Transverse mode coupling instability of the bunch with oscillating wake field and space charge

TL;DR

This paper analyzes how oscillating wake fields and space charge effects influence the transverse mode coupling instability thresholds in particle bunches, providing formulas and insights for different wake phase advances.

Contribution

It introduces a detailed analysis of the combined effects of oscillating wake fields and space charge on instability thresholds, including asymptotic formulas for various phase advances.

Findings

Space charge can either raise or lower the instability threshold depending on wake phase advance.

The wake phase advance from 0 to 4π significantly affects the instability behavior.

Simple asymptotic formulas for thresholds are derived for different regimes.

Abstract

Transverse mode coupling instability of a single bunch caused by oscillating wake field is considered in the paper. The instability threshold is found at different frequencies of the wake with space charge tune shift taken into account. The wake phase advance in the bunch length from 0 up to $4\pi$ is investigated. It is shown that the space charge can push the instability threshold up or down dependent on the phase advance. Transition region is investigated thoroughly, and simple asymptotic formulas for the threshold are represented.