Scaling law of fringe fields as functions of stored energy and maximum magnetic field for SMES configurations

Although a SMES (Superconducting Magnetic Energy Storage System) has attractive potential for power management and quality control, the fringe field from the SMES restricts its site location. The fringe field outside a coil is expanded in a series of Legendre polynomials. The results are applied to the fringe fields of various SMES configurations, such as a single solenoid coil, toroidal coil, axially displaced coil. The derived fringe fields are scaled as functions of both the stored energy E and the maximum magnetic field B _m, which are the main parameters of superconducting coil design. The fringe fields decrease as E/B_m, (E⁽ⁿ⁺²⁾/B ⁽²ⁿ⁺¹⁾)^1/3, and (E⁵/B_m ⁷)^1/3, for a single solenoid, toroidal coll, and axially-displaced coil configurations, respectively, where n is the number of coils.