UMD Theses and Dissertations
Permanent URI for this collectionhttp://hdl.handle.net/1903/3
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Item Magnetic Field Effects on the Motion of Circumplanetary Dust(2012) Jontof-Hutter, Daniel; Hamilton, Douglas P; Astronomy; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Hypervelocity impacts on satellites or ring particles replenish circumplanetary dusty rings with grains of all sizes. Due to interactions with the plasma environment and sunlight, these grains become electrically charged. We study the motion of charged dust grains launched at the Kepler orbital speed, under the combined effects of gravity and the electromagnetic force. We conduct numerical simulations of dust grain trajectories, covering a broad range of launch distances from the planetary surface to beyond synchronous orbit, and the full range of charge-to-mass ratios from ions to rocks, with both positive and negative electric potentials. Initially, we assume that dust grains have a constant electric potential, and, treating the spinning planetary magnetic field as an aligned and centered dipole, we map regions of radial instability (positive grains only), where dust grains are driven to escape or collide with the planet at high speed, and vertical instability (both positive and negative charges) whereby grains launched near the equatorial plane and are forced up magnetic field lines to high latitudes, where they may collide with the planet. We derive analytical criteria for local stability in the equatorial plane, and solve for the boundaries between all unstable and stable outcomes. Comparing our analytical solutions to our numerical simulations, we develop an extensive model for the radial, vertical and azimuthal motions of dust grains of arbitrary size and launch location. We test these solutions at Jupiter and Saturn, both of whose magnetic fields are reasonably well represented by aligned dipoles, as well as at the Earth, whose magnetic field is close to an anti-aligned dipole. We then evaluate the robustness of our stability boundaries to more general conditions. Firstly, we examine the effects of non-zero launch speeds, of up to 0.5 km s$^{-1}$, in the frame of the parent body. Although these only weakly affect stability boundaries, we find that the influence of a launch impulse on stability boundaries strongly depends on its direction. Secondly, we focus on the effects of higher-order magnetic field components on orbital stability. We find that vertical stability boundaries are particularly sensitive to a moderate vertical offset in an aligned dipolar magnetic field. This configuration suffices as a model for Saturn's full magnetic field. The vertical instability also expands to cover a wider range of launch distances in slightly tilted magnetic dipoles, like the magnetic field configurations for Earth and Jupiter. By contrast, our radial stability criteria remain largely unaffected by both dipolar tilts and vertical offsets. Nevertheless, a tilted dipole magnetic field model introduces non-axisymmetric forces on orbiting dust grains, which are exacerbated by the inclusion of other higher-order magnetic field components, including the quadrupolar and octupolar terms. Dust grains whose orbital periods are commensurate with the spatial periodicities of a rotating non-axisymmetric magnetic field experience destabilizing Lorentz resonances. These have been studied by other authors for the largest dust grains moving on perturbed Keplerian ellipses. With Jupiter's full magnetic field as our model, we extend the concept of Lorentz resonances to smaller dust grains and find that these can destabilize trajectories on surprisingly short timescales, and even cause negatively-charged dust grains to escape within weeks. We provide detailed numerically-derived stability maps highlighting the destabilizing effects of specific higher-order terms in Jupiter's magnetic field, and we develop analytical solutions for the radial locations of these resonances for all charge-to-mass ratios. We include stability maps for the full magnetic field configurations of Jupiter, Saturn, and Earth, to compare with our analytics. We further provide numerically-derived stability maps for the tortured magnetic fields of Uranus and Neptune. Relaxing the assumption of constant electric charges on dust, we test the effects of time-variable grain charging on dust grain motion in two distinct environments. Firstly, we examine orbital stability in the tenuous plasma of Jupiter's main ring and gossamer ring where sunlight, the dominant source of grain charging, is periodically interrupted by transit through the planetary shadow. This dramatically expands dynamical instabilities to cover a large range of grain sizes. Secondly, we study the motion of dust grain orbits in the dense plasma environment of the Io torus. Here dust grain charges deviate little from equilibrium, and our stability map conforms closely to that of constant, negatively-charged dust grains. Finally, we focus on the poorly understood spokes in Saturn's B ring, highlighting the observational constraints on spokes, and present our hypothesis for spoke formation.Item Quantitative modeling of mantle heterogeneity and structure(2010) Arevalo, Jr., Ricardo David; McDonough, William F; Geology; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Mantle-derived rocks, particularly mid-ocean ridge basalts (MORB) and intraplate ocean island basalts (OIB), provide insights into the compositional heterogeneity and first-order structural make-up of the modern mantle; laser ablation (LA-) ICP-MS analysis provides the ideal analytical tool for the in situ chemical characterization of these materials. The silicate Earth, as defined by the MORB and OIB source regions plus the continental crust, is determined to have a representative W/U and K/U ratio of 0.65 ± 0.45 (2σ) and 13,800 ± 2600 (2σ), respectively, equating to 13 ± 10 ng/g W and 280 ± 120 μg/g K in the silicate Earth. Although both the isotopic composition of W and the constancy of the terrestrial W/U ratio may serve as tracers of putative core-mantle interactions, both of these proxies are sensitive to the chemical composition of the mantle source and have yet to resolve a core signal in Hawaiian picrites. The abundance of K in the silicate Earth indicates a current convective Urey ratio of ~0.34 and mantle cooling rate of 70-130 K*Gyr−1, after taking into account potential heat flux across the core-mantle boundary. The Earth's balance of radiogenic heat and budget of 40Ar necessitate a lower mantle reservoir enriched in radioactive elements. The bulk Earth Pb/U ratio, determined here to be ~85, suggests ~1200 ng/g Pb in the bulk Earth and ≥3300 ng/g Pb in the core. A compositional model of MORB, which is derived from a suite of sample measurements augmented by a critically compiled data set, shows that Atlantic, Pacific and Indian MORB can be distinguished based on both trace element abundances and ratios. The geochemical signatures associated with global MORB are not entirely complementary to the continental crust, and require an under-sampled reservoir enriched in Ti, Nb and Ta. A compositional model of OIB, which is based on the inferred chemical composition of OIB parental melts from Hawaiian shield volcanoes as well as the Austral-Cook islands, indicates that the OIB source region may only be ≥1.0x as enriched in incompatible elements as the unfractionated silicate Earth, and constitute up to ≤50% of the modern mantle mass.Item Melting and Phase Relations in Iron-Silicon Alloys with Applications to the Earth's Core(2009) Miller, Noah Andrew; Campbell, Andrew; Geology; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Experiments were performed on iron-silicon alloys to determine their suitability as analog compositions for the Earth's core. Starting compositions with 9 wt.% silicon and 16 wt.% silicon were compressed in diamond anvil cells and laser-heated. The melting temperatures of the alloys were measured up to 52 GPa using a recently developed optical system. Both curves show a melting point depression from pure iron but intersect at ~50 GPa. The two starting compositions were also studied up to 90 GPa and over 3500 K in synchrotron x-ray diffraction experiments, and phase diagrams were constructed for both compositions that show significant deviation from the pure iron phase diagram. Based on this synchrotron data, a model was produced which predicts the core to contain 8.6 to 11.1 wt.% silicon for a core-mantle boundary temperature of 4000 K.Item Liquid sodium model of Earth's outer core(2004-08-27) Shew, Woodrow Lee; Lathrop, Daniel P.; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Convective motions in Earth's outer core are responsible for the generation of the geomagnetic field. We present liquid sodium convection experiments in a spherical vessel, designed to model the convective state of Earth's outer core. Heat transfer, zonal fluid velocities, and properties of temperature fluctuations were measured for different rotation rates and temperature drops across the convecting sodium. The small scale fluid motion was highly turbulent, despite the fact that less than half of the total heat transfer was due to convection. Retrograde zonal velocities were measured at speeds up to 0.02 times the tangential speed of the outer wall of the vessel. Power spectra of temperature fluctuations indicate a well defined knee characterizing the convective energy input. This frequency is proportional to the ballistic velocity estimate. In the context of Earth's outer core, our observations imply a thermal Rayleigh number Ra=10^22, a convective velocity near 10^-5 m/s, and length and time scales of convective motions of 100 m and 2 days.