The aim of this research program is the establishment of the physical mechanisms underlying the magnetically dominated energy- conversion processes that drive solar-terrestrial activity. Significant progress in developing two new computer codes for the treatment of MHD instabilities in sheared magnetic fields has been made. This grant will extend both the physical accuracy and solar applications of the computer experiments. It is intended to add more realistic boundaries, dissipative and gravitational effects, and a full third dimension. These powerful simulation instruments will be used to detail the saturation process for flare reconnection, the final equilibrium state of a filament and its stable magnetic-support mechanism, the efficiency of Alfven wave heating, and the acceleration dynamics of coronal mass ejections. 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.