Harmonic structure of cylindrical imaging coils.

Presented is a derivation of an exact closed-form expression for the spectra of resonant frequencies for magnetic resonance imaging birdcage coils in the limit of long coils with many elements. Results of the analysis are compared with observation in a variety of birdcage coils where it is shown that for even relatively short coils the progression of resonant frequencies are of the form omega m = omega 1m +/- 1/2 + low pass; -high pass, with m integer and omega 1 the primary resonance.