Head-Tail Modes for Strong Space Charge

TL;DR

This paper analyzes head-tail modes in strong space charge conditions, deriving a general equation, exploring mode shapes and frequencies, and explaining how space charge suppresses transverse mode coupling instability.

Contribution

It introduces a comprehensive equation for head-tail modes under strong space charge and investigates their properties and damping mechanisms.

Findings

Derived a general equation for head-tail modes with strong space charge

Explored mode shapes, frequencies, and growth rates

Explained suppression of transverse mode coupling instability

Abstract

The head-tail modes are described for the space charge tune shift significantly exceeding the synchrotron tune. A general equation for the modes is derived. The spatial shapes of the modes, their frequencies, and coherent growth rates are explored. The Landau damping rates are also found. The suppression of the transverse mode coupling instability by the space charge is explained.