The near acoustic field of a subscale ducted fan was experimentally measured for the purposeof understanding the physics of sound generation and refining low-order models for aft-emitted tonal fan noise. To properly resolve the detailed features of the pressure field, measurements were obtained using a phased microphone array comprising of fixed and scanning sensors. The traversing of a sensor through a spatially-varying acoustic field introduces signal non-stationarity which must be addressed by dividing the complete signal into quasistationary blocks and applying a frequency-dependent window during spectral estimation. The harmonic content of the pressure along the scan line was obtained from the signals of the axially scanning sensors using the Vold-Kalman (VK) filter and partial fields decomposition (PFD). Accurate construction of the axial pressure distribution from the microphone measurements required advanced interpolation and filtering techniques based on the the decomposition of the pressure into its unwrapped phase and amplitude. The resulting axial pressure field has sufficient spatial resolution to perform space-time correlations and calculate the convective Mach number distribution. The azimuthal distribution of the tonal pressure field was obtained from the fixed sensors using the VK filter and can be combined with the axial pressure distribution to generate a cylindrical radiation surface. The radiation surface can then be implemented into propagation and scattering tools, such as the boundary element method (BEM), to efficiently predict acoustic emission in isolated and installed configurations. The near-field measurements are compared to the predictions of a model for aft tonal emission where the source features are partially informed by the internal duct acoustics. Reasonable agreement is found in the axial pressure distributions and space-time correlations. The near-field measurements can provide guidance for refinement of the model.

In low-dimensional topology one often decomposes a space into pieces that can be individually understood then put back together, yielding a combinatorial description, and such descriptions can be used for diagrammatic reasoning, computations of algebraic invariants, constructions of new objects, and so on. A powerful tool for this is singularity theory, where a classification of the types of singularities that generically might be present (for example, Morse critical points) leads to systematic approaches to decompositions, and in the ideal case the classification reduces to analyzing singularities of polynomial functions. We develop singularity theory relevant to "n-categorical" decompositions of smooth manifolds, in which pieces each have a recursive decomposition of their boundaries. In particular, we study smooth functions from manifolds to flag-foliated R^n, which serves as a model for the composition laws of an n-category. We use a refinement of the jet transversality techniques for the Thom--Boardman singularity types to define dense sets of functions that are suitably generic with respect to the foliations. We show how to compute codimensions of the submanifolds that correspond to a singularity type. For a few situations, for instance surfaces with embedded curves, we carry out a classification of the germs that appear in this dense set up to structure-preserving diffeomorphism. To this end, we prove stability results that aid in proving equivalence of germs and in finding polynomial representatives.

We explain how to use this classification of singularities to give a presentation of the symmetric monoidal 2-category of curves with embedded curves. As an application, we give a way to compute the Krushkal polynomial, which is a combinatorial invariant of graphs in surfaces, using an extended TQFT on the symmetric monoidal 2-category of surfaces that are decomposed into black and white regions.

There is interest in using short-pulse x-rays that are small in source size, broad in energy spectrum, and high in photon number to probe and visualize the evolution of hot, dense material for both research and industrial applications. One method to produce such x-rays is to collide an energetic electron beam with a high-Z material, which will then emit bremsstrahlung radiation with many of the desired source characteristics. In this dissertation we study the physical processes of generating energetic electrons from laser–plasma interactions in both underdense and overdense plasmas.

These laser–plasma interactions are nonlinear and kinetic in nature. Therefore, the particle-in-cell (PIC) algorithm is often the tool of choice for the simulations discussed within this dissertation, with length and time scales on the order of a millimeter and picosecond, respectively. Such simulations require the use of massively parallel computers. However, these simulations often suffer from having a large concentration of particles processed by relatively few computing elements, leading to decreases in performance due to a computational load imbalance. We present a dynamic load balancing technique for the PIC algorithm that effectively balances computational load across distributed-memory processes, in addition using a hybrid shared-memory scheme to increase scalability with shared-memory thread number by an order of magnitude and boost overall performance by a factor of two. Another useful PIC algorithm relevant to this work invokes a cylindrical geometry and azimuthal mode decomposition to yield proper three-dimensional geometric effects at the computational cost of a two-dimensional simulation. We also discuss improvements to this algorithm, where modifications to the particle initialization and field solver at the cylindrical axis eliminate spurious electromagnetic fields at the axis that have long been observed for this method.

The second part of this dissertation explores the mechanism of direct laser acceleration (DLA) in laser-based plasma acceleration. This process occurs when the channel-guided laser fields overlap electrons either in the plasma wave wake or within an ion channel, and the frequency of the electron transverse motion matches the Doppler-shifted laser frequency. We first utilize the cylindrical mode decomposition to more accurately account for the energy gain from the DLA process compared to traditional methods, then show that laser wakefield accelerators (LWFAs) in both the self-modulated (SM-LWFA) and bubble regimes exhibit comparable contributions in energy from the wakefields and DLA process for the most energetic electrons. A customized finite-difference Maxwell field solver is then presented that corrects the dispersion relation of light in vacuum and removes a time-discretization error in the Lorentz force compared to the standard PIC algorithm. This solver is especially valuable when investigating DLA, and simulations using the customized solver demonstrate better agreement with experiment and with numerically integrated equations of motion. Single-particle motion is analyzed to study resonant motion in the DLA process, where electrons are observed to gain significant energy from laser fields but do not readily transition between different orders of resonance to gain further energy. We also simulate the motion of an electron probe beam propagating across an LWFA perpendicular to the laser propagation direction, which is timed with the laser pulse and measured far from the plasma to image the dynamics of the plasma wave wake. Although some qualitative agreement is observed between simulation and experiment, further investigation is needed to discern wakefield properties from the radiograph image alone.

In the last part of this dissertation, we present simulations of laser–solid interactions to investigate the dynamics of energetic electron generation in the density upramp before an overdense plasma. These electrons propagate through the target and are then collided with a high-Z material to emit bremsstrahlung radiation. We first detail the requisite simulation techniques to correctly model this process, namely the splitting of energetic macro-particles to reduce enhanced wakefields, an extended particle absorber to prevent reflux at the boundary and a large transverse domain size to resolve long-wavelength magnetic field modes in the low- density plasma. A series of simulations are then carried out with varied laser amplitude and duration at constant energy to determine the laser configuration that yields the largest dose of few-MeV x-rays. We find that the high-amplitude laser pulses generate higher-temperature electron spectra, which in turn produce more x-rays at the desired energy. In addition, the shortest pulses generate many energetic electrons before the formation of self-generated magnetic fields, resulting in more directional beams of electrons and x-rays.