Impedance of Small Obstacles and Rough Surfaces

We calculate the longitudinal impedance for small obstacles of arbitrary shape located on the surface of a round perfectly conducting pile. Calculations are carried out in a small{angle approximation that assumes a smallness of the angle between the surface of the obstacle and the unperturbed surface of the pipe. As an illustration of the accuracy of this approach, we compare the impedance of the triangular mask and an ellipsoidal protrusion in small{angle approximation with a more general result known from the literature. We also apply our theory to the calculation of the impedance due to the roughness of the wall surface in terms of the spectral function characterizing statistical properties of the microscopic surface landscape. Submitted to Physical Review Special Topics: Accelerators and Beams Work supported by Department of Energy contract DE{AC03{76SF00515.