A calculation of the effect of coaxial superconducting shields on the flux sensitivity of SQUID pick-up coils

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Abstract
Two methods based on the use of mutual inductance are given for the calculation of the field surrounding a shielded circular loop carrying unit current. Taken in conjunction with a reciprocity theorem of electromagnetism this calculation provides values for the sensitivity of any shielded, elemental coil to changes in flux brought about by changes in the position or the moment of a nearby point dipole. The authors present an exact method to calculate the distribution of shielding currents set up on the inside of the coaxial shield and an approximate image-like method in which the effect of the entire shield is mimicked by a single coil of slightly larger radius than the shield. Detailed numerical comparisons are made both between the two methods and between the calculations and experimental results for a particular shielded coil. The authors demonstrate how the effect of a coaxial shield on the flux sensitivity of SQUID pick-up coils may be calculated and present a table of results for a range of coil-to-shield radius ratios.