Plasma physics, differential geometry, magnetohydrodynamics
Much progress has been made in understanding of plasmas through the use of the MHD equations and newer models such as Hall MHD and electron MHD. As with most equations of fluid behavior, these equations are nonlinear, and no general solutions can be found. The use of invariant structures allows limited predictions of fluid behavior without requiring a full solution of the underlying equations. The use of gauge transformation can allow the creation of new invariants, while differential geometry offers useful tools for constructing additional invariants from those that are already known. Using these techniques, new geometric, integral and topological invariants are constructed for Hall and electron MHD models. Both compressible and incompressible models are considered, where applicable. An application of topological invariants to magnetic reconnection is provided. Finally, a particular geometric invariant, which can be interpreted as the fluid impulse density, is studied in greater detail, its nature and invariance in plasma models is demonstrated, and its behavior is predicted in particular geometries under different models.
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Doctor of Philosophy (Ph.D.)
College of Sciences
Length of Campus-only Access
Doctoral Dissertation (Open Access)
Dissertations, Academic -- Sciences, Sciences -- Dissertations, Academic
Michalak, Martin, "Dynamical Invariants And The Fluid Impulse In Plasma Models" (2013). Electronic Theses and Dissertations. 2954.