TMCI threshold with space charge and different wake fields

TL;DR

This paper analyzes the transverse mode coupling instability (TMCI) threshold in particle bunches considering space charge effects and various wake fields, providing a comprehensive dispersion relation and exploring how thresholds change with space charge tune shifts.

Contribution

It introduces a dispersion equation for TMCI with space charge and arbitrary wake fields using a basis of eigenfunctions, including realistic wake models.

Findings

Negative wake TMCI threshold increases with space charge tune shift.

Positive wake TMCI threshold decreases as space charge tune shift increases.

The bunch spectrum analysis explains the threshold behavior.

Abstract

Transverse mode coupling instability of a bunch with space charge and wake field is considered within the frameworks of the boxcar model. Eigenfunctions of the bunch without wake are used as a basis for the solution of the equations with the wake field included. A dispersion equation for constant wake is presented in the form of an infinite continued fraction and also as the recursive relation with an arbitrary number of the basis functions. Realistic wake fields are considered as well including resistive wall, square, and oscillating wakes. It is shown that the TMCI threshold of the negative wake grows up in absolute value when the SC tune shift increases. Threshold of positive wake goes down at the increasing SC tune shift. The explanation is developed by an analysis of the bunch spectrum.