Longitudinal beam dynamics II. Lecture 2: intensity effects and beam instabilities

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