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Dynamical Invariants and the Fluid Impulse in Plasma Models

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Date Issued:
2013
Abstract/Description:
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.
Title: Dynamical Invariants and the Fluid Impulse in Plasma Models.
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Name(s): Michalak, Martin, Author
Shivamoggi, Bhimsen, Committee Chair
Mohapatra, Ram, Committee Member
Brennan, Joseph, Committee Member
Eastes, Richard, Committee Member
University of Central Florida, Degree Grantor
Type of Resource: text
Date Issued: 2013
Publisher: University of Central Florida
Language(s): English
Abstract/Description: 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.
Identifier: CFE0005382 (IID), ucf:50442 (fedora)
Note(s): 2013-12-01
Ph.D.
Sciences, Mathematics
Doctoral
This record was generated from author submitted information.
Subject(s): plasma physics -- differential geometry -- magnetohydrodynamics
Persistent Link to This Record: http://purl.flvc.org/ucf/fd/CFE0005382
Restrictions on Access: campus 2017-06-15
Host Institution: UCF

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