Discussion on the Relation between Stored Energy and Current Density of Superconducting Magnets

Abstract

It is useful for designing superconducting magnets to find the relation between the stored energy and the composite current density: Here we discuss the relation using the requirements for the full stabilization and energy dumping. Comparing our arguments with the performance of the magnets built before, we find that the relation can be devided into following three regions;
(1) Energy Dumping Limit, where the current density is inversely proportional to the square root of the stored energy.
(2) Full Stability Limit, where the current density is almost independent of the stored energy.
(3) Superconductor Limit, where magnets can be wound without the liquid helium cooling channels, and the current density is determined by the critical current density of the conductor.
Then we figure out the problems to be solved to develop large-scale superconducting magnets.