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Increasingly Parallel Pressure Anisotropic Ballooning Instability: a New Mechanism for Magnetospheric Substorm Onset

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Increasingly Parallel Pressure Anisotropic Ballooning Instability: a New Mechanism for Magnetospheric Substorm Onset Increasingly Parallel Pressure Anisotropic Ballooning Instability: A New Mechanism for Magnetospheric Substorm Onset by Luke Oberhagemann A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science Department of Physics University of Alberta © Luke Oberhagemann, 2019 Abstract Geomagnetic substorms are a process through which energy stored in Earth’s magnetosphere is suddenly and violently released. On the ground, this process is largely observed as a vibrant and dancing display in the aurorae and is well documented, while the sequence of events that occurs in the magnetosphere is less understood and is the subject of ongoing debate. The work presented here offers a novel perspective on this sequence of events, focusing on ballooning instabilities, a type of plasma instability in which a weak portion of a magnetic flux tube bulges outward. Ballooning instabilities have been linked to ground-based auroral observations at the time the main phase of a substorm begins, known as onset, through observations of auroral beads, a periodic brightness feature that exists on the most equatorward auroral arc immediately prior to onset for the vast majority of substorms. First, a numerical model of ballooning instabilities in magnetospheric conditions is applied to determine under what circumstances these instabilities may form. The main parameters that impact the formation of ballooning instabilities in this model are the plasma 훽, which is a ratio of the thermal pressure to the magnetic pressure, the pressure gradient, and the pressure anisotropy. The pressure anisotropy is a measure of how different the pressure in the direction parallel to a magnetic field line is from the pressure perpendicular to that field line, with the term parallel anisotropy denoting larger parallel than perpendicular pressure. It is found that, for constant values of the other parameters, an increase in plasma 훽 and an increase in the pressure gradient create conditions that are more ballooning unstable. Significantly, it is also found that a change in the pressure anisotropy towards a parallel anisotropic configuration, ii without the parallel pressure necessarily exceeding the perpendicular pressure in absolute terms, is destabilising. Based on these findings, a second numerical model is used to examine the evolution of particle distributions as the geomagnetic tail stretches prior to substorm onset. In particular, the evolution of particles that originate in less stretched, earlier tail configurations and periodically drift around Earth, completing a full orbit to return to the tail in a more stretched configuration immediately prior to substorm onset is examined. It is found that particles follow drift orbits that depend on their pitch angle, the angle between their velocity vector and the local magnetic field, in a well-understood process called drift shell splitting. In the context examined here, drift shell splitting causes a mixing of particles from regions with varying pressures in a manner that leads to increasingly parallel pressure anisotropy, i.e., a more ballooning unstable distribution. In addition, the transport of particles from a less stretched early tail configuration to more stretched, immediate pre-onset field lines causes a decrease in particle energy that is stronger in the direction perpendicular to the magnetic field, further increasing parallel pressure anisotropy. Therefore, the results presented here combine to form a picture of the time sequence of events leading to substorm onset in which particles drift from less stretched to more stretched tail configurations, resulting in an increasingly parallel pressure anisotropy and, consequently, the triggering of a ballooning instability. The high 훽 and high pressure gradient requirements for triggering ballooning instability are met in the same radially localized equatorial region in Earth’s magnetotail that is found to be most conducive to causing increasingly parallel pressure anisotropy for drifting particles. The two models used, therefore, self-consistently predict a region for ballooning instability that agrees with existing predictions. In addition, the prediction that increasingly parallel pressure anisotropies should precede substorm onset and be concurrent iii with periods of tail stretching show very good agreement with existing in-situ satellite observations immediately prior to onset. Therefore, the work presented here suggests a self- consistent and observationally testable novel mechanism for substorm onset. iv Preface The research presented here was completed by the author, with chapters 4 and 6 containing manuscripts completed in collaboration with Ian Mann and prepared for submission to Geophysical Research Letters and Journal of Geophysical Research respectively. Chapter 4 describes the numerical examination of ballooning instability thresholds in the magnetosphere. I was responsible for writing the code for the calculation of these thresholds based on the Chan et al. (1994) model, conducting primary analysis of the results, and manuscript composition. Chapter 6 describes the numerical tracing of particles through a model magnetic field. I was responsible for writing code based on the Kabin et al. (2011) model, conducting primary analysis of the results, and manuscript composition. v Acknowledgements I would like to thank my supervisor Ian Mann for his support and guidance throughout the completion of this work. I would also like to thank my friends and family for their continued support. This work was supported by the NSERC CREATE grant for the International Space Masters (ISM) program. vi Table of Contents Abstract ................................................................................................................................ ii Preface .................................................................................................................................. v Acknowledgements .............................................................................................................. vi Chapter 1: Introduction.......................................................................................................... 1 Chapter 2: Background: The Solar-Terrestrial Environment .................................................... 3 2.1 The Solar Wind .........................................................................................................................3 2.2 Magnetic Tension and Pressure ................................................................................................5 2.3 Earth’s Magnetosphere ............................................................................................................7 2.4 Single Particle Motion ..............................................................................................................9 2.5 Magnetohydrodynamic waves ................................................................................................ 13 2.6 Geomagnetic Storms .............................................................................................................. 14 2.7 Substorms .............................................................................................................................. 15 Chapter 3: Review of Plasma Instabilities ............................................................................. 19 3.1 General Overview of Instabilities ............................................................................................ 19 3.1.1 Anisotropic Plasma Equilibria .................................................................................................................... 20 3.1.2 MHD Instabilities ....................................................................................................................................... 25 3.2 Numerical Approach ............................................................................................................... 30 3.2.1 Selection of a Root Finding Algorithm....................................................................................................... 31 3.2.2 Code Used for Solving for the Eigenvalue ................................................................................................. 33 3.2.3 Calculations for Stable Eigenmodes .......................................................................................................... 34 3.2.4 Calculations of the Ballooning instability thresholds ................................................................................ 36 Chapter 4: Paper Examining Ballooning Instability Thresholds Prepared for Submission ....... 38 Chapter 5: Review of Particle Tracing ................................................................................... 58 5.1 Tracing Particles Through a Model Magnetic Field ................................................................... 58 5.1.1 Particles Moving in a Stationary Magnetic Field ....................................................................................... 58 5.1.2 Particles Moving in a Changing Magnetic Field ......................................................................................... 59 5.1.3 The Quasi-Stationary Approach ................................................................................................................ 59 5.2 Numerical Particle Tracing ...................................................................................................... 60 5.2.1 Code Structure .........................................................................................................................................
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