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(⟨A · B⟩), 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