In the aerospace industry, gas discharges have gained importance with the exploration of their performance and capabilities for flow control and combustion. Tunable properties of plasma make gas discharges efficient tools for various purposes. Since the scales of plasma and the available technology limit the knowledge gained from experimental studies, computational studies are essential to understand the results of experimental studies. The temporal and spatial scales of plasma also restrict the numerical studies. It is a necessity to use an idealized model, in which enough physics is captured, while the computational costs are acceptable.<br><br>In this work, numerical simulations of different low-pressure gas discharges are presented with a detailed analysis of the numerical approach. A one moment model is employed for DC glow discharges and nanosecond-pulse discharges. The cheap-est method regarding the modeling and simulation costs is chosen by checking the requirements of the fundamental processes of gas discharges. The verification of one-moment 1-D glow discharges with constant electron temperature variation is achieved by comparing other computational results.<br><br>The one moment model for pulse discharge simulation aims to capture the information from the experimental data for low-pressure argon discharges. Since the constant temperature assumption is crude, the local field approximation is investigated to obtain the data for electron temperature. It was observed that experimental data and computational data do not match because of the stagnant decay of electron number densities and temperatures. At the suggestion of the experimental group, water vapor was added as an impurity to the plasma chemistry. Although there was an improvement with the addition of water vapor, the results were still not in good agreement with experiment.<br><br>The applicability of the local field approximation was investigated, and non-local effects were included in the context of an averaged energy equation. A 0-D electron temperature equation was employed with the collision frequencies obtained from the local field approximation. It was observed that the shape of the decay profiles matched with the experimental data. The number densities; however, are less almost an order of magnitude.<br><br>As a final step, the two-moment model, one-moment model plus thermal electron energy equation, was solved to involve non-local effects. The two-moment model allows capturing of non-local effects and improves agreement with the experimental data. Overall, it was observed that non-local regions dominate low-pressure pulsed discharges. The local field approximation is not adequate to solve these types of discharges.

<div>Developments in modern electronics drive device design to smaller scale and higher electric fields and currents. Device size reductions to microscale and smaller have invalidated the assumption of avalanche formation for the traditional Paschen’s law for predicting gas breakdown. Under these conditions, the stronger electric fields induce field emission driven microscale gas breakdown; however, these theories often rely upon semi-empirical models to account for surface effects and the dependence of gas ionization on electric field, making them difficult to use for predicting device behavior a priori.</div><div>This dissertation hypothesizes that one may predict a priori how to tune emission physics and breakdown conditions for various electrode conditions (sharpness and surface roughness), gap size, and pressure. Specifically, it focuses on experiments to demonstrate the implications of surface roughness and emitter shape on gas breakdown for microscale and nanoscale devices at atmospheric pressure and simulations to extend traditional semi-empirical representations of the ionization coefficient to the relevant electric fields for these operating conditions.</div><div>First, this dissertation reports the effect of multiple discharges for 1 μm, 5 μm, and 10 μm gaps at atmospheric pressure. Multiple breakdown events create circular craters to 40 μm deep with crater depth more pronounced for smaller gap sizes and greater cathode surface roughness. Theoretical models of microscale breakdown using this modified effective gap distance agree well with the experimental results.</div><div>We next investigated the implications of gap distance and protrusion sharpness for nanoscale devices made of gold and titanium layered onto silicon wafers electrically isolated with SiO2 for gas breakdown and electron emission at atmospheric pressure. At lower voltages, the emitted current followed the Fowler-Nordheim (FN) law for field emission (FE). For either a 28 nm or 450 nm gap, gas breakdown occurred directly from FE, as observed for microscale gaps. For a 125 nm gap, emission current begins to transition toward the Mott-Gurney law for space-charge limited emission (SCLE) with collisions prior to undergoing breakdown. Thus, depending upon the conditions, gas breakdown may directly transition from either SCLE or FE for submicroscale gaps.</div><div>Applying microscale gas breakdown theories to predict this experimental behavior requires appropriately accounting for all physical parameters in the model. One critical parameter in these theories is the ionization coefficient, which has been determined semi-empirically with fitting parameters tabulated in the literature. Because these models fail at the strong electric fields relevant to the experiments reported above, we performed particle-in-cell simulations to calculate the ionization coefficient for argon and helium at various gap distances, pressures, and applied voltages to derive more comprehensive semi-empirical relationships to incorporate into breakdown theories.</div><div>In summary, this dissertation provides the first comprehensive assessment of the implications of surface roughness on microscale gas breakdown, the transition in gas breakdown and electron emission mechanisms at nanoscale, and the extension of semi-empirical laws for ionization coefficient. These results will be valuable in developing theories to predict electron emission and gas breakdown conditions for guiding nanoscale device design.</div>

<p>Multiple industry applications, including combustion, flow control, and medicine, have leveraged nanosecond pulsed plasma (NPP) discharges to create plasma generated reactive species (PGRS). The PGRS are essential to induce plasma-assisted mechanisms, but the rate of generation and permanence of these species remains complex. Many of the mechanisms surrounding plasma discharge have been discovered through experiments, but a consistent challenge of time scales limits the plasma measurements. Thus, a well-constructed model with experimental research will help elucidate complex plasma physics. The motivation of this work is to construct a feasible physical model within the additional numerical times scale limitations and computational resources. This thesis summarizes the development of a one-moment fluid model for NPP discharges, which are applied due to their efficacy in generating ionized and excited species from vacuum to atmospheric pressure. </p><p>From a pulsed power perspective, the influence of pulse parameters, such as electric field intensity, pulse shape and repetition rate, are critical; however, the effects of these parameters on PGRS remain incompletely characterized. Here, we assess the influence of pulse conditions on the electric field and PGRS computationally by coupling a quasi-one-dimensional model for a parallel plate geometry, with a Boltzmann solver (BOLSIG+) used to improve plasma species characterization. We first consider a low-pressure gas discharge (3 Torr) using a five-species model for argon. <a>We then extend to a 23 species model with a reduced set of reactions for air chemistry remaining at low pressure.</a> The foundations of a single NPP is first discussed to build upon the analysis of repeating pulses. Because many applications use multiple electric pulses (EPs) the need to examine EP parameters is necessary to optimize ionization and PGRS formation. </p><p>The major goal of this study is to understand how the delivered EP parameters scale with the generated species in the plasma. Beginning with a similar scaling study done by Paschen we examine the effects of scaling pressure and gap length when the product remains constant for the two models. This then leads to our study on the relationship of pulsed power for different voltages and pulse widths of EPs. By fixing the energy delivered to the gap for a single pulse we determine that the electron and ion number densities both increased with decreasing pulse duration; however, the rate of this increase of number densities appeared to reach a limit for 3 ns. These results suggest the feasibly of achieving comparable outputs using less expensive pulse generators with higher pulse duration and lower peak voltage. Lastly, we study these outcomes when increasing the number of pulses and discuss the effects of pulse repetition and the electron temperature.</p><p>Future work will extend this parametric study to different geometries (i.e. pin-to-plate, and pin-to pin) and ultimately incorporate this model into a high-fidelity computational fluid dynamics (CFD) model that may be compared to spectroscopic results under quiescent and flowing conditions will be discussed.<br></p>

<p> In the past two decades, great interest in weakly ionized plasmas sustained by high voltage nanosecond pulsed plasmas at high repetition rates has emerged. For such plasmas, the electron number density does not significantly decay between pulses, unlike the electron temperature. Such conditions are favorable to reconfigurable plasma antennas where the low electron temperature may enable the reduction of the Johnson–Nyquist thermal noise if an antenna is operated in the plasma afterglow. Moreover, it may be possible to sustain such conditions with RF pulses. Doing so could enable a plasma antenna that transmits the driving frequency when the pulse is applied and receives other frequencies with low thermal noise between pulses.</p> <p>To study nanosecond pulsed plasmas, experiments were performed in a parallel-plate electrode configuration in argon and nitrogen gas at a pressure of several Torr and repetition frequencies of 30-75 kHz. To measure the time-resolved electron number density in the afterglow of each pulse, a custom 58.1 GHz homodyne microwave interferometer was constructed. The voltage and current measurements were made using a back current shunt (BCS). Initial analysis of the measured electron density in both plasmas indicated that the electron thermalization was much faster than the electron decay. In the nitrogen plasma, dissociative recombination with cluster ions was the dominant electron loss mechanism. However, the dissociative recombination rates of the electrons in the argon plasma suggested the presence of molecular impurities, such as water vapor. Therefore, to better understand the recombination mechanisms in argon plasma with trace amounts (0.1% or less by volume) of water vapor under the experimental conditions, a 0-D kinetic model was developed and fit to the experimental data. The influence of trace amounts of water on the electron temperature and density decay was studied by solving electron energy and continuity equations. It was found that in pure argon, Ar⁺ ions dominate while the electrons are very slow to thermalize and recombine. Including trace amounts of water impurities drastically reduces the time for electrons to thermalize and increases their rate of recombination. </p> <p>In addition to large quasi-steady electron number densities and low electron temperature in the plasma afterglow, plasmas sustained by nanosecond pulses use a lower power budget than those sustained by RF or DC supplies. The efficiency of the power budget can be characterized by measuring the ionization cost per electron, defined as the ratio of the energy deposited in a pulse to the total number of electrons created. This was experimentally determined in air and argon plasmas at 2-10 Torr sustained by 1-7 kV nanosecond pulses at repetition frequencies of 0.1-30 kHz. The number of electrons were determined from the measured electron density through microwave interferometry and assuming a plasma volume equivalent to the volume between electrodes. The energy deposited was calculated from voltage and current measurements using both a BCS as well as high frequency resistive voltage divider and fast current transformer (FCT). It was found that the ionization cost in all conditions was within a factor of three of Stoletov’s point (the theoretical minimum ionization cost) and two orders of magnitude less than RF plasma.</p><p> </p><p>Having shown that it is possible to generate high electron density, low electron temperature plasmas with nanosecond pulses, it was necessary to now create a plasma antenna prototype. Initially, commercial fluorescent light bulbs were used and ignited using surface wave excitation at various RF frequencies and powers. The S₁₁ of the antenna response was measured by a VNA through a novel coupling circuit, while the deposited power was measured using a bi-directional coupler. Next, a custom plasma antenna was created in which the pressure and gas composition could be varied. In addition to the S₁₁ and deposited power, the antenna gain, and the electron number density were also measured for a pure argon plasma antenna at pressures of 0.3-1 Torr. Varying the applied power shifts the antenna resonance frequency while increasing the excitation frequency caused an increase in measured electron density for the same deposited power. Initial tests using direct electrode excitation of a twin-tube integrated compact fluorescent light bulb with nanosecond pulses have successfully been achieved. Future efforts include designing the proper circuitry to time-gate out the large pulse voltage to facilitate safe antenna measurements in the plasma afterglow.<br></p>

<p>Constructive elastic microwave scattering, or, historically, coherent microwave scattering (CMS), refers to the inference of small plasma object characteristics via in-phase electromagnetic scattering – and has become a valuable technique in applications ranging from photoionization and electron-loss rate measurements to trace species detection, gaseous mixture and reaction characterization, molecular spectroscopy, and standoff measurement of local vector magnetic fields in gases through magnetically-induced depolarization. Notable advantages of the technique include a high sensitivity, good temporal resolution, low shot noise, non-intrusive probing, species-selectivity when coupled with resonance-enhanced multiphoton ionization (REMPI), single-shot acquisition, and the capability of time gating due to continuous scanning.</p> <p>Originally, the diagnostic was used for the measurement of electron total populations and number densities in collisional, weakly-ionized, and unmagnetized small plasma objects – so called collisional scattering. However, despite increased interest in recent years, the technique’s applicability to collisionless plasmas has remained relatively unexplored. This dissertation intends to expand upon the theoretical, mathematical, and experimental basis for CMS and demonstrate the constructive Thomson & Rayleigh scattering regimes for the first time. Furthermore, this work seeks to explore other novel and relevant capabilities of CMS including electron momentum-transfer collision frequency measurements via scattered phase information and spatially-resolved electron number characterizations of elongated plasma filament structures.</p> <p>This dissertation additionally leverages the technique to diagnose microplasmas and situations of particular interest. Primarily, photoionization (PI) – including UV resonance-enhanced multiphoton ionization, non-resonant visible PI, and mid-IR tunneling ionization in gaseous media. Such processes bear importance to studies on nonequilibrium plasmas, soft ionization in mass spectrometry, the development of compact particle accelerators, X-ray and deep UV radiation sources, laser-assisted combustion, laser-induced breakdown spectroscopy, species detection, mixture characterization and spectroscopy, studies on nonlinear beam propagation (filamentation, self-trapping and pulse splitting, dispersion, modulation instabilities), and so on. Finally, the application of CMS to ion thrusters is demonstrated.</p>

<p dir="ltr">In recent years, nanosecond repetitively pulsed (NRP) plasma discharges have garnered significant interest due to their rapid generation of reactive excited-state species, reactive radicals, and localized heat release within nanosecond (ns) timescale. To effectively harness these plasmas for altering system-level thermal and chemical behavior, a thorough understanding of their governing physics is crucial. This knowledge enables the development of predictive plasma kinetic models for tailoring NRP plasmas to specific applications. However, achieving this requires high-fidelity experimental data to validate models and deepen our understanding of fundamental plasma physics. Advancing experimental spectroscopy and laser diagnostics methods is essential for probing such temporally highly dynamic and optically complex nonequilibrium environments. This includes developing novel <i>test platforms</i>, conducting <i>fundamental research</i> to address existing knowledge gaps, and constructing custom <i>ultrafast laser architectures</i> for probing plasma properties. </p><p dir="ltr">The pioneering development of Streak-based <i>test platform</i> in the diagnostics field of nanosecond pulsed plasmas and its successful application towards inferring the underlying ultrafast spatio-temporal evolution of nanosecond pulsed plasma discharges with an unprecedented time-resolution as short as ~25 ps is presented for the first time. Spectrally filtered, 1D line-imaging of nanosecond pulsed plasma discharges in a single-shot, jitter-free, continuously sweeping manner is obtained, and differences in discharge dynamics of air and N2 plasma environments are studied. Successive <i>test platform</i> advancement includes spectrally resolved Streak-spectroscopy measurements of thermal regime-transition evolution from early-nonequilibrium to local-thermal-equilibrium (LTE) to attain time-resolved quantitative insights into N2(C) state rotational/vibrational nonequilibrium temperatures, electron temperature/density, and spectral lifetime dynamics. </p><p dir="ltr">Ultrafast laser-based progression includes detailed <i>fundamental</i> investigation of higher-order optical nonlinearity perturbations of fs-EFISH by considering of – self-phase modulation induced spectral characteristic of fs-EFISH signal, calibration mapping during-below-and-beyond optical breakdown regime, optical Kerr effect consequences, impact of femtosecond (fs) laser seeding on the noninvasiveness of fs-EFISH, and spectral emission characteristics of fs laser filaments. To infer N2(X) state nonequilibrium of NRP pulsed plasmas, two hybrid fs/ps ro-vibrational coherent anti-Stokes Raman scattering (CARS) <i>ultrafast laser architectures</i> are developed. First architecture, single-laser-solution, reduces system’s energy budget by ~3 mJ/pulse for generating narrowband (~21 ps), high-energy (~420 μJ/pulse), 532 nm probe pulses through incorporation of custom built visible fs optical parametric amplifier (OPA) coupled with an Nd:YAG power amplifier module. The second architecture, two-laser-solution, improves system’s robustness through the development of a 1 kHz, 532 nm, high-energy (~600 μJ/pulse), low-jitter (<1 ps), narrowband (~27 ps), master-oscillator-power-amplification (MOPA) based picosecond probe pulse laser time-synchronized with fs master-oscillator. Single-shot, hybrid fs/ps narrowband ro-vibrational CARS demonstration in a combusting flame up to temperatures of ~2400 K is demonstrated. Experimental ro-vibrational CARS investigation includes polarization based nonresonant background suppression and demonstration of preferential Raman coherence excitation shift, a temperature sensitivity enhancing strategy for vibrationally hot mediums like nanosecond pulsed plasmas. Lastly, an ultrafast pulse-friendly optically accessible vacuum cell is designed and fabricated for controlled experiments of NRP fs/ps CARS. Special care is taken to prevent self-focusing and spectral-temporal chirp of fs CARS beams while maintaining Gaussian focusing beam caustic.</p>