Envelope instability as a source of diffusion

Electron cooling increases the phase space density of the cooled particles up to a certain limit. This limit is normally characterized by a strong space charge tune shift, about 0.2-0.3. This tune shift is high enough to bring the cooled beam to the threshold of the envelope instability. The envelope instability can be in a kind of dynamic equilibrium with the cooling, keeping the cooled beam at a threshold with a high level of the coherent noise. This noise acts as a diffusion for the halo particles which puts a limit on the stored current. (C) 2000 Elsevier Science B.V. All rights reserved.