Landau damping

Section 2.5.8 of the Handbook of Accelerator Physics and Engineering on Landau damping is rewritten. An solvable example is first given to demonstrate the interplay between Landau damping and decoherence. This example is an actual one when the beam oscillatory motion is driven by a wake force. The dispersion relation is derived and its implication on Landau damping is illustrated. The rest of the article touches on the Landau damping of transverse and longitudinal beam oscillations. The stability criteria are given for a bunched beam and the changes of the criteria when the beam is lengthened and becomes unbunched.