Minimum structure magnetic energy storage solenoids with a toroidal insert

Force-free magnetic energy storage devices are not possible and a theoretical minimum structural mass is required as determined by the virial theorem. The support structure required for a given system depends on geometry as well as current distribution. This paper considers an arbitrary cross-section energy storage solenoid carrying a given poloidal surface current distribution. To reduce the mass of the required structure, a toroidal current is provided on the inner surface of the solenoid cross-section to partially overcome the radially outward magnetic forces generated by the poloidal current. A minimum mass energy storage solenoid is obtained by determining the optimum cross-section and the corresponding optimum surface current distribution. The structural mass obtained for the optimized solenoid is only a few percent greater than the structural mass required based on the virial theorem and thus is more efficient superconducting magnetic energy storage devices are possible.