Introducing a description of the collective transverse dynamics of charged (proton) beams in the stability regime by suitable classical stochastic fluctuations, we show that the transition probabilities associated to Nelson processes can be exploited to model evolutions suitable to control the transverse beam dynamics. In particular we show how to control, in the quadrupole approximation to the beam-field interaction, both the focusing and the transverse oscillations of the beam, either together or independently.
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