all functions ###
 def error(code, *info):
 if (len(info) == 0):
 info=[??]
 message = {
 "CD01" : "Unknown set type {0}".format(info[0]),
 "CD02" : "Incorrect file type for set type {0}".format(info[0]),
 "ED01" : "Unknown set type for extraction",
 "ED02" : "Data set not compatible with set type",
 "EX01" : "Extractor {0} found no data head".format(info[0]),
 "EX02" : "Extractor failed to find {0} calibration values"
 :: .format(info[0])
 }
 print("ERR {0}: ".format(code) + message[code])
 ### Data Analysis Routines ###
 317
def time_convert(d,s):
 J2000=946728000.0
 return J2000+24.*360.*d+s/1e6
 def interpolate(x,y,width=20):
 y_new=zeros(len(y))
 for i in range(len(y)):
 if isnan(y[i]):
 x2=[]
 y2=[]
 for j in range(i-width/2,i+width/2):
 if isnan(y[j])==False:
 x2.append(x[j])
 y2.append(y[j])
 f=interp1d(x2,y2,kind=?cubic?)
 y_new[i]=f(x[i])
 else:
 y_new[i]=y[i]
 return y_new
 318
E.2.2 champformats.py
 # champformats: data file formatting details
 # Rev. A1 20 Jan 2011
 tim = [ (?int?,4), # year
 (?int?,2), # month
 (?int?,2), # day
 (?int?,2), # hours
 (?int?,2), # minutes
 (?float?,10) ] # seconds
 acl = [ (?blank?,4),
 (?float?,13), # linear ax
 (?float?,13), # linear ay
 (?float?,13), # linear az
 (?int?,5), # samples nx
 (?int?,5), # samples ny
 (?int?,5) ] # samples nz
 aca = [ (?blank?,4),
 (?float?,13), # angular aphi
 (?float?,13), # angular atheta
 (?float?,13), # angular apsi
 (?int?,5), # samples nphi
 (?int?,5), # samples ntheta
 (?int?,5) ] # samples npsi
 att = [ (?bin?,4), # star camera flags
 (?float?,13), # attitude quaternions
 (?float?,13), # q1, q2, q3: vector part
 (?float?,13),
 (?float?,13), # q4: scalar part
 (?float?,4) ] # quaternion accuracy
 319
E.2.3 CHAMP stats.py
 from matplotlib.pyplot import *
 from pylab import find
 from math import pi
 from numpy import array,zeros,arange,isnan,nansum,nanmin,log10,r_,delete,fft,
 ::: nan,mean,concatenate
 from scipy.stats import stats
 from scipy.interpolate import interp1d
 import process
 import pickle
 import plot_setup
 import time
 basedir="/home/david/research/CHAMP/data/"
 filesuff="-b3.pkl"
 def get_averages(orbits,bd_append,type=?raw?):
 f_basedir="/home/david/research/FAST/data/"
 mt=[]
 mdcy=[]
 milt=[]
 mmlt=[]
 for o in orbits:
 print("Geting averages for orbit {0}".format(o))
 f=open(f_basedir+bd_append+o+"/FAST_"+o+"-a-1.71-py2.pkl",?rb?)
 fd=pickle.load(f)
 f.close()
 i=min(find(fd[?data?][?Outflow?]==1))
 j=max(find(fd[?data?][?Outflow?]==1))+1
 doy=time.gmtime(fd[?data?][?Time?][i])[7]
 if time.gmtime(fd[?data?][?Time?][j])[7]!=doy:
 print("Error! Orbit {0} overlaps two days!".format(o))
 d1=time.gmtime(fd[?data?][?Time?][0])[7]
 d2=time.gmtime(fd[?data?][?Time?][-1])[7]
 if d1==d2:
 cd1={}
 f=open(basedir+"RSO_2002_{0:03}".format(d1)+filesuff,?rb?)
 d=pickle.load(f)
 cd1[?rso?]=d
 f.close()
 f=open(basedir+"ACC_2002_{0:03}".format(d1)+filesuff,?rb?)
 d=pickle.load(f)
 320
cd1[?acc?]=d
 f.close()
 cd2=cd1
 else:
 cd1={}
 f=open(basedir+"RSO_2002_{0:03}".format(d1)+filesuff,?rb?)
 d=pickle.load(f)
 cd1[?rso?]=d
 f.close()
 f=open(basedir+"ACC_2002_{0:03}".format(d1)+filesuff,?rb?)
 d=pickle.load(f)
 cd1[?acc?]=d
 f.close()
 cd2={}
 f=open(basedir+"RSO_2002_{0:03}".format(d2)+filesuff,?rb?)
 d=pickle.load(f)
 cd2[?rso?]=d
 f.close()
 f=open(basedir+"ACC_2002_{0:03}".format(d2)+filesuff,?rb?)
 d=pickle.load(f)
 cd2[?acc?]=d
 f.close()
 cd={}
 cd[?acc?]={}
 cd[?rso?]={}
 if d1==d2:
 cd[?acc?][?t?]=cd1[?acc?][?t?]
 cd[?acc?][?dcy?]=cd1[?acc?][?dcy?]
 cd[?acc?][?filtered t?]=cd1[?acc?][?filtered t?]
 cd[?acc?][?filtered day?]=cd1[?acc?][?filtered day?]
 cd[?rso?][?t?]=cd1[?rso?][?t?]
 cd[?rso?][?ipos?]=cd1[?rso?][?ipos?]
 else:
 cd[?acc?][?t?]=concatenate((cd1[?acc?][?t?],cd2[?acc?][?t?]))
 cd[?acc?][?dcy?]=concatenate((cd1[?acc?][?dcy?],cd2[?acc?][?dcy?]))
 if type==?change?:
 cd[?acc?][?filtered t?]=concatenate((
 ::: cd1[?acc?][?filtered t?],cd2[?acc?][?filtered t?]))
 cd[?acc?][?filtered day?]=concatenate((
 ::: cd1[?acc?][?filtered day?],cd2[?acc?][?filtered day?]))
 cd[?rso?][?t?]=concatenate((cd1[?rso?][?t?],cd2[?rso?][?t?]))
 321
cd[?rso?][?ipos?]=concatenate((
 ::: cd1[?rso?][?ipos?],cd2[?rso?][?ipos?]))
 t1=min(find(cd[?rso?][?t?]>fd[?data?][?Time?][0]))
 t2=min(find(cd[?rso?][?t?]>fd[?data?][?Time?][-1]))
 ilt1=fd[?data?][?Invariant Position?][0][i]
 ilt2=fd[?data?][?Invariant Position?][0][j]
 min_ilt=min(ilt1,ilt2)
 max_ilt=max(ilt1,ilt2)
 t=[]
 dcy=[]
 ILT=[]
 MLT=[]
 if type==?raw?:
 f=interp1d(cd[?acc?][?t?],cd[?acc?][?dcy?],kind=?linear?)
 elif type==?change?:
 f=interp1d(cd[?acc?][?filtered t?],cd[?acc?][?filtered day?],
 ::: kind=?linear?)
 for k in range(t1,t2):
 ilt=cd[?rso?][?ipos?][k,0]*180/pi
 mlt=cd[?rso?][?ipos?][k,1]
 if ilt > min_ilt and ilt < max_ilt:
 if mlt > 6. and mlt < 18.:
 dcy.append(f(cd[?rso?][?t?][k]))
 ILT.append(ilt)
 MLT.append(mlt)
 t=mean(cd[?rso?][?t?][t1:t2])
 mt.append(t)
 mdcy.append(mean(dcy))
 milt.append(mean(ILT))
 mmlt.append(mean(MLT))
 return array(mt),array(mdcy),array(milt),array(mmlt)
 def time_to_latitude(ends,days,lat):
 for d in days:
 print(d)
 f=open(basedir+"RSO_"+d+filesuff,?rb?)
 rso=pickle.load(f)
 f.close()
 f=open(basedir+"ACC_"+d+filesuff,?rb?)
 acc=pickle.load(f)
 322
f.close()
 tr=rso[?t?]
 ilt=rso[?ipos?][:,0]*180./pi
 ta=acc[?filtered t?]
 if len(days)==1:
 a=min(find(ends[0]<ta))
 b=min(find(ends[1]<ta))
 else:
 if d==days[0]:
 a=min(find(ends[0]<ta))
 b=len(ta)
 else:
 a=0
 b=min(find(ends[1]<ta))
 print(a,b)
 ta=ta[a:b]
 ay=acc[?filtered ay?][a:b]
 nilt=nan*zeros(len(ta))
 a=0
 b=len(ta)
 for i in range(len(ta)):
 if ta[i]<tr[0]:
 a=i+1
 if ta[i]>tr[-1]:
 b=i
 print(a,b)
 nilt[a:b]=process.interp(tr,ilt,ta[a:b],100.)
 lay=zeros(len(lat))
 n=zeros(len(lat))
 for i in range(len(ta)):
 if nilt[i]>lat[0] and nilt[i]<(2*lat[-1]-lat[-2]):
 nogo=isnan(ay[i])
 if not nogo:
 j=0
 while j<len(lat) and lat[j]<nilt[i]:
 j+=1
 j-=1
 lay[j]+=ay[i]
 n[j]+=1
 return lay,n
 def get_latavg(t,lat=arange(70.,80.,0.5)):
 323
size=(len(t),len(lat))
 ay=zeros(size)
 cts=zeros(size)
 used=[]
 for i in range(len(t)):
 print("Time Range {0}".format(i))
 print(" Finding used sets...")
 used.append([])
 d0=time.gmtime(t[i])[7]
 if i<len(t)-1:
 d1=time.gmtime(t[i+1])[7]
 ends=[t[i],t[i+1]]
 else:
 d1=time.gmtime(2*t[i]-t[i-1])[7]
 ends=[t[i],2*t[i]-t[i-1]]
 day0="{0}_{1}".format(time.gmtime(t[i])[0],d0)
 day1="{0}_{1}".format(time.gmtime(t[i])[0],d1)
 if day0==day1:
 used[i].append(day0)
 else:
 used[i].append(day0)
 used[i].append(day1)
 print(" Allocating data...")
 ay[i],cts[i]=time_to_latitude(ends,used[i],lat)
 return ay,cts
 def update_acc_pickle(days,notch=??):
 for d in days:
 print("Updating {0}...".format(d))
 f=open(basedir+"ACC_"+d+filesuff,?rb?)
 acc=pickle.load(f)
 f.close()
 t=acc[?t?]
 ay=-acc[?dcy?]
 t_interp=arange(t[0],t[-1]+10.,10.)
 ay_interp=process.interp(t,ay,t_interp,100.)
 ay_fft=fft.fft(ay_interp)
 ay_frq=fft.fftfreq(ay_fft.size, d=10.)
 if notch==??:
 P=zeros(ay_fft.size)
 for i in range(P.size):
 324
P[i]=ay_fft[i].real**2+ay_fft[i].imag**2
 plot(ay_frq,P)
 notch = raw_input("max freq: ")
 for i in range(ay_fft.size):
 if abs(ay_frq[i])>notch:
 ay_fft[i]=0
 new_ay=fft.ifft(ay_fft).real
 acc[?filtered ay?]=new_ay
 acc[?filtered t?]=t_interp
 acc[?filtered day?]=ay_interp-new_ay
 f=open(basedir+"ACC_"+d+filesuff,?wb?)
 pickle.dump(acc,f)
 f.close()
 def create_pickle(days):
 for d in days:
 print("Creating Pickle for {0}...".format(d))
 f=open(basedir+"ACC_"+d+filesuff,?rb?)
 acc=pickle.load(f)
 f.close()
 f=open(basedir+"RSO_"+d+filesuff,?rb?)
 rso=pickle.load(f)
 f.close()
 t=arange(rso[?t?][0]//10*10.+10.,rso[?t?][-1]//10*10.+10.,10.)
 print(" interpolating invariant latitude...")
 ilt=process.interp(rso[?t?],rso[?ipos?][:,0]*180./pi,t,100.)
 print(" interpolating magnetic local time...")
 mlt=process.interp(rso[?t?],rso[?ipos?][:,1],t,100.)
 print(" interpolating altitude...")
 alt=process.interp(rso[?t?],rso[?ipos?][:,2],t,100.)
 print(" interpolating x velocity...")
 vx=process.interp(rso[?t?],rso[?vel?][:,0],t,100.)
 print(" interpolating y velocity...")
 vy=process.interp(rso[?t?],rso[?vel?][:,1],t,100.)
 print(" interpolating z velocity...")
 vz=process.interp(rso[?t?],rso[?vel?][:,2],t,100.)
 print(" interpolating decceleration...")
 dcy=process.interp(acc[?t?],acc[?dcy?],t,100.)
 data={?t?:t, ?ipos?:array([ilt,mlt,alt]), ?vel?:array([vx,vy,vz]),
 ::: ?dcy?:dcy}
 f=open(basedir+"CHAMP_"+d+filesuff,?wb?)
 pickle.dump(data,f)
 f.close()
 325
print(" done!")
 def find_upwelling(fa_orbit,fa_basedir):
 plot_setup.set_params(10,?default?,16)
 f=open(fa_basedir+fa_orbit+?/FAST_?+fa_orbit+?-a-1.71-py2.pkl?,?rb?)
 fd = pickle.load(f)
 f.close()
 d1=time.gmtime(fd[?data?][?Time?][0])[7]
 d2=time.gmtime(fd[?data?][?Time?][-1])[7]
 if d1==d2:
 f=open(basedir+?CHAMP_2002_{0:03}-b3.pkl?.format(d1),?rb?)
 cd=pickle.load(f)
 f.close()
 else:
 f=open(basedir+?CHAMP_2002_{0:03}-b3.pkl?.format(d1),?rb?)
 cd1=pickle.load(f)
 f.close()
 f=open(basedir+?CHAMP_2002_{0:03}-b3.pkl?.format(d2),?rb?)
 cd2=pickle.load(f)
 f.close()
 cd={}
 cd[?t?]=concatenate((cd1[?t?],cd2[?t?]))
 cd[?ipos?]=zeros((3,len(cd[?t?])))
 cd[?ipos?][0]=concatenate((cd1[?ipos?][0],cd2[?ipos?][0]))
 cd[?ipos?][1]=concatenate((cd1[?ipos?][1],cd2[?ipos?][1]))
 cd[?ipos?][2]=concatenate((cd1[?ipos?][2],cd2[?ipos?][2]))
 cd[?vel?]=concatenate((cd1[?vel?],cd2[?vel?]))
 cd[?dcy?]=concatenate((cd1[?dcy?],cd2[?dcy?]))
 i=min(find(fd[?data?][?Outflow?]==1))
 j=max(find(fd[?data?][?Outflow?]==1))
 ilt_min=min(fd[?data?][?Invariant Position?][0][i],
 ::: fd[?data?][?Invariant Position?][0][j])
 ilt_max=max(fd[?data?][?Invariant Position?][0][i],
 ::: fd[?data?][?Invariant Position?][0][j])
 cusp=zeros(len(cd[?t?]))
 fast=zeros(len(cd[?t?]))
 for k in range(cusp.size):
 if cd[?ipos?][0][k]>ilt_min and cd[?ipos?][0][k]<ilt_max:
 if cd[?ipos?][1][k]>6. and cd[?ipos?][1][k]<18.:
 cusp[k]=1
 326
if cd[?t?][k]>fd[?data?][?Time?][i] and
 ::: cd[?t?][k]<fd[?data?][?Time?][j]:
 fast[k]=1
 t0=fd[?data?][?Time?][0]
 close()
 figure()
 subplot(212)
 plot(fd[?data?][?Time?]-t0,fd[?data?][?Invariant Position?][0],?r-?)
 plot(cd[?t?]-t0,cd[?ipos?][0],?b-?)
 axis([0,fd[?data?][?Time?][-1]-t0,-90,90])
 legend([?FAST?,?CHAMP?],loc=?best?)
 xlabel(?Time (s)?)
 ylabel(?Invariant Latitude (deg)?)
 subplot(211)
 plot(cd[?t?]-t0,-1000*cd[?dcy?])
 fill_between(cd[?t?]-t0,0,2,where=(fast==1),facecolor=?red?,alpha=0.5)
 fill_between(cd[?t?]-t0,0,2,where=(cusp==1),facecolor=?green?,alpha=0.5)
 axis([0,fd[?data?][?Time?][-1]-t0,0,1.1*max(-1000*cd[?dcy?])])
 ylabel(?Decceleration ($\mu$m/s$^2$)?)
 good=?n?
 while(good!=?y?):
 ax=gca()
 if len(ax.lines)>3:
 ax.lines=ax.lines[:3]
 draw()
 start=float(raw_input("Enter starting time: "))
 stop=float(raw_input("Enter stopping time: "))
 plot([start,start],[0,2],?k--?)
 plot([stop,stop],[0,2],?k--?)
 good=raw_input("Good times (y/n): ")
 a=min(find(cd[?t?]>start+t0))
 b=min(find(cd[?t?]>stop+t0))
 t_interp=concatenate((cd[?t?][2*a-b:a],cd[?t?][b:2*b-a]))
 dcy_interp=concatenate((cd[?dcy?][2*a-b:a],cd[?dcy?][b:2*b-a]))
 f=interp1d(t_interp,dcy_interp,kind=?linear?)
 base=zeros(b-a)
 for i in range(b-a):
 base[i]=f(cd[?t?][a+i])
 plot(cd[?t?][a:b]-t0,-1000*base,?r--?)
 327
raw_input("Press Enter to continue.")
 spike=array(cd[?dcy?][a:b]-base)
 subplot(212)
 ax=gca()
 ax.clear()
 plot(cd[?t?][a:b]-t0,-1000*spike,?m-?)
 plot(cd[?t?][a:b]-t0,zeros(b-a),?k--?)
 axis([cd[?t?][a]-t0,cd[?t?][b]-t0,min(-1000*spike)*0.9,max(-1000*spike)*1.1])
 return mean(-1000*spike),max(-1000*spike)
 E.3 Coordinate System Transformation
 E.3.1 cstrans2.py
 # :: cstrans.py ::
 #
 # Coordinate System Transformation tools
 # v0.2
 #
 # David K. Olson Jul 2011
 # NASA/Goddard Space Flight Center
 # david.olson@nasa.gov
 #
 # Requires IGRF.py to do magnetic-aligned coordinate systems.
 #
 # ::::::::::::::::::::
 from numpy import array,matrix,zeros,dot,cross,sign
 from math import sqrt,sin,asin,cos,acos,tan,atan,atan2,pi
 from datetime import datetime
 from time import gmtime
 from calendar import timegm
 from spacepy import time as spt
 import IGRF
 known_systems=[?GEO?,?GEI?]
 # centered dipole calculation from IGRF
 # see eg. http://www.spenvis.oma.be/help/background/magfield/cd.html
 def get_dipole(model,year,eccentric=False):
 g,h=IGRF.load_IGRF(model,year)
 B0=sqrt(g[1,0]**2+g[1,1]**2+h[1,1]**2)
 328
c11=sqrt(g[1,1]**2+h[1,1]**2)
 theta=acos(-g[1,0]/B0)
 phi=asin(-h[1,1]/c11)
 if eccentric:
 L0=2*g[1,0]*g[2,0]+sqrt(3)*(g[1,1]*g[2,1]+h[1,1]*h[2,1])
 L1=-g[1,1]*g[2,0]+sqrt(3)*(g[1,0]*g[2,1]+g[1,1]*g[2,2]+h[1,1]*h[2,2])
 L2=-h[1,1]*g[2,0]+sqrt(3)*(g[1,0]*h[2,1]-h[1,1]*g[2,2]+g[1,1]*h[2,2])
 E=(L0*g[1,0]+L1*g[1,1]+L2*h[1,1])/(4*B0**2)
 x=array([(L1-g[1,1]*E)/(3*B0**2),(L2-h[1,1]*E)/(3*B0**2),
 ::: (L0-g[1,0]*E)/(3*B0**2)])*6371.2
 else:
 x=array([cos(pi/2-theta)*cos(phi),cos(pi/2-theta)*sin(phi),
 ::: sin(pi/2-theta)])
 return theta,phi,x
 def jd(t,Julian=False):
 t_ex=gmtime(t)
 y=t_ex[0]
 m=t_ex[1]
 d=t_ex[2]
 H=t_ex[3]
 M=t_ex[4]
 S=t_ex[5]+t-int(t)
 fd = d+(H+(M+(S/60.))/60.)/24.
 if m<=2:
 y-=1
 m+=12
 A=y//100
 if Julian:
 B=0
 else:
 B=2-A+A//4
 return int(365.25*(y+4716))+int(30.6001*(m+1))+fd+B-1524.5
 # Greenwich mean Sidereal Time from Meeus
 def gst(t):
 djm=jd(t)-2451545.0
 T=djm/36525.
 return (280.46061837 + 360.98564736629*djm+3.87933e-4*T**2-T**3/3.871e7)%360.
 329
# Greenwich mean Sidereal Time from Russell
 def gst2(t):
 date=gmtime(t)
 y=date[0]
 d=date[7]
 fd=(date[3]+(date[4]+(date[5]+(t-int(t)))/60.)/60.)/24.
 dj=365.*(y-1900)+(y-1901)/4.+d+fd-0.5
 T=dj/36525.
 return (279.690983+0.9856473354*dj+360.*fd+180.)%360.
 def gst3(t):
 t=spt.Ticktock(t,?UNX?)
 mjd=t.MJD[0]
 T0=(mjd-51544.5)/36525.0
 return (100.461+36000.770*T0+15.04107)
 def sun(t):
 date=gmtime(t)
 y=date[0]
 d=date[7]
 fd=(date[3]+(date[4]+(date[5]+(t-int(t)))/60.)/60.)/24.
 dj=365.*(y-1900)+(y-1901)/4+d+fd-0.5
 T=dj/36525.
 vl=(279.696678+0.9856473354*dj)%360.
 gst=(279.690983+0.9856473354*dj+360.*fd+180.)%360.
 g=((358.475845+0.985600267*dj)%360.)*pi/180.
 slong=vl+(1.91946-0.004789*T)*sin(g)+0.020094*sin(2.*g)
 obliq=(23.45229-0.0130125*T)*pi/180.
 slp=(slong-0.005686)*pi/180.
 sind=sin(obliq)*sin(slp)
 cosd=sqrt(1.-sind**2)
 sdec=180./pi*atan(sind/cosd)
 srasn=180.-180./pi*atan2(sind/cosd/tan(obliq),-cos(slp)/cosd)
 r=149598000.
 x=r*cos(srasn*pi/180.)*cos(sdec*pi/180.)
 y=r*sin(srasn*pi/180.)*cos(sdec*pi/180.)
 z=r*sin(sdec*pi/180.)
 return array([x,y,z])
 330
def geo2gei(x_geo,t):
 theta=gst2(t)*pi/180.
 x_gei=zeros(len(x_geo))
 x_gei[0]=x_geo[0]*cos(theta)-x_geo[1]*sin(theta)
 x_gei[1]=x_geo[0]*sin(theta)+x_geo[1]*cos(theta)
 x_gei[2]=x_geo[2]
 return x_gei
 def gei2geo(x_gei,t):
 theta=gst2(t)*pi/180.
 x_geo=zeros(len(x_gei))
 x_geo[0]=x_gei[0]*cos(theta)+x_gei[1]*sin(theta)
 x_geo[1]=-1*x_gei[0]*sin(theta)+x_gei[1]*cos(theta)
 x_geo[2]=x_gei[2]
 return x_geo
 def gei2gsm(x_gei,t):
 theta,phi,D=get_dipole(7,1995)
 Dp=geo2gei(D,t)
 S=sun(t)
 DpS=cross(Dp,S)
 Y=DpS/sqrt(sum(DpS**2))
 Z=cross(S,Y)
 x_gsm=zeros(3)
 x_gsm[0]=dot(S,x_gei)
 x_gsm[1]=dot(Y,x_gei)
 x_gsm[2]=dot(Z,x_gei)
 return x_gsm
 def gei2sm(x_gei,t):
 theta,phi,D=get_dipole(7,1995)
 Dp=geo2gei(D,t)
 S=sun(t)
 DpS=cross(Dp,S)
 Y=DpS/sqrt(sum(DpS**2))
 X=cross(Y,Dp)
 x_sm=zeros(3)
 x_sm[0]=dot(X,x_gei)
 x_sm[1]=dot(Y,x_gei)
 x_sm[2]=dot(Dp,x_gei)
 331
return x_sm
 def transform(x,fr,to):
 error=False
 if fr not in known_systems:
 print("Unknown system {0}.".format(fr))
 error=True
 if to not in known_systems:
 print("Unknown system {0}.".format(to))
 error=True
 if len(x) != 3:
 print("Vector length needs to be 3 components.")
 error=True
 if error==True:
 return []
 T={?geogei?:1, ?geigeo?:2}
 v=array([[x[0]],[x[1]],[x[2]]])
 return T[fr+to]*v
 ###
 #def solar_pos_GEI(year,day,time):
 # if year<1901 or year>2099:
 # print("year out of range for solar position.")
 # return
 # else:
 # if len(time)==3:
 # ftime=(time[0].+(time[1]+(time[2]/60.))/60.)/24.
 # elif len(time)==1:
 # ftime=time/86400.
 # else:
 # print("time formatting error: use either [hh,mm,ss.ss] or ss.sss")
 # return
 #
 # DJ=365*(year-1900)+(year-1901)/4+day+ftime-0.5
 # T=DJ/36525.
 # VL=(279.696678+0.9856473354*DJ)%360.
 # GST=(279.690983+0.9856473354*DJ+360*ftime+180.)%360.
 # G=(358.475845+0.985600267*DJ)%360.*180./pi
 # SLONG=VL+(1.91946-0.
 ###
 332
def rotate_x(v,theta):
 R=array([[1.,0.,0.],[0.,cos(theta),-sin(theta)],[0.,sin(theta),cos(theta)]])
 return dot(R,v)
 def rotate_y(v,theta):
 R=array([[cos(theta),0.,sin(theta)],[0.,1.,0.],[-sin(theta),0.,cos(theta)]])
 return dot(R,v)
 def rotate_z(v,theta):
 R=array([[cos(theta),-sin(theta),0.],[sin(theta),cos(theta),0.],[0.,0.,1.]])
 return dot(R,v)
 def gei2mag(Xgei,t):
 X=gei2geo(Xgei,t)
 theta,phi,off=get_dipole(7,1995,eccentric=True)
 Xm=rotate_y(rotate_z(X-off,-phi),-theta)
 S=gei2geo(sun(t),t)
 Sm=rotate_y(rotate_z(S-off,-phi),-theta)
 mrad=sqrt(sum(Xm**2))
 mlat=asin(Xm[2]/mrad)
 mlon=atan2(Xm[1],Xm[0])
 slon=atan2(Sm[1],Sm[0])
 ilat=sign(Xm[2])*acos(min(1.,sqrt(6371.2/mrad)*cos(mlat)))
 if slon-mlon>pi:
 alpha=slon-mlon-2*pi
 elif slon-mlon<-pi:
 alpha=slon-mlon+2*pi
 else:
 alpha=slon-mlon
 mlt=12.-alpha*12./pi
 return Xm,ilat,mlt
 333
E.4 Other Code
 E.4.1 nantools.py
 from numpy import nansum
 from math import sqrt
 def nanmean(a):
 return nansum(a)/nansum(a/a)
 def nanstd(a):
 return sqrt(nanmean((a-nanmean(a))**2))
 E.4.2 plot setup.py
 from math import sqrt
 from pylab import rcParams as rc
 shapes={?default?: 0.774193548387, ?golden mean?: (sqrt(5)-1)/2,
 ::: ?square?: 1., ?portrait?: 11./8.5, ?landscape?: 8.5/11.,
 ::: ?long?: 1.5}
 pti=72.27
 def set_params(width=??,shape=??,fontsize=??,linewidth=2.):
 if width==??:
 width=rc[?figure.figsize?][0]
 if shape==??:
 w,h=rc[?figure.figsize?]
 mt=1-rc[?figure.subplot.top?]
 mb=rc[?figure.subplot.bottom?]
 ml=rc[?figure.subplot.left?]
 mr=1-rc[?figure.subplot.right?]
 factor=h*(1-mt-mb)/w/(1-ml-mr)
 else:
 if not shapes.has_key(shape):
 print("Unkown shape.")
 return
 factor=shapes[shape]
 if fontsize==??:
 fontsize=rc[?text.fontsize?]
 else:
 fontsize=int(fontsize)
 334
print("Using width {0}, factor {1}, fontsize {2}".format(
 :: width,factor,fontsize))
 ml = 6.0225*fontsize/pti
 mr = 4.8180*fontsize/pti
 mt = 3.6135*fontsize/pti
 mb = 3.6135*fontsize/pti
 pw = width - ml - mr
 ph = factor*pw
 height = mt + ph + mb
 params = { ?lines.linewidth?: linewidth,
 ?figure.figsize?: [width,height],
 ?figure.subplot.bottom?: mb/height,
 ?figure.subplot.top?: 1-mt/height,
 ?figure.subplot.left?: ml/width,
 ?figure.subplot.right?: 1-mr/width,
 ?font.size?: fontsize }
 rc.update(params)
 335
Bibliography
 [1] E.N. Parker, Newton, Maxwell, and Magnetospheric Physics, in Magnetospheric
 Current Systems, Geophys. Monogr. Ser., 118, edited by S.-I. Ohtani et al., 1-
 10, AGU, Washington, D.C. (2000).
 [2] McGraw-Hill Concise Encyclopedia of Science & Technology, Troposphere,
 (1984).
 [3] M.C. Kelley, The Earth?s Ionosphere: Plasma Physics & Electrodynamics, El-
 sevier Inc., London (2009).
 [4] A.E. Hedin, J. Geophys. Res., 96, 1159 (1991).
 [5] Data obtained via http://ccmc.gsfc.nasa.gov/modelweb/models/msis vitmo.php
 (last retrieved 7 Feb 2012).
 [6] C.Y. Johnson, \Ion and neutral composition of the ionosphere", Annals of the
 IQSY, 5, 197 (1969).
 [7] H. Alfv en, L. Danielsson, C.G. F althammer, and L. Lindberg, Natural Electro-
 magnetic Phenomena Below 30 kc/s, pp. 33{48, edited by D.F. Bleil, Plenum,
 New York (1964).
 [8] J. Larmor, Rep. of the British Assoc., 87, 159 (1919).
 [9] IGRF details can be found at: http://www.ngdc.noaa.gov/IAGA/vmod/igrf.html
 [10] M.F. Smith and M. Lockwood, Rev. Geophys., 34, 233 (1996).
 [11] N. Meyer-Vernet, Basics of the Solar Wind, Cambridge Atmospheric and Space
 Science Series, Cambridge University Press, Cambridge (2009).
 [12] T.E. Moore and J.L. Horwitz, Rev. Geophys., 45, RG3002 (2007).
 [13] M.F. Shea, R.D. Sharp, and M.B. McElroy, J. Geophys. Res., 73, 4199{4212
 (1968).
 [14] W.G. Pilipp, H. Miggenrieder, M.D. Montgomery, K.-H. M uhlh auser, H. Rosen-
 bauer, and R. Schwenn, J. Geophys. Res., 92, 1075{1092 (1987).
 336
[15] G.R. Wilson, D.R. Weimer, J.O. Wise, and F.A. Marcos, J. Geophys. Res.,
 111, A10314 (2006).
 [16] A.D. Richmond and J.P. Thayer, Ionospheric electrodynamics: A tutorial, in
 Magnetospheric Current Systems, Geophys. Monogr. Ser., vol. 118, edited by
 S.-I. Ohtani et al., 131-146, AGU, Washington, D.C. (2000).
 [17] B. Gustavsson, M.T. Reitveld, N.V. Ivchenko, and M.J. Kosch, J. Geophys.
 Res., 115, A12332 (2010).
 [18] E.N. Parker, J. Geophys. Res., 62, 509 (1957).
 [19] L.G. Jacchia and J. Slowey, J. Geophys. Res., 69, 905-910 (1964).
 [20] H. L uhr, M. Rother, W. K ohler, P. Ritter, and L. Grunwaldt, Geophys. Res.
 Lett., 31 , 6805 (2004).
 [21] J.H. Clemmons, J.H. Hecht, D.R. Salem, and D.J. Strickland, Geophys. Res.
 Lett., 35, L24103 (2008).
 [22] K. Schlegel, H. L uhr, J.P. St. Maurice, G. Crowley, and C. Hackert, Ann.
 Geophy., 23, 1659 (2005).
 [23] H.G. Demars and R.W. Schunk, J. Atmos. Solar-Terr. Phy., 69, 649 (2007).
 [24] Various Authors, Measurement Techniques in Space Plasmas: Particles, Geo-
 phys. Monogr. Ser., 102, edited by R.F. Pfa , J.E. Borovsky, and D.T. Young,
 AGU, Washington, D.C. (1998).
 [25] J.L. Wiza, Nucl. Inst. And Meth., 162, 587-601 (1979).
 [26] E.J. Gamboa, C.M. Huntington, E.C. Harding, and R.P. Drake, Rev. Sci. Inst.,
 81, 10E310 (2010).
 [27] K. Furuya and Y. Hatano, Int. J. of Mass Spectrom., 218, 237 (2002).
 [28] D.T. Young, Measurement Techniques in Space Plasmas: Particles, Geophys.
 Monogr. Ser., 102, 1 (1998).
 [29] J. Oberheide, P. Wilhelms, and M. Zimmer, Meas. Sci. Technol., 8, 351 (1997).
 [30] R.E. Ergun et al., Geophys. Res. Lett., 25, 2041 (1998).
 337
[31] W.K. Peterson et al., Geophys. Res. Lett, 25, 2081 (1998).
 [32] R. Lysak, Geophys. Res. Lett, 25, 2089 (1998).
 [33] H. L uhr, S. Maus, and M. Rother, J. Geophys. Res., 109, A01306 (2004).
 [34] H. L uhr, S. Maus, and M. Rother, Gephys. Res. Lett., 29, 1489 (2002).
 [35] C. Stolle, H. L uhr, M. Rother, and G. Balasis, J. Geophys. Res., 111, A02304
 (2006).
 [36] R. Pfa , C. Carlson, J. Watzin, D. Everett, and T. Gruner, Space Sci. Rev.,
 98, 1 (2001).
 [37] R.E. Ergun et al., Space Sci. Rev., 98, 67 (2001).
 [38] R.C. Elphic, J.D. Means, R.C. Snare, R.J. Strangeway, L. Kepko, and R.E.
 Ergun, Space Sci. Rev., 98, 151 (2001).
 [39] C.W. Carlson, J.P. McFadden, P. Turin, D.W. Curtis, and A. Magoncelli, Space
 Sci. Rev., 98, 33 (2001).
 [40] C. Reigber, H. L uhr, and P. Schwintzer, \Announcement of Opportunity for
 CHAMP", CH-GFZ-AO-001, GFZ Potsdam, Germany (2001).
 [41] S. Bruinsma, D. Tamagnan, and R. Biancale, Planet Space Sci., 52, 297 (2004).
 [42] T.E. Moore et al., Geophys. Res. Lett., 26, 2339 (1999).
 [43] R.J. Strangeway et al., J. Geophys. Res., 105, 21,129 (2000).
 [44] R.J. Strangeway, R.E. Ergun, Y.-J. Su, C.W. Carlson, and R.C. Elphic, J.
 Geophys. Res., 110, A03221 (2005).
 [45] K.J. Zahnle and D.C. Catling, "Our Planet?s Leaky Atmosphere," Scienti c
 American, May 2009.
 [46] R.D. Sharp, R.G. Johnson, and E.G. Shelley, J. Geophys. Res., 82, 3324 (1977).
 [47] D.J. Gorney, A. Clarke, D. Croley, J. Fennell, J. Luhmann, and P. Mizera, J.
 Geophys. Res., 86, 83 (1981).
 338
[48] C.R. Chappell, T.E. Moore, and J.H. Waite Jr., J. Geophys. Res., 92, 5896
 (1987).
 [49] M.-C. Fok, T.E. Moore, and M.R. Collier, J. Geophys. Res., 109, A01206
 (2004).
 [50] R.L. Lysak and M. Andr e, Phys. Chem. Earth (C), 26, 3 (2001).
 [51] K.A. Lynch et al., Ann. Geophys., 25, 1967 (2007).
 [52] M. Andre, J. Atmos. Terr. Phys., 59, 1687 (1997).
 [53] Y. Zheng, T.E. Moore, F.S. Mozer, C.T. Russell, and R.J. Strangeway, J.
 Geophys. Res., 110, A07210 (2005).
 [54] C.T. Russell, Cosmic Electrodynamics, 2, 184 (1971).
 [55] C.C. Finlay et al., Geophys. J. Int., 183, 1216 (2010).
 [56] Available at http://realterm.sourceforge.net
 [57] The Fast Auroral SnapshoT Explorer, http://sprgl.ssl.berkeley.edu/fast
 [58] CDF Home Page, http://cdf.gsfc.nasa.gov
 [59] The Information System and Data Center, http://isdc.gfx-potsdam.de
 [60] Numerical Python, http://numpy.scipy.org
 [61] Scienti c Tools for Python, http://www.scipy.org
 [62] The matplotlib Plotting Library for Python, http://matplotlib.sourceforge.net
 [63] Python-based Tools for the Space Science Community, http://spacepy.lanl.gov
 [64] C. F orste, P. Schwintzer, and C. Reigber, \The CHAMP Data Format", CH-
 GFZ-FD-001, GFZ Potsdam, Germany (2002).
 [65] R. K onig, P. Schwintzer, and C. Reigber, \The CHAMP Orbit Format
 CHORB", CH-GFZ-FD-002, GFZ Potsdam, Germany (2001).
 339
[66] P. Schwintzer, H. L uhr, C. Reigber, L. Grunwaldt, and C. F orste, \CHAMP
 Reference Systems, Transformations and Standards", CH-GFZ-RS-002, GFZ
 Potsdam, Germany (2002).
 340