Coherent instabilities of intense high-energy 'white' charged-particle beams in the presence of nonlocal effects within the context of the Madelung fluid description

摘要

A hydrodynamical description of coherent instabilities that take place in thelongitudinal dynamics of a charged-particle coasting beam in a high-energyaccelerating machine is presented. This is done in the framework of theMadelung fluid picture provided by the Thermal Wave Model. The well knowncoherent instability charts in the complex plane of the longitudinal couplingimpedance for monochromatic beams are recovered. The results are alsointerpreted in terms of the deterministic approach to modulational instabilityanalysis usually given for monochromatic large amplitude wave train propagationgoverned by the nonlinear Schr\"odinger equation. The instability analysis isthen extended to a non-monochromatic coasting beam with a given thermalequilibrium distribution, thought as a statistical ensemble of monochromaticincoherent coasting beams ("white" beam). In this hydrodynamical framework, thephenomenon of Landau damping is predicted without using any kinetic equationgoverning the phase space evolution of the system.