Abstract
The perturbation method of Chatard-Moulin and Papiernik is used to calculate the longitudinal and transverse impedances, Z(ω) and Z⊥(ω), of a bellows. The bellows shape is defined by its radius a(z) = a (1 + es(z)), where a is the mean radius, e a small parameter, and s(z) describes the convolution of the bellows. We consider a finite wall conductivity and determine the resonant contribution to the impedance above the cutoff frequency of the unperturbed chamber, obtaining analytic approximations to the resonant frequencies, quality factors, and shunt impedances. The relation Z⊥(ω) = (2c/a2)Z(ω)/ω, of course, does not hold as an identity, but it is found to be a useful relation for the shunt impedances, holding exactly for one family of transverse modes and providing an upper bound on the shunt impedances of the second set of transverse modes.
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