# Longitudinal instabilities & Intensity effects

- Institution: CERN
- Department: CAS - CERN Accelerator School
- Speaker: Elena Shaposhnikova
- Year: 2023
- Level: Graduate
- Language: English
- Source: [CERN](https://videos.cern.ch/record/3014447)
- 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)

In this lecture, dealing with intensity effects, the equations of motion with induced beam voltage are analysed. This allows, first, to describe single-bunch potential well distortion and loss of Landau damping. Then the linearised Vlasov equation is used to derive step-by-step the Lebedev equation. This matrix equation is applied to find the thresholds, growth rates and spectra of unstable multi-bunch beam. The lecture is concluded by discussion of possible beam-instability cures.

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## Lectures

1. [Longitudinal instabilities & Intensity effects](https://invisiblenetwork.ai/learn/cern/3014447/1a04f2cf3489), 55 min (CERN's player)