Theses and Dissertations at Montana State University (MSU)
Permanent URI for this collectionhttps://scholarworks.montana.edu/handle/1/733
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Item Twist in coronal magnetic fields(Montana State University - Bozeman, College of Letters & Science, 2010) Malanushenko, Anna Viktorovna; Chairperson, Graduate Committee: Dana W. LongcopeTwist of magnetic field is believed to play important role in driving instabilities that result in eruptive events on the Sun. This thesis provides different methods to measure twist in the solar corona. First, given a model of coronal field, twist of a magnetic domain (i.e., a volume that contains all field lines connecting two regions of interest in the photosphere) is well studied for cases when the domain is a thin cylinder. For cases when such approximation is inapplicable a generalization of twist can be derived from a quantity called additive self-helicity. I develop explicit numerical methods to compute generalized twist. I also demonstrate that such a quantity sets a threshold on kink instability like the traditional twist does for thin cylinders. In a more realistic scenario, coronal magnetic field is not known and so neither is its helicity. There are two principal methods to overcome this problem. The first is to integrate helicity flux across the photosphere (as helicity is believed to be approximately conserved in the corona) using magnetic field on Sun's surface. There is little published evidence as yet that coronal helicity indeed corresponds to its integrated photospheric flux. The second is to extrapolate the coronal magnetic field using surface measurements as boundary conditions and use this extrapolation for helicity computation; for fields with complicated structure such extrapolations are extremely challenging and suffer from major drawbacks. I develop a method to estimate twist of coronal fields without attempting complicated extrapolations or studying helicity flux. The method builds a simple uniformly-twisted magnetic field and adjusts its properties until there is one line in this field that matches one coronal loop; this is repeated for all evident coronal loops resulting in twist measurements for each individual loop. I use this method to demonstrate that the rate of change of twist in the solar corona is indeed approximately equal to the one derived from photospheric helicity flux. The results of this dissertation are useful for better understanding of magnetic topology in general. They are also extremely promising for extrapolating coronal magnetic fields. Measurements of coronal twist might aid in predicting magnetic instabilities.Item On the geometry and topology of the angular momentum of light(Montana State University - Bozeman, College of Letters & Science, 2010) Gelbord, Todd Richard; Chairperson, Graduate Committee: Sachiko TsurutaThe classical field theory approach to the angular momentum of light, specifically how it represents the spin angular momentum of light, has been a matter of controversy for some time. This thesis analyses the aforementioned approach from the point of view of the Exterior Calculus and de Rham Cohomology. It is found purely mathematically that the spin angular momentum of a circularly polarized plane wave of light must be identically zero. It is concluded that the classical formulation of the angular momentum of a plane wave of light is, on some level, incomplete.