In this thesis we follow on the mathematical aspects of the previous work of Shivamoggi (2009) on the Parker problem in Hall magnetohydrodynamics (MHD). We will present an analysis involving detailed analytical and numerical solutions to the Parker problem in Hall MHD. We give an analytical formulation for the Parker problem in Hall MHD, involving an initial value problem (IVP) associated with a first order Riccati equation (RE). We present Mathematica software exact solutions directly with special functions and more straightforward solutions that use the change of variables and power series methods without special functions. We give an asymptotic formulation for the solution using the method of dominant balance in the various regions of interest. These regions describe the triple-deck spatial structure of the magnetic field profile for the Parker problem in Hall MHD. We then give a numerical solution using Runge-Kutta (RK 4) method which offers a comparable solution to the RE IVP with an acceptable number of points and error. We use the Picard iteration method (PIM) to give a unique solution to the RE IVP that can be extended from its initial point with an acceptable number of terms and computing time. The analytical, asymptotic analysis and numerical solutions results are shown to be in agreement with the various special solutions given by Shivamoggi (2009). We discuss the theoretical underpinnings for our solution of the RE IVP associated with the Parker problem in Hall MHD provided by the usual existence and uniqueness theorems.
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Master of Science (M.S.)
College of Sciences
Length of Campus-only Access
Masters Thesis (Open Access)
Malott, Chad, "The Parker Problem in Hall Magnetohydrodynamics Analytical and Numerical Solutions" (2022). Electronic Theses and Dissertations, 2020-. 1050.