Abstract
A semianalytic formalism is constructed for investigating the transverse dynamics of intense, mismatched charged-particle beams which are centered on, and propagate through, focusing channels. It uses the Fokker-Planck equation to account for the rapid evolution of the coarse-grained distribution function in the phase space of a single beam particle. It also incorporates the space-charge potential, which is calculated from Poisson’s equation using the coarse-grained density. A simple phenomenological model of dynamical friction and diffusion represents the effects of turbulence triggered by charge redistribution. Sheet beams and fully two-dimensional beams are both considered in detail. In addition, closed-form solutions are presented for beams in which the space charge is negligible and noise arises from other stochastic processes.
- Received 7 April 1994
DOI:https://doi.org/10.1103/PhysRevE.50.1516
©1994 American Physical Society