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

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.