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 sim- plify 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 trans- verse 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 compar- isons between analytical formulas and 3D electromagnetic CST simulations.