Magnetic-field calculation for a high-temperature superconducting cryogenic current comparator (Q873173)

This paper is concerned with the study of the magnetic field of a cryogenic current comparator. In the case of a toroidal superconducting shield with an infinitesimal radial cut it is deduced the expression of the magnetic vector potential. This analysis is based on the study of a related Fredholm integral equation, which enables the author to establish an analytic expression for the current distribution on the outer surface. The ratio error formula shows that the error decreases by increasing the toroidal radius, and decreasing the inner radius of the shield. Moreover, since the dependence of the error on cut thickness is logarithmic then, in order to minimize the error, currents should be concentrated around the shield axis.