Convective Instabilities of Bunched Beams with Space Charge

TL;DR

This paper investigates how strong space charge affects beam stability in circular accelerators, revealing new convective instabilities that challenge previous assumptions about the stability thresholds of bunches.

Contribution

It introduces a novel analysis method and identifies two new instability types, SCI and ACI, explaining complex stability behavior under strong space charge conditions.

Findings

Strong space charge suppresses TMCI but induces convective amplifications.

Two new instability types, SCI and ACI, are identified.

Beam stability can be compromised even when traditional modes are stable.

Abstract

For a single hadron bunch in a circular accelerator at zero chromaticity, without multi-turn wakes and without electron clouds and other beams, only one transverse collective instability is possible, the mode-coupling instability, or TMCI. For sufficiently strong space charge (SC), the instability threshold of the wake-driven coherent tune shift normally increases linearly with the SC tune shift, as independently concluded by several authors using different methods. This stability condition has, however, a very strange feature: at strong SC, it is totally insensitive to the number of particles. Thus, were it correct, such a beam with sufficiently strong SC, being stable at some intensity, would remain stable at higher intensity, regardless of how much higher! This paper suggests a resolution of this conundrum: while SC suppresses TMCI, it introduces head-to-tail convective amplifications, which could make the beam even less stable than without SC, even if all the coherent tunes are real, i.e. all the modes are stable in the conventional {\it absolute} meaning of the word. This is done using an effective new method of analysis of the beam's transverse spectrum for arbitrary space charge and wake fields. Two new types of beam instabilities are introduced: the {\it saturating convective instability}, SCI, and the {\it absolute-convective instability}, ACI.