Explicit treatment of mutual inductance in eight-column birdcage resonators

A formulation has been developed for the determination of self and mutual inductances in unloaded, eight-column symmetric birdcage coils using their expected resonant mode current patterns and well-known inductance formulas. The average frequency differences between theory and experiment for mode one resonances for nine low-pass coils were 0.66 (+/- 0.57) MHz and 2.14 (+/- 2.08) MHz using effective (self plus mutual) and self inductances, respectively, and similarly, for three high-pass coils, 1.19 (+/- 0.56) MHz and 2.79 (+/- 2.20) MHz. These frequency differences were more pronounced for the higher modes; for mode four, the differences neglecting mutual inductance were 14.30 (+/- 11.10) MHz and 10.42 (+/- 4.60) MHz for the low- and high-pass coils, respectively. This analysis provides the first explicit evaluation of the total end-ring and column inductances L1 and L2 within each birdcage section at resonance with resulting excellent agreement in resonant frequencies between theory and experiment.