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This paper presents the theory of the quadrature birdcage coil wound on an elliptic cylindrical former. A conformal transformation of the ellipse to a circular geometry is used to derive the optimal sampling of the continuous surface current distribution to produce uniform magnetic fields within an elliptic cylinder. The analysis is rigorous for ellipses of any aspect ratio and shows how to produce quadrature operation of the elliptic birdcage with a conventional hybrid combiner. Insight gained from the transformation is also used to analyze field homogeneity, find the optimal RF shield shape, and specify component values to produce the correct current distribution in practice. Measurements and images from a 16-leg elliptic birdcage coil at both low and high frequencies show good quadrature performance, homogeneity, and sensitivity.

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This paper presents details of an unusual clip-on nanoammeter. The device utilizes a toroidal magnetic flux sensor which is split to allow its placement around a continuous current carrying filament, and is coupled to a sensitive superconducting current amplifier. Optimization formulas allow the design of an instrument having the greatest possible signal-to-noise ratio consistent with the physical volume available for the sensing element. A prototype exhibited 125-nA current sensitivity at 25 Hz with a noise level of 40 nA/Hz1/2. The performance of this instrument verified the predictions of the theory. The optimization analysis for this probe demonstrated that the signal-to-noise ratio could have been doubled by a slight change in toroid dimensions. It was shown that SQUID noise is negligible for this instrument, justifying the assumption of a noiseless amplifier in the original calculation. Finally, the conditions under which an impedance matching transformer can reduce the importance of the SQUID noise relative to the Johnson noise are derived, and the required inductances are given.