Longitudinal Equilibrium Distributions of Ion Beams in Storage Rings with Internal Targets and Electron Cooling

A derivation of the model used to describe the longitudinal drag rate is presented along with analytic equations to describe various aspects of the longitudinal equilibrium of an ion beam in a storage ring with internal targets and electron cooling. The effects of transverse and longitudinal heating, cathode power supply ripple voltage, and the electron beam space charge depression are discussed.