Transverse modes and instabilities of a bunched beam with space charge and resistive wall impedance

TL;DR

This paper analyzes the transverse instabilities of bunched beams considering space charge, resistive wall effects, and synchrotron oscillations, providing detailed insights into growth rates, thresholds, and damping mechanisms.

Contribution

It introduces a comprehensive analysis of beam instabilities using a boxcar model combined with Gaussian distributions, including effects of chromaticity and internal oscillations.

Findings

Instability thresholds vary with mode and parameters.

Landau damping from space charge can stabilize certain modes.

Effects of resistive wall impedance are quantitatively characterized.

Abstract

Transverse instability of a bunched beam is investigated with synchrotron oscillations, space charge, and resistive wall wakefield taken into account. Boxcar model is used for all-round analysis, and Gaussian distribution is invoked for details. The beam spectrum, instability growth rate and effects of chromaticity are studied in a wide range of parameters, both with head-tail and collective bunch interactions included. Effects of the internal bunch oscillations on the of collective instabilities is investigated thoroughly. Landau damping caused by the space charge tune spread is discussed, and the instability thresholds of different modes of Gaussian bunch are estimated.