A stochastic-hydrodynamic model of halo formation in charged particle beams
arXiv:cond-mat/0302382 · doi:10.1103/PhysRevSTAB.6.034206
Abstract
The formation of the beam halo in charged particle accelerators is studied in the framework of a stochastic-hydrodynamic model for the collective motion of the particle beam. In such a stochastic-hydrodynamic theory the density and the phase of the charged beam obey a set of coupled nonlinear hydrodynamic equations with explicit time-reversal invariance. This leads to a linearized theory that describes the collective dynamics of the beam in terms of a classical Schrödinger equation. Taking into account space-charge effects, we derive a set of coupled nonlinear hydrodynamic equations. These equations define a collective dynamics of self-interacting systems much in the same spirit as in the Gross-Pitaevskii and Landau-Ginzburg theories of the collective dynamics for interacting quantum many-body systems. Self-consistent solutions of the dynamical equations lead to quasi-stationary beam configurations with enhanced transverse dispersion and transverse emittance growth. In the limit of a frozen space-charge core it is then possible to determine and study the properties of stationary, stable core-plus-halo beam distributions. In this scheme the possible reproduction of the halo after its elimination is a consequence of the stationarity of the transverse distribution which plays the role of an attractor for every other distribution.
arXiv comment18 pages, 20 figures, submitted to Phys. Rev. ST AB
References in corpus (5)
- Stochastic collective dynamics of charged--particle beams in the stability regime
- Quantum-like approach to the transversal and longitudinal beam dynamics. The halo problem
- Stochastic effects in real and simulated charged particle beams
- Controlled quantum evolutions and transitions
- Inference of Planck action constant by a classical fluctuative postulate holding for stable microscopic and macroscopic dynamical systems