Analytically Regularized Evaluation of the Wakefield of a Particle Travelling through a Plane Conducting Ring

In this work the wakefield of a charged particle traveling through a plane conducting ring is evaluated. The problem is formulated in the spectral domain as integral equations of Fredholm type, solved by Galerkin method employing entire domain functions factorizing the correct edge behavior of the unknown induced current. As a result, high accuracy and numerical stability are achieved, allowing the calculation of parameters relevant to accelerator physics, such as longitudinal impedance and wakefield.