A method is described of calculating the resonant frequencies of cylindrical re-entrant electromagnetic cavities, which provides upper and lower bounds to the required frequency. These bounds converge towards each other as the number of terms in certain harmonic expansions is increased. The lower bound is increased by subtracting from the total field a singular part caused by the presence of sharp corners. Application to cavities of interest in the design of proton linear accelerators shows that accuracies of better than 1 per cent can be obtained without excessive computing time.
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Ron Taylor (1961) studied this question.