Transverse Instabilities of a Bunch with Space Charge, Wake and Feedback

TL;DR

This paper investigates the complex interplay of space charge, wakefields, and feedback in beam stability, revealing new instability modes and behaviors relevant for accelerator physics.

Contribution

It introduces a detailed analysis of combined feedback, wake, and space charge effects, identifying new instability modes and their characteristics.

Findings

Identification of feedback-wake instability (FWI) with a gain-dependent pattern.

Discovery of a new transverse mode-coupling instability (3FMCI) at high fields and gain.

Observation of growth rate saturation in the 3FMCI mode.

Abstract

When a resistive feedback and single-bunch wake act together, it is known that some head-tail modes may become unstable even without space charge. This feedback-wake instability, FWI, modified by space charge to a certain degree, is shown to have a special single-maximum increasing- dropping pattern with respect to the gain. Also, at sufficiently large Coulomb and wake fields, as well as the feedback gain, a new type of transverse mode-coupling instability is shown to take place, 3FMCI, when head-to-tail amplified positive modes couple and the growth rate saturates with the gain.