Theory and Simulation of Magnetohydrodynamic Dynamos and Faraday Rotation for Plasmas of General Composition

Many astrophysical phenomena depend on the underlying dynamics of magnetic fields. The observations of accretion disks and their jets, stellar coronae, and the solar corona are all best explained by models where magnetic fields play a central role. Understanding these phenomena requires studying the basic physics of magnetic field generation, magnetic energy transfer into radiating particles, angular momentum transport, and the observational implications of these processes. Each of these topics comprises a large enterprise of research. However, more practically speaking, the nonlinearity in large scale dynamo is known to be determined by magnetic helicity(>), the topological linked number of knotted magnetic field. Magnetic helicity, which is also observed in solar physics, has become an important tool for observational and theoretical study. The first part of my work addresses one aspect of the observational implications of magnetic fields, namely Faraday rotation. It is shown that plasma composition affects the interpretation of Faraday rotation measurements of the field, and in turn how this can be used to help constrain unknown plasma composition. The results are applied to observations of astrophysical jets. The thesis then focuses on the evolution of magnetic fields. In particular, the dynamo amplification of large scale magnetic fields is studied with an emphasis on the basic physics using both numerical simulations and analytic methods. In particular, without differential rotation, a two and three scale mean field (large scale value + fluctuation scales) dynamo theory and statistical methods are introduced. The results are compared to magnetohydrodynamic (MHD) simulations of the Pencil code, which utilizes high order finite difference methods. Simulations in which the energy is initially driven into the system in the form of helical kinetic energy (via kinetic helicity) or helical magnetic energy (via magnetic helicity) reveal the exponential growth of seed magnetic fields by a mechanism known as ``alpha effect." The generalized theory systematically explains the simulation results, showing how magnetic energy is inversely cascaded from small to large scales, and how the large scale field growth saturates. In addition to work on the nonlinear saturation of large scale magnetic fields, the thesis also includes a study of the influence of the magnitude and distribution of the magnetic energy on the large scale field growth rate in the last chapter. Since the large scale dynamos of most astrophysical objects are likely not yet in a resistively saturated state (due to the high conductivity of astrophysical plasmas), the evolution of the magnetic field in the pre-saturation regime is most important. The results show that, within the limitations of the present study, the effect of the initial field distribution on the large scale field growth is limited only to the early growth regime, not the saturated time regime.