Landau damping

Abstract

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.Submitted to 3rd edition of Handbook of Accelerator Physics and Engineering

Transverse mode coupling instability of the bunch with oscillating wake field and space charge

“…In particular, the blue lines form the chart which is well known as the TMCI tunes without space charge ∆Q = 0 (see e.g. [8]). At κ = 0.5, the instability appears because of coalescence of the modes m = 0 and m = ±1 having the threshold |q 0 |/Q s0 = 0.81 (0.57 at κ = 0 or with the square wake model).…”

Selected Topics in Microwave Instabilities and Linacs

“…Spread in oscillation frequency accelerates damping and decelerates growths. This is called Landau Damping [7,8] Illustration of Landau Damping [9] Consider transverse oscillation of a particle in an unbunched beam…”