Electron cooler impedances

An electron beam of a cooler in an ion storage ring can be considered as a medium which responds to fields generated by an ion bean. Electron density perturbations awaken by the ion beam act back on it, which can give rise to instabilities. This reaction can be described in terms of an impedance introduced in the ring by the electron beam. Longitudinal and transverse impedances of an electron cooler are derived here, increments and thresholds of corresponding instabilities are estimated.