Threshold of transverse mode coupling instability with arbitrary space charge

TL;DR

This paper develops a new method to calculate the threshold of transverse mode coupling instability considering arbitrary space charge effects, showing that the threshold increases indefinitely with tune shift and comparing results across different wake models.

Contribution

A novel calculation approach for the instability threshold that extends beyond traditional methods and applies to various wake functions and potential well shapes.

Findings

Instability threshold increases without limit as space charge tune shift grows.

The new method is applicable to square, resistive, and exponential wakes.

Results resemble those for parabolic potential wells, with explanations provided.

Abstract

Threshold of the transverse mode coupling instability is calculated in frameworks of the square well model at arbitrary value of space charge tune shift. A new method of calculation is developed beyond the traditional expansion technique. The square, resistive, and exponential wakes are investigated. It is shown that the instability threshold goes up without limit when the tune shift increases. A resemblance of the results to conventional case of the parabolic potential well is demonstrated and explained.