Theory of electron cooling

We consider the process of cooling of a heavy particle beam in a co-moving electron beam of low temperature guided by a solenoidal magnetic field. This paper summarizes the main results of theoretical studies of this process conducted by the author during a period of several years. The main result of these studies is a conclusion that magnetization of the electron beam can provide the possibility of drastic enhancement of the cooling rate of a heavy particle beam with achieving equilibrium temperatures that are much lower than the transverse temperatures of the electron beam. Magnetized electron cooling is proposed for cooling of ion beams in high-luminosity colliders.