A 50-MJ superconducting magnetic energy storage plant has been proposed. A discussion is presented of the design study for the plant's coil system. The 5-m diameter coil is divided into six sections that will be transported from the factory and assembled on site. The authors describe the superconducting cables, electromagnetic forces and stresses on the coil structure, the helium and vacuum vessels used, the coil's thermal insulating support structures, cooling system, and coil protection system.>