The theory of an arbitrarily perturbed bird-cage resonator, and a simple method for restoring it to full symmetry

Abstract

The first-order theory of a low-pass bird-cage resonator perturbed at a single capacitor [J. Tropp, J. Magn. Reson. 82, 51 (1989)] is extended by explicit calculation to cover a low-pass bird cage perturbed arbitrarily at every reactance, provided that a first-order condition is satisfied. It is shown that the effect of arbitrary perturbation, i.e., the splitting of resonances and rotation of the polarization axes, can be exactly mimicked (in first order) by a pair of capacitors spaced by an azimuth of π 4 . This result may be extended by symmetry arguments to the high-pass and simple band-pass bird cage. A method of correcting symmetry (abolishing the splitting of the useful eigenstates) is then derived, which provides near-perfect correction by the application of two capacitors, typically spaced π 4 on the resonator azimuth. Experimental results are given for a low-pass bird-cage; and the correction procedure is verified and demonstrated in practical detail; and it is shown that the limit of the first-order theory is that the first of the two requisite correction capacitors should be within 7 or 8% of the nominal bird-cage capacitance. Practical examples of symmetry correction outside the first-order regime are also given.