Transverse Mode Coupling Instability with Space Charge

TL;DR

This paper analyzes the transverse mode coupling instability in particle bunches considering space charge effects using the boxcar model, revealing how wake sign influences the instability threshold and spectrum.

Contribution

It introduces a dispersion equation for eigentunes incorporating space charge and wake effects, providing new insights into the instability behavior with different wake signs.

Findings

Space charge effects depend on wake sign, affecting instability thresholds.

Negative wake thresholds increase with small space charge and decrease at higher space charge.

The spectrum analysis explains the observed behavior of the instability.

Abstract

Transverse mode coupling instability of a bunch with space charge and wake field is considered in frameworks of the boxcar model. Eigenfunctions of the bunch without wake are used as the basis for solution of the equations with the wake field included. Dispersion equation for the bunch eigentunes is obtained in the form of an infinite continued fraction. It is shown that influence of space charge on the instability essentially depends on the wake sign. In particular, threshold of the negative wake increases in absolute value until the space charge tune shift is rather small, and goes to zero at higher space charge. The explanation of this behavior is developed by analysis of the bunch spectrum. A comparison of the results with published articles is represented.