Coupled-Beam and Coupled-Bunch Instabilities

TL;DR

This paper analyzes coupled-beam instabilities in a multibunch accelerator, specifically addressing how different revolution frequencies affect growth rates and exploring stabilization methods like chromaticity and feedback.

Contribution

It provides a general analytical framework for coupled-beam instability with different revolution frequencies and applies it to the Fermilab Recycler Ring.

Findings

Sharing of inter-bunch growth rates between intra-bunch modes is characterized.

Stabilization strategies using chromaticity and feedback are evaluated.

The analysis enhances understanding of coupled-beam dynamics in multibunch accelerators.

Abstract

A problem of coupled-beam instability is solved for two multibunch beams with slightly different revolution frequencies, as in the Fermilab Recycler Ring (RR). Sharing of the inter-bunch growth rates between the intra-bunch modes is described. The general analysis is applied to the RR; possibilities to stabilize the beams by means of chromaticity and feedback are considered.