A stochastic-hydrodynamic model of halo formation in charged particle beams

TL;DR

This paper introduces a stochastic-hydrodynamic model for charged particle beams that explains halo formation and stability, using coupled nonlinear equations analogous to quantum many-body theories, revealing stationary core-plus-halo configurations.

Contribution

It develops a novel stochastic-hydrodynamic framework for beam dynamics, linking classical collective motion to quantum-like equations, and analyzes stable halo formation in charged particle beams.

Findings

Derivation of coupled nonlinear hydrodynamic equations for beam dynamics

Identification of stationary, stable core-plus-halo distributions

Demonstration of halo reproduction as an attractor in the distribution space

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 Schr\"odinger 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.