  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.
