Thick Scatterers seen through the Twiss Functions

A treatment of multiple scattering for thick and thin scatterers is derived using the sigma-formalism which is then used to give a statistical description of the Twiss functions with the scattering included. Full account is taken of the geometric correlation which occurs between the scattering angle and displacement of the scattered particle. The formalism is first derived for uncoupled beams, but is then extended to take coupling into account. Excellent agreement is demonstrated with Monte-Carlo data. The Twiss-Scatterer relations presented make it possible to include arbitrarily, thick scatterers as elements in accelerator codes.