Stochastic collective dynamics of charged-particle beams in the stability regime - art. no. 016501

We introduce a description of the collective transverse dynamics of charged (proton) beams in the stability regime by suitable classical stochastic fl uctuations. In this scheme, the collective beam dynamics is described by ti me-reversal invariant diffusion processes deduced by stochastic variational principles (Nelson processes). By general arguments, we show that the diff usion coefficient, expressed in units of length, is given by lambda (c)root N, when N is the number of particles in the beam and lambda (c) the Compton wavelength of a single constituent. This diffusion coefficient represents an effective unit of beam emittance. The hydrodynamic equations of the stoc hastic dynamics can be easily recast in the form of a Schrodinger equation, with the unit of emittance replacing the Planck action constant. This fact provides a natural connection to the so-called "quantum-like approaches'' to beam dynamics. The transition probabilities associated to Nelson process es can be exploited to model evolutions suitable to control the transverse beam dynamics. In particular we show how to control, in the quadrupole appr oximation to the beam-field interaction, both the focusing and the transver se oscillations of the beam, either together or independently.