Impedances and Instabilities

TL;DR

This paper introduces the concepts of wake fields and impedance in particle accelerators, explaining their effects on beam stability, and discusses how chamber geometry and materials influence these phenomena.

Contribution

It provides a comprehensive overview of wake fields, impedance, and their relation to beam instabilities, including models and examples relevant to accelerator design.

Findings

Impedance affects beam stability and current limits.

Cavity mode impedance can be modeled with equivalent circuits.

Geometry and materials of vacuum chambers influence impedance.

Abstract

The concepts of wake fields and impedance are introduced to describe the electromagnetic interaction of a bunch of charged particles with its environment in an particle accelerator. The wake fields can act back on the beam and lead to instabilities, which may limit the achievable current per bunch, the total current, or even both. Some typical examples are used to illustrate the wake function and its basic properties. Then the frequency-domain view of the wake field or impedance is explained, and basic properties of the impedance are derived. The impedance of a cavity mode is illustrated using an equivalent circuit model. The relation of wake field effects to important beam parameters is treated in the rigid beam approximation. Several examples are employed to illustrate the impact of the geometry and the material properties of the vacuum chamber on the impedance. Finally, a basic introduction to beam instabilities based on a head tail model of the beam is given.