Stochastic cooling of particle beams

This lecture note describes the main analytical approaches to stochastic cooling. The first is the time-domain picture in which the beam is rapidly sampled and a statistical analysis is used to describe the cooling behaviour. The second is the frequency-domain picture, which is particularly useful since the observations made on the beam are mainly in this domain. This second picture is developed in detail to assess ingredients of modern cooling theory like mixing and signal shielding and to illustrate some of the diagnostic methods. Finally the use of a distribution function and the Fokker-Plank equation are discussed, which give the most complete description of the beam during the cooling.