Useful formulas for non-magnetized electron cooling

Abstract

Recent success of Low Energy RHIC Electron Cooler (LEReC) opened a road for development of high energy electron coolers based on non-magnetized electron bunches accelerated by RF cavities. Electrons in such coolers can have velocity distribution with various unequal horizontal, vertical and longitudinal velocity spreads. In this paper we revisit a formula of friction force in non-magnetized cooling and derive a number of useful expressions for different limiting cases.