Chairperson, Graduate Committee: Dana W. LongcopeTarr, Lucas AdrianDana W. Longcope was a co-author of the article, 'Calculating energy storage due to topological changes in emerging active region NOAA 11112' in the journal 'The astrophysical journal' which is contained within this thesis.Dana W. Longcope and Margaret Millhouse were co-authors of the article, 'Calculating separate magnetic free energy estimates for active regions producing multiple flares: NOAA AR11158' in the journal 'The astrophysical journal' which is contained within this thesis.Dana W. Longcope, David McKenzie, and Keiji Yoshimura were co-authors of the article, 'Quiescent reconnection rate between emerging active regions and preexisting field, with associated heating: NOAA AR11112' submitted to the journal 'Solar physics' which is contained within this thesis.2014-04-022014-04-022013https://scholarworks.montana.edu/handle/1/2917When magnetic field in the solar convection zone buoyantly rises to pierce the visible solar surface (photosphere), the atmosphere (corona) above this surface must respond in some way. One response of the coronal field to photospheric forcing is the creation of stress in the magnetic field, generating large currents and storing magnetic free energy. Using a topological model of the coronal magnetic field we will quantify this free energy. We find the free energy just prior to major flares in active regions to be between 30% and 50% of the potential field energy. In a second way, the coronal field may topologically restructure to form new magnetic connections with newly emerged fields. We use our topological model to quantify the rapid restructuring in the case of solar flare and coronal mass ejections, finding that between 1% and 10% of total active region flux is exchanged. Finally, we use observational data to quantify the slow, quiescent reconnection with preexisting field, and find that for small active regions between 20% and 40% of the total emerged flux may have reconnected at any given time.enCC BY-NC-SA 3.0https://creativecommons.org/licenses/by-nc-sa/3.0/Cosmic magnetic fieldsSolar energyDissertationCopyright 2013 by Lucas Adrian Tarr