Storage ring longitudinal instabilities

The FEL gain is proportional to the particle density n ∝ Iσs. Both the beam current and the bunch length are influenced by electromagnetic fields, generated by the bunched beam. The longitudinal oscillations of single electrons or the whole bunch can be excited by these fields. This effect causes a blow-up of the bunch dimensions or even the loss of the beam. The only cure against these instabilities is the design of a vacuum chamber with extremely low impedance.