https://doi.org/10.1140/epjb/e2006-00067-3
How the coherent instabilities of an intense high-energy charged-particle beam in the presence of nonlocal effects can be explained within the context of the Madelung fluid description
1
Dipartimento di Scienze Fisiche, Università Federico II and INFN Sezione di Napoli, Complesso Universitario di M.S. Angelo, via Cintia, 80126 Napoli, Italy
2
Department of Electromagnetics, Chalmers University of Technology, Göteborg, Sweden
Corresponding author: a renato.fedele@na.infn.it
Received:
3
November
2005
Revised:
28
December
2005
Published online:
27
February
2006
A hydrodynamical description of coherent instabilities that take place in the longitudinal dynamics of a charged-particle coasting beam in a high-energy accelerating machine is presented. This is done within the framework of the Madelung fluid picture provided by the Thermal Wave Model. The well known coherent instability charts in the complex plane of the longitudinal coupling impedance for monochromatic beams are recovered. The results are also interpreted in terms of the deterministic approach to modulational instability analysis usually given for monochromatic large amplitude wave propagation governed by the nonlinear Schrödinger equation. The instability analysis is then extended to a non-monochromatic coasting beam with a given thermal equilibrium distribution, thought of as a statistical ensemble of monochromatic incoherent coasting beams (“white” beam). In this hydrodynamical framework, the phenomenon of Landau damping is predicted without using any kinetic equation governing the phase space evolution of the system.
PACS: 29.27.Bd – Beam dynamics, collective effects and instabilities / 05.45.-a – Nonlinear dynamics and nonlinear dynamical systems / 03.75.-b – Matter waves
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2006