Conceptual foundation of the Fokker-Planck approach to space-charge effects

An rms-mismatched beam can evolve rapidly to a configuration of quasiequilibrium under the influence of space-charge forces. As sit evolves, its emittance grows and a diffuse halo forms. The beam's distribution function accounts for all the complicated dynamics. Unfortunately, the distribution function is difficult to calculate in as much as the physics lies at the interface between classical mechanics and thermodynamics. This paper presents the foundation for a statistical theory of the dynamics of nonequilibrium space-charge-dominated beams. Within certain approximations, the theory takes on a Fokker-Planck form. Key questions arise concerning the nature of the dynamical friction and diffusion in the beam's phase space and of the quasiequilibrium configuration that ensues