Quantification of resistive wall instability for particle accelerator machines

Abstract

The aim of this study is to quantify longitudinal resistive wall impedances, corresponding wake functions, and wake potentials for different accelerator machines of interest. Accurate calculations of wake potentials by particle-in-cell codes are extremely difficult for the investigated parameters; therefore, we use an analytical approach and consider large domains with fine discretization for the required numerical integrations. The semianalytical wake potential computations are benchmarked against numerical general purpose 2D/3D Maxwell solver software codes and a different analytical approach for a certain set of parameters. We report examples to illustrate limitations of wake potential estimations from coupling impedances, and computations for the machines using realistic beam parameters and machine conditions. A numerical example where the aim is to find the wake potential of the machine from the 5$\%$ noisy impedance data is given.