Acoustical-based imaging systems have found merit in determining the behavior of vibrating structures. This thesis focuses on the continued development of the nearfield acoustic holography (NAH) approach. Conventional NAH consists of first measuring the pressure field on a two-dimensional conformal surface and then propagating this data back to the vibrating structure to obtain information about the source, such as the normal velocity distribution. Recent work has been done which incorporates particle velocity information into the traditional NAH measurements to reduce the number of measurements required. This advancement has made NAH a more affordable tool for acoustical imaging and sound field characterization. It is proposed that the inclusion of velocity information into traditional NAH can further increase its usefulness. By propagating the velocity and pressure values independently and recombining them on the reconstruction surface, the pressure field and energy density fields can be predicted at any point in the sound field. It is also proposed that the same NAH measurement can be used to predict farfield directivity. The inclusion of velocity values into the NAH technique also provides a means for predicting energy density (ED) anywhere within the acoustic field. These two developments would allow a single NAH measurement to provide much more information about an acoustic source and its radiated sound field. Experimental testing shows that NAH is successful at predicting the shape of the resulting ED field and directivity pattern with some error in amplitude. The best performance of the technique is with a planer source resulting in an average amplitude error of 18.5% over the entire field.

In order to facilitate the acquisition and accurate interpretation of intensity and energy density data in high-amplitude pressure fields, the expressions for intensity and energy density are examined to ascertain the impact of nonlinear processes on the standard expressions. Measurement techniques for estimating acoustic particle velocity are presented. The finite-difference method is developed in an alternate manner and presented along with bias and confidence estimates. Additionally, two new methods for estimating the local particle velocity are presented. These methods appears to eliminate the errors and bias associated with the finite-difference technique for certain cases.

Equalization of loudspeakers and enclosed sound fields has been a topic of considerable interest for decades. Confusion has often arisen among audio professionals regarding the feasibility of simultaneously equalizing a loudspeaker and the enclosed field (i.e., the “room”) it excites. Because of frustrations encountered in such efforts, some have advocated abandoning simultaneous equalization altogether. This dissertation discusses the drawbacks of this approach as well as traditional in situ equalization methods. It demonstrates that many problems with traditional equalization stem from the use of measured acoustic pressure at a discrete point in a sound field as the system output. The dissertation presents analytical models and experiments involving the equalization of loudspeakers and both one-dimensional and three-dimensional sound fields. Equalization using total energy density at a point in either a one-dimensional or three-dimensional field produces better global equalization of the pressure field. In the one-dimensional case, it allows simultaneous correction of spectral loudspeaker and global sound-field response anomalies in a nearly optimal sense.

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The current driven electrothermal instability (ETI) forms when the material resistivity is temperature dependent, occurring in nearly all Z-pinch-like high energy density platforms. ETI growth for high-mass density materials is predominantly striation form which corresponds to magnetically perpendicular mode growth. The striation form is caused by a resistivity that increases with temperature, which is often the case for high-mass density materials. In contrast, low-density ETI growth is mainly filamentation form, magnetically aligned modes, because the resistivity tends to decrease with temperature. Simulating ETI is challenging due to the coupling of magnetic field transport to equation of state over a large region of state space spanning solids to plasmas. This dissertation presents a code-code verification study to effectively model the ETI. Specifically, this study provides verification cases which ensure the unit physics components essential to modeling ETI are accurate. This provides a way for fluid-based codes to simulate linear and nonlinear ETI. Additionally, the study provides a sensitivity analysis of nonlinear ETI to equation of state, vacuum resistivity, and vacuum density. Simulations of ETI typically use a collisional form of the resistivity as provided, e.g., in a Lee-More Desjarlais conductivity table. In regions of low-mass density, collision-less transport needs to be incorporated to properly simulate the filamentation form of ETI growth. Anomalous resistivity (AR) is an avenue by which these collision-less micro-turbulent effects can be incorporated into a collisional resistivity. AR directly changes the resistivity which will directly modify the linear growth rate of ETI, so a new linear growth rate is derived which includes AR's added dependency on current density. This linear growth rate is verified through a filamentation ETI simulation using an ion acoustic based AR model. Kinetically based simulations of vacuum contaminant plasmas provide a physical platform to study the use of AR models in pulsed-power platforms. Using parameters from the Z-machine pulsed-power device, the incorporation of AR can increase a collisional-based resistivity by upwards of four orders of magnitude. The presence of current-carrying vacuum contaminant plasmas can indirectly affect nonlinear ETI growth through modification of the magnetic diffusion wave. The impact of AR on nonlinear ETI is explored through pulsed-power simulations of a dielectrically coated solid metallic liner surrounded by a low-density vacuum contaminant plasma. / Doctor of Philosophy / High-energy-density physics (HEDP) is the study of materials with pressures that exceed 1Mbar, and is difficult to reach here on Earth. Inertial confinement fusion concepts and experiments are the primary source for achieving these pressures in the laboratory. Inertial confinement fusion (ICF) is a nuclear fusion concept that relies on the inertia of imploding materials to compress a light fuel (often deuterium and tritium) to high densities and temperatures to achieve fusion reactions. The imploding materials in ICF are driven in many ways, but this dissertation focuses on ICF implosions driven by pulsed-power devices. Pulsed-power involves delivering large amounts of capacitive energy in the form of electrical current over very short time scales (nanosecond timescale). The largest pulsed-power driver is the Z-machine at Sandia National Laboratory (SNL) which is capable of delivering upwards of 30 MA in 130 ns approximately. During an ICF implosion there exists instabilities that disrupt the integrity of the implosion causing non-ideal lower density and temperature yields. One such instability is the Rayleigh-Taylor instability where a light fluid supports a heavy fluid under the influence of gravity. The Rayleigh-Taylor is one of the most detrimental instabilities toward achieving ignition and was one of the main research topics in the early stages of this Ph.D. The study of this instability provided a nice intro for modeling in the HEDP regime, specifically, in the uses of tabulated equations-of-state and tabulated transport coefficients (e.g., resistivity and thermal conductivity). The magneto Rayleigh-Taylor instability occurs in pulsed-power fusion platforms where the heavy fluid is now supported by a magnetic field instead of a light fluid. The magneto Rayleigh-Taylor instability is the most destructive instability in many pulsed-power fusion platforms, so understanding seeding mechanisms is critical in mitigating its impact. Magnetized liner inertial fusion (MagLIF) is a pulsed-power fusion concept that involves imploding a solid cylindrical metal annulus on laser-induced pre-magnetized fuel. The solid metal liners have imperfections and defects littered throughout the surface. The imperfections on the surface create a perturbation during the initial phases of the implosion when the solid metal liner is undergoing ohmic heating. Because a solid metal has a resistivity that increases with temperature, as the metal heats the resistivity increases causing more heating which creates a positive feedback loop. This positive feedback loop is similar to the heating process in a nichrome wire in a toaster, and is the fundamental bases of the main instability studied in this dissertation, the electrothermal instability (ETI). ETI is present in all pulsed-power fusion platforms where a current-carrying material has a resistivity that changes with temperature. In MagLIF, ETI is dominant in the early stages of a current pulse where the resistivity of the metal increases with temperature. An increasing resistivity with temperature is connected to the axially growing modes of ETI which is denoted as the striation form of ETI. Contrary to the striation form of ETI, the filamentation form of ETI occurs when resistivity decreases with temperature and is associated with the azimuthally growing modes of ETI. Chapter 2 in this dissertation details a study of how to simulate striaiton ETI for a MagLIF-like configuration across different resistive magnetohydrodynamics (MHD) codes. Resistivity that decreases with temperature typically occurs in low-density materials which are often in a gaseous or plasma state. Low density plasmas are nearly collision-less and have resistivity definitions that often overestimate the conductivity of a plasma in certain experiments. Anomalous resistivity (AR) addresses this overestimation by increasing a collisional resistivity through micro-turbulence driven plasma phenomenon that mimic collisional behavior. The creation of AR involves reduced-modeling of micro-turbulence driven plasma phenomenon, such as the lower hybrid drift instability, to construct an effective collision frequency based on drift speeds. Because AR directly modifies a collisional resistivity for certain conditions, it will directly alter the growth of ETI which is the topic of Chapter 3. The current on the Z-machine is driven by the capacitor bank through the post-hole convolute, the magnetically insulated transmission lines, and then into the chamber. Magnetically insulated transmission lines have been shown to create low-density plasma through desorption processes in the vacuum leading to a load surrounded by a low-density plasma referred to as a vacuum contaminant plasmas (VCP). VCP can divert current from the load by causing a short between the vacuum anode and cathode gap. In simulations, this plasma would be highly conducting when represented by a collisionally-based resistivity model resulting in non-physical vacuum heating that is not observed in experiments. VCP are current-carrying low-density and high-temperature plasmas which make them ideal candidates to study the role of AR as described in Chapter 4. Chapter 4 investigates the role AR in a VCP would have on striation ETI for a MagLIF-like load.

An active noise control (ANC) system has been applied to the problem of attenuating low-frequency tonal noise inside small enclosures. The intended target application of the system was the reduction of the engine firing frequency inside heavy equipment cabins. The ANC system was based on a version of the filtered-x LMS adaptive algorithm, modified for the minimization of acoustic energy density (ED), rather than the more traditional minimization of squared acoustic pressure (SP). Three loudspeakers produced control signals within a mock cabin composed of a steel frame with plywood sides and a Plexiglas® front. An energy density sensor, capable of measuring acoustic pressure as well as acoustic particle velocity, provided the error signal to the control system. The ANC system operated on a single reference signal, which, for experiments involving recorded tractor engine noise, was derived from the engine's tachometer signal. For the low frequencies at which engine firing occurs, experiments showed that ANC systems minimizing ED and SP both provided significant attenuation of the tonal noise near the operator's head and globally throughout the small cabin. The tendency was for ED control to provide a more spatially uniform amount of reduction than SP control, especially at the higher frequencies investigated (up to 200 Hz). In dynamic measurement conditions, with a reference signal swept in frequency, the ED control often provided superior results, struggling less at frequencies for which the error sensor was near nodal regions for acoustic pressure. A single control channel often yielded performance comparable to that of two control channels, and sometimes produced superior results in dynamic tests. Tonal attenuation achieved by the ANC system was generally in excess of 20 dB and reduction in equivalent sound level for dynamic tonal noise often exceeded 4 dB at the error sensor. It was shown that temperature changes likely to be encountered in practice have little effect on the initial delay through the secondary control path, and are therefore unlikely to significantly impact ANC system stability in the event that a fixed set of system identification filter coefficients are employed.

Sound pressure equalization of audio signals using digital signal processors has been a subject of ongoing study for many years. The traditional approach is to equalize sound at a point in a listening environment, but because of its specific dependence on the room frequency response between a source and receiver position, this equalization generally causes the spectral response to worsen significantly at other locations in the room. This work presents both a time-invariant and a time-varying implementation of an adaptive acoustic energy density equalization filter for a one-dimensional sound field. Energy density equalization addresses the aforementioned challenge and others that relate to sound equalization. The theory and real-time implementation of time-invariant sound pressure and energy density equalizers designed using the least-squares method are presented, and their performances are compared. An implementation of a time-varying energy density equalizer is also presented. Time-invariant equalization results based on real-time measurements in a plane-wave tube are presented. A sound pressure equalizer results in a nearly flat spectral magnitude at the point of equalization. However, it causes the frequencies corresponding to spatial nulls at that point to be undesirably boosted elsewhere in the sound field, where those nulls do not exist at the same frequencies. An energy density equalization filter identifies and compensates for all resonances and other global spectral effects of the tube and loudspeaker. It does not attempt to equalize the spatially varying frequency nulls caused by local pressure nodes at the point of equalization. An implementation of a time-varying energy density equalizer is also presented. This method uses the filtered-x filter update to adjust the filter coefficients in real-time to adapt to changes in the sound field. Convergence of the filter over time is demonstrated as the closed end of the tube is opened, then closed once again. Thus, the research results demonstrate that an acoustic energy density filter can be used to time-adaptively equalize global spectral anomalies of a loudspeaker and a one-dimensional sound field.

Measuring different acoustical properties have been the key in reducing noise and improving the sound quality from various sources. In this report, a broadband (200 Hz – 6.5 kHz) three-dimensional seven-microphone intensity probe system is developed to measure the sound intensity, and total energy density in different acoustical environments. Limitations of most commercial intensity probes in measuring the three-dimensional intensity for a broadband sound field was the main motivation in developing this probe. The finite-difference error and the phase mismatch error which are the two main errors associated with the intensity measurements are addressed in this report. As for the physical design, seven microphones were arranged in a two-concentric arrays with one microphone located at the center of the probe. The outer array is for low-frequencies (200 Hz – 1.0 kHz), and the inner one is for high-frequencies (1.0 kHz – 6.5 kHz). The screw adjustable center microphone is used for the microphone calibration, and as the reference microphone of the probe. The simultaneous calibrations of all the microphones in the probe were done in the anechoic room. Theories for the intensity and the energy densities calculations for the probe were derived from the existing four-microphone probe configuration. Reflection and diffraction effects on the intensity measurements due to the presence of the microphones, and the supporting structures were also investigated in this report. Directivity patterns of the calculated intensity showed the omnidirectional nature of the probe. The intensity, and total energy density were calculated and compared with the ideal values in the anechoic room environment. Characterization of sound fields in a reverberant enclosed space, and sound source identification are some applications that were investigated using this probe. Results of different measurements showed effectiveness of the probe as a tool to measure key acoustical properties in many practical environments. / text

Experiments in high energy density (HED) plasma physics have become more accessible with the increasing availability of high-intensity pulsed lasers. Extending the experiment parameters to include magnetized HED plasmas requires a field source that can generate fields of order 100 tesla. This dissertation discusses the design and implementation of a pulsed field driver with a designed maximum of 2.2 MA from a 160 kJ capacitor bank. Faraday rotation measurement of 63 T for a 1.0 MA discharge supported Biot-Savart estimates for a single-turn coil with a 1 cm bore. After modification, the field driver generated up to 15 T to magnetize supernova-like spherical blast waves driven by the Texas Petawatt Laser. The presence of the high field suppressed blast wave expansion, and had the additional effect of revealing a cylindrical plasma along the laser axis. / text

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