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A detailed analysis is given of the procedures involved in balancing second order axial gradiometers using superconducting vanes. Building on this analysis a very simple practical procedure emerges that provides a means of quantifying the initial imbalance and correcting it in an iterative manner. The method is illustrated by comparing experimental data with numerical calculations. The effects of test field inhomogeneities and eddy current sources on the balancing procedure and the degree of noise rejection obtained are discussed.

In order to describe the response of an RF SQUID to current flowing in a signal coil to which it is inductively coupled, the authors introduce the idea that currents flowing in the SQUID body are divided into two components, which they term coil-screening and flux-screening currents. They develop a more precise definition of what is usually called the mutual inductance of the SQUID, and obtain an expression for it. For the case of the two-hole SQUID, this expression is compared with the experimentally known relationship. Several other useful relations for the SQUID are obtained. Using these concepts they have analysed the dependence of the period of the response on the SQUID geometry. Experimental results for two-hole and toroidal SQUIDS support this analysis.

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