An analytical framework is presented which justifies the use of a confocal elliptical shield (previously adopted on empirical or numerical grounds) to limit the spatial extent of the radiofrequency (RF) field produced by an elliptical birdcage coil, while concurrently minimizing field inhomogeneities. From this analytical capability it is further shown that the relative linear mode geometric sensitivities depend only on the shield dimensions and can be readily evaluated, thus providing an upper bound to the improvement in signal-to-noise ratio (SNR) of the damped elliptical birdcage over a circular coil of similar dimensions. The mismatch in the linear mode sensitivities can also be evaluated, and a method for the design of an appropriate feed configuration that ensures quadrature operation is given.
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