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Observational Signatures of Nonlinear Interactions in the Solar Wind Observational Signatures of Nonlinear Interactions in the Solar Wind by Trevor Bowen A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Physics in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Stuart Bale, Chair Professor Jonathan Wurtele Professor Eliot Quataert Spring 2019 Copyright 2019 by Trevor Bowen Abstract Observational Signatures of Nonlinear Interactions in the Solar Wind by Trevor Bowen Doctor of Philosophy in Physics University of California, Berkeley Professor Stuart Bale, Chair Spacecraft observations from the interplanetary medium of our solar system reveal the presence of a magnetized super-sonic flow emanating from the sun, commonly known as the solar wind. Empiri- cally, in-situ measurements from spacecraft suggest that the solar wind is in a turbulent state frequently occurring fluid-like systems. Though theories of non-magnetized hydrodynamic turbulence have been successfully adapted to account for plasma dynamics relevant to the solar wind (e.g. strong magneti- zation, multi-particle composition, non-viscous dissipation, and weak collisionality), there is lacking consensus regarding the physical processes responsible for empirically observed phenomena: e.g. com- pressible fluctuations, intermittent coherent features, injection of energy at large scales, and particle heating. Interpreting in-situ spacecraft measurements is often complicated by limitations associated with single point me which most often consist of a single point (or at best a few points) located near Earth. At the largest physical scales, processes associated with solar wind generation and evolution consist of temporal variation over the 11 year solar cycle, with spatial gradients extending over the large scale heliosphere, ∼ 200 AU. At the smallest scales, heating and dissipation process can occur on electron kinetic scales corresponding to ∼ kHz frequencies and centimeter length scales in the inner heliosphere. Even in observing fluid-like magnetohydrodynamic (MHD) fluctuations of the solar wind, “easily” measurable by spacecraft at 1 AU, significant ambiguity exists in distinguishing effects associ- ated with plasma transport from the processes related to the generation (heating and acceleration) of the solar wind in the inner-heliosphere. The source of the solar wind is the corona, a hot magnetized upper-atmosphere of our sun with ambient temperatures ranging from ∼ 105-106 Kelvin: orders of magnitude larger than the solar pho- tospheric surface at 5800 Kelvin. Even the roughest estimation of the coronal energy budgets suggest that the magnetic field must be responsible for heating the corona to these temperatures. However, the specific processes which drive coronal heating, and subsequently accelerate the solar wind, are yet 1 unknown; though many models of coronal heating exist, little empirical evidence is currently available to distinguish between theories. The NASA Parker Solar Probe (PSP) mission, launched in August 2018, recently became the closest human-made object to orbit the sun. During its closest perihelion approach, PSP will reach an alti- tude of 9.8 solar radii (0.045 AU), well within the expected boundary between the solar wind corona, known as the Alfvén point. By measuring the local plasma environment, PSP will provide an empiri- cal understanding of the processes responsible for coronal heating and solar wind acceleration which cannot be observed using remote sensing techniques. In addition, through studying the turbulent en- vironment present in the inner heliosphere, PSP will inevitably make significant contribution to our understanding of magnetized turbulence and the role it plays in shaping astrophysical systems. This dissertation highlights the development of observational techniques and instrumentation used in studying nonlinear dynamic processes, e.g. turbulence and plasma instabilities, in astrophysical plas- mas. Part I consists of a discussion of incompressible magnetohydrodynamic turbulence in the solar wind and the observed coupling with compressible fluctuations. Chapter 1 contains an overview of the historical and mathematical development of MHD turbulence based on both empirical observations from spacecraft and theory of hydrodynamic turbulence. Chapter 2 contains original research on the effect of intermittency on the observational signatures of MHD turbulence. Chapter 3 discusses the the nature of compressible fluctuations in the solar wind based on the mathematical and observational techniques developed in Chapter 2. Chapter 4 describes an observational study which examines the existence of parametric mode coupling in the solar wind which could drive compressible fluctuations as well as initiate non-linear turbulent interactions in the heliosphere. Part II surveys the calibration and operation of the PSP/FIELDS magnetometer suite. Chapter 5 highlights the operation and calibration of the PSP/FIELDS DC fluxgate magnetometer (MAG). Chap- ter 6 consists of an overview of the PSP/FIELDS search coil magnetometer (SCM) and an in depth dis- cussion of instrument calibration through the framework of linear time invariant filter design. Chapter 7 describes a merged fluxgate and search coil data product for PSP created using optimal filter design techniques. 2 ACKNOWLEDGMENTS I exited “high-school #1” after a single year with an impressively miserable GPA and an algebra teacher convinced that I needed remedial course work. The experiences with teachers in a nontraditional high- school largely inspired me to pursue an education in science. Lisa Luhn ran a class which facilitated student internships with local scientists, providing my first experience with research: Professor Brian Hynek mentored me for two years and deserves immense credit for letting a crusty high-school student map out river valley systems and impact craters on floor-size printouts of the Martian surface. My experience with nontraditional education led me to liberal arts school. Professor Travis Norsen (who would regularly commute to campus in blizzard conditions to chat about quantum mechanics) was pivotal in pushing me to explore off-campus research opportunities. Professor Sara Salimbeni was key in helping me learn to communicate scientific ideas through various forms and to manage the goals of an open ended research project. I first worked with Dr. Katharine Reeves and Dr. Paola Testa as a summer intern, both are largely responsible for my continued enthusiasm in doing research. After finishing college, Kathy and Paola hired me to wrap up our project on solar flares. I was simultaneously applying to graduate programs, though it seemed like a reach, Kathy advised me to apply to Berkeley. Their efforts and kind mentorship are definitely what prepared me most for graduate school. I started at Berkeley jaded by course work and the concept of attending 100+ person early morning lectures. The friendships solidified during these first two years (Robert Kealhofer, Dr. Parker Fagrelius, Halleh Balch, Dr. Alison Saunders, Dr. Carolyn Kierans, Lex Kosieradzki, Taylor Burrows, Marcelo Caceres) provided support which kept me enrolled in graduate school long enough to see it through. The successful completion of this thesis is due to mentorship provided by Professor Stuart Bale, who has regularly provided intellectually stimulating problems and projects. Though absent from this the- sis, a significant portion of my graduate work was done with Professors Jonathan Wurtele and Dmitry Budker who brought me onto a project to study magnetic fields in urban areas, providing an oppor- tunity to hone technical skills with interdisciplinary relevance. I would also like to acknowledge Sam Badman and Dr. Alfred Mallet, who have coauthored work central to this thesis, as well as Professor Thierry Dudok de Wit and Dr. John Bonnell who are invaluable mentors that have helped me learn many fundamental aspects of signal processing. A lot of this work was made possible by everyone in the Silver-260 office (Dr. David Sundkvist, Dr. Marc Pulupa, Dr. Juan Carlos Martinez-Oliveros, Dr. Chadi Salem, Yuguang Tong, Juan Camilo Buitrago-Casas, et al.) who always assist with little questions and provide advice and friendly chatter. I am truly indebted to friends and family who have always supported these endeavors; there are countless people who have positively contributed to the work in this thesis and who I am dearly thank- ful for their presence in my life. i CONTENTS I TURBULENCE IN THE SOLAR WIND 1 1 INTRODUCTION TO TURBULENCE IN THE SOLAR WIND 2 1.1 Early Observations of Solar Wind Turbulence . 2 1.2 A Mathematical Introduction to Turbulence . 4 1.2.1 Turbulence in Hydrodynamics . 4 1.3 Energy (Power) Spectra . 7 1.4 Magnetohyrdrodynamic Turbulence . 10 1.5 Early Observations of Anisotropic Turbulence . 13 1.6 Critical Balance . 14 1.7 Dynamic Alignment & 3D Anisotropy Boldyrev . 16 1.8 Intermittency . 19 1.9 Compressible Turbulence and Scalar Fluctuations . 20 1.10 Observing Turbulence in the Solar Wind . 24 1.10.1 Single Point Measurements & Taylor Hypothesis . 25 1.10.2 Reduced Spectra . 27 1.10.3 Statistical Studies of Plasma Instabilities . 28 1.10.4 Kinetic and Dissipation Scale Turbulence . 31 1.10.5 Outer Scale Turbulence . 31 2 IMPACT OF RESIDUAL ENERGY ON SOLAR WIND TURBULENT SPECTRA 34 2.1 Introduction . 34 2.2 Data . 36 2.3 Spectral Fitting . 38 2.4 Results . 39 2.5 Discussion . 43 3 SPECTRAL AND INTERMITTENT SIGNATURES OF COMPRESSIVE FLUCTUATIONS
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