Electromagnetic field and short-range wake function in a beam pipe of elliptical cross section

Abstract

Within the ultrarelativistic limit, analytical expressions are found for the high-frequency resistive-wall coupling impedance of an elliptical cross-section vacuum chamber. Subsequently, the corresponding wake functions are derived by performing inverse Fourier transformations numerically. The electromagnetic fields have been developed working out two systems of solutions, namely for the vacuum and for the resistive wall. The constants involved in these systems have been determined by matching boundary conditions at the interface vacuum wall. Several study cases have been considered concerning the aspect ratio of the elliptical cross section and the transverse position of the leading charge in order to exemplify the behavior of the longitudinal and transverse wake functions. © 2008 The American Physical Society.