This research is concerned with the physical processes underlying the magnetically dominated energy-conversion processes that drive solar-terrestrial activity. The methodology involves the formation of an MHD treatment of transport-enriched evolution and instability processes, and their multi-dimensional nonlinear simulation onsupercomputers. The proposed program involves analytical and computational plasma physics, illuminated by the study of solar-activity measurements. It is planned to extend both the physical accuracy and solar applications of past computer simulations. Convective energization and reconnection of magnetic structures will be detailed, as well as the dynamic magnetic response (and support of) gravitating prominences, the speed-up of flare reconnection, and the evolution and activity of coronal streamers. These studies are motivated by the desire to understand related phenomena in the wider universe of astrophysics, and by the need to predict their consequences in the solar-terrestrial system.