We investigated the phenomena of self-stimulation of incoherent emission from an undulator installed in the linear accelerator or quasi-isochronous storage ring. We discuss possible applications of these phenomena for the beam physics also.
The evolution of the phase space density of particle beams in external fields is found proceeding from the continuity equation in the six-dimensional (6D) phase space (mu-space). The Robinson theorem, which includes the Liouville theorem as a special
case, was proved in a more simple and consistent alternative way valid for arbitrary external fields, averaged fields of the beam (self-generated electro-magnetic fields except intrabeam scattering) and arbitrary frictional forces (linear, nonlinear). It includes particle accelerators as a special case. The limits of the applicability of the Robinson theorem in case of cooling of excited ions having a finite living time are presented.
