Plasma, one of the four fundamental states of matter, prevails the universe and accounts for 90\% of the known masses. Interaction between the solar wind, a space plasma with solar origin, and the terrestrial magnetic field shapes the space climate that is crucial for our modern society that heavily dependent on electricity, electronics and satellites. Waves ubiquitously grow, propagate, interact with other waves and plasmas, and eventually damps away in plasmas, significantly altering plasma dynamics and energy transport. Measurements of both plasma particles and electromagnetic fields allow probing wave-plasma interactions of interest.

Part one of the thesis presents a few new results relating to the electron heat flux in the solar wind. Electron heat flux is a poorly understood quantity in weakly collisional or collisionless astrophysical and space plasmas, but it is crucial to modeling large scale systems such as galaxy clusters and stellar winds. We present a statistical study of the electron heat flux in the solar wind and confirm that it is bounded from above by power laws of electron beta. We consider various collisionless processes that potentially reduce the heat flux. In particular, the whistler heat flux instability (WHFI) has long been considered to constrain heat flux in the high beta regime. We show for the first time local generation of whistler waves in the solar wind using high-cadence simultaneous particles and wave measurements onboard ARTEMIS spacecraft. We present the statistical properties of the whistler waves in the solar wind at 1 AU, with evidence supporting WHFIs generating the observed whistler waves. However, we argue that the wave amplitude is too small to effectively reduce the electron heat flux. Accompanied by the electron heat flux is measurable electron bulk drifts with respect to the solar wind protons, which significantly modify Landau resonance of kinetic Alfv\'en waves (KAWs). We consider the effects of potential KAW instabilities in the context of electron heat flux inhibition.

Part two of the thesis considers a type of electrostatic structure known as the electron phase space hole (EPSH). It is formed in the non-linear stage of plasma streaming instabilities and remains highly stable for long duration. We address for the first time 3D configuration of EPSHs by analyzing multi-spacecraft (using NASA MMS) passing of the same EPSH. The length scale perpendicular to the background magnetic field is directly measured with significant implications to electron motions inside EPSHs. In addition, statistical study of such multi-spacecraft observation reveals strong correlation among parameters of fast EPSHs.

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. Empirically, 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 magnetization, multi-particle composition, non-viscous dissipation, and weak collisionality), there is lacking consensus regarding the physical processes responsible for empirically observed phenomena: e.g. compressible 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 associated 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 10^5-10^6 Kelvin: orders of magnitude larger than the solar photospheric 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 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 altitude of 9.8 solar radii (0.045 AU), well within the expected boundary between the solar wind corona, known as the Alfven point. By measuring the local plasma environment, PSP will provide an empirical 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 environment 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 plasmas. Part 1 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 2 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). Chapter 6 consists of an overview of the PSP/FIELDS search coil magnetometer (SCM) and an in depth discussion 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.

The Sun’s atmosphere is a complex and dynamic magnetized plasma and extends all theway from its visible surface out into interplanetary space, carving out a bubble in the inter- stellar medium which is called the heliosphere. All interactions between the Sun and life on Earth are channelled through this medium. Of particular importance to making Sun-Earth connections are the regions called the corona and the inner heliosphere. These two regimes are strongly coupled together but their mutual boundary may be regarded as the location where the dynamic pressure of the outflowing solar wind overcomes the magnetic pressure of the Sun’s intrinsic field. By inner heliosphere, we focus on the portion of the Sun’s sphere of influence which extends out to 1 au and therefore is most relevant to the Earth and humanity.

Our most complete understanding of the corona and heliosphere comes from large scalephysical models which can fill in information about a plasma on a 3D grid. In 2018, Parker Solar Probe (PSP) was launched into an orbit taking it closer to the Sun than any human- made object in history. This has presented an opportunity to directly probe regions of the heliosphere which had hitherto could only be accessed with global modelling. In this body of work we use new data from PSP to improve our knowledge and understanding of this global structure and further derive novel constraints on plasma models of the corona and heliosphere.

Specifically, we first introduce a framework for evaluating models of the coronal magneticfield, which sets how the solar wind emerges and shapes the inner heliosphere. In addition to new PSP data which provides direct boundary conditions on the magnetic skeleton of the corona, we show how it is important to make use of pre-existing observational capabilities to constrain the sizes of coronal holes and the locations of high plasma density indicating the topology of the coronal streamer belt. We illustrate how models must be constrained at multiple boundaries to give an accurate representation and that focusing on individual specific metrics can lead to different conclusions about optimum model parameters.

Next, we use the full data set of the heliospheric magnetic field taken by Parker Solar Probein its first four years on orbit to directly measure the heliospheric magnetic field down to 0.13 au and compare directly to the large scale expectations of the Parker magnetic field. We present evidence that at 0.13 au the heliospheric magnetic field remains latitudinally isotropic, indicating the coronal field has already relaxed to this state within this radius. We measure the open magnetic flux and confirm it is conserved between 1 au and PSP’s closest approach to date. This conservation implies a deficit in open magnetic flux according to coronal models with typically accepted model parameters. We also compare the mean direction of the heliospheric magnetic field to the expectation of the Parker spiral model, finding very good agreement which is tending to improve with closing distance from the sun as the ratio of average field strength to random fluctuations increases.

Third, we present a study in which we determine Parker Solar Probe’s magnetic connectivityback to specific coronal sources for its first solar encounter. This exercise allows determi- nation of specific locations on the Sun which emit solar wind plasma later measured by PSP, and therefore contextualises its measurements. This application of combining coronal modelling and PSP data shows how making these connections is a vital building block for understanding other peculiar plasma physics observed as PSP as it has explored new re- gions of the inner heliosphere. Further, it allows disambiguation of spatial and temporal phenomena.

Finally, we present recent work using observations by Parker Solar Probe and other 1 auspacecraft to localise type III radio bursts, an impulsive solar ejection of electron beams, from emission at the solar surface out into the inner heliosphere. These events have the potential to act as passive tracers of coronal and heliospheric structure. We comment on the future prospects of using this localisation to constrain magnetic connectivity and density structure.

We close with a summary of these results and the outlook for further improvement of ourunderstanding of the coupled corona and inner heliosphere ans PSP continues to approach the Sun and as other advances in space based instrumentation are made, such as the gradual escape of the Solar Orbiter to higher latitudes.

The individual investigations, which are briefly introduced above, are united in highlightingseveral specific advances in our understanding of the Sun’s atmosphere facilitated by the ad- dition of Parker Solar Probe to humanity’s suite of heliospheric instrumentation. Specifically, we exemplify how multi-point, multi-spacecraft and multi-messenger observations at differ- ent heliographic locations are vital in making progress in constraining our physical models; using just one vantage point or one physical observable can lead to false conclusions about model optimisation. We also observe an underlying thread of the surprising utility of the very simplest model representations of the corona and heliosphere, for example a current- free corona and essentially hydrodynamic heliosphere can accurately predict the magnetic polarity structure, and even the velocity stream structure measured in situ by PSP. Lastly, we verify that as one would expect from sending an instrument to never-before explored regions of interplanetary space, new gaps in our understanding are identified. For example, confirming that coronal models do not open enough magnetic flux to the inner heliosphere, or showing at several points that while we make substantial progress exploring closer to the Sun, a lack of far-side and high latitude remote sensing (most critically of the photospheric magnetic field), remains a big limitation to accurately reproducing the physical structure of the heliosphere.

Radio waves at the local plasma frequency and its harmonic are generated upstream of collisionless shocks in foreshock regions which are magnetically connected to the shock. The radio waves are created in a multi-step process which involves the acceleration of electrons at the shock front, growth of electrostatic Langmuir waves driven by the accelerated electron beam, and conversion of the Langmuir waves into radio waves.

These radio waves can be used to remotely determine properties of the shock. For example, Type II solar radio burst observations yield information about the radial speed and angular extent of the coronal mass ejection-driven shock associated with the burst. However, in order to completely understand the generation of the radio waves and interpret the remote observations, in situ spacecraft measurements of the shock-accelerated electrons and Langmuir waves are necessary.

In this thesis, a brief introduction to the heliospheric environment is followed by a survey of the basic principles of collisionless shocks, a detailed discussion of the process of generating shock-accelerated electrons and the resulting plasma waves, and a description of the relevant instrumentation on board the Wind and STEREO spacecraft. Following this review material, several results based on in situ observations are presented:

(1) High cadence electron measurements made by Wind in the foreshock region of several IP shocks allow for a determination of the spatial scales of the source regions of Type II radio bursts. The sizes of the observed foreshock source regions are comparable to the size of the terrestrial bow shock.

(2) Langmuir waves upstream of IP shocks can be used as a diagnostic signature of foreshock electrons. Using a large database of shocks observed by Wind, different shock parameters are statistically tested for their effectiveness at accelerating electrons.

(3) Using a new type of electron detector on STEREO, the limits of the Fast Fermi theory for electron acceleration at suprathermal energies are examined. Preliminary results suggest that the mechanism may hold beyond the regime where the Larmor radius of electrons is much smaller than the scale sizes of the shock.

The prospects for future work in this area are discussed in the conclusion, and a description of an experimental antenna calibration procedure known as rheometry is included as an appendix.

Low-frequency $\nu < 10$ MHz astrophysical flux typically does not penetrate the Earth's ionosphere, so can only be precisely measured using space-based radio instruments. The restrictions on data volume and instrument size that this imposes have stimulated the development of specialized analysis techniques for radio measurements from spacecraft. One such technique is the decomposition of the spectra recorded by co-located electrically short antennas into the $l=0$ and $l=2$ spherical harmonic expansion coefficients of the measured brightness distribution.

I apply this decomposition to radio data from Parker Solar Probe (PSP) to analyze the diffuse galactic and extragalactic synchrotron background. The $\nu < 10$ MHz frequency regime notably features free-free absorption of this radiation by interstellar ionized hydrogen. Between $\nu = 10$ MHz and $\nu = 3$ MHz, the optical depth due to this plasma to a typical region in the galaxy increases from roughly zero to one. As a result, the brightness distribution on the sky at $\nu \lesssim 3$ MHz is determined as much by free-free absorption as by synchrotron emission. Measurements of the sky's $l=0$ and $l=2$ expansion coefficients from PSP provide new constraints on the agents of this radiation transfer, most significantly the free electrons in the galaxy.

The $l=2$ coefficients can also be used as a reference source for calibrating electrically short antennas. PSP data allowed this to be conducted in parallel with measurement of the coefficients. The calibration results will improve the accuracy of direction-finding analyses using PSP radio spectra. As typically implemented for spacecraft data, this technique can jointly determine the angular coordinates as well as the $I$ and $V$ Stokes parameters of point-source radiation, such as that from Jupiter or the Sun when these bodies are sufficiently distant.

Limited data telemetry also motivates close examination of the random statistical errors in spectral measurements and their correlations. Such an inquiry shows, for example, that these errors can sometimes impede direction-finding using two antennas, which in part prompted the calibration of additional antennas on PSP. Also, this calibration itself and the spherical harmonic coefficient results benefited from fitting procedures that compensated for the statistical errors.

Although basing radio instruments in space bypasses the ionosphere, ambient interplanetary plasma gives rise to novel sources of noise. Electrostatic plasma fluctuations produce so-called quasi-thermal noise, which presented the most severe impediment to the spherical harmonic analysis of PSP's measurements. Due to this noise's unique importance for space-based instruments, I start by approximating its spectral density in PSP's radio data.

Laser-plasma interactions have become a rapidly growing area of modern plasma physics and an important subfield of it is laser-plasma acceleration. Using high-intensity lasers, one can drive a plasma structure with electric-field gradients three orders of magnitude higher than the gradients found in traditional, radio-frequency accelerators. This promises to enable great technological advances in medicine, spectroscopy, and experimental particle physics, as well as to open up new avenues of studying matter under extreme conditions.

An important aspect of laser-plasma acceleration is how the transverse electromagnetic field of the laser affects and drives an accelerated particle via longitudinal waves in the plasma. To understand how the laser interacts with the plasma, it is necessary to understand that the transverse characteristics of the laser dictate its longitudinal propagation dynamics. The transverse radiation field of the laser pulse can be described in various ways and decomposed into bases of orthogonal modes. The presence of multiple higher-order modes, copropagating through the plasma, leads to mode beating. Likewise, these modes propagate at different velocities through the plasma and are susceptible to nonlinear interactions with the plasma to varying degrees.

The primary objective of this thesis is to understand how higher-order laser modes interact with the plasma and with one another. In this work, we discuss the detrimental consequences that mode beating may have on a laser-plasma accelerator and how higher-order modes can be filtered out using specially designed plasma structures. Also discussed is how higher-order mode content can be controlled and utilized to shape and control the wakefields. These ideas are extended to the concept of the plasma undulator as a plasma-based light source. Lastly, we discuss how nonlinear effects can excite higher-order mode content as path to understanding laser pulse break up into multiple filaments.

The Earth's ionosphere is a region of plasma embedded within and on top of the Earth's atmosphere. As the Sun-Earth interaction medium closest to Earth, the ionosphere has many important implications for humankind. The ionosphere affects radio wave propagation, GPS performance, and both space- and ground-based asset response to space weather, to name just a few technological impacts. From a scientific perspective, there are a plethora of interesting and open plasma physics questions that can be studied in such a planetary-scale plasma laboratory. For this reason we strive to understand the ionosphere's properties and characteristics. In this dissertation, we specifically study the large-scale electrodynamics in the northern, polar region of the ionosphere. We also present developments in electric and magnetic field-sensing instruments that are necessary to obtain more accurate, sensitive, and cost-effective measurements of the ionosphere.

We begin by discussing measurements from a sounding rocket, TRICE-2, that observed multi-scale, large amplitude electric (E) and magnetic (B) field structures in the polar ionosphere. These structures indicated fast plasma convection speeds. At high latitudes, it is well established that ionospheric plasma convects in a two cell pattern, transporting plasma throughout the magnetosphere and informing on forcing from the Sun at the magnetopause. TRICE-2 made some of the first observations of very fast convection in the polar region of the ionosphere. Fast flows are associated with reconnection in the northern hemisphere of the magnetopause and lead to GPS scintillation. Meso- and small-scale E and B field structures are also expected to correlate and give a measure of the ionospheric conductance. Ionospheric conductance is crucial to studying how currents close in the ionosphere and how the magnetosphere is coupled to the ionosphere. TRICE-2 found many structures where the fields did not correlate, indicating that more careful treatment of in-situ calculations of conductance are required.

Next, we discuss an interesting and rarely studied electric probe phenomenon called sheath rectification. In this process, large amplitude waves of certain frequencies cause baseline shifts and very low frequency signatures that can be mistaken for geophysical processes. Identifying and characterizing these events is important in understanding how to prevent them from occurring and affecting data interpretation. TRICE-2 also observed hundreds of these events during its 20 minute flight. We discuss the characteristic signatures and how they were produced on TRICE-2 as well as potential design implementations that could minimize this in the future. Although there is no way to completely avoid rectification, we can design the instrument such that this occurs for higher frequency incident waves, whose amplitudes (and consequently rectification signatures) are significantly smaller.

Finally, we present a novel, space-based anisotropic magneto-resistive (AMR) magnetometer, named the MRM, utilizing small and cheap commercial off-the-shelf components to provide sensitive and scientifically useful B field measurements. Currently, the magnetometry field utilizes fluxgate and search coil magnetometers, which are comparatively larger in volume and cost more to manufacture, operate, and develop. Although those technologies are more sensitive, the AMR magnetometer is useful for measurements of larger amplitude phenomena and structures. For example the MRM would have been sensitive enough to detect the magnetic field structures observed by TRICE-2. Development culminated in two space flights, one on the sounding rocket, VIPER, and another on the CURIE cubesat. The VIPER flight proved the concept of the magnetometer but revealed some electrical engineering design flaws. CURIE has yet to receive radio communications and, consequently, has still not provided any MRM data. However, we expect careful design changes to lead to a viable space-flight rated magnetometer. As the space sciences field moves towards constellation and multi-point measurements of the magnetosphere, a small, cheap magnetometer like the MRM will prove useful.

We end with a summary of our results and potential future research. In presenting novel instrument developments and data analysis techniques we have furthered our knowledge of the near Earth ionosphere environment. Such analysis is important in understanding the Earth's connection to the interplanetary medium and its response to plasma events originating from the Sun. The knowledge obtained about these instruments is crucial to supporting data interpretation of future plasma missions such as TRACERS, which is scheduled to launch in March, 2025, and creating ever cheaper, smaller, and more sensitive instruments. Lastly, as all of the data utilized here comes from sounding rocket missions, this dissertation highlights that important science can be performed using quick and cheap missions. Sounding rockets provide an excellent platform to test new technologies and study rare or intermittent phenomena. Furthermore, their timelines are ideal for training future generations of scientists.

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