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.