Longitudinal coupling impedance of a particle traveling in PEC rings: A regularised analysis

Abstract

Abstract The analysis of a charged particle traveling through one, two, or infinite conducting rings is presented. The problem is formulated in the spectral domain as integral equations of Fredholm type, solved by Galerkin's method employing entire domain functions factorising the correct edge behaviour of the unknown induced current. As a result, high accuracy and numerical stability are achieved. Numerical results are presented, proving the effectiveness of the method, and the parameters relevant to accelerator physics are calculated.

Keywords

• Galerkin method
• Fredholm integral equations
• numerical stability
• electromagnetic wave diffraction