Longitudinal coupling impedance of a plane conducting ring

Abstract

In this paper, we propose a new method to evaluate the longitudinal coupling impedance of a charged particle passing perpendicularly through the center of a plane conducting ring. It is shown that the solution of the problem can be expressed as a double Neumann series, whose expansion coefficients can be easily computed. Moreover, we show the causality of the wake potential for a particle traveling at the speed of light.