Textbooks on particle physics and free electron lasers treat fluctuations in particle beams by introducing summation over individual particles, in sharp contrast to the formalism of the distribution functions that represent the beam as a continuous medium evolving in phase space. In this talk, I advocate the use of the approach developed in the kinetic theory of gases that treats fluctuations in the context of distribution functions. The method is simple and at the same time powerful enough to address many problems in beam physics. Its usage is illustrated with selected problems from FEL theory, theory of stochastic cooling, and noise suppression in beams.
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