Stochastic collective dynamics of charged-particle beams in the stability regime.
We introduce a description of the collective transverse dynamics of charged (proton) beams in the stability regime by suitable classical stochastic fluctuations. In this scheme, the collective beam dynamics is described by time-reversal invariant diffusion processes deduced by stochastic variational principles (Nelson processes). By general arguments, we show that the diffusion coefficient, expressed in units of length, is given by lambda(c)sqrt[N], where 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 stochastic dynamics can be easily recast in the form of a Schrödinger 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 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.
Petroni
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Dipartimento Interateneo di Fisica dell'Università e del Politecnico di Bari, INFN Sezione di Bari and INFM Unità di Bari, Via G. Amendola 173, 70126 Bari, Italy. cufaro@ba.infn.it
De Martino
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De Siena
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Illuminati
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