Impedance of periodic irises in a beam pipe

In a recent paper, we constructed a variational form to calculate both the longitudinal and transverse impedance of a thick iris in a beam pipe. Implementation of this calculation led to rapidly converging and accurate values for these impedances for a circular beam pipe and iris. We have now constructed an analogous variational form for the longitudinal and transverse impedance of periodic irises in a beam pipe, with similar convergence and accuracy properties. In this case the numerically calculated impedance is imaginary, except for isolated narrow resonances corresponding to modes propagating with the velocity of light. The real part of impedance is obtained by using causality. Analysis and numerical results are discussed and presented