# Longitudinal HI ring beam-instabilities + mitigations II

- Institution: CERN
- Department: CAS - CERN Accelerator School
- Speaker: Ivan Karpov
- Year: 2025
- Level: Graduate
- Language: English
- Source: [CERN](https://videos.cern.ch/record/3023601)
- Licence: [CERN](https://copyright.web.cern)
- Who can watch: Teens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

The interaction of charged particles with the beam coupling impedance can lead to undamped or exponentially increasing oscillations in the longitudinal plane. To ensure the stability and reproducibility of beam parameters, many hadron synchrotrons must rely on Landau damping or active damping provided by feedback systems. Understanding the intensity threshold and beam evolution after perturbation is essential for pushing the performance of existing and future facilities. In these lectures, we first discuss the fundamentals of synchrotron motion and the role of the beam coupling impedance. Then, van Kampen modes and the formalisms for analysing beam stability are introduced. We use them to determine the threshold at which Landau damping is lost and examine two mechanisms of longitudinal single-bunch instabilities: azimuthal and radial mode coupling. Finally, the latest developments regarding multi-bunch instabilities are presented, and possible mitigation strategies are briefly discussed.

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## Lectures

1. [Longitudinal HI ring beam-instabilities + mitigations II](https://invisiblenetwork.ai/learn/cern/3023601/2a4fbdadefba), 44 min (CERN's player)