Transverse impedance of an iris in a beam pipe

In an earlier paper the longitudinal impedance of an iris was obtained in the form of an integral equation by matching the fields in the planes perpendicular to the axis at the ends of the iris. This equation was solved by expanding the field components into a complete set of azimuthally symmetric TM modes in the iris region and numerical results were obtained, particularly for large beam pipe radii. The same method is now applied to the calculation of the transverse impedance, where both asymmetric TM and TE modes are needed in the expansions. Once again the results are obtained for large beam pipe radius and a wide range of values of the relative values of the iris radius, the iris thickness, and the wavelength