Generalized threshold of longitudinal multi-bunch instability in synchrotrons

TL;DR

This paper presents a unified approach to analyze longitudinal multi-bunch instability thresholds in synchrotrons, revealing how Landau damping loss can influence coupled-bunch instability limits, with implications for future accelerator designs.

Contribution

It introduces a numerical method and analytical threshold that integrate short- and long-range wakefield effects, advancing understanding of beam stability limits.

Findings

LLD can lower the multi-bunch instability threshold

The new approach explains observations in CERN SPS

Implications for future accelerators like HL-LHC and FCC

Abstract

Beam stability is an essential requirement for particle accelerators. Longitudinal coupled-bunch instabilities (CBI) are driven by beam interaction with long-range wakefields induced in the resonant structures with narrow-band impedance. Single-bunch loss of Landau damping (LLD) is mainly determined by short-range wakefields excited at any geometry change of the beam pipe (broadband impedance) and leads to undamped bunch oscillations. Up to now, to define the threshold beam intensity or impedance, these two effects were evaluated separately. We developed an approach to numerically solve the stability problem in a more general case and derived a new analytical threshold. We have shown that LLD can modify the mechanism of multi-bunch instability and reduce the CBI threshold below the LLD threshold. This effect explains the existing observations in the CERN SPS and should be considered for future accelerators, such as HL-LHC, EIC, FCC, and others.