Emerick, Andrew2013-08-092013-08-092013-08-09https://hdl.handle.net/11299/155303Magnetic fields play an important role in astrophysical objects, in everything from planet for- mation through large scale structure evolution. The understanding of how these fields evolve and affect the medium in which they are contained has been bolstered through complex computational simulations of both the micro physics involved, and on cosmological scales. I focus on the context of magnetic fields in diffuse plasmas such as that present in the intracluser medium (ICM) of galaxy clusters. In this paper, I examine the evolution of initially weak magnetic fields through solenoidally driven turbulence in a plasma medium. This evolution is expected to be controlled predominantly by the small scale turbulent dynamo until the system reaches equillibrium. The relevant time domain in galaxy clusters, with eddy turnover times on the order of a few to several Myr, corresponds to well before the equillibrium stage. I focus then on the early magnetic field evolution and turbulent amplification under three initial magnetic field conditions utilizing an ideal, isothermal MHD code. I examine the detailed time and power spectra evolution of both the kinetic and magnetic energies, and compare to what would be expected in the small scale dynamo picture. In addition, I examine the prospects of distinguishing initial magnetic field structures within the ICM.en-USSumma Cum LaudeAstrophysicsCollege of Science and EngineeringThesis or Dissertation