Single bunch transverse instability in a circular accelerator with chromaticity and space charge

TL;DR

This paper introduces a new tree-modes model for analyzing transverse bunch instability in circular accelerators, incorporating chromaticity and space charge effects, and explores how wake shape influences stability.

Contribution

A novel, flexible tree-modes model that includes chromaticity and space charge, applicable to any bunch and wake form, with detailed analysis of space charge effects on stability.

Findings

Instability parameters are sensitive to wake shape.

Negative wake fields can enhance bunch stability.

Resistive wall wake effects are thoroughly analyzed.

Abstract

The transverse instability of a bunch in a circular accelerator is elaborated in this paper. A new tree-modes model is proposed and developed to describe the most unstable modes of the bunch. This simple and flexible model includes chromaticity and space charge, and can be used with any bunch and wake forms. The dispersion equation for the bunch eigentunes is obtained in form of a third-order algebraic equation. The known head-tail and TMCI modes appear as the limiting cases which are distinctly bounded at zero chromaticity only. It is shown that the instability parameters depend only slightlyon the bunch model but they are rather sensitive to the wake shape. In particular, space charge effects are investigated in the paper and it is shown that their influence depends on sign of wake field enhancing the bunch stability if the wake is negative. The resistive wall wake is considered in detail including a comparison of single and collective effects. A comparison of the results with earlier publications is carried out.