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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 at a high rate 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 and the numerical cooling simulations are mainly in this domain. This second picture is developed in detail to assess key components 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, which offer the most complete description of the beam during the cooling, are discussed.
Content Level »Research
Keywords »Fokker-Plank equation - Nobel Prize in Physics 1984 - Simon van der Meer - accelerator physics - beam cooling - beam cooling methods and diagnostics - betatron oscillations - stochastic cooling of particle beams
Foreword.- Introduction.- Simplified Theory, Time-domain Picture.- Pickup and Kicker Impedance.- Frequency-domain Picture.- A More Detailed Derivation of Betatron and Filter Cooling (Frequency-Domain Picture).- Feedback via the Beam and Signal Shielding.- The Distribution Function and Fokker-Planck Equations.- Some Special Applications.- References.- Glossary.