Design of magnets inside cylindrical superconducting shields

Abstract

We discuss the design of magnets inside closed, cylindrical, superconducting shields. We give the Green function for the magnetic vector potential for cylindrically symmetric currents inside such a shield. The magnetic field everywhere inside the shield can be obtained from this function, which includes the effects of the induced shield currents exactly. We give the field for a thin solenoid as an example and discuss the convergence of the series solution for this case. The shield can significantly reduce the strength and improve the homogeneity of a magnet. The improvement in homogeneity is of particular importance in the design of correction coils. These effects, and the maximum field on the shield, are examined for a typical solenoid. The results given are also useful, although not exact, for long shields with one or two open ends.