Transverse impedance of a resistive cylinder of finite length

In this report we calculate the transverse impedance of a charged particle beam, displaced from the axis of a circular cylindrical beam pipe which has finite resistivity only over a finite length. For this purpose we replace it with a cavity filled with the resistive material and connected to the region surrounding the beam by a gap of the same length. Matching of the electro-magnetic fields on both sides of the gap leads to an infinite set of linear equations for the field expansion coefficients with terms given by infinite sums over integrals which are evaluated by summing over their residues. By truncating these sums one can determine the transverse impedance and evaluate it numerically. Keeping only the lowest terms gives simple approximate expressions which are often sufficient to estimate the values and parameter dependence of the impedance.