Optimization of field homogeneity of Helmholtz-like coils for measuring the balance of planar gradiometers

Measuring the balance of planar SQUID gradiometers using a relatively small Helmholtz-like coil system requires a careful design of the coils in order to have a high degree of field uniformity along the radial direction. The level to which planar gradiometers can be balanced will be affected by any misalignment of the gradiometer relative to the ideal central position. The refore, the maximum degree of balancing possible is calculated numerically for the Helmholtz geometry under various perturbations, including misalignm ent of the gradiometer along the cylindrical and the radial axis, and angul ar tilting relative to the normal plane. Furthermore, if the ratio between the coil separation and coil radius is chosen to be less than unity, calcul ations show that the expected radial uniformity of the field can be improve d considerably compared to the traditional Helmholtz geometry. The optimize d coil geometry is compared to the Helmholtz geometry and is found to yield up to an order of magnitude improvement of the worst case error signal wit hin a volume spanned by the uncertainty in the alignment.