Simplified calculus for the design of a cryogenic current comparator

The calculation of inductances of superconducting structures like the cryogenic current comparator (CCC) is not straightforward due to image effects and unknown current distributions. By treating the problem as a magnetic circuit, an approximate analytical expression for the self-inductance of the shielded CCC is obtained. This formula can be used to derive a "rule of thumb" for maximizing the value of an inductance inside a superconducting shield. Using this rule the design of an optimum CCC is simplified.