The Hanle effect has been proposed as a new diagnostic of circumstellar magnetic fields for early-type stars, for which it is sensitive to field strengths in the 1-300 G range. In this paper we compute the polarized P Cygni line profiles that result from the Hanle effect. For modeling the polarization, we employ a variant of the "last scattering approximation." For cases in which the Sobolev optical depths are greater than unity, the emergent line intensity is assumed to be unpolarized, while for smaller optical depths, the Stokes source functions for the Hanle effect with optically thin line scattering are used. For a typical P Cygni line, the polarized emission forms in the outer wind, because the Sobolev optical depth is large at the inner wind. For low surface field strengths, weak P Cygni lines are needed to measure the circumstellar field. For high values of the surface fields, both the Zeeman and Hanle diagnostics can be used, with the Zeeman effect probing the photospheric magnetic fields and the Hanle effect measuring the magnetic field in the wind flow. Polarized line profiles are calculated for a self-consistent structure of the flow and the magnetic geometry based on the WCFields model, which is applicable to slowly rotating stellar winds with magnetic fields drawn out by the gas flow. For surface fields of a few hundred gauss, we find that the Hanle effect can produce line polarizations in the range of a few tenths of a percent up to about 2%.

The measurement of vector magnetic fields on the sun is one of the most important diagnostic tools for characterizing solar activity. The ubiquitous solar wind is guided into interplanetary space by open magnetic field lines in the upper solar atmosphere. Highly-energetic solar flares and Coronal Mass Ejections (CMEs) are triggered in lower layers of the solar atmosphere by the driving forces at the visible ``surface'' of the sun, the photosphere. The driving forces there tangle and interweave the vector magnetic fields, ultimately leading to an unstable field topology with large excess magnetic energy, and this excess energy is suddenly and violently released by magnetic reconnection, emitting intense broadband radiation that spans the electromagnetic spectrum, accelerating billions of metric tons of plasma away from the sun, and finally relaxing the magnetic field to lower-energy states. These eruptive flaring events can have severe impacts on the near-Earth environment and the human technology that inhabits it. This dissertation presents a novel inversion method for inferring the properties of the vector magnetic field from telescopic measurements of the polarization states (Stokes vector) of the light received from the sun, in an effort to develop a method that is fast, accurate, and reliable. One of the long-term goals of this work is to develop such a method that is capable of rapidly-producing characterizations of the magnetic field from time-sequential data, such that near real-time projections of the complexity and flare-productivity of solar active regions can be made. This will be a boon to the field of solar flare forecasting, and should help mitigate the harmful effects of space weather on mankind's space-based endeavors. To this end, I have developed an inversion method based on genetic algorithms (GA) that have the potential for achieving such high-speed analysis.

The primary goal of this research was to investigate the effects associated with the application of magnetic fields to single electrodes.

<p> The de Haas-van Alphen (dHvA) effect has been studied in single crystals of calcium using the modulation method in magnetic fields up to 55 kOe. Four distinct orbits were observed with dHvA frequency minima at the [110] or [100] directions. The results do not support calculations predicting a disconnected first-band Fermi surface for calcium. The dHvA data of crystalline calcium is consistent with the topology of the two-OPW model in which the first band is connected and pockets of electrons are about the point L of the second zone.</p> / Thesis / Master of Science (MSc)

<p> Field modulation techniques were used to observe the de Haas-van Alphen effect in magnetic fields up to 5.5 tesla and at temperatures below 1.1°K. A data acquisition system recorded on magnetic tape the large amount of data necessary for computer fourier analysis of the oscillations. All of the orbits predicted by Keeton and Loucks' model of the Fermi surface of mercury were at least tentatively identified. The data on the β, τ and α orbits were in essential agreement with previous work. The γ and X-face orbits were also investigated in some detail, while tentative identification was made of the μ and T-face orbits. When the data permitted, the areas were fitted to ellipsoids or hyperboloids of revolution by a least squares calculation.</p> <p> A search was made for modifications to the de Haas-van Alphen theory due to phonons. Accurate torque de Haas-van Alphen amplitude measurements were taken as a function of temperature and magnetic field. The analysis of the results revealed no systematic dependence of either the cyclotron effective mass or the Dingle temperature on temperature from 1.25°K to 4.2°K or on magnetic field from 1.5 tesla to 2.3 tesla. Thus no effects due to phonons were observed.</p> <p> A method of observing the open orbits in metallic single crystals was developed and used to observe the open orbits in mercury. The method utilized the eddy currents induced in the sample by the rotation of a magnetic field. This provided a signal which was dependent on the conductivity in the plane perpendicular to the open orbit. The torque amplitude, which indicated the number of open orbit carriers, was used to detect the angular range of the bands of open orbits in mercury. The method was experimentally simple since no special sample geometry was necessary and no electrical connections to the sample were needed.</p> / Thesis / Doctor of Philosophy (PhD)

This thesis is a work divided into two parts on aspects of three-dimensional (3D) magnetic fields: (I) magnetic reconnection treated from a strictly 3D viewpoint and (II) the design of coils for producing the 3D magnetic fields of optimized stellarators. In astrophysical settings, magnetic fields are generically 3D. 3D divergence-free fields have rich topological structures such as magnetic nulls and chaotic field line structures. Standard reconnection literature identifies magnetic nulls as locations of magnetic reconnection, and that intense currents will build up around them. This idea is explored with a key realization that by placing a vanishingly small sphere around the null, boundary conditions on field lines passing through the sphere may be sorted out. The main result here is (1) the dismissal of the notion that nulls are crucial places for magnetic reconnection and current accumulation, instead identifying separatrices of topological type on the boundaries of null-passing field lines to be crucial. Standard reconnection literature dismisses chaotic flows yet 3D fields generically have chaotic flows. An inherent property of chaotic flows is exponentiation. The main result here is (2) the identification of exponentiation as a natural mechanism for magnetic reconnection and that the associated current builds up linearly in time in contradiction to standard results requiring the formation of high-density current sheets. The magnetic fields of optimized stellarators are intricate, producing complex 3D magnetic surfaces. These fields are conventionally generated by non-planar electromagnetic coils, though these coils are costly to manufacture, slow device assembly, and hinder stellarator maintenance. Part II of this thesis explores methods of stellarator coil simplification that do not involve modular coils. All of this work uses current potentials, which are stream functions of the current sheets that produce magnetic surfaces. We begin with a result found using analytic methods on current potentials that (1) there may be an inherent limitation in the ability of modular coils to produce fields at a distance. This result is not surprising, though further analysis is necessary to work out some complexities of the result. Next, (2) a novel method to produce localized patches of current potential, representative of patches of current sheets, is developed and used to identify crucial locations of current placement for shaping magnetic surfaces. Most notably, these current sheet patches are able to produce much of the surface shaping while occupying a small fraction of the winding surface, resulting in good open-access stellarator coil configurations. Continuing the trend away from modular coils, (3) helical coils are optimized to support stellarator magnetic fields. This work agrees with related work on the optimization of helical coils, finding them unsuitable to the precise production of equilibria generated by modular coils. To improve this result, we use coil sets of mixed-type: helical coils with windowpane coils or permanent magnets, to mitigate field error left behind by the helical coils. Finally, (4) the development of a generalized method to cut modular, helical, and windowpane coils out of current potentials and to identify the associated coil currents is developed and used in coil optimization.

The intent of this thesis is to simulate the effect of a background magnetic field on Rayleigh-Taylor (RT) instability morphology and evolution in support of a Discovery Science campaign at the National Ignition Facility. The RT instability is relevant in High Energy Density (HED) systems including supernova remnants such as the Crab Nebula and inertial fusion confinement (ICF). Magnetic fields affect RT evolution and can suppress small-scale fluid motion. Thus far no experimental work has quantified the effect of a B-field on RT evolution morphology. RT evolution under a B-field was examined in three-dimensional magnetohydrodynamic (MHD) simulations using the hydrocode ARES, developed by Lawrence Livermore National Laboratory. The parameter space of the experiment is explored to determine the parameters that yield a visible effect on RT evolution. The effect of resistive MHD and conductivity is examined to further establish the desired parameter space to observe the suppression of RT morphology.

No description available.

No description available.

No description available.