Stochastic collective dynamics of charged--particle beams in the stability regime

Abstract

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.

15 pages, 9 figures

References in corpus (4)

• Quantum-like approach to the transversal and longitudinal beam dynamics. The halo problem
• Radiation Damping and Quantum Excitation for Longitudinal Charged Particle Dynamics in the Thermal Wave Model
• Controlled quantum evolutions and transitions
• Inference of Planck action constant by a classical fluctuative postulate holding for stable microscopic and macroscopic dynamical systems

Cited by in corpus (6)

• Quantum mechanics of Dirac particle beam optics: Single-particle theory
• Mixtures in non stable Levy processes
• A stochastic-hydrodynamic model of halo formation in charged particle beams
• Lévy-Schrödinger wave packets
• Levy-Student Distributions for Halos in Accelerator Beams
• Markov processes and generalized Schroedinger equations