Some aspects of electron cooling technique at different energies

The cooling rate depends on the property of collision between an ion and electron. The magnetized electron cooling is able to strongly increase the cooling rate and enables it to obtain higher parameters of the ion (proton) beams. At medium and high energies of the electron beam it is difficult to have magnetized motion of electron at a whole cooling device. The length of the Larmor spiral is larger or almost equal to the characteristic length of parts of a cooler device, moreover it is difficult to combine the longitudinal magnetic field with RF accelerating structures. So, the special methods for the electron transport along a cooler are necessary. In this article, the different ways of problem solving are described. The merits and demerits of variants with continuous and discontinuous longitudinal magnetic fields are discussed.