The mode matching technique applied to the transverse beam coupling impedance calculation of azimuthally symmetric devices of finite length

The infinite length approximation is often used to simplify the calculation of the beam coupling impedance of accelerator elements. This is expected to be a reasonable assumption for devices whose length is greater than the transverse dimension but may be a less accurate approximation for segmented devices. In this contribution we present the extension of the study of the beam coupling impedance of a finite length device to the transverse plane. In order to take into account the finite length, we decompose the fields in the cavity and in the beam pipe into a set of orthonormal modes and apply the Mode Matching method to obtain the impedance. To validate our method, we will present comparisons between analytical formulas and 3D electromagnetic CST simulations.