Analysis of coupling impedance bench measurements using Bethe's diffraction theory

Abstract

In this paper we study the validity of coupling impedance bench measurements, comparing two of the most commonly used formulas to the result obtained applying a modified version of Bethe's theory of diffraction to a lumped impedance in a coaxial beam pipe. The equations found provide a quantitative expression for the influence of the wire thickness used in the measurement of the real and imaginary part of the longitudinal impedance. The precision achievable in an actual measurement is therefore discussed. The method presented can also be applied in the presence of distributed impedances as well as to the analysis of transverse impedance measurements.