The virial theorem and scaling laws for superconducting magnet systems

The structural masses of over thirty superconducting magnet designs are shown to exceed that required by the virial theorem by factors of from 2 to 10 or more. Designs for magnetohydrodynamic and toroidal field fusion magnets from many different magnet groups around the world appear to obey a stored energy-mass scaling law of the form E=CM4/3. This scaling law appears to be valid over three to four orders of magnitude of stored magnetic energy. The 4/3 power law differs from the linear scaling derived from the virial theorem and may be related in part to the thermal stability requirements of the superconductor. However, the masses of large-scale magnets are approaching the regime where the structural mass required by the virial theorem will place greater constraints on the design than thermal stability.