  A recent proposal (see quant-ph/9803068) to simulate semiclassical
corrections to classical dynamics by suitable classical stochastic fluctuations
is applied to the specific instance of charged beam dynamics in particle
accelerators. The resulting picture is that the collective beam dynamics, at
the leading semiclassical order in Planck constant can be described by a
particular diffusion process, the Nelson process, which is time-reversal
invariant. Its diffusion coefficient $\sqrt{N}\lambda_{c}$ represents a
semiclassical unit of emittance (here $N$ is the number of particles in the
beam, and $\lambda_{c}$ is the Compton wavelength). The stochastic dynamics of
the Nelson type can be easily recast in the form of a Schroedinger equation,
with the semiclassical 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
collective coherent effects.
