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The longitudinal coupling impedance of a cylindrical beam pipe for arbitrary relativistic energy and mode frequency is obtained analytically for finite wall conductivity and finite wall thickness. Closed form expressions for the electromagnetic fields excited by a beam perturbation are derived analytically. General expressions for the resistive-wall impedance in the presence of a metallic shield and for the rf shielding effectiveness of the beam pipe have been obtained. The results are applieddoi:10.1063/1.1949565 fatcat:olm7pliddnewvdhiau6eeipgom