# Wakefields, Landau damping and beam instabilities

- Institution: CERN
- Department: CERN Academic Training Lecture,284
- Speaker: Albert Hofmann
- Year: 1993
- Level: Graduate
- Language: English
- Source: [CERN](https://videos.cern.ch/record/3024610)
- Licence: [CERN](http://copyright.web.cern.ch)
- Who can watch: Teens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

The concepts of wake potential and impedance are introduced in the example of a single mode cavity. Longitudinal beam dynamics is then briefly discussed and the Vlasov equation derived. With this as a base, the effects of a broad band reactive impedance on the bunch (potential bunch lengthening) and of a narrow band resistive impedance on the bunch stability (Robinson instability) are calculated. The concept of Landau damping is introduced by calculating the response of coasting beam with frequency spread to a transverse excitation (transfer function). The obtained result is used to obtain a transverse beam stability criterion. Finally, the response of a bunched beam is investigated..

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## Lectures

1. [Wakefields, Landau damping and beam instabilities](https://invisiblenetwork.ai/learn/cern/3024610/08b3de6f78de), 47 min (CERN's player)