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Abstract
Magnetohydrodynamics (MHD), a fluid model of the low-frequency behavior of magnetized plasma, provides the most successful framework for understanding the equilibrium and large-scale stability of magnetically confined plasma. The success of this model is due in large part to its simplicity relative to more complete models. Much of this simplicity comes at the expense of the omission of non-ideal effects, which include dissipation, two-fluid and finite Larmor radius effects, micro-turbulence, and wave-particle interactions, among others. Often, the inclusion of these effects leads to important and unexpected phenomena. However, incorporating some of these effects, which may occur on vastly disparate spatial and temporal scales, introduces significant mathematical complexity and makes obtaining numerical solutions substantially more difficult. This dissertation investigates methods for numerically solving fluid models that have been extended to include some of these non-ideal effects, and to use these methods together with analytic theory to explore non-ideal effects on the steady-states and stability of magnetized plasmas.
An overview of the two-fluid model of a magnetized plasma is given. This overview includes discussion of various methods of closing the fluid equations, and the physical effects included (or excluded) by each method. A method for the solution of a generic set of collisional two-fluid equations is described, and results from an implementation of this method, the numerical code M3D- C1, are presented. The importance of two-fluid effects and gyroviscosity on the linear growth rate of three instabilities—the gravitational instability, the magnetorotational instability, and the magnetothermal instability—is demonstrated analytically. It is shown that gyroviscosity, in particular, may play an important role in the stability threshold of these instabilities. Toroidal axisymmetric steady-states of the two-fluid model are obtained using M3D-C1 for magnetic configurations typical of the National Spherical Torus Experiment (NSTX). These steady-states represent the first such states obtained with self-consistently determined flow of a dissipative model in realistic geometry. Resistively-driven radial flows are shown to be in excellent agreement with Pfirsch-Schlüter theory. Qualitative and quantitative agreement is found with comparable results for resistively-driven toroidal edge flows. New results, including toroidal rotation and oscillation due to gyroviscosity, are characterized and discussed.