Analysis of the longitudinal space charge impedance of a round uniform beam inside parallel plates and rectangular chamber

TL;DR

This paper presents a comprehensive analysis of the longitudinal space charge impedance of a uniform round beam in rectangular and parallel plate chambers, using the image charge method valid for all wavelengths.

Contribution

It introduces a fast-converging method for calculating LSC impedance with minimal image charges and discusses the impact of beam offset.

Findings

Few image charges suffice for high accuracy

The method is valid for arbitrary wavelengths

Beam offset effects are analyzed

Abstract

This paper analyzes the longitudinal space charge (LSC) impedances of a round uniform beam inside a rectangular and parallel plate chambers using the image charge method. This analysis is valid for arbitrary wavelengths and the calculation converges fast. The research shows that only a few of the image beams are needed to obtain a relative error less than 0.1%. The beam offset effect is also discussed in the analysis.