99 8 A stochastic model for the semiclassical collective dynamics of charged beams in particle accelerators 1

In this paper we briefly review the main aspects of a recent proposal to simulate semiclassical corrections to classical dynamics by suitable classical stochastic fluctuations, and we apply it to the specific instance of charged beams in particle accelerators. The resulting picture is that the collective beam dynamics, at the leading semiclassi-cal order in Planck constant can be described by a particular diffusion process, the Nelson process, that is time–reversal invariant. Its diffusion coefficient √ Nλ c represents a semiclassical unit of emittance (here N is the number of particles in the beam, and λ c is the Comp-ton wavelength). The stochastic dynamics of the Nelson type can be easily recast in the form of a Schroedinger equation, with the semi-classical unit of emittance replacing Planck constant. Therefore we provide a physical foundation to the several quantum–like models of beam dynamics proposed in recent years. We also briefly touch upon applications of the Nelson and Schroedinger formalisms to incorporate the description of coherent collective effects.