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_m^{(2 n+1)})¹3/, and ( E⁵/B_m⁷)¹3/, for a single solenoid, toroidal coil, and axially-displaced coil configurations, respectively, where n is the number of coils.