Instabilities in Linear Accelerators

As a charged particle beam moves through perfectly conducting structures with varying cross-sectional boundaries - such as RF cavities, tapers, bellows, kickers, ... - it induces both longitudinal and transverse electromagnetic fields called wakefields. In this lecture, we explore the fundamental characteristics of wakefields and illustrate key concepts using simple cases in cylindrical geometry, including a perfectly conducting pipe and the resonant modes of an RF cavity. Finally, we examine how wakefields influence beam dynamics in a LINAC, focusing on beam breakup instabilities and potential mitigation strategies.