Thesis (Ph.D)--Aerospace Engineering, Georgia Institute of Technology, 2009. / Committee Chair: Menon Suresh; Committee Co-Chair: Jagoda Jeff; Committee Member: Ruffin Stephen; Committee Member: Thorsten Stoesser; Committee Member: Walker Mitchell. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Thesis (Ph. D.)--University of Wisconsin, 1967. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Magnetic field permeates the solar atmosphere and plays a crucial role in the dynamics, energetics and structures observed. In particular, magnetic flux tubes provide the structure for coronal loops that extend from the solar surface into the corona. In this thesis, we present 3D numerical simulations examining the heating produced by reconnection between flux tubes driven by rotational footpoint motions. The basic model consists of two, initially aligned, flux tubes that are forced to interact by rotational driving velocities on the flux concentrations on the boundaries. A single, twisted current layer is created in the centre of the domain and strong, localised heating is produced. We extend this model by altering the number, distribution and strength of the sources, while maintaining the same total magnetic flux on the boundaries. The dynamical evolution and the resultant magnitude, distribution and timing of the heating events are examined for the different flux distributions. In all cases, the magnetic field is stressed by the boundary motions and a current grows within the domain. A comparison of cases with two and four sources shows that there are more locations of current concentrations, but with reduced maximum current density values, for the four source case. This produces weaker reconnection and less efficient heating. In addition, for the case with two sources, we also consider the effect of splitting up one of the sources into many smaller flux fragments. The evolution and heating are shown to be very similar to the two source case. The impact of increasing the strength of the background field between the flux tubes is also examined and we find that it delays and increases the strength of the heating, although by how much depends on the distribution of the flux sources.

In highly conductive plasmas described by the ideal magnetohydrodynamics (MHD), magnetic field lines are frozen-in to the plasma. The contrary process takes place when the localized non-ideal and diffusive effects allow the field lines to break and reform, and therefore, called "magnetic reconnection" process. Magnetic reconnection is well recognized as an important plasma process capable of converting enormous amounts of stored magnetic energy to both thermal energy and bulk acceleration of the plasma. Single-fluid MHD model of this process can not explain the rate of magnetic reconnection observed in the space and laboratory plasmas, but the two-fluid model has raised the promises of explaining the magnetic reconnection satisfactorily. This thesis by employing the two-fluid MHD model of the magnetic reconnection studies theoretically this process.

The Richtmyer-Meshkov instability (RMI) in the convergent geometry is numerically studied in the framework of ideal magnetohydrodynamics (MHD) and two-fluid plasma in this thesis. The converging RMI usually occurs along with the Rayleigh-Taylor instability (RTI) due to the non-uniform motion or continuous acceleration of the interface. First, we investigate the interaction between a converging cylindrical shock and double density interfaces in the presence of a saddle magnetic field with ideal MHD model. We show that the RMI is suppressed by the magnetic field . However, the extent of the suppression varies on the interface which leads to non-axisymmetric growth of the perturbations. The degree of asymmetry increases when the seed field strength increases. The perturbation amplitude is affected by the competition mechanism between RMI and RTI. It increases when RMI dominates RTI while decreases when RTI dominates. Then, we research the two-fluid plasma RMI of a cylindrical density interface without an initial magnetic field. Varying the Debye length scale, we examine the effects of the coupling between the electron and ion fluids. The charge separation is responsible for the self-generated electromagnetic fields. We show that the Biermann battery effect dominates the generation of magnetic field when the coupling effect is weak. In addition to the RT stabilization effect during flow deceleration, the interfaces are accelerated by the induced Lorentz force. As a consequence, the perturbations develop into the RTI, leading to an enhancement of the perturbation amplitude compared with the hydrodynamic case. Finally, we investigate the linear evolution of two-fluid plasma RMI. We show that the increase of perturbation amplitude is almost contributed by the ion shock-interface interaction. We also examine the effect of magnetic field in the streamwise direction. For a short duration after the ion shock-interface interaction, the growth rate is similar for different initial magnetic field strengths. As time progresses the suppression of the instability due to the magnetic field is observed. The growth rate shows oscillations with a frequency that is related to the ion or electron cyclotron frequency. The instability is suppressed due to the vorticity being transported away from the interface.

The framework for the Hall magnetohydrodynamic (MHD) model for plasma physics is built up from kinetic theory and used to analytically solve problems of interest in the field. The Hall MHD model describes fast magnetic reconnection processes in space and laboratory plasmas. Specifically, the magnetic reconnection process at an X-type neutral point, where current sheets form and store enormous amounts of magnetic energy which is later released as magnetic storms when the sheets break up, is investigated. The phenomena of magnetic flux pile-up driving the merging of antiparallel magnetic fields at an ion stagnation-point flow in a thin current sheet, called the Parker problem, also receives rigorous mathematical analysis.

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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Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Earth and Planetary Sciences, 1981. / Microfiche copy available in Archives and Science. / Bibliography: leaves 171-173. / by Adolfo Figueroa Vinãs. / Ph.D.