Magnetic and Acoustic Investigations of Turbulent Spherical Couette Flow

Title of dissertation: MAGNETIC AND ACOUSTIC INVESTIGATIONS OF TURBULENT SPHERICAL COUETTE FLOW Matthew M. Adams, Doctor of Philosophy, 2016 Dissertation directed by: Professor Daniel Lathrop Department of Physics This dissertation describes experiments in spherical Couette devices, using both gas and liquid sodium. The experimental geometry is motivated by the Earth's outer core, the seat of the geodynamo, and consists of an outer spherical shell and an inner sphere, both of which can be rotated independently to drive a shear flow in the fluid lying between them. In the case of experiments with liquid sodium, we apply DC axial magnetic fields, with a dominant dipole or quadrupole component, to the system. We measure the magnetic field induced by the flow of liquid sodium using an external array of Hall effect magnetic field probes, as well as two probes inserted into the fluid volume. This gives information about possible velocity patterns present, and we extend previous work categorizing flow states, noting further information that can be extracted from the induced field measurements. The limitations due to a lack of direct velocity measurements prompted us to work on developing the technique of using acoustic modes to measure zonal flows. Using gas as the working fluid in our 60~cm diameter spherical Couette experiment, we identified acoustic modes of the container, and obtained excellent agreement with theoretical predictions. For the case of uniform rotation of the system, we compared the acoustic mode frequency splittings with theoretical predictions for solid body flow, and obtained excellent agreement. This gave us confidence in extending this work to the case of differential rotation, with a turbulent flow state. Using the measured splittings for this case, our colleagues performed an inversion to infer the pattern of zonal velocities within the flow, the first such inversion in a rotating laboratory experiment. This technique holds promise for use in liquid sodium experiments, for which zonal flow measurements have historically been challenging.

SPACE-DEPLOYED, THIN-WALLED ENCLOSURE FOR A CRYOGENICALLY-COOLED HIGH TEMPERATURE SUPERCONDUCTING COIL

The interaction of magnetic fields generated by large superconducting coils has multiple applications in space, including actuation of spacecraft or spacecraft components, wireless power transfer, and shielding of spacecraft from radiation and high energy particles. These applications require coils with major diameters as large as 20 meters and a thermal management system to maintain the superconducting material of the coil below its critical temperature. Since a rigid thermal management system, such as a heat pipe, is unsuitable for compact stowage inside a 5 meter payload fairing, a thin-walled thermal enclosure is proposed. A 1.85 meter diameter test article consisting of a bladder layer for containing chilled nitrogen vapor, a restraint layer, and multilayer insulation was tested in a custom toroidal vacuum chamber. The material properties found during laboratory testing are used to predict the performance of the test article in low Earth orbit. Deployment motion of the same test article was measured using a motion capture system and the results are used to predict the deployment in space. A 20 meter major diameter and coil current of 6.7 MA is selected as a point design case. This design point represents a single coil in a high energy particle shielding system. Sizing of the thermal and structural components of the enclosure is completed. The thermal and deployment performance is predicted.

A Search for Muon Neutrinos in Coincidence with Gamma-Ray Bursts in the Southern Hemisphere Sky Using the IceCube Neutrino Observatory

The origin of observed ultra-high energy cosmic rays (UHECRs, energies in excess of $10^{18.5}$ eV) remains unknown, as extragalactic magnetic fields deflect these charged particles from their true origin. Interactions of these UHECRs at their source would invariably produce high energy neutrinos. As these neutrinos are chargeless and nearly massless, their propagation through the universe is unimpeded and their detection can be correlated with the origin of UHECRs. Gamma-ray bursts (GRBs) are one of the few possible origins for UHECRs, observed as short, immensely bright outbursts of gamma-rays at cosmological distances. The energy density of GRBs in the universe is capable of explaining the measured UHECR flux, making them promising UHECR sources. Interactions between UHECRs and the prompt gamma-ray emission of a GRB would produce neutrinos that would be detected in coincidence with the GRB’s gamma-ray emission. The IceCube Neutrino Observatory can be used to search for these neutrinos in coincidence with GRBs, detecting neutrinos through the Cherenkov radiation emitted by secondary charged particles produced in neutrino interactions in the South Pole glacial ice. Restricting these searches to be in coincidence with GRB gamma-ray emis- sion, analyses can be performed with very little atmospheric background. Previous searches have focused on detecting muon tracks from muon neutrino interactions fromthe Northern Hemisphere, where the Earth shields IceCube’s primary background of atmospheric muons, or spherical cascade events from neutrinos of all flavors from the entire sky, with no compelling neutrino signal found. Neutrino searches from GRBs with IceCube have been extended to a search for muon tracks in the Southern Hemisphere in coincidence with 664 GRBs over five years of IceCube data in this dissertation. Though this region of the sky contains IceCube’s primary background of atmospheric muons, it is also where IceCube is most sensitive to neutrinos at the very highest energies as Earth absorption in the Northern Hemisphere becomes relevant. As previous neutrino searches have strongly constrained neutrino production in GRBs, a new per-GRB analysis is introduced for the first time to discover neutrinos in coincidence with possibly rare neutrino-bright GRBs. A stacked analysis is also performed to discover a weak neutrino signal distributed over many GRBs. Results of this search are found to be consistent with atmospheric muon backgrounds. Combining this result with previously published searches for muon neutrino tracks in the Northern Hemisphere, cascade event searches over the entire sky, and an extension of the Northern Hemisphere track search in three additional years of IceCube data that is consistent with atmospheric backgrounds, the most stringent limits yet can be placed on prompt neutrino production in GRBs, which increasingly disfavor GRBs as primary sources of UHECRs in current GRB models.

Radio Frequency Superconducting Quantum Interference Device Meta-atoms and Metamaterials: Experiment, Theory, and Analysis

Metamamterials are 1D, 2D or 3D arrays of articial atoms. The articial atoms, called "meta-atoms", can be any component with tailorable electromagnetic properties, such as resonators, LC circuits, nano particles, and so on. By designing the properties of individual meta-atoms and the interaction created by putting them in a lattice, one can create a metamaterial with intriguing properties not found in nature. My Ph. D. work examines the meta-atoms based on radio frequency superconducting quantum interference devices (rf-SQUIDs); their tunability with dc magnetic field, rf magnetic field, and temperature are studied. The rf-SQUIDs are superconducting split ring resonators in which the usual capacitance is supplemented with a Josephson junction, which introduces strong nonlinearity in the rf properties. At relatively low rf magnetic field, a magnetic field tunability of the resonant frequency of up to 80 THz/Gauss by dc magnetic field is observed, and a total frequency tunability of 100% is achieved. The macroscopic quantum superconducting metamaterial also shows manipulative self-induced broadband transparency due to a qualitatively novel nonlinear mechanism that is different from conventional electromagnetically induced transparency (EIT) or its classical analogs. A near complete disappearance of resonant absorption under a range of applied rf flux is observed experimentally and explained theoretically. The transparency comes from the intrinsic bi-stability and can be tuned on/ off easily by altering rf and dc magnetic fields, temperature and history. Hysteretic in situ 100% tunability of transparency paves the way for auto-cloaking metamaterials, intensity dependent filters, and fast-tunable power limiters. An rf-SQUID metamaterial is shown to have qualitatively the same behavior as a single rf-SQUID with regards to dc flux, rf flux and temperature tuning. The two-tone response of self-resonant rf-SQUID meta-atoms and metamaterials is then studied here via intermodulation (IM) measurement over a broad range of tone frequencies and tone powers. A sharp onset followed by a surprising strongly suppressed IM region near the resonance is observed. This behavior can be understood employing methods in nonlinear dynamics; the sharp onset, and the gap of IM, are due to sudden state jumps during a beat of the two-tone sum input signal. The theory predicts that the IM can be manipulated with tone power, center frequency, frequency difference between the two tones, and temperature. This quantitative understanding potentially allows for the design of rf-SQUID metamaterials with either very low or very high IM response.

Tensor Completion for Multidimensional Inverse Problems with Applications to Magnetic Resonance Relaxometry

This thesis deals with tensor completion for the solution of multidimensional inverse problems. We study the problem of reconstructing an approximately low rank tensor from a small number of noisy linear measurements. New recovery guarantees, numerical algorithms, non-uniform sampling strategies, and parameter selection algorithms are developed. We derive a fixed point continuation algorithm for tensor completion and prove its convergence. A restricted isometry property (RIP) based tensor recovery guarantee is proved. Probabilistic recovery guarantees are obtained for sub-Gaussian measurement operators and for measurements obtained by non-uniform sampling from a Parseval tight frame. We show how tensor completion can be used to solve multidimensional inverse problems arising in NMR relaxometry. Algorithms are developed for regularization parameter selection, including accelerated k-fold cross-validation and generalized cross-validation. These methods are validated on experimental and simulated data. We also derive condition number estimates for nonnegative least squares problems. Tensor recovery promises to significantly accelerate N-dimensional NMR relaxometry and related experiments, enabling previously impractical experiments. Our methods could also be applied to other inverse problems arising in machine learning, image processing, signal processing, computer vision, and other fields.